diff options
| author | kinitrupti | 2017-05-12 18:40:35 +0530 |
|---|---|---|
| committer | kinitrupti | 2017-05-12 18:40:35 +0530 |
| commit | d36fc3b8f88cc3108ffff6151e376b619b9abb01 (patch) | |
| tree | 9806b0d68a708d2cfc4efc8ae3751423c56b7721 /Strength_Of_Materials_by_B_K_Sarkar | |
| parent | 1b1bb67e9ea912be5c8591523c8b328766e3680f (diff) | |
| download | Python-Textbook-Companions-d36fc3b8f88cc3108ffff6151e376b619b9abb01.tar.gz Python-Textbook-Companions-d36fc3b8f88cc3108ffff6151e376b619b9abb01.tar.bz2 Python-Textbook-Companions-d36fc3b8f88cc3108ffff6151e376b619b9abb01.zip | |
Revised list of TBCs
Diffstat (limited to 'Strength_Of_Materials_by_B_K_Sarkar')
17 files changed, 0 insertions, 12724 deletions
diff --git a/Strength_Of_Materials_by_B_K_Sarkar/chapter_10_som.ipynb b/Strength_Of_Materials_by_B_K_Sarkar/chapter_10_som.ipynb deleted file mode 100755 index 6fa2bde1..00000000 --- a/Strength_Of_Materials_by_B_K_Sarkar/chapter_10_som.ipynb +++ /dev/null @@ -1,689 +0,0 @@ -{
- "metadata": {
- "name": "chapter 10 som.ipynb"
- },
- "nbformat": 3,
- "nbformat_minor": 0,
- "worksheets": [
- {
- "cells": [
- {
- "cell_type": "heading",
- "level": 1,
- "metadata": {},
- "source": [
- "Chapter 10:Analysis Of Framed Structures"
- ]
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 10.1,Page No.249"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "#Consider Equilibrium of joint A\n",
- "#As there are no Load applied at A members AC and AB have nothing to Balance \n",
- "#So they are null members\n",
- "F_AB=0\n",
- "F_AC=0\n",
- "\n",
- "#Consider Equilibrium of joint B\n",
- "\n",
- "#Applying the summation of horizontal forces we get\n",
- "F_DB=4*(cos(45*pi*180**-1))**-1\n",
- "\n",
- "#Applying the summation of vertical forces we get\n",
- "F_BC=F_DB*sin(45*pi*180**-1)\n",
- "\n",
- "#Consider Equilibrium of joint B\n",
- "\n",
- "#Applying the summation of vertical forces we get\n",
- "F_CE=4*(sin(45*pi*180**-1))**-1\n",
- "\n",
- "#Applying the summation of horizontal forces we get\n",
- "F_DC=F_CE*cos(45*pi*180**-1)\n",
- "\n",
- "#Result\n",
- "print\"The Forces in Each members are as follows:F_AB\",F_AB,\"KN\"\n",
- "print\" :F_AC\",F_AC,\"KN\"\n",
- "print\" :F_DB\",round(F_DB,2),\"KN(compression)\"\n",
- "print\" :F_BC\",round(F_BC,2),\"KN(Tension)\"\n",
- "print\" :F_CE\",round(F_CE,2),\"KN(Tension)\"\n",
- "print\" :F_DC\",round(F_DC,2),\"KN (compression)\" "
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Forces in Each members are as follows:F_AB 0 KN\n",
- " :F_AC 0 KN\n",
- " :F_DB 5.66 KN(compression)\n",
- " :F_BC 4.0 KN(Tension)\n",
- " :F_CE 5.66 KN(Tension)\n",
- " :F_DC 4.0 KN (compression)\n"
- ]
- }
- ],
- "prompt_number": 12
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 10.2,Page No.250"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "#Taking moment at Pt A we get\n",
- "R_B=100*8*4**-1\n",
- "\n",
- "#Applying the summation of vertical forces we get\n",
- "R_AV=-R_B\n",
- "\n",
- "#Applying the summation of horizontal forces we get\n",
- "R_H=100\n",
- "\n",
- "#joint B\n",
- "\n",
- "#Applying the summation of vertical forces we get\n",
- "F_CB=R_B\n",
- "\n",
- "#Applying the summation of horizontal forces we get\n",
- "F_AB=0 #As there is no force to balance in horizontal direction\n",
- "\n",
- "#joint A\n",
- "\n",
- "#Applying the summation of horizontal forces we get\n",
- "F_AC=R_H*(cos(45*pi*180**-1))**-1\n",
- "\n",
- "#Applying the summation of vertical forces we get\n",
- "F_AD=200-F_AC*sin(45*pi*180**-1)\n",
- "\n",
- "#joint C\n",
- "\n",
- "#Applying the summation of vertical forces we get\n",
- "F_EC=200-F_AC*cos(45*pi*180**-1)\n",
- "\n",
- "#Applying the summation of horizontal forces we get\n",
- "F_DC=F_AC*cos(45*pi*180**-1)\n",
- "\n",
- "#joint D\n",
- "\n",
- "#Applying the summation of horizontal forces we get\n",
- "F_DE=F_DC*(cos(45*pi*180**-1))**-1\n",
- "\n",
- "#DF and EF are null members at this joint as each member individually has nothing to balance\n",
- "F_DF=0\n",
- "F_EF=0\n",
- "\n",
- "#Result\n",
- "print\"The Forces in Each members are as follows:F_AB\",F_AB,\"KN\"\n",
- "print\" :F_CB\",F_CB,\"KN(compressive)\"\n",
- "print\" :F_AC\",round(F_AC,2),\"KN(Tensile)\"\n",
- "print\" :F_AD\",F_AD,\"KN(Tensile)\"\n",
- "print\" :F_EC\",F_EC,\"KN(Compressive)\"\n",
- "print\" :F_DC\",F_DC,\"KN(compressive)\"\n",
- "print\" :F_DE\",round(F_DE,2),\"KN(Tensile)\"\n",
- "print\" :F_DF\",F_DF,\"KN\"\n",
- "print\" :F_EF\",F_EF,\"KN\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Forces in Each members are as follows:F_AB 0 KN\n",
- " :F_CB 200.0 KN(compressive)\n",
- " :F_AC 141.42 KN(Tensile)\n",
- " :F_AD 100.0 KN(Tensile)\n",
- " :F_EC 100.0 KN(Compressive)\n",
- " :F_DC 100.0 KN(compressive)\n",
- " :F_DE 141.42 KN(Tensile)\n",
- " :F_DF 0 KN\n",
- " :F_EF 0 KN\n"
- ]
- }
- ],
- "prompt_number": 34
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 10.3,Page No.252"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "#taking moment at pt A we get\n",
- "R_D=(90*6+120*3)*9**-1 #Reaction at Pt D\n",
- "\n",
- "#Joint D\n",
- "\n",
- "#Applying the summation of vertical forces we get\n",
- "F_GD=100*(sin(60*pi*180**-1))**-1\n",
- "\n",
- "#Applying the summation of horizontal forces we get\n",
- "F_DC=F_GD*cos(60*pi*180**-1)\n",
- "\n",
- "#Joint G\n",
- "\n",
- "#Applying the summation of vertical forces we get\n",
- "F_GC=F_GD\n",
- "\n",
- "#Applying the summation of horizontal forces we get\n",
- "F_FG=F_GD*cos(60*pi*180**-1)+F_GC*cos(60*pi*180**-1)\n",
- "\n",
- "#joint C\n",
- "\n",
- "#Applying the summation of vertical forces we get\n",
- "F_FC=(115.5*sin(60*pi*180**-1)-90)*(sin(60*pi*180**-1))**-1\n",
- "\n",
- "#Applying the summation of horizontal forces we get\n",
- "F_CB=F_DC+F_GC*cos(60*pi*180**-1)+F_FC*cos(60*pi*180**-1)\n",
- "\n",
- "#joint F\n",
- "\n",
- "#Applying the summation of vertical forces we get\n",
- "F_FB=F_FC\n",
- "\n",
- "#Applying the summation of horizontal forces we get\n",
- "F_EF=F_FG+F_FC*cos(60*pi*180**-1)+F_FB*cos(60*pi*180**-1)\n",
- "\n",
- "#Joint B\n",
- "\n",
- "#Applying the summation of vertical forces we get\n",
- "F_EB=(120-F_FB*sin(60*pi*180**-1))*(sin(60*pi*180**-1))**-1\n",
- "\n",
- "#Applying the summation of horizontal forces we get\n",
- "F_BA=F_CB+F_FB*cos(60*pi*180**-1)-F_EB*cos(60*pi*180**-1)\n",
- "\n",
- "#Joint E\n",
- "\n",
- "#Applying the summation of vertical forces we get\n",
- "F_AE=F_EB\n",
- "\n",
- "#Result\n",
- "print\"Forces in Each members are as follows:F_GD\",round(F_GD,1),\"KN(compression)\"\n",
- "print\" :F_DC\",round(F_DC,2),\"KN(Tension)\" \n",
- "print\" :F_GC\",round(F_GC,1),\"KN(Tension)\" \n",
- "print\" :F_FG\",round(F_FG,1),\"KN(compression)\"\n",
- "print\" :F_FC\",round(F_FC,1),\"KN(compression)\"\n",
- "print\" :F_CB\",round(F_CB,2),\"KN(Tension)\"\n",
- "print\" :F_FB\",round(F_FB,1),\"KN(Tension)\"\n",
- "print\" :F_EF\",round(F_EF,2),\"KN(compression)\"\n",
- "print\" :F_EB\",round(F_EB,2),\"KN(Tension)\"\n",
- "print\" :F_BA\",round(F_BA,2),\"KN(Tension)\"\n",
- "print\" :F_AE\",round(F_AE,2),\"KN(compression)\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Forces in Each members are as follows:F_GD 115.5 KN(compression)\n",
- " :F_DC 57.74 KN(Tension)\n",
- " :F_GC 115.5 KN(Tension)\n",
- " :F_FG 115.5 KN(compression)\n",
- " :F_FC 11.6 KN(compression)\n",
- " :F_CB 121.26 KN(Tension)\n",
- " :F_FB 11.6 KN(Tension)\n",
- " :F_EF 127.05 KN(compression)\n",
- " :F_EB 126.99 KN(Tension)\n",
- " :F_BA 63.55 KN(Tension)\n",
- " :F_AE 126.99 KN(compression)\n"
- ]
- }
- ],
- "prompt_number": 5
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 10.4,Page No.253"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "#JOint D\n",
- "\n",
- "#Applying the summation of vertical forces we get\n",
- "F_1=6*sin(30*pi*180**-1)**-1\n",
- "\n",
- "#Applying the summation of horizontal forces we get\n",
- "F_5=F_1*cos(30*pi*180**-1)\n",
- "\n",
- "#Joint C\n",
- "\n",
- "#Resolving forces perpendicular to plane\n",
- "F_6=10*cos(30*pi*180**-1)\n",
- "\n",
- "#Resolving forces parallel to plane\n",
- "F_2=F_1+10*cos(60*pi*180**-1)\n",
- "\n",
- "#Joint E\n",
- "\n",
- "#Applying the summation of vertical forces we get\n",
- "F_7=(8+F_6*sin(60*pi*180**-1))*(sin(60*pi*180**-1))**-1\n",
- "F_4=F_5+F_6*cos(60*pi*180**-1)+F_7*cos(60*180**-1*pi)\n",
- "\n",
- "#Resolving forces perpendicular to plane\n",
- "F_3=F_7*sin(60*pi*180**-1)\n",
- "\n",
- "#Resolving forces parallel to plane\n",
- "F_8=F_2+F_7*cos(30*pi*180**-1)\n",
- "\n",
- "#Result\n",
- "print\"Forces in Each members are as follows:F_1\",round(F_1,2),\"KN(Tension)\"\n",
- "print\" :F_5\",round(F_5,2),\"KN(compression)\"\n",
- "print\" :F_6\",round(F_6,2),\"KN(compression)\"\n",
- "print\" :F_2\",round(F_2,2),\"KN(Tension)\"\n",
- "print\" :F_7\",round(F_7,2),\"KN(Tension)\"\n",
- "print\" :F_4\",round(F_4,2),\"KN(compression)\"\n",
- "print\" :F_3\",round(F_3,2),\"KN(compression)\"\n",
- "print\" :F_8\",round(F_8,2),\"KN(Tension)\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Forces in Each members are as follows:F_1 12.0 KN(Tension)\n",
- " :F_5 10.39 KN(compression)\n",
- " :F_6 8.66 KN(compression)\n",
- " :F_2 17.0 KN(Tension)\n",
- " :F_7 17.9 KN(Tension)\n",
- " :F_4 23.67 KN(compression)\n",
- " :F_3 15.5 KN(compression)\n",
- " :F_8 32.5 KN(Tension)\n"
- ]
- }
- ],
- "prompt_number": 7
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 10.5,Page No.256"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "BC=6 #m\n",
- "\n",
- "#Calculations\n",
- "\n",
- "AB=2*BC*(3**0.5)**-1\n",
- "\n",
- "#Taking moment about B we get\n",
- "R_A=-(-2000*3-1000*6)*(12*(3**0.5)**-1)**-1 #reaction at the roller support A\n",
- "\n",
- "#The resultant of all the three Loads is 4000 N acting at right angle to BC at D\n",
- "\n",
- "#Resolving it vertically we have\n",
- "V=4000*sin(60*pi*180**-1)\n",
- "\n",
- "#Resolving it horizontal we have\n",
- "H=4000*cos(60*pi*180**-1)\n",
- "\n",
- "#Applying the summation of vertical forces we get\n",
- "R_B_v=V-R_A\n",
- "\n",
- "#Applying the summation of horizontal forces we get\n",
- "R_B_h=H\n",
- "R_B=((R_B_v)**2+(R_B_h)**2)**0.5\n",
- "\n",
- "tan_theta=R_B_v*R_B_h**-1\n",
- "\n",
- "#Joint B\n",
- "\n",
- "#Applying the summation of vertical forces we get\n",
- "F_BD=1000*(3**0.5)*2\n",
- "\n",
- "#Applying the summation of horizontal forces we get\n",
- "F_BE=R_B_h+F_BD*cos(30*pi*180**-1)\n",
- "\n",
- "#Joint D\n",
- "F_DE=2000 #N\n",
- "F_CD=F_BD\n",
- "\n",
- "#Consider equilibrium of truss to the Left of section 2-2\n",
- "F_CE=R_A*AB*(sin(30*pi*180**-1)*6)**-1\n",
- "\n",
- "#Joint A\n",
- "\n",
- "#Applying the summation of vertical forces we get\n",
- "F_AC=R_A*(sin(60*pi*180**-1))**-1\n",
- "\n",
- "#Applying the summation of horizontal forces we get\n",
- "F_AE=F_AC*cos(60*pi*180**-1)\n",
- "\n",
- "#Result\n",
- "print\"Forces in Each members are as follows:F_BD\",round(F_BD,2),\"KN(compression)\"\n",
- "print\" :F_BE\",round(F_BE,2),\"KN(Tension)\"\n",
- "print\" :F_DE\",round(F_DE,2),\"KN(compression)\"\n",
- "print\" :F_CD\",round(F_CD,2),\"KN(compression)\"\n",
- "print\" :F_CE\",round(F_CE,2),\"KN(Tension)\"\n",
- "print\" :F_AC\",round(F_AC,2),\"KN(compression)\"\n",
- "print\" :F_AE\",round(F_AE,2),\"KN(Tension)\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Forces in Each members are as follows:F_BD 3464.1 KN(compression)\n",
- " :F_BE 5000.0 KN(Tension)\n",
- " :F_DE 2000.0 KN(compression)\n",
- " :F_CD 3464.1 KN(compression)\n",
- " :F_CE 4000.0 KN(Tension)\n",
- " :F_AC 2000.0 KN(compression)\n",
- " :F_AE 1000.0 KN(Tension)\n"
- ]
- }
- ],
- "prompt_number": 31
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 10.6,Page No.258"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#Taking moment of the Forces about the hinge A\n",
- "P=1000*2**0.5*1.2*(0.9)**-1\n",
- "\n",
- "#Let R_AH be the Horizontal component of the reaction at A\n",
- "R_AH=P-1000*2**0.5\n",
- "R_A=((R_AH)**2+(1000*2**0.5)**2)**0.5\n",
- "\n",
- "#Resolving the forces vertically we get\n",
- "R_AV=1000*2**0.5 #vertical component of the reaction at A\n",
- "\n",
- "#joint A\n",
- "\n",
- "#Resolving vertically we get\n",
- "F_BA=1000*2**0.5*(sin(30*pi*180**-1))**-1\n",
- "\n",
- "#Resolving horizontally we get\n",
- "F_AD=2000*2**0.5*3**0.5*2**-1-1000*2**0.5*3**-1 #N\n",
- "\n",
- "#Joint C\n",
- "\n",
- "BD=1.2*sin(30*pi*180**-1)\n",
- "BE=0.6*sin(30*pi*180**-1)\n",
- "ED=0.6*cos(30*pi*180**-1)\n",
- "CE=0.9-0.52\n",
- "\n",
- "theta=arctan(BE*CE**-1)*(180*pi**-1)\n",
- "\n",
- "F_CB=P*(sin(38.29*pi*180**-1))**-1\n",
- "\n",
- "#Resolving vertically\n",
- "F_CD=F_CB*cos(theta*pi*180**-1)\n",
- "\n",
- "#Joint D\n",
- "\n",
- "#Resolving horizontally\n",
- "F_DB=(F_AD-1000*2**0.5)*(cos(60*pi*180**-1))**-1\n",
- "\n",
- "#Result\n",
- "print\"The Pull in chain is\",round(P,2),\"N\"\n",
- "print\"Force in the each members are as follows:F_BA\",round(F_BA,2),\"KN(compressive)\"\n",
- "print\" :F_AD\",round(F_AD,2),\"KN(Tensile)\"\n",
- "print\" :F_CB\",round(F_CB,2),\"KN(compression)\"\n",
- "print\" :F_CD\",round(F_CD,2),\"KN(Tensile)\"\n",
- "print\" :F_DB\",round(F_DB,2),\"KN(compressive)\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Pull in chain is 1885.62 N\n",
- "Force in the each members are as follows:F_BA 2828.43 KN(compressive)\n",
- " :F_AD 1978.09 KN(Tensile)\n",
- " :F_CB 3043.08 KN(compression)\n",
- " :F_CD 2388.46 KN(Tensile)\n",
- " :F_DB 1127.74 KN(compressive)\n"
- ]
- }
- ],
- "prompt_number": 3
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 10.7,Page No.261"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Calculations\n",
- "\n",
- "theta=arctan(1*2**-1)*(180*pi**-1) #Radian\n",
- "\n",
- "#Taking moment about A\n",
- "R_EH=10*8*4**-1\n",
- "\n",
- "#Horizontal component of reaction at A\n",
- "R_AH=20 #KN\n",
- "\n",
- "#Applying the summation of horizontal forces we get\n",
- "F_AB=20*cos(theta*pi*180**-1)**-1\n",
- "\n",
- "#Applying the summation of vertical forces we get\n",
- "R_AV=10*5**0.5*sin(theta*pi*180**-1)\n",
- "\n",
- "#Vertical Reaction at E\n",
- "R_EV=0\n",
- "\n",
- "#Joint C\n",
- "\n",
- "#Applying the summation of vertical forces we get\n",
- "F_DC=10*sin(theta*pi*180**-1)**-1\n",
- "\n",
- "#Applying the summation of horizontal forces we get\n",
- "F_CB=F_DC*cos(theta*pi*180**-1)\n",
- "\n",
- "#Joint D\n",
- "\n",
- "#Applying the summation of vertical forces we get\n",
- "F_DB=F_DC*sin(theta*pi*180**-1)\n",
- "\n",
- "#Applying the summation of horizontal forces we get\n",
- "F_DE=F_DC*cos(theta*pi*180**-1)\n",
- "\n",
- "#Joint E\n",
- "\n",
- "#Applying the summation of vertical forces we get\n",
- "F_EB=R_EV*sin(theta*pi*180**-1)\n",
- "\n",
- "#Result\n",
- "print\"Forces in Each members are as follows:F_AB\",round(F_AB,2),\"KN(Tensile)\"\n",
- "print\" :F_DC\",round(F_DC,2),\"KN(compression)\"\n",
- "print\" :F_CB\",round(F_CB,2),\"KN(Tensile)\"\n",
- "print\" :F_DB\",round(F_DB,2),\"KN(Tensile)\" \n",
- "print\" :F_DE\",round(F_DE,2),\"KN(compression)\"\n",
- "print\" :F_EB\",round(F_EB,2),\"KN\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Forces in Each members are as follows:F_AB 22.36 KN(Tensile)\n",
- " :F_DC 22.36 KN(compression)\n",
- " :F_CB 20.0 KN(Tensile)\n",
- " :F_DB 10.0 KN(Tensile)\n",
- " :F_DE 20.0 KN(compression)\n",
- " :F_EB 0.0 KN\n"
- ]
- }
- ],
- "prompt_number": 7
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 10.8,Page No.262"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "F_c=20 #KN #Force at C\n",
- "F_d=5 #KN #Force at D\n",
- "F_e=15 #KN #Force at E\n",
- "F_f=10 #KN #Force at F\n",
- "L_CD=3.6 #m #Length of CD\n",
- "L_DE=3.6 #m #Length of DE\n",
- "L_EF=4.8 #m #Length of EF\n",
- "L_AD=L_BE=3.6 #m #Length of AD & BE\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#Let R_A and R_B be the reactions at pts at A and B\n",
- "\n",
- "#Taking moment at A\n",
- "R_B=-(-F_f*(L_DE+L_EF)+F_c*L_CD-F_e*L_DE)*(L_DE)**-1\n",
- "R_A=50-R_B\n",
- "\n",
- "#Considering section 1-1 through members AB,DB,DE and taking F.B.D of left side of section 1-1\n",
- "\n",
- "#Taking moment at B\n",
- "sigma_1=(F_d*L_DE+F_c*(L_CD+L_DE)-R_A*L_DE)*L_AD**-1 #Force i member DE\n",
- "\n",
- "#Taking moment @ D\n",
- "sigma_3=(F_c*L_CD)*L_AD**-1 #KN #force in member AB\n",
- "\n",
- "\n",
- "#Consider triangle DBE\n",
- "theta=arctan(L_BE*L_DE**-1)*(180*pi**-1)\n",
- "\n",
- "#Taking moment @ A\n",
- "sigma_2=(-sigma_1*L_AD+F_c*L_CD)*(L_AD*cos(theta*pi*180**-1))**-1 #Force in member F_DE\n",
- "\n",
- "#Now considering section 2-2 passing through members AB,AD,CD and taking left hand F.B.D\n",
- " \n",
- "#Taking moment @C\n",
- "sigma_5=(R_A*L_CD-sigma_3*L_AD)*L_CD**-1 #Force in member AD\n",
- "\n",
- "#Taking moment @A=0\n",
- "sigma_4=F_c*L_CD*L_AD**-1 #Force in member CD\n",
- "\n",
- "\n",
- "#Result\n",
- "print\"Force in member CD is\",round(sigma_4,2),\"KN(Compressive)\"\n",
- "print\"Force in member AD is\",round(sigma_5,2),\"KN(Tensile)\"\n",
- "print\"Force in member BD is\",round(sigma_2,2),\"KN(Compression)\"\n",
- "print\"Force in member AB is\",round(sigma_1,2),\"KN(Tension)\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Force in member CD is 20.0 KN(Compressive)\n",
- "Force in member AD is 11.67 KN(Tensile)\n",
- "Force in member BD is 9.43 KN(Compression)\n",
- "Force in member AB is 13.33 KN(Tension)\n"
- ]
- }
- ],
- "prompt_number": 26
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [],
- "language": "python",
- "metadata": {},
- "outputs": []
- }
- ],
- "metadata": {}
- }
- ]
-}
\ No newline at end of file diff --git a/Strength_Of_Materials_by_B_K_Sarkar/chapter_11_som.ipynb b/Strength_Of_Materials_by_B_K_Sarkar/chapter_11_som.ipynb deleted file mode 100755 index 25a93e73..00000000 --- a/Strength_Of_Materials_by_B_K_Sarkar/chapter_11_som.ipynb +++ /dev/null @@ -1,402 +0,0 @@ -{
- "metadata": {
- "name": "chapter 11 som.ipynb"
- },
- "nbformat": 3,
- "nbformat_minor": 0,
- "worksheets": [
- {
- "cells": [
- {
- "cell_type": "heading",
- "level": 1,
- "metadata": {},
- "source": [
- "Chapter no 11:Combined Direct And Bending Stresses"
- ]
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 11.1,Page no.273"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "P=10 #KN #Load\n",
- "e=0.06 #m #eccentricity\n",
- "b=0.240 #m #width of column\n",
- "d=0.150 #m #depth of column\n",
- "\n",
- "#Calculations\n",
- "\n",
- "sigma_d=P*(b*d)**-1 #KN/m**2\n",
- "M=P*e #KN*m #Moment due to eccentricity\n",
- "Z=(d*(b)**2)*6**-1 #mm**3\n",
- "\n",
- "sigma_b=M*Z**-1 #KN/m**2\n",
- "\n",
- "sigma_CD=sigma_d+sigma_b\n",
- "sigma_AB=sigma_d-sigma_b\n",
- "\n",
- "#Result\n",
- "print\"Stress at face CD is\",round(sigma_CD,2),\"KN/m**2\"\n",
- "print\"Stress at face AB is\",round(sigma_AB,2),\"KN/m**2\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Stress at face CD is 694.44 KN/m**2\n",
- "Stress at face AB is -138.89 KN/m**2\n"
- ]
- }
- ],
- "prompt_number": 8
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 11.2,Page no.274"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "d=2 #cm #Diameter of specimen\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#Let P be the Load on the section\n",
- "\n",
- "A=pi*4**-1*d**2 #cm**2 #Area of section\n",
- "I=pi*64**-1*d**4 #cm**4 #M.I of the section\n",
- "y=d*2**-1 #cm\n",
- "Z=I*y**-1 #cm**3 #Section modulus\n",
- "#M=P.e #Moment\n",
- "\n",
- "#Stress due to direct load\n",
- "#sigma_d=(4*P)*(pi*d**2)**-1 #N/cm**2\n",
- "\n",
- "#stress due to moment\n",
- "#sigma_b=(32*P*e)*(pi*d**3)**-1 N/cm**2\n",
- "\n",
- "#Maximum stress\n",
- "#sigma_r_max=(((4*P)*(pi*d**2)**-1)+((32*P*e)*(pi*d**3)**-1))\n",
- "\n",
- "#Mean stress \n",
- "#sigma_r_mean=((4*P)*(pi*d**2)**-1) \n",
- "\n",
- "#Since the maximum stress is 20% greater than the mean stress \n",
- "#(((4*P)*(pi*d**2))+((32*P*e)*(pi*d**3)))=1.2*4*P*(pi*d**2)**-1\n",
- "\n",
- "#After substituing values and simplifyinf we get\n",
- "\n",
- "e=0.2*d*8**-1 #cm #distance of line of thrust from the axis\n",
- "\n",
- "#Result\n",
- "print\"The distance of line of thrust from the axis is\",round(e,2),\"cm\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The distance of line of thrust from the axis is 0.05 cm\n"
- ]
- }
- ],
- "prompt_number": 1
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 11.3,Page no.274"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "A=300 #cm**2 #Area of column\n",
- "e=5 #cm #eccentricity\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#sigma_d=P*A**-1 #Direct compressive stress\n",
- "#M=P*e #Bending Moment\n",
- "Z=((20**4-10**4)*(6*20)**-1) #cm**3 #Section modulus\n",
- "\n",
- "#sigma_b=M*Z**-1=P*250**-1 \n",
- "\n",
- "#Now sigma_d+sigma_b=60*10**2\n",
- "\n",
- "#P*300**-1+P*250**-1=6000\n",
- "\n",
- "#After simplifying we get\n",
- "P_1=6000*300*250*550**-1 #N #Load\n",
- "\n",
- "#sigma_b-sigma_d=300 \n",
- "\n",
- "P_2=300*300*250*50**-1 #N #Load \n",
- "\n",
- "#Result\n",
- "print\"The maximum load column can carry\",round(P_2,2),\"N\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The maximum load column can carry 450000.0 N\n"
- ]
- }
- ],
- "prompt_number": 3
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 11.4,Page no.275"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "D=40 #cm #External diameter of column\n",
- "d=30 #cm #Internal diameter of column\n",
- "e=20 #cm #Eccentricity\n",
- "P=150 #KN #Load\n",
- "\n",
- "#calculations\n",
- "\n",
- "A=pi*4**-1*(D**2-d**2) #cm**2 #Area of the column\n",
- "Z=pi*32**-1*((D**4-d**4)*D**-1) #cm**3 #Section modulus\n",
- "M=P*10**3*e #N*cm #Moment\n",
- "\n",
- "sigma_r_max=((P*10**3*A**-1)+(M*Z**-1)) #N/cm**2 #Max stress \n",
- "sigma_r_min=((P*10**3*A**-1)-(M*Z**-1)) #N/cm**2 #Min stress \n",
- "\n",
- "#Result\n",
- "print\"Max intensities of stress in the section is\",round(sigma_r_max,2),\"N/cm**2\"\n",
- "print\"Min intensities of stress in the section is\",round(sigma_r_min,2),\"N/cm**2(tension)\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Max intensities of stress in the section is 971.3 N/cm**2\n",
- "Min intensities of stress in the section is -425.63 N/cm**2(tension)\n"
- ]
- }
- ],
- "prompt_number": 9
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 11.5,Page no.277"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "b=4 #m #width of pier\n",
- "d=3 #m #depth of pier\n",
- "e_x=1 #m #distance from y axis\n",
- "e_y=0.5 #m #distance from x axis\n",
- "P=80 #KN #Load\n",
- "\n",
- "#Calculations\n",
- "\n",
- "A=b*d #m**2 #Area of pier\n",
- "I_x_x=b*d**3*12**-1 #m**4 #M.I about x-x axis\n",
- "I_y_y=d*b**3*12**-1 #m**4 #M.I about y-y axis\n",
- "M_x=P*e_y #KN*m #Moment about x-x axis\n",
- "M_y=P*e_x #KN*m #Moment about y-y axis\n",
- "\n",
- "x=2 #m #Distance between y-y axis and corners A and B\n",
- "y=1.5 #m ##Distance between x-x axis and corners A and D\n",
- "\n",
- "#Part-1\n",
- "#Stress developed at each corner\n",
- "\n",
- "\n",
- "sigma_A=P*A**-1+M_x*y*I_x_x**-1-M_y*x*I_y_y**-1 #KN/m**2 #stress at A\n",
- "sigma_B=P*A**-1+M_x*y*I_x_x**-1+M_y*x*I_y_y**-1 #KN/m**2 #stress at B\n",
- "sigma_C=P*A**-1-M_x*y*I_x_x**-1+M_y*x*I_y_y**-1 #KN/m**2 #stress at C\n",
- "sigma_D=P*A**-1-M_x*y*I_x_x**-1-M_y*x*I_y_y**-1 #KN/m**2 #stress at D\n",
- "\n",
- "#Part-2\n",
- "#Let f be the additional load that should be placed at centre\n",
- "\n",
- "#sigma_c=F*A**-1 #KN/m**2 #compressive stress\n",
- "\n",
- "#For no tension in pier section, compressive stress is equal to tensile stress\n",
- "sigma_c=10 #KN/m**2\n",
- "F=sigma_c*A #KN\n",
- "\n",
- "#Part-3\n",
- "\n",
- "sigma=F*A**-1 #KN/m**2 #stress due to additional load of 120 KN\n",
- "\n",
- "sigma_A_1=sigma_A+10 #stress at A\n",
- "sigma_B_1=sigma_B+10 #stress at B\n",
- "sigma_C_1=sigma_C+10 #stress at C\n",
- "sigma_D_1=sigma_D+10 #stress at D\n",
- "\n",
- "#Result\n",
- "print\"Stress at each corner are as follows:stress_A\",round(sigma_A,2),\"KN/m**2\"\n",
- "print\" :stress_B\",round(sigma_B,2),\"KN/m**2\"\n",
- "print\" :stress_C\",round(sigma_C,2),\"KN/m**2\"\n",
- "print\" :stress_D\",round(sigma_D,2),\"KN/m**2(tensile)\"\n",
- "\n",
- "print\"Additional load that should be placed at centre is\",round(F,2),\"KN\"\n",
- "\n",
- "print\"Stresses at the corners with the additional load in centre are as follows:Stress_A_1\",round(sigma_A_1,2),\"KN/m**2\"\n",
- "print\" :Stress_B_1\",round(sigma_B_1,2),\"KN/m**2\"\n",
- "print\" :Stress_C_1\",round(sigma_C_1,2),\"KN/m**2\"\n",
- "print\" :Stress_D_1\",round(sigma_D_1,2),\"KN/m**2\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Stress at each corner are as follows:stress_A 3.33 KN/m**2\n",
- " :stress_B 23.33 KN/m**2\n",
- " :stress_C 10.0 KN/m**2\n",
- " :stress_D -10.0 KN/m**2(tensile)\n",
- "Additional load that should be placed at centre is 120.0 KN\n",
- "Stresses at the corners with the additional load in centre are as follows:Stress_A_1 13.33 KN/m**2\n",
- " :Stress_B_1 33.33 KN/m**2\n",
- " :Stress_C_1 20.0 KN/m**2\n",
- " :Stress_D_1 0.0 KN/m**2\n"
- ]
- }
- ],
- "prompt_number": 27
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 11.11.6,Page no.278"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "#d=Diameter of rod\n",
- "P=500 #KN\n",
- "e=0.75 #cm #eccentricity\n",
- "\n",
- "#calculation\n",
- "\n",
- "#A=pi*d**2*4**-1 #cm**2 #Area of rod\n",
- "#sigma_d=P*A**-1 #KN/cm**2 #stress due to direct load\n",
- "\n",
- "#After substituting value and simplifying we get,\n",
- "#sigma_d=2000*(pi*d**2)**-1 #KN/cm**2 \n",
- "\n",
- "M=P*e #Kn*cm #Moment\n",
- "\n",
- "#Z=pi*d**3*32**-1 #cm**3 #section modulus\n",
- "#sigma_b=M*Z**-1 #KN/cm**2 #Stress due to moment\n",
- "\n",
- "#After substituting value and simplifying we get,\n",
- "#sigma_b=12000*(pi*d**3)**-1 #KN/cm**2\n",
- "\n",
- "#Max stress \n",
- "#sigma=sigma_d+sigma_b \n",
- "\n",
- "#After substituting value and simplifying we get,\n",
- "#2000*(pi*d**2)**-1+12000*(pi*d**3)**-1=12.5\n",
- "\n",
- "#After simplifying we get,\n",
- "#d**3-53.05*d-318.3=0\n",
- "\n",
- "#From Synthetic Division we get d**2+4.73*d-42.918\n",
- "a=1\n",
- "b=-4.73\n",
- "c=-42.918\n",
- "\n",
- "X=b**2-(4*a*c)\n",
- "\n",
- "d_1=(-b+X**0.5)*(2*a)**-1\n",
- "d_2=(-b-X**0.5)*(2*a)**-1\n",
- "\n",
- "#Result\n",
- "print\"The minimum diameter of tie rod is\",round(d_1,2),\"cm\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The minimum diameter of tie rod is 9.33 cm\n"
- ]
- }
- ],
- "prompt_number": 5
- }
- ],
- "metadata": {}
- }
- ]
-}
\ No newline at end of file diff --git a/Strength_Of_Materials_by_B_K_Sarkar/chapter_12_som.ipynb b/Strength_Of_Materials_by_B_K_Sarkar/chapter_12_som.ipynb deleted file mode 100755 index fd200d5e..00000000 --- a/Strength_Of_Materials_by_B_K_Sarkar/chapter_12_som.ipynb +++ /dev/null @@ -1,425 +0,0 @@ -{
- "metadata": {
- "name": "chapter 12 som.ipynb"
- },
- "nbformat": 3,
- "nbformat_minor": 0,
- "worksheets": [
- {
- "cells": [
- {
- "cell_type": "heading",
- "level": 1,
- "metadata": {},
- "source": [
- "Chapter 12:Propped Cantilever"
- ]
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 12.1,Page No.286"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "L=6 #m #Length of Beam\n",
- "L_1=4 #m #Length of Beam with udl Load\n",
- "w=10 #KN/m #u.d.l\n",
- "\n",
- "#Calculation\n",
- "\n",
- "#Deflection of cantileverat C due to udl on AB\n",
- "y_c=w*L_1**4*8**-1+w*L_1**3*6**-1*(L-L_1) \n",
- "\n",
- "#Deflection of cantileverat C due to prop reaction alone\n",
- "#y_c_2=R_c*L**3*3**-1\n",
- "\n",
- "#Since both Deflection are Equal\n",
- "#y_c=y_c_2\n",
- "\n",
- "R_c=y_c*(6**3)**-1*3 #Reaction at C\n",
- "\n",
- "#Result\n",
- "print\"The Reaction at End C is\",round(R_c,3),\"KN\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Reaction at End C is 7.407 KN\n"
- ]
- }
- ],
- "prompt_number": 8
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 12.2,Page No.286"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "L=10 #m #Length\n",
- "b=15 #cm #Width\n",
- "d=40 #cm #Depth\n",
- "y_c=1.5*10**-2 #m #Deflection\n",
- "E=120*10**9 \n",
- "y=0.2\n",
- "sigma=10*10**6 #Bending stress\n",
- "\n",
- "#Calculations\n",
- "\n",
- "I=b*d**3*12**-1*10**-8 #cm #M.I\n",
- "\n",
- "#From Deflection at the centre of cantilever we get\n",
- "w=y_c*192*E*I*(L**4)**-1*10**-3 #udl distributed over the cantilever\n",
- "\n",
- "#From Bending Moment Equation we get\n",
- "w_2=sigma*I*y**-1*16*(L**2)**-1*10**-3 #udl distributed over the cantilever\n",
- "\n",
- "#Result\n",
- "print\"The safe uniformly Distributed Load is\",round(w_2,2),\"KN/m\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The safe uniformly Distributed Load is 6.4 KN/m\n"
- ]
- }
- ],
- "prompt_number": 23
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 12.3,Page No.287"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "L=6 #m #span of beam\n",
- "w=30*10**3 #KN/m #u.d.l\n",
- "P=160*10**3 #N #concentrated Load\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#Consider a section at a distance x from the fixed end A and B.M at x\n",
- "#M_x=R_b*(6-x)-30*2**-1*(6-x)**2-160*(3-x)\n",
- "\n",
- "#E*I*d**2y*(dx**2)**-1=-M_x=-R_b*(6-x)+15*(6-x)+160*(3-x)\n",
- "\n",
- "#Now Integrating above term we get\n",
- "#E*I*dy*(dx)**-1=R_b*2**-1*(6-x)**2-5*(6-x)**3-80*(3-x)**2+C_1 (Equation 1)\n",
- "\n",
- "#Now on Integrating we get\n",
- "#E*I*y=-R_b*6**-1*(6-x)**3+5*4**-1*(6-x)**2+80*3**-1*(3-x)**3+C_1*x+C_2 (Equation 2)\n",
- "\n",
- "#At x=0,dy*dx**-1=0\n",
- "#substituting in equation 1 we get\n",
- "#C_1=1800-R_b\n",
- "\n",
- "#At x=0,y=0\n",
- "#substituting in equation 2 we get\n",
- "#C_2=36*R_b-2340\n",
- "\n",
- "#At x=6,y=0\n",
- "R_b=72**-1*(10800-2340)\n",
- "\n",
- "#At x=0\n",
- "x=0\n",
- "M_x=R_b*(6-x)-30*2**-1*(6-x)**2-160*(3-x)\n",
- "\n",
- "#Result\n",
- "print\"Bending Moment at A is\",round(M_x,2),\"KNm\"\n",
- "print\"The Reaction at B\",round(R_b,2),\"KN\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Bending Moment at A is -315.0 KNm\n",
- "The Reaction at B 117.5 KN\n"
- ]
- }
- ],
- "prompt_number": 5
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 12.4,Page No.288"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "L=4 #span of beam\n",
- "w_1=20*10**3 #Nm #u.d.l\n",
- "w_2=30*10**3 #Nm #u.d.l\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#consider a section at a distance x from A and B.M at this section is \n",
- "#M_x=R_b*(3-x)-10*x**2+90*x-195\n",
- "\n",
- "#Now integrating above equation we get\n",
- "#E*I*dy*(dx)**-1=-R_b(3*x-x**2*2**-1)+10*x**3*3**-1-45*x**2+195*x+C_1\n",
- "\n",
- "#again on Integrating we get\n",
- "#E*I*y=-R_b*(3*x**2*2**-1-x**3*6**-1)+10*x**4*12**-1-15*x**3+195*x**2*2**-1+C_1*x+C_2\n",
- "\n",
- "#At x=0,dy*(dx)**-1=0 Therefore C_1=0\n",
- "\n",
- "#At x=0,y=0 Therefore C_2=0\n",
- "\n",
- "#At x=3m, y=0\n",
- "x=3\n",
- "C_1=0\n",
- "C_2=0\n",
- "R_b=-(-10*x**4*12**-1+15*x**3-195*x**2*2**-1-C_1*x-C_2)*(3*x**2*2**-1-x**3*6**-1)**-1\n",
- "\n",
- "#result\n",
- "print\"Load taken by prop is\",round(R_b,2),\"KN\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Load taken by prop is 60.0 KN\n"
- ]
- }
- ],
- "prompt_number": 3
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 12.5,Page No.289"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "L=2 #m #Span of beam\n",
- "w=10 #KN/m #u.d.l\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#Downward deflection at B(of Beam AB) due to u.d.l of 10 KN/m is\n",
- "Y_B_1=w*L**4*8**-1 \n",
- "\n",
- "#Upward deflection at B due to reaction at C alone is\n",
- "#Y_B_2=R_c*8*3**-1\n",
- "\n",
- "#Net downward deflection of cantilever at AB at B\n",
- "#Y_B=Y_B_1-Y_B_2\n",
- "\n",
- "#Downward Deflection of Beam CD at C due to the reaction\n",
- "#R_c=R_c*(3*E*I)**-1\n",
- "\n",
- "#since both deflection at C and B are equal\n",
- "R_c=20*(1*3**-1+8*3**-1)**-1\n",
- "\n",
- "#Result\n",
- "print\"Reaction at C is\",round(R_c,2),\"KN\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Reaction at C is 6.67 KN\n"
- ]
- }
- ],
- "prompt_number": 7
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 12.8,Page No.292"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "%matplotlib inline\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "L=8 #m #span\n",
- "W=24*10**3 #N/m #U.D.L\n",
- "y=2*10**-2 #m #deflection\n",
- "E=20*10**9\n",
- "I=10**-5 #m**4\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#The Downward deflection at C Due to u.d.l\n",
- "#Y_c=5*W*L**3*(384*E*I)**-1\n",
- "\n",
- "#The Upward Deflection at C due to prop Reaction P \n",
- "#Y_c_1=P*L**3*(48*E*I)**-1\n",
- "\n",
- "#Since the prop is at the same level as end supports\n",
- "#Y_c_1=Y_c\n",
- "P_1=5*W*8**-1*10**-3 #KN\n",
- "\n",
- "#The reaction at A and B is equal\n",
- "R_a=R_b=(24-15)*2**-1\n",
- "\n",
- "#Shear Force at B\n",
- "V_B=4.5 #KN\n",
- "\n",
- "#Shear Force at C\n",
- "V_C1=4.5-24*2**-1\n",
- "V_C2=4.5-24*2**-1+15\n",
- "\n",
- "#Shea rForce at A\n",
- "V_A=-4.5 #KN\n",
- "\n",
- "#B.M at C due to u.d.l\n",
- "M_C1=W*L*8**-1*10**-3 #KN*m\n",
- "\n",
- "#B.M due to only prop reaction P=15 KN\n",
- "P=15\n",
- "M_C2=-P*L*4**-1 #KN*m\n",
- "\n",
- "#B.M at D\n",
- "M_D=4.5*1.5-24*8**-1*1.5**2*2**-1\n",
- "\n",
- "#In second case prop sinks by 2 cm\n",
- "#Y_c-Y_c_1=2 \n",
- "\n",
- "#So Further simplifying and sunstituting values in above equation we get\n",
- "P=-(2*100**-1-(5*W*L**3*(384*E*I)**-1))*(L**3*(48*E*I)**-1)**-1\n",
- "\n",
- "#Let Each end reaction be X\n",
- "X=(24-14.625)*2**-1\n",
- "\n",
- "#Result\n",
- "print\"prop reaction is\",round(P_1,2),\"KN\"\n",
- "print\"The End Reaction is\",round(X,2),\"KN\"\n",
- "\n",
- "#Plotting the SHear Force Diagram\n",
- "\n",
- "X1=[0,4,4,8,8]\n",
- "Y1=[V_B,V_C1,V_C2,V_A,0]\n",
- "Z1=[0,0,0,0,0]\n",
- "plt.plot(X1,Y1,X1,Z1)\n",
- "plt.xlabel(\"Length x in m\")\n",
- "plt.ylabel(\"Shear Force in kN\")\n",
- "plt.show()\n",
- "\n",
- "#Plotting the Bendimg Moment Diagram\n",
- "\n",
- "X2=[0,4,4]\n",
- "Y2=[0,M_C1,0]\n",
- "Z2=[0,0,0]\n",
- "plt.plot(X2,Y2)\n",
- "plt.xlabel(\"Lenght in m\")\n",
- "plt.ylabel(\"Bending Moment in kN.m\")\n",
- "plt.show()"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "prop reaction is 15.0 KN\n",
- "The End Reaction is 4.69 KN\n"
- ]
- },
- {
- "metadata": {},
- "output_type": "display_data",
- "png": "iVBORw0KGgoAAAANSUhEUgAAAX8AAAEPCAYAAACqZsSmAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
- "text": [
- "<matplotlib.figure.Figure at 0x56bdc90>"
- ]
- },
- {
- "metadata": {},
- "output_type": "display_data",
- "png": "iVBORw0KGgoAAAANSUhEUgAAAYIAAAEPCAYAAABP1MOPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nzqsRe/u3SQAAAABJRU5ErkJggg==\n",
- "text": [
- "<matplotlib.figure.Figure at 0x5651370>"
- ]
- }
- ],
- "prompt_number": 12
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [],
- "language": "python",
- "metadata": {},
- "outputs": []
- }
- ],
- "metadata": {}
- }
- ]
-}
\ No newline at end of file diff --git a/Strength_Of_Materials_by_B_K_Sarkar/chapter_13_som.ipynb b/Strength_Of_Materials_by_B_K_Sarkar/chapter_13_som.ipynb deleted file mode 100755 index 6f724b86..00000000 --- a/Strength_Of_Materials_by_B_K_Sarkar/chapter_13_som.ipynb +++ /dev/null @@ -1,694 +0,0 @@ -{
- "metadata": {
- "name": "chapter 13 som.ipynb"
- },
- "nbformat": 3,
- "nbformat_minor": 0,
- "worksheets": [
- {
- "cells": [
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Chapter No.13:Shear Stress in Beams"
- ]
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 13.2,Page No.301"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "#W=10*w #KN/m #u.d.l\n",
- "sigma=805*10**6 #Pa #Bending stress\n",
- "Tou=0.85*10**6 #Pa #Shear stress\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#M=W*L**2*10**-4*8**-1 #Max B.M\n",
- "#F=W*L*10**-2*2**-1 #Max S.F\n",
- "#y=h*2**-1 #depth\n",
- "#A-b*h #Area of c/s\n",
- "\n",
- "#Now using relation we get\n",
- "#sigma=M*h*(2*I)**-1 #Bending stress\n",
- "\n",
- "#AFter substituitng values we get\n",
- "#805*10**6=w*l**2*h*(16*10**5*I)**-1 #Equation 1\n",
- "\n",
- "#Again using the relation we get \n",
- "#tou=F*A*y_bar*(I*b)**-1 #shear atress\n",
- "\n",
- "#AFter substituitng values we get\n",
- "#0.85*10**6=w*L*h**2*(16*10**5*I)**-1 #Equation 2\n",
- "\n",
- "#Dividing equation 1 & 2 we get\n",
- "#L*h**-1=10\n",
- "#Let L*h**-1=Z\n",
- "z=10\n",
- "\n",
- "#Result\n",
- "print\"The Ratio of span to depth ratio is\",round(z,2)"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Ratio of span to depth ratio is 10.0\n"
- ]
- }
- ],
- "prompt_number": 1
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 13.3,Page No.302"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "%matplotlib inline\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "L=2 #m #span\n",
- "w=20*10**3 #N/m #u.d.L\n",
- "b=12.5 #cm #width of Flange\n",
- "t=2.5 #cm #flange thickness\n",
- "w_t=2.5 #cm #web thickness\n",
- "D=20 #cm #Overall depth\n",
- "w_d=17.5 #m #Depth of web\n",
- "\n",
- "#Calculations\n",
- "\n",
- "F=w*L*2**-1 #N #Max S.F\n",
- "a_1=b*t #Area of flange\n",
- "a_2=w_d*w_t #Area of web\n",
- "y_1=t*2**-1 #C.G of flange\n",
- "y_2=w_d*2**-1+t #C.G of web\n",
- "\n",
- "#C.G of c/s\n",
- "Y=(a_1*y_1+a_2*y_2)*(a_1+a_2)**-1 \n",
- "\n",
- "#M.I about N.A\n",
- "I=b*t**3*12**-1+b*t*(Y-y_1)**2+w_t*w_d**3*12**-1+w_t*w_d*(y_2-Y)**2 \n",
- "\n",
- "#Shear Stress in flange at the junction with web\n",
- "#Let tou(Shear stress)=S \n",
- "#Change in the notifications of Shear Stress For convenience\n",
- "S_1=(F*a_1*(Y-y_1)*10**-6)*(I*10**-8*b*10**-2)**-1*10**-3 \n",
- "\n",
- "#Shear Stress in web at the junction with flange \n",
- "S_2=(F*a_1*(Y-y_1)*10**-6)*(I*10**-8*w_t*10**-2)**-1*10**-3 \n",
- "\n",
- "#Max Shear Stres at N.A\n",
- "S_max=(F*(a_1*(Y-y_1)+(w_t*(Y-t))*((Y-t)*2**-1))*10**-6)*(I*10**-8*w_t*10**-2)**-1*10**-3\n",
- "\n",
- "#Result\n",
- "print\"The Max shear stress in the beam is\",round(X_max,2),\"KN/m**2\"\n",
- "\n",
- "print\"Shear stress distribution Diagram\"\n",
- "\n",
- "#Plotting the Shear stress distribution Diagram\n",
- "\n",
- "X_1=[0,2.5,2.5,4.58,15.42]\n",
- "Y_1=[0,S_1,S_2,S_max,0]\n",
- "Z_1=[0,0,0,0,0]\n",
- "plt.plot(X_1,Y_1,X_1,Z_1)\n",
- "plt.xlabel(\"Length x in m\")\n",
- "plt.ylabel(\"Shear Stress in kN/m**2\")\n",
- "plt.show()"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Max shear stress in the beam is 5644.64 KN/m**2\n",
- "Shear stress distribution Diagram\n"
- ]
- },
- {
- "metadata": {},
- "output_type": "display_data",
- "png": "iVBORw0KGgoAAAANSUhEUgAAAY4AAAEPCAYAAABV6CMBAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nHEIIISpFCocQQohK+f/7gGcS8RurtQAAAABJRU5ErkJggg==\n",
- "text": [
- "<matplotlib.figure.Figure at 0x57624b0>"
- ]
- }
- ],
- "prompt_number": 24
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 13.4,Page No.303"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "F=100*10**3 #N #Shear Force\n",
- "I=11340*10**-8 #m**4 #M.I\n",
- "b=20 #cm #width of Flange\n",
- "t=5 #cm #thickness of flange\n",
- "w_d=20 #cm #Depth of web\n",
- "w_t=5 #cm #thickness of web\n",
- "\n",
- "#Calculations\n",
- "\n",
- "a_1=b*t #cm**2 #Area of flange\n",
- "a_2=w_d*w_t #cm**2 #Area of web\n",
- "y_1=t*2**-1 #cm #C.G of flange\n",
- "y_2=t+w_d*2**-1\n",
- "\n",
- "#C.G of C/s\n",
- "Y=(a_1*y_1+a_2*y_2)*(a_1+a_2)**-1\n",
- "\n",
- "#Shear Stress in flange at the junction with web\n",
- "#Let tou(Shear stress)=S \n",
- "#Change in the notifications of Shear Stress For convenience\n",
- "S_1=(F*a_1*(Y-y_1)*10**-6)*(I*b*10**-2)**-1*10**-3 \n",
- "\n",
- "#Shear Stress in web at the junction with flange \n",
- "S_2=(F*a_1*(Y-y_1)*10**-6)*(I*w_t*10**-2)**-1*10**-3 \n",
- "\n",
- "#Max Shear Stres at N.A\n",
- "S_max=(F*(a_1*(Y-y_1)+(w_t*(Y-t))*((Y-t)*2**-1))*10**-6)*(I*w_t*10**-2)**-1*10**-3\n",
- "\n",
- "#Result\n",
- "print\"Shear Stress in flange at the junction with web\",round(S_1,2),\"KN/m**2\"\n",
- "print\"Shear Stress in web at the junction with flange\",round(S_2,2),\"KN/m**2\"\n",
- "print\"Max Shear Stres at N.A\",round(S_max,2),\"KN/m**2\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Shear Stress in flange at the junction with web 2755.73 KN/m**2\n",
- "Shear Stress in web at the junction with flange 11022.93 KN/m**2\n",
- "Max Shear Stres at N.A 11642.97 KN/m**2\n"
- ]
- }
- ],
- "prompt_number": 38
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 13.5,Page No.304"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "from scipy.integrate import quad\n",
- "\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "D=50 #cm #Overall depth\n",
- "b=19 #cm #width of flange\n",
- "t=2.5 #cm #Thickness of Flange\n",
- "w_t=1.5 #cm #Web thickness\n",
- "w_d=45 #cm #web thickness\n",
- "F=400*10**3 #N #Shear Force\n",
- "I=64500*10**-8 #m**4 #M.I\n",
- "\n",
- "#Calculations (Part-1)\n",
- " \n",
- "a_1=b*t #cm**2 #Area of flange\n",
- "a_2=w_d*w_t #cm**2 #Area of web\n",
- "y_1=t*2**-1 #cm #C.G of flange\n",
- "y_2=t+w_d*2**-1\n",
- "\n",
- "#As section is symmetrical \n",
- "Y=D*2**-1 #cm\n",
- "\n",
- "#Shear Stress in flange at the junction with web\n",
- "#Let tou(Shear stress)=S \n",
- "#Change in the notifications of Shear Stress For convenience\n",
- "S_1=(F*a_1*(Y-y_1)*10**-6)*(I*b*10**-2)**-1*10**-3 \n",
- "\n",
- "#Shear Stress in web at the junction with flange \n",
- "S_2=(F*a_1*(Y-y_1)*10**-6)*(I*w_t*10**-2)**-1*10**-3 \n",
- "\n",
- "#Max Shear Stres at N.A\n",
- "S_max=(F*(a_1*(Y-y_1)+(w_t*(Y-t))*((Y-t)*2**-1))*10**-6)*(I*w_t*10**-2)**-1*10**-3\n",
- "\n",
- "#Calculations (Part-2)\n",
- "\n",
- "#consider a strip in the flange of thickness dy at a distance y from N.A \n",
- "\n",
- "#S=F*(b*(Y-y)*(Y+y)*2**-1*10**-6)*(I*b*10**-2)**-1\n",
- "#after substituting values we get\n",
- "#S=625-y**2*(3225*10**-8)**-1\n",
- "\n",
- "#shear force carried by small strip\n",
- "#F_1=625-y**2*(3225*10**-8)**-1*b*dy*10**-4\n",
- "\n",
- "#Now Integrating above Equation we get\n",
- "def integrand(y, a, b):\n",
- " return 625-y**2\n",
- "a =625\n",
- "b =-1\n",
- "I = quad(integrand, 22.5, 25, args=(a,b))\n",
- "\n",
- "#Shear force carried by one flange\n",
- "F_1=19*3225**-1*10**4*I[0]\n",
- "\n",
- "#Shear force carried by two flange\n",
- "F_2=2*F_1\n",
- "\n",
- "#Shear force carried by web\n",
- "F_3=F-F_2\n",
- "\n",
- "#Result\n",
- "print\"The shear Force int the section is\",round(S_max,2),\"Pa\"\n",
- "print\"Total Shear Force in the web is\",round(F_3,2),\"N\"\n",
- "\n",
- "\n",
- "print\"Shear stress distribution Diagram\"\n",
- "\n",
- "#Plotting the Shear stress distribution Diagram\n",
- "\n",
- "X_1=[0,2.5,2.5,25,47.5,47.5,50]\n",
- "Y_1=[0,S_1,S_2,S_max,S_2,S_1,0]\n",
- "Z_1=[0,0,0,0,0,0,0]\n",
- "plt.plot(X_1,Y_1,X_1,Z_1)\n",
- "plt.xlabel(\"Length x in m\")\n",
- "plt.ylabel(\"Shear Stress in kN/m**2\")\n",
- "plt.show()"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The shear Force int the section is 62338.5 MPa\n",
- "Total Shear Force in the web is 382202.84 N\n",
- "Shear stress distribution Diagram\n"
- ]
- },
- {
- "metadata": {},
- "output_type": "display_data",
- "png": "iVBORw0KGgoAAAANSUhEUgAAAZQAAAEPCAYAAABlZDIgAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nUERExC0UKCIi4hYKFBERcYv/D6L3iyTClBJuAAAAAElFTkSuQmCC\n",
- "text": [
- "<matplotlib.figure.Figure at 0x5633a10>"
- ]
- }
- ],
- "prompt_number": 7
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 13.6,Page No.305"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "F=5*10**3 #N #shea Force\n",
- "b=20 #cm #width of Flange\n",
- "t=6 #cm #Thickness of flange\n",
- "w_d=20 #cm #depth of web\n",
- "w_t=6 #cm #thickness of web\n",
- "X=700 #N #Shear Looad\n",
- "\n",
- "#Calculations\n",
- "\n",
- "a_1=b*t #cm**2 #Area ofFlange\n",
- "a_2=w_d*w_t #cm**2 #Area of web\n",
- "y_1=t*2**-1 #cm #C.G of Flange\n",
- "y_2=t+w_d*2**-1 #cm #C.G of Web\n",
- "\n",
- "Y=(a_1*y_1+a_2*y_2)*(a_1+a_2)**-1\n",
- "\n",
- "#M.I about N.A\n",
- "I=b*t**3*12**-1+b*t*(Y-y_1)**2+w_t*w_d**3*12**-1+w_t*w_d*(y_2-Y)**2 \n",
- "\n",
- "#Shear Force per metre Length in Plane of contact of two Planks \n",
- "#Let Shear Force per metre Length=F_1 \n",
- "F_1=(F*a_1*(Y-y_1)*10**-6)*(I*10**-8)**-1\n",
- "\n",
- "#Spacing of nails\n",
- "s=X*F_1**-1*100\n",
- "\n",
- "#Result\n",
- "print\"The spacing of nails along the Length of beam is\",round(s,2),\"cm\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The spacing of nails along the Length of beam is 2.6 cm\n"
- ]
- }
- ],
- "prompt_number": 74
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 13.7,Page No.306"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "L=3 #m #span\n",
- "d=5 #cm #depth of each plank\n",
- "b=15 #cm #width of plank\n",
- "d_1=1.9 #cm #Diameter of bolt\n",
- "s=12.5 #cm #spacing of bolt\n",
- "w=3.3*10**3 #N.m #u.d.l\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#Shear Force at 1.5m from support\n",
- "F=w*1.5\n",
- "\n",
- "I=b*(5*d)**3*12**-1 #M.I\n",
- "A=pi*4**-1*d_1**2 #area of Bolt\n",
- "Y=5*d*2**-1 #C.G of beam\n",
- "y_1=d*2**-1 #c.G of top plank\n",
- "\n",
- "#Shear Force per metre Length \n",
- "F_1=F*b*d*(Y-y_1)*10**-6*(I*10**-8)**-1\n",
- "\n",
- "#Load carried by bolt\n",
- "W_1=F_1*s*10**-2\n",
- "\n",
- "#shear stress\n",
- "X_1=W_1*(round(A,3))**-1*10**+4\n",
- "\n",
- "#Shear Force per metre Length \n",
- "F_2=F*b*2*d*((d+y_1)-Y*10**-6)*(I*10**-8)**-1*10**-6\n",
- "\n",
- "#Load carried by bolt\n",
- "W_2=F_2*s*10**-2\n",
- "\n",
- "#shear stress\n",
- "X_2=W_2*(A*10**-4)**-1*10**-3\n",
- "\n",
- "#Reult\n",
- "print\"Shear stress in a bolt Located at 1.5 m from support is\",round(X_2,2),\"KN/m**2\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Shear stress in a bolt Located at 1.5 m from support is 12570.13 KN/m**2\n"
- ]
- }
- ],
- "prompt_number": 23
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 13.8,Page No.307"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\\\n",
- "\n",
- "b=15 #cm #width of plank\n",
- "t=2.5 #cm #thickness of planf\n",
- "F_1=1250 #N #Shear Force\n",
- "F_2=5*10**3 #shaear force transmitted by screw\n",
- "d=15 #cm #Depth of plank\n",
- "D=20 #cm #Overall depth\n",
- "\n",
- "#Calculations\n",
- "\n",
- "Y=D*2**-1 #C.G of beam\n",
- "y_1=t*2**-1 #C.G of flange\n",
- "\n",
- "I=((b*D**3)-(D*2**-1*b**3))*12**-1 #cm**4 #M.I\n",
- "\n",
- "#Shear Stress in the Flange at 7.5 cm from N.A\n",
- "X_1=F_2*b*t*(Y-y_1)*10**-6*(I*10**-8*d*10**-2)**-1*10**-3\n",
- "\n",
- "#Shear Stress in the web at 7.5 cm from N.A\n",
- "X_2=X_1*d*(2*t)**-1\n",
- "\n",
- "#shear stress at N.A\n",
- "X_max=F_2*(b*t*(Y-y_1)+2*t*d*2**-1*d*4**-1)*10**-6*(I*10**-8*2*t*10**-2)**-1*10**-3\n",
- "\n",
- "#horizontal shear force per pitch length to the shearing strength of two bolts we have\n",
- "#X_h=X_2*10**3*2*t*10**-2*p\n",
- "\n",
- "#Equating horizontal shear force per pitch length to the shearing strength of two bolts we have\n",
- "p=F_1*2*(X_2*10**3*2*t*10**-2)**-1*10**2\n",
- "\n",
- "#Result\n",
- "print\"The Min spacing of screw along the beam is\",round(p,2),\"cm\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Min spacing of screw along the beam is 10.95 cm\n"
- ]
- }
- ],
- "prompt_number": 18
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 13.9,Page No.308"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "L=4 #m #span\n",
- "w=80*10**3 #N/m #u.d.l\n",
- "D=35 #cm #Overall depth\n",
- "b=15 #cm #width of Flange\n",
- "t=2.5 #cm #Thickness of flange\n",
- "w_d=30 #cm #Depth of web\n",
- "w_t=1.2 #cm #thickness of web\n",
- "\n",
- "#Calculations\n",
- "\n",
- "R_a=R_b=160 #KN #Reactions at supports\n",
- "\n",
- "#Shear FOrce at 1m from left support\n",
- "F=R_a*10**3-w\n",
- "\n",
- "M=R_a*10**3-w*2**-1 #B.M at 1m From support\n",
- "\n",
- "I=(b*D**3-((b-w_t)*w_d**3))*12**-1 #cm**4\n",
- "\n",
- "y=w_d*2**-1\n",
- "sigma=M*I**-1*y #N/m**2\n",
- "\n",
- "#Shear stress in Flange at the junction with web\n",
- "X_1=w*b*t*(w_d*2**-1+t*2**-1)*10**-6*(I*10**-8*b*10**-2)**-1*10**-3\n",
- "\n",
- "#Shear stress in web at the junction with Flange \n",
- "X_2=X_1*15*1.2**-1\n",
- "\n",
- "#Result\n",
- "print\"The Magnitude of Bending is\",round(sigma,2),\"N/m**2\"\n",
- "print\"Shear stress in web at the junction with Flange\",round(X_1,2),\"KN/m**2\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Magnitude of Bending is 79.84 N/m**2\n",
- "Shear stress in web at the junction with Flange 1441.64 KN/m**2\n"
- ]
- }
- ],
- "prompt_number": 16
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 13.10,Page No.309"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "b=25 #cm #width of top FLange\n",
- "t=5 #cm #thickness of top Flange\n",
- "D=35 #cm #Depth of overall section\n",
- "w_d=25 #cm #depth of web\n",
- "w_t=5 #cm #thickness of web\n",
- "t_1=5 #cm #thickness of bottom Flange\n",
- "b_1=15 #cm #width of bottom Flange\n",
- "sigma=17.5*10**6\n",
- "F=100*10**3 #N #S.F\n",
- "\n",
- "#Calculations\n",
- "\n",
- "a_1=b*t #area of top flange\n",
- "a_2=w_d*w_t #area of web\n",
- "a_3=b_1*t_1 #area of bottom Flange\n",
- "y_1=t*2**-1 #C.G of top flange\n",
- "y_3=D-(t_1*2**-1) #C.G of bottom Flange \n",
- "y_2=D*2**-1 #c.G of Web\n",
- "\n",
- "Y=(a_1*y_1+a_2*y_2+a_3*y_3)*(a_1+a_2+a_3)**-1\n",
- "\n",
- "I=b*t**3*12**-1+b*t*(Y-y_1)**2+w_t*w_d**3*12**-1+w_t*w_d*(D*2**-1-Y)**2+b_1*t_1**3*12**-1+b_1*t_1*(y_3-Y)**2\n",
- "\n",
- "M=sigma*I*10**-8*(Y*10**-2)**-1 #B.M\n",
- "\n",
- "#Shear Stress in upper Flange at the junction with web\n",
- "S_1=F*b*t*(Y-y_1)*10**-6*(I*10**-8*b*10**-2)**-1*10**-3\n",
- "\n",
- "#Shear Stress in web at the junction with upper Flange \n",
- "S_2=S_1*b*t**-1\n",
- "\n",
- "#Max shear stress at the N.A\n",
- "S=F*(b*t*(Y-y_1)+w_t*(Y-t)*(Y-t)*2**-1)*10**-6*(I*10**-8*w_t*10**-2)**-1*10**-3\n",
- "\n",
- "#Shear Stress in Lower Flange at the junction with web\n",
- "S_3=F*(a_3*(D-Y-t_1*2**-1))*10**-6*(I*10**-8*b_1*10**-2)**-1*10**-3\n",
- "\n",
- "#Shear Stress in web at the junction with Lower Flange \n",
- "S_4=S_3*b_1*t_1**-1\n",
- "\n",
- "#Result\n",
- "print\"The Bending Moment section can take is\",round(M,2),\"N-m\"\n",
- "print\"The shear stress Distribution Diagram\"\n",
- "\n",
- "#Plotting the Shear stress distribution Diagram\n",
- "\n",
- "X_1=[0,5,5,15.19,30,30,35]\n",
- "Y_1=[0,S_1,S_2,S,S_3,S_4,0]\n",
- "Z_1=[0,0,0,0,0,0,0]\n",
- "plt.plot(X_1,Y_1,X_1,Z_1)\n",
- "plt.xlabel(\"Length x in m\")\n",
- "plt.ylabel(\"Shear Stress in kN/m**2\")\n",
- "plt.show()\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Bending Moment section can take is 57821.07 N-m\n",
- "The shear stress Distribution Diagram\n"
- ]
- },
- {
- "metadata": {},
- "output_type": "display_data",
- "png": "iVBORw0KGgoAAAANSUhEUgAAAY4AAAEPCAYAAABV6CMBAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nu0jiEEIIYRdJHEIIIezy/0Du21HzYcG/AAAAAElFTkSuQmCC\n",
- "text": [
- "<matplotlib.figure.Figure at 0x5641790>"
- ]
- }
- ],
- "prompt_number": 11
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [],
- "language": "python",
- "metadata": {},
- "outputs": []
- }
- ],
- "metadata": {}
- }
- ]
-}
\ No newline at end of file diff --git a/Strength_Of_Materials_by_B_K_Sarkar/chapter_14_som.ipynb b/Strength_Of_Materials_by_B_K_Sarkar/chapter_14_som.ipynb deleted file mode 100755 index 636bc8f6..00000000 --- a/Strength_Of_Materials_by_B_K_Sarkar/chapter_14_som.ipynb +++ /dev/null @@ -1,971 +0,0 @@ -{
- "metadata": {
- "name": "chapter 14 som.ipynb"
- },
- "nbformat": 3,
- "nbformat_minor": 0,
- "worksheets": [
- {
- "cells": [
- {
- "cell_type": "heading",
- "level": 1,
- "metadata": {},
- "source": [
- "Chapter 14:Dams and Retaining Walls"
- ]
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 14.1,Page No.325"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "%matplotlib inline\n",
- "\n",
- "#Initilization of variables\n",
- "b=2 #m #width \n",
- "FOS=1.5 #Factor of safety\n",
- "#rho_mason=2.5*rho_w\n",
- "mu=0.5 #coeffeicient of friction\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#Let L=1 m (length of dam)\n",
- "L=1\n",
- "#W=b*H*L*rho\n",
- "#After substituting values and Further simplifying we get\n",
- "#W=2*H*rho\n",
- "\n",
- "#Total Pressure\n",
- "#P=W*H**2*2**-1\n",
- "\n",
- "x_bar=b*2**-1 #Distance of Line of action of W from waterface\n",
- "\n",
- "#Distance of pt where resultant cuts the base measured from Line of action\n",
- "#x=P*W**-1*H*3**-1\n",
- "#After substituting values and Further simplifying we get\n",
- "#x=H**2*30**-1\n",
- "\n",
- "#x_bar+x=2*b*3**-1\n",
- "#After substituting values and Further simplifying we get\n",
- "#1+H**2*30**-1=2*b*3**-1\n",
- "H=(30*(2*b*3**-1-1))**0.5 #height of dam\n",
- "\n",
- "#Frictional Resistance offered at the base\n",
- "#F=mu*W\n",
- "#After substituting values and Further simplifying we get\n",
- "#F=3.16*rho\n",
- "\n",
- "#Total Lateral Pressure\n",
- "#P=W*H**2*2**-1\n",
- "#P=4.99*W\n",
- "\n",
- "#Factor of safety against sliding\n",
- "#FOS1=F*P**-1=3.16*4.99**-1*rho_mason*rho_w**-1\n",
- "FOS1=3.16*4.99**-1*2.5\n",
- "\n",
- "#FOS1>FOS\n",
- "\n",
- "#Result\n",
- "print\"Dam is safe against sliding\",round(FOS1,2)"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Dam is safe against sliding 1.58\n"
- ]
- }
- ],
- "prompt_number": 2
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 14.2,Page No.327"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "%matplotlib inline\n",
- "\n",
- "#Initilization of variables\n",
- "D=2 #m #External Diameter\n",
- "d=1.5 #m #Internal Diameter\n",
- "P=1600 #N/m**2 #N/m**2 #Wind Pressure\n",
- "W=19200 #N/m**2 #Weight of masonry\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#Let H be max height of dam\n",
- "\n",
- "#W2=pi*4**-1*(D**2-d**2)*H*W #weight of chimney\n",
- "#W2=26400*H\n",
- "\n",
- "#Eccentricrty\n",
- "x=(D**2+d**2)*(8*D)**-1\n",
- "\n",
- "#P2=H*D*P #Lateral thrust of wind on chimney\n",
- "#P2=3200*H\n",
- "\n",
- "#Now by using the relation we get P*W**-1=x*(H*2**-1)**-1\n",
- "#After substituting values and Further simplifying we get\n",
- "H=0.39*2*26400*3200**-1\n",
- "\n",
- "#result\n",
- "print\"The Height of Dam is\",round(H,2),\"m\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Height of Dam is 6.44 m\n"
- ]
- }
- ],
- "prompt_number": 3
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 14.3,Page No.327"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "%matplotlib inline\n",
- "\n",
- "#Initilization of variables\n",
- "rho_w=10 #KN/m**3 #Density of water\n",
- "rho_mason=22.4 #KN/m**3 #Density of mason\n",
- "H=6 #m #height of dam\n",
- "a=1 #m #width of top\n",
- "b=4 #m #bottom width\n",
- "h=5.5 #m #Weight of water depth \n",
- "\n",
- "#Calculations\n",
- "\n",
- "#Let L=1 m (length of dam)\n",
- "L=1\n",
- "\n",
- "#weight of dam\n",
- "W=(a+b)*2**-1*H*a*rho_mason\n",
- "\n",
- "#Lateral thrust\n",
- "P=rho_w*h**2*a*2**-1\n",
- "\n",
- "#distance of Line of action of W measured from vertical face\n",
- "x_bar=(b**2+b*a+a**2)*(3*(b+a))**-1\n",
- "\n",
- "#distance of pt where resultant cuts the base\n",
- "x=P*W**-1*h*3**-1\n",
- "\n",
- "#Eccentricity\n",
- "e=x_bar+x-b*2**-1\n",
- "\n",
- "#Stress at Pt B\n",
- "sigma1=W*b**-1*(1-6*e*b**-1)\n",
- "\n",
- "#stress at Pt C\n",
- "sigma2=W*b**-1*(1+6*e*b**-1)\n",
- "\n",
- "#Result\n",
- "print\"Max stress intensities at the base is\",round(sigma2,2),\"KN/m**2\"\n",
- "print\"Min stress intensities at the base is\",round(sigma1,2),\"KN/m**2\"\n",
- "\n",
- "#Plotting the Shear Force Diagram\n",
- "\n",
- "X1=[0,L,L]\n",
- "Y1=[sigma2,sigma1,0]\n",
- "Z1=[0,0,0]\n",
- "plt.plot(X1,Y1,X1,Z1)\n",
- "plt.xlabel(\"Length x in m\")\n",
- "plt.ylabel(\"Shear Force in kN\")\n",
- "plt.show()\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Max stress intensities at the base is 112.38 KN/m**2\n",
- "Min stress intensities at the base is 55.62 KN/m**2\n"
- ]
- },
- {
- "metadata": {},
- "output_type": "display_data",
- "png": "iVBORw0KGgoAAAANSUhEUgAAAYgAAAEPCAYAAABY9lNGAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
- "text": [
- "<matplotlib.figure.Figure at 0x55942b0>"
- ]
- }
- ],
- "prompt_number": 29
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 14.4,Page No.329"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "%matplotlib inline\n",
- "\n",
- "#Initilization of variables\n",
- "H=10 #m #height od dam\n",
- "a=2 #m #top width\n",
- "b=5 #m #bottom width\n",
- "W=25 #KN/m**3 #weight of mason\n",
- "rho_w=10 #KN/m**3 #density of water\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#Let L=1 m (length of dam)\n",
- "L=1\n",
- "\n",
- "#weight of dam\n",
- "W2=(b+a)*H*L*W*2**-1\n",
- "\n",
- "##Lateral thrust\n",
- "P=rho_w*H**2*L*2**-1 \n",
- "\n",
- "#Resultant thrust\n",
- "R=(P**2+W**2)**0.5\n",
- "\n",
- "#Distance of Line of action from vertical base\n",
- "x_bar=(b**2+b*a+a**2)*(3*(b+a))**-1\n",
- "\n",
- "##distance of pt where resultant cuts the base\n",
- "x=P*W2**-1*H*3**-1\n",
- "\n",
- "#Eccentricity\n",
- "e=x_bar+x-b*2**-1\n",
- "\n",
- "#Stress at Pt B\n",
- "sigma1=W2*b**-1*(1-6*e*b**-1)\n",
- "\n",
- "#stress at Pt C\n",
- "sigma2=W2*b**-1*(1+6*e*b**-1)\n",
- "\n",
- "#Result\n",
- "print\"The Resultant Thrust on the base is\",round(R,2),\"KN\"\n",
- "\n",
- "#Plotting the Shear Force Diagram\n",
- "\n",
- "X1=[0,L,L]\n",
- "Y1=[-sigma2,-sigma1,0]\n",
- "Z1=[0,0,0]\n",
- "plt.plot(X1,Y1,X1,Z1)\n",
- "plt.xlabel(\"Length x in m\")\n",
- "plt.ylabel(\"Shear Force in kN\")\n",
- "plt.show()\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Resultant Thrust on the base is 500.62 KN\n"
- ]
- },
- {
- "metadata": {},
- "output_type": "display_data",
- "png": "iVBORw0KGgoAAAANSUhEUgAAAZAAAAEPCAYAAABsj5JaAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
- "text": [
- "<matplotlib.figure.Figure at 0x5657d50>"
- ]
- }
- ],
- "prompt_number": 28
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 14.5,Page No.330"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "%matplotlib inline\n",
- "\n",
- "#Initilization of variables\n",
- "H=30 #m #height of Dam\n",
- "h=29 #m #height of water\n",
- "rho_w=9810 #N/m**3 \n",
- "rho_mason=22560 #N/m**3\n",
- "sigma1=0 #KN/m**3\n",
- "sigma2=880 #KN/m**3\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#Let L=1 m (length of dam)\n",
- "L=1\n",
- "\n",
- "#weight of dam\n",
- "#W=(a+b)*2**-1*L*H*rho_mason*10**-3\n",
- "#After substituting values and Further simplifying we get\n",
- "#W=338.4*(a+b) #equation1\n",
- "\n",
- "#Pressure at B=0, Sinc etension at base has just been avoided\n",
- "\n",
- "#Eccentricity\n",
- "e=b*6**-1 #as sigma1=0\n",
- "\n",
- "#Pressure at C\n",
- "#sigma2=W2*b**-1*(1+6*e*b**-1)\n",
- "#After substituting values and Further simplifying we get\n",
- "#W=440*b\n",
- "\n",
- "#From equation1,440*b=338*(a+b)\n",
- "#b=3.33*a\n",
- "\n",
- "#the distance of C.Gof dam\n",
- "#x_bar=(b**2+b*a+a**2)*(3*(b+a))**-1\n",
- "#After substituting values and Further simplifying we get\n",
- "#x_bar=1.187*a\n",
- "\n",
- "#distance of pt where resultant cuts the base\n",
- "#x=P*W2**-1*H*3**-1\n",
- "#After substituting values and Further simplifying we get\n",
- "#x=27.214*a**-1\n",
- "\n",
- "#Now x_bar+x=2*3**-1*b\n",
- "#After substituting values and Further simplifying we get\n",
- "a=(27.17*(2.22-1.187)**-1)**0.5\n",
- "b=3.33*a\n",
- "\n",
- "#Result\n",
- "print\"The top width dam is\",round(a,2),\"m\"\n",
- "print\"The bottom width dam is\",round(b,2),\"m\"\n",
- "\n",
- "\n",
- "#Plotting the Shear Force Diagram\n",
- "\n",
- "X1=[0,L,L]\n",
- "Y1=[sigma2,sigma1,0]\n",
- "Z1=[0,0,0]\n",
- "plt.plot(X1,Y1,X1,Z1)\n",
- "plt.xlabel(\"Length x in m\")\n",
- "plt.ylabel(\"Shear Force in kN\")\n",
- "plt.show()\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The top width dam is 5.13 m\n",
- "The bottom width dam is 17.08 m\n"
- ]
- },
- {
- "metadata": {},
- "output_type": "display_data",
- "png": "iVBORw0KGgoAAAANSUhEUgAAAYkAAAEPCAYAAAC3NDh4AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nhIiI1EhJQkREavT/G7kEgAv8kjUAAAAASUVORK5CYII=\n",
- "text": [
- "<matplotlib.figure.Figure at 0x5650490>"
- ]
- }
- ],
- "prompt_number": 35
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 14.6,Page No.332"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "%matplotlib inline\n",
- "\n",
- "#Initilization of variables\n",
- "H= 4 #m #height of dam\n",
- "a=1 #m #Top width\n",
- "b=3 #m #bottom width\n",
- "rho1=9810 #N/m**3 #weight of water\n",
- "rho2=19620 #n/m**3 #Weight of mason\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#Let L=1 m (length of dam)\n",
- "L=1\n",
- "\n",
- "#weight of dam\n",
- "W=(a+b)*2**-1*L*H*rho2*10**-3\n",
- "\n",
- "##Lateral thrust\n",
- "P=rho1*H**2*L*2**-1*10**-3 \n",
- "\n",
- "#Distance of Line of action from vertical base\n",
- "x_bar=(b**2+b*a+a**2)*(3*(b+a))**-1\n",
- "\n",
- "#distance of pt where resultant cuts the base\n",
- "x=P*W**-1*H*3**-1\n",
- "\n",
- "#Eccentricity\n",
- "e=x_bar+x-b*2**-1\n",
- "\n",
- "#Stress at Pt B\n",
- "sigma1=W*10**3*b**-1*(1-6*e*b**-1)\n",
- "\n",
- "#stress at Pt C\n",
- "sigma2=W*10**3*b**-1*(1+6*e*b**-1)\n",
- "\n",
- "#Stresses at the base when resorvoir is empty\n",
- "\n",
- "e2=x_bar-b*2**-1\n",
- "\n",
- "#Minus sign indicates sigma_b>sigma_c\n",
- "\n",
- "#Stress at C\n",
- "sigma2_2=W*10**3*b**-1*(1+6*round(e2,2)*b**-1)\n",
- "\n",
- "#Stress at Pt B\n",
- "sigma1_2=W*10**3*b**-1*(1-6*round(e2,2)*b**-1)\n",
- "\n",
- "#result\n",
- "print\"When the Reservoir is full :sigma1\",round(sigma1,2),\"KN/m**2\"\n",
- "print\" :sigma2\",round(sigma2,2),\"KN/m**2\"\n",
- "print\"When the Reservoir is empty:sigma1_2\",round(sigma1_2,2),\"KN/m**2\"\n",
- "print\" :sigma2_2\",round(sigma2_2,2),\"KN/m**2\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "When the Reservoir is full :sigma1 26160.0 KN/m**2\n",
- " :sigma2 78480.0 KN/m**2\n",
- "When the Reservoir is empty:sigma1_2 96268.8 KN/m**2\n",
- " :sigma2_2 8371.2 KN/m**2\n"
- ]
- }
- ],
- "prompt_number": 21
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 14.7,Page No.333"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "%matplotlib inline\n",
- "\n",
- "#Initilization of variables\n",
- "H=8 #m #height of dam\n",
- "h=7.5 #m #Height of water\n",
- "a=1 #m #top width\n",
- "mu=0.6 #Coeffeicient of friction\n",
- "rho_mason=22.4 #KN/m**3 #weight of mason\n",
- "rho_w=9.81 #KN/m**3 #density of water\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#weight of dam\n",
- "#W=(a+b)*2**-1*L*H*rho2*10**-3\n",
- "#After substituting values and further simplifying we get\n",
- "#W=89600*(b+1)\n",
- "\n",
- "#Distance of Line of action from vertical base\n",
- "#x_bar=(b**2+b*a+a**2)*(3*(b+a))**-1\n",
- "#After substituting values and further simplifying we get\n",
- "#x_bar=(1+b+b**2)*(3*(1+b))**-1\n",
- "\n",
- "#Lateral thrust\n",
- "P=rho_w*h**2*2**-1\n",
- "\n",
- "#Min width to avoid tension at base\n",
- "#Z=x_bar+P*W**-1*h*3**-1\n",
- "#Z=2*3**-1*b\n",
- "#After substituting values and further simplifying we get\n",
- "#b**2+b-24.09=0\n",
- "a=1\n",
- "b=1\n",
- "c=-24.09\n",
- "\n",
- "X=b**2-4*a*c\n",
- "\n",
- "b1=(-b+X**0.5)*(2*a)**-1\n",
- "b2=(-b-X**0.5)*(2*a)**-1\n",
- "\n",
- "#Thus width cannot be negative,b1 is considered\n",
- "\n",
- "#Min width to avoid sliding\n",
- "#mu*W>P\n",
- "#After substituting values and further simplifying we get\n",
- "b=P*10**3*(mu*89600)**-1-1\n",
- "\n",
- "#Result\n",
- "print\"The Min bottom width is\",round(b,2),\"m\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Min bottom width is 4.13 m\n"
- ]
- }
- ],
- "prompt_number": 30
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 14.8,Page No.334"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "%matplotlib inline\n",
- "\n",
- "#Initilization of variables\n",
- "H=10 #m #height of dam\n",
- "a=1 #m #top width\n",
- "b=7 #m #Bottom width\n",
- "rho_mason=19620 #N/m**3 #weight of mason\n",
- "rho_w=9810 #N/m**3 #density of water\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#Lateral thrust\n",
- "P=rho_w*H**2*2**-1\n",
- "\n",
- "#weight of dam\n",
- "W=(rho_w*H*2**-1*a)+(rho_mason*(a+b)*2**-1*H)\n",
- "\n",
- "#Taking Moment at B,M_B=0\n",
- "x_bar=((rho_w*H*2**-1*1*3**-1)+(rho_mason*H*2**-1*2*3**-1)+(rho_mason*H*1.5)+(rho_mason*H*5*11*2**-1*3**-1))*W**-1\n",
- "\n",
- "#Now using relation we get\n",
- "x=P*W**-1*H*3**-1\n",
- "\n",
- "#Eccentricity\n",
- "e=x_bar+x-b*2**-1\n",
- "\n",
- "#Max stress\n",
- "sigma_max=W*b**-1*(1+6*round(e,2)*b**-1)\n",
- "\n",
- "#Min stress\n",
- "sigma_min=W*b**-1*(1-6*round(e,2)*b**-1)\n",
- "\n",
- "#Result\n",
- "print\"The Max stresses on the base is\",round(sigma_max,2),\"N/m**2\"\n",
- "print\"The Min stresses on the base is\",round(sigma_min,2),\"N/m**2\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Max stresses on the base is 228372.8 N/m**2\n",
- "The Min stresses on the base is 9870.06 N/m**2\n"
- ]
- }
- ],
- "prompt_number": 47
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 14.10,Page No.337"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "%matplotlib inline\n",
- "\n",
- "#Initilization of variables\n",
- "H=6 #m #height of dam\n",
- "a=1 #m #top width\n",
- "b=3 #m #Bottom width\n",
- "rho_mason=22 #KN/m**3 #weight of mason\n",
- "rho_earth=16 #KN/m**3 #density of water\n",
- "phi=30 #Degree #angle of repose\n",
- "mu=0.5 #Coeffecient of friction\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#Let Length of dam ,L=1 m\n",
- "L=1 #m\n",
- "\n",
- "#weight of dam\n",
- "W=(a+b)*2**-1*L*H*rho_mason\n",
- "\n",
- "#Lateral thrust\n",
- "P=rho_earth*H**2*L*2**-1*((1-sin(30*pi*180**-1))*(1+sin(phi*pi*180**-1))**-1)\n",
- "\n",
- "#Distance of Line of action from vertical base\n",
- "x_bar=(b**2+b*a+a**2)*(3*(b+a))**-1\n",
- "\n",
- "#distance of pt where resultant cuts the base\n",
- "x=P*W**-1*H*3**-1\n",
- "\n",
- "#Eccentricity\n",
- "e=x_bar+x-b*2**-1\n",
- "e_max=b*6**-1\n",
- "\n",
- "#stress at toe\n",
- "sigma2=W*10**3*b**-1*(1+6*round(e,2)*b**-1)*10**-3\n",
- "\n",
- "#Safe agaainst bearing\n",
- "\n",
- "#Frictional Resistance \n",
- "F=mu*W\n",
- "\n",
- "#Hence F>P,so it is safe against sliding\n",
- "\n",
- "#Result\n",
- "print\"Safe against bearing as well as sliding\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Safe against bearing as well as sliding\n"
- ]
- }
- ],
- "prompt_number": 69
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 14.11,Page No.338"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "%matplotlib inline\n",
- "\n",
- "#Initilization of variables\n",
- "H=8 #m #height of dam\n",
- "a=1 #m #top width\n",
- "b=4.5 #m #Bottom width\n",
- "rho_mason=24 #KN/m**3 #weight of mason\n",
- "rho_earth=20 #KN/m**3 #density of water\n",
- "phi=30 #Degree #angle of repose\n",
- "mu=0.5 #Coeffecient of friction\n",
- "BC=120 #KN/m**2\n",
- "\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#Let Length of dam ,L=1 m\n",
- "L=1 #m\n",
- "\n",
- "#weight of dam\n",
- "W=(a+b)*2**-1*L*H*rho_mason\n",
- "\n",
- "#Rankine's coeff earth pressure\n",
- "K=((1-sin(30*pi*180**-1))*(1+sin(phi*pi*180**-1))**-1)\n",
- "\n",
- "#Lateral thrust\n",
- "P=rho_earth*H**2*L*2**-1*round(K,2)\n",
- "\n",
- "#Distance of Line of action from vertical base\n",
- "x_bar=(b**2+b*a+a**2)*(3*(b+a))**-1\n",
- "\n",
- "#distance of pt where resultant cuts the base\n",
- "x=P*W**-1*H*3**-1\n",
- "\n",
- "#Eccentricity\n",
- "e=x_bar+x-b*2**-1\n",
- "\n",
- "#Pressure at heel B\n",
- "sigma1=W*b**-1*(1-6*round(e,2)*b**-1)\n",
- "\n",
- "#Pressure at heel C\n",
- "sigma2=W*b**-1*(1+6*round(e,2)*b**-1)\n",
- "\n",
- "#sigma2>120 #KN/m**2,so it is unsafe against bearing capacity of the soil\n",
- "\n",
- "#result\n",
- "print\"Unsafe against the bearing capacity of soil\" \n",
- "\n",
- "#Plotting the Shear Force Diagram\n",
- "\n",
- "X1=[0,L,L]\n",
- "Y1=[sigma2,sigma1,0]\n",
- "Z1=[0,0,0]\n",
- "plt.plot(X1,Y1,X1,Z1)\n",
- "plt.xlabel(\"Length x in m\")\n",
- "plt.ylabel(\"Shear Force in kN\")\n",
- "plt.show()\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Unsafe against the bearing capacity of soil\n"
- ]
- },
- {
- "metadata": {},
- "output_type": "display_data",
- "png": "iVBORw0KGgoAAAANSUhEUgAAAYgAAAEPCAYAAABY9lNGAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzt3XlYlXX+//HnQchMLXcoYMJAQ8Q990zIcCvNXChsQck2\n09L5Tuk08yutmSRnGtdsqsklW6y0ESszLUUrMTRNTUpcQBHU0ZTMTBG4f3988uRyEATOuQ/welzX\nua5z7nPOfb+7LztvPtv747Asy0JEROQ8PnYHICIi3kkJQkREXFKCEBERl5QgRETEJSUIERFxSQlC\nRERccluCSEhIwN/fnxYtWjiPpaam0qFDB9q0aUP79u1Zv369871JkybRpEkTwsPDWb58ubvCEhGR\nEnK4ax3EF198Qa1atbjvvvvYunUrAFFRUfz5z3+mV69efPLJJ0yePJlVq1aRlpbG0KFDWb9+PdnZ\n2dxyyy2kp6fj46MGjoiIXdz2C9ytWzfq1q17zrGrr76an376CYDc3FwCAwMBSEpKIi4uDj8/P0JC\nQggLCyM1NdVdoYmISAn4evJiiYmJ3HjjjfzpT3+isLCQlJQUAHJycujUqZPzc0FBQWRnZ3syNBER\nOY9H+3Duv/9+pk+fzt69e5kyZQoJCQlFftbhcHgwMhEROZ9HWxCpqal89tlnAAwePJgRI0YAEBgY\nSFZWlvNz+/btc3Y/nS0sLIxdu3Z5JlgRkUoiNDSUnTt3XvL3PNqCCAsLY/Xq1QCsXLmSpk2bAtC/\nf38WLFhAXl4eGRkZ7Nixgw4dOlzw/V27dmFZlh6WxTPPPGN7DN7y0L3QvdC9uPijtH9Yu60FERcX\nx+rVqzl8+DDBwcE8++yzvPrqqzz66KOcOnWKGjVq8OqrrwIQERFBbGwsERER+Pr6MmvWLHUxiYjY\nzG0J4p133nF5/Ouvv3Z5/KmnnuKpp54q9rwTJ8LDD4O/f5nCExGRYlS4hQY5ORAeDgkJsGWL3dHY\nJyoqyu4QvIbuxe90L36ne1F2blso5w4OhwPLsjh8GF55BV56CZo1g7FjoW9f0Lo6EZELnfntvOTv\nVcQEcUZeHrz3HkyZAsePw+OPQ3w81KxpY5AiIl6mSiaIMywLvvgCpk6FNWvg/vth1CgIDrYhSBER\nL1PaBFEpOmUcDrjpJvjgA0hNhVOnoFUriIuDIsbERUSkGJWiBeHKTz/B7NkwfTpcfbUZp7jjDvD1\n6NJAERH7VekupovJz4ekJDNOkZUFo0fDiBFQp46bghQR8TJVuovpYnx9YdAg+PJLWLgQNm2C666D\nxx6DUqw8FxGpMip9gjhb+/bw1luwdSvUqgWdO8Ptt0NyshnoFhGR31X6LqaLOXEC3njDzH6qUQPG\njIG77oLq1cvtEiIittMYRBkUFsKnn5pxiq1bYeRIU86jYcNyv5SIiMdpDKIMfHygTx9YvhxWrIC9\ne6FpUzOY/d13dkcnImIPJYjzREbCa69Bejpcey3ExEDPnrB0qWlpiIhUFepiKsapU/Duu6b76eRJ\nU87jvvvgiis8GoaISKlpDMLNLAtWrzaJYu1a0/00ahS42PhORMSraAzCzRwOiIoyi+5SUuCXX6BF\nC7j7btiwwe7oRETKn9sSREJCAv7+/rRo0eKc4zNmzKBZs2ZERkYybtw45/FJkybRpEkTwsPDWb58\nubvCKhdhYaaEx+7d0LatWYh3442waBEUFNgdnYhI+XBbF9MXX3xBrVq1uO+++9i6dSsAq1at4vnn\nn2fp0qX4+flx6NAhGjZsSFpaGkOHDmX9+vVkZ2dzyy23kJ6ejs95GzzY2cV0Mfn58N//mu6n/fvN\nKu2EBLjqKrsjExHxwi6mbt26Ubdu3XOOvfzyy/z5z3/Gz88PgIa/LTRISkoiLi4OPz8/QkJCCAsL\nIzU11V2hlTtfXxgyxIxNLFhgKso2bmwW3u3ebXd0IiKl49ExiB07drBmzRo6depEVFQUG37rvM/J\nySEoKMj5uaCgILKzsz0ZWrnp2BHeeQc2bzYrsjt0MFVk16xROQ8RqVg8Wvw6Pz+fo0ePsm7dOtav\nX09sbCy7i/gT2+FwuDw+YcIE5/OoqCiv3Xc2OBheeAGefhrmzTOznmrXNmXHY2PhssvsjlBEKqvk\n5GSSk5PLfB6PJoigoCAGDhwIQPv27fHx8eHw4cMEBgaSlZXl/Ny+ffsILGL+6NkJoiKoWfP30h1L\nl5q6T+PGmWMPPQQNGtgdoYhUNuf/8Txx4sRSncejXUwDBgxg5cqVAKSnp5OXl0eDBg3o378/CxYs\nIC8vj4yMDHbs2EGHDh08GZrb+fjAbbfBZ5/BJ5/Arl3QpIlJEmlpdkcnInIhtyWIuLg4unTpQnp6\nOsHBwcyZM4eEhAR2795NixYtiIuL44033gAgIiKC2NhYIiIi6NOnD7NmzSqyi6kyaNnS7Hb3ww9w\nzTVw883Qu7cpGKhxChHxFlpJ7QVOnjQD21OmmCmzY8bAvfeaEuQiImWlUhuVgGXBqlUmUXz9NTz4\nIDz6qNlTW0SktLxuHYRcOofDdDd9+KHZIjU3FyIiTGti40a7oxORqkYJwks1bQozZ5qFdi1amK1R\nu3c3K7ZVzkNEPEFdTBXE6dPwwQem++nQod/LedSubXdkIuLt1MVUyfn5wZ13wrp18Oab8NVXEBIC\nf/wjZGbaHZ2IVEZKEBVQ587w3ntmXKJaNWjXDgYPNuMWVbSBJSJuoC6mSuDnn005j2nToE4dU85j\nyBDT6hAR0TRXoaAAPv7YjFPs2GF2vHvwQahXz+7IRMROGoMQqlWD/v3NWoqPPjIrtUND4ZFHzHMR\nkUuhBFFJtW4Nc+fC999Do0ZmimzfvrBihcYpRKRk1MVURZw8CW+9ZbqfHA5TzmPoUJXzEKkKNAYh\nJWJZ8PnnJlFs2GCqyY4cCQEBdkcmIu6iMQgpEYcDbrnFDGavXm0W3TVrBsOGwbff2h2diHgTJYgq\nLDwcXn7Z7E0RHm72q4iOhiVLVM5DRNTFJGc5fRref990Px09Co8/DsOHQ61adkcmImWhMQgpN5YF\na9eaRJGcbJLE6NHwhz/YHZmIlIbXjUEkJCTg7+9PixYtLnjvxRdfxMfHhyNHjjiPTZo0iSZNmhAe\nHs7y5cvdFZaUgMMBXbvCwoWwfj0UFkKbNhAbCykpdkcnIp7itgQxfPhwli1bdsHxrKwsVqxYwbXX\nXus8lpaWxrvvvktaWhrLli1j5MiRFBYWuis0uQSNG8OLL0JGhkka99wDnTrBggWmS0pEKi+3JYhu\n3bpRt27dC47/8Y9/ZPLkyeccS0pKIi4uDj8/P0JCQggLCyM1NdVdoUkpXHmlGZNIT4fx483gdmgo\nTJ5sxitEpPLx6CympKQkgoKCaNmy5TnHc3JyCAoKcr4OCgoiOzvbk6FJCVWrBgMGmCmyixfDd9/B\nddeZrVHT0+2OTkTKk6+nLnTixAmef/55VqxY4Tx2sUETh8Ph8viECROcz6OiooiKiiqvEOUStW0L\nb7wBOTkwaxbceCN07GhWad98sxnLEBHPS05OJjk5uczncesspszMTPr168fWrVvZunUrt9xyC1dc\ncQUA+/btIzAwkK+//po5c+YAMH78eAB69+7NxIkT6dix47nBahaTV/v1V7OZ0dSp4OtrEkVcHFx+\nud2RiVRtXjnN9ewEcb7GjRvzzTffUK9ePdLS0hg6dCipqalkZ2dzyy23sHPnzgtaEUoQFYNlwfLl\nZprst9+aarIPPwz+/nZHJlI1ed0017i4OLp06UJ6ejrBwcHOVsIZZ//4R0REEBsbS0REBH369GHW\nrFlFdjGJ93M4oFcvWLYMVq40XVDh4WYP7S1b7I5OREpKC+XEIw4fhldfhZdeMsli7FhTftxHxV5E\n3M4ru5jKmxJExZeXZ/bTnjIFjh83U2fj46FmTbsjE6m8lCCkQrEs+PJLkyjWrIH77zdbpAYH2x2Z\nSOXjdWMQIhfjcEC3bvDBB5CaCqdOQatWZtbT11/bHZ2IgFoQ4kV++glmz4bp0+Hqq804xR13mCmz\nIlJ66mKSSiM/3+xJMWUK7N1rKsmOGAF16tgdmUjFpC4mqTR8fWHgQPjiC1i0CDZtMuU8HnsMdu60\nOzqRqkMJQrzaDTfAW2/B1q1m46LOneH2280+FWpMiriXupikQjlxwtR/mjoVatQw5TzuuguqV7c7\nMhHvpTEIqVIKC+HTT804xdatMHKkKefRsKHdkYl4H41BSJXi4wN9+piaTytWmMHspk3NYPZ339kd\nnUjloAQhFV5kJLz2mtmP4tprISYGevaEpUtNS0NESkddTFLpnDoF775rup9OnjTlPO67D36rNC9S\n5WgMQuQ8lmV2vps6Fb76ynQ/jRoFgYF2RybiWRqDEDmPwwFRUWZr1JQU+OUXaNEC7r4bNmywOzoR\n76cWhFQpubnw+uumnEdwsCnnMWCA2WtbpLIq9y6m6OjoIi8EsHLlyku+WFkpQUh5yc+H//7XdD/l\n5JhV2gkJcNVVdkcmUv7KPUFsOKsNfiYprFu3jhdeeIFGjRqd874rCQkJfPzxxzRq1Mi55egTTzzB\nRx99xGWXXUZoaChz5szhqt/+j5w0aRKzZ8+mWrVqTJ8+nZ49e5bbf6TIxaSmmgHtTz81g9mPPWZK\ne4hUFqX+7bRKYNWqVVaPHj2sLl26WEuXLi3JV6w1a9ZYGzdutCIjI53Hli9fbhUUFFiWZVnjxo2z\nxo0bZ1mWZW3bts1q1aqVlZeXZ2VkZFihoaHOz52thOGKlMrevZY1bpxl1a9vWQMGWNbq1ZZVWGh3\nVCJlV9rfzosOUi9btoxu3brx3HPP8Ze//IWvvvqKPn36lCjxdOvWjbp1655zLCYmBp/f9pjs2LEj\n+/btAyApKYm4uDj8/PwICQkhLCyM1NTUS892ImUQHAyJibBnj1lL8cADphbUm2+anfBEqpoiK+23\nb9+eQ4cO8ac//YnOnTsDsHHjRuf7bdu2LdOFZ8+eTVxcHAA5OTl06tTJ+V5QUBDZ2dllOr9IadWs\n+Xvpjk8+Md1P48aZYw89BA0a2B2hiGcUmSBq1qxJzZo1WbRoEYsWLbrg/VWrVpX6on//+9+57LLL\nGDp0aJGfOTPucb4JEyY4n0dFRREVFVXqOEQuxscHbr3VPLZsMQPaTZpAbKxZfBcRYXeEIq4lJyeT\nnJxc5vMUmSDOnLywsNDZLXTGyZMnS33BuXPnsnTpUj7//HPnscDAQLKyspyv9+3bR2ARq5nOThAi\nntKypdntbtIk+Pe/4eaboXVrM022Z0+z5kLEW5z/x/PEiRNLdZ5iF8qNGDHinNfHjx+nb9++pbrY\nsmXL+Mc//kFSUhKXX36583j//v1ZsGABeXl5ZGRksGPHDjp06FCqa4i4k78/PPMMZGaaMuNPPgnN\nm8Orr8Kvv9odnUj5KjZBBAYGMnLkSACOHj1Kz549uffee4s9cVxcHF26dGH79u0EBwcze/ZsRo8e\nzfHjx4mJiaFNmzbO80ZERBAbG0tERAR9+vRh1qxZRXYxiXiDyy+HYcPg229h5kz48ENTKPCvf4X9\n++2OTqR8lGgl9RNPPMGxY8f45ptvGD9+PIMHD/ZEbBfQOgjxZunpZoX222+bcYuxY6GMczlEykW5\nL5Q7MzB95sTPPfcc7du3p3fv3jgcDgYOHFi2iEtBCUIqgqNHTfnxmTOhcWOz613//irnIfYp9wQx\nbNiwc7p5LMs65/WcOXNKEWbZKEFIRXL6NHzwgZkme+jQ7+U8ate2OzKpalTuW8SLpaSYabKffQbx\n8SZZhITYHZVUFSr3LeLFOnc2mxht2mS6mtq1g8GD4csvzb4VIt5ILQgRGxw/DnPnwrRpUKeOGdAe\nMgT8/OyOTCojdTGJVEAFBfDxx6b7KT3d7Hj34INQr57dkUll4rYEcfLkSRYtWkRmZib5+fnOiz39\n9NOli7QMlCCkMvv2W5MokpLMIrzHH4fwcLujksrAbWMQt99+O0uWLMHPz49atWpRq1YtatasWaog\nRaRorVubbqfvv4dGjaB7d+jbF1as0DiF2KPYFkRkZCTfffedp+K5KLUgpCo5eRLeesu0KsCspxg6\nFGrUsDcuqXjc1oLo0qULW7ZsKVVQIlJ6l18O999vKslOmWLWVISEwNNPw4EDdkcnVUGxLYhmzZqx\nc+dOGjduTPXq1c2XHA5bkoZaEFLV/fCDmfm0YAHcfrtpVbRubXdU4u3cNkidmZnp8niIDat8lCBE\njCNHTAXZmTPNHhVjx5r6TyrnIa6Ue4I4duwYV155JUeOHHH5xXo2zMNTghA51+nTsHCh6YI6csTM\nfBo+HGrVsjsy8SblniBuvfVWPv74Y0JCQi4ove1wONi9e3fpIi0DJQgR1ywL1q41iSI52SSJ0aPh\nD3+wOzLxBlooJyKA2cxoxgwzZbZHD9P99Nu28lJFeV0tpoSEBPz9/WnRooXz2JEjR4iJiaFp06b0\n7NmT3Nxc53uTJk2iSZMmhIeHs3z5cneFJVLphYTAiy+aRHHjjXDPPdCpkxnYPn3a7uikInFbghg+\nfDjLli0751hiYiIxMTGkp6fTo0cPEhMTAUhLS+Pdd98lLS2NZcuWMXLkSAoLC90VmkiVULu2qRqb\nng7jx8PLL0NoKEyebPasECmO2xJEt27dqFu37jnHlixZQnx8PADx8fEsXrwYgKSkJOLi4vDz8yMk\nJISwsDBSU1PdFZpIlVKtGgwYAKtXw+LF8N13JlE8+qhJHiJFKVGC+OKLL5wbBB06dIiMjIxSXezg\nwYP4+/sD4O/vz8GDBwHIyckhKCjI+bmgoCCys7NLdQ0RKVrbtvDGGyZJ1K1ruqD69YOVK1XOQy5U\nbIKYMGECkydPZtKkSQDk5eVxzz33lPnCDofjgtlR578vIu5xzTXwt7/Bnj1mO9TRo82CuzlzTIkP\nEQDf4j7w3//+l02bNtGuXTsAAgMD+fnnn0t1MX9/fw4cOEBAQAD79++nUaNGznNmZWU5P7dv3z4C\nAwNdnmPChAnO51FRUURFRZUqFhExdZ0eeABGjDBFAadMgT//GR55BB5+GH5r8EsFk5ycTHJyctlP\nZBWjffv2lmVZVuvWrS3Lsqzjx49bLVq0KO5rlmVZVkZGhhUZGel8/cQTT1iJiYmWZVnWpEmTrHHj\nxlmWZVnbtm2zWrVqZZ06dcravXu3dd1111mFhYUXnK8E4YpIGW3bZlkPPmhZdepY1vDhlrV5s90R\nSVmV9rez2C6mIUOG8NBDD5Gbm8urr75Kjx49GDFiRLGJJy4uji5durB9+3aCg4OZM2cO48ePZ8WK\nFTRt2pSVK1cyfvx4ACIiIoiNjSUiIoI+ffowa9YsdTGJ2CQiAl55BXbsgLAw6NPHrKf46CPQ5MKq\npUQL5ZYvX+5cm9CrVy9iYmLcHpgrWign4nl5efDee6b76fhxU84jPh60LUzF4baV1BkZGQQEBFDj\ntyL0v/76KwcPHlSxPpEqxrLgyy9NolizxpQiHzUKgoPtjkyK47aV1IMHD6baWSUifXx8GDx48CVf\nSEQqNocDunUz+1KkppqWRevWEBcHX39td3TiDsUmiIKCAi677DLn6+rVq3Na6/VFqrTrrjMtiYwM\n6NDB7KHdpQu8/z78tnW9VALFJogGDRqQlJTkfJ2UlESDBg3cGpSIVAxXXmmKAe7cCX/6E0yfblZp\n//OfcFapNamgih2D2LlzJ3fffTc5OTmAWeU8f/58wsLCPBLg2TQGIeL9Nmww+2gvXWoKBT72mJkN\nJfYp7W/nRRfKFRQU8O9//5uvv/7auTiudu3apYtQRKqEG26AN9+E7Gx46SVTarxLF9PS6N7djGVI\nxVBsC6JTp06kpKR4xboEtSBEKp4TJ2D+fNOquPxykyjuvBN+2+JePMBt01wffvhhcnJyGDJkCFdc\ncYXzYgMHDixdpGWgBCFScRUWwqefmkSxZQuMHGnKeTRsaHdklZ/bEsSwYcOcFzjbmequnqQEIVI5\nbNtmEsXChTBoEIwZA5GRdkdVeWnLURGpcA4dgn//G2bNghYtTPdTr17g47adaqomty2Uy8rK4o47\n7qBhw4Y0bNiQQYMGsW/fvlIFKSJytoYN4f/9P7M96j33wFNPQfPmJmmcOGF3dFJsghg+fDj9+/cn\nJyeHnJwc+vXrx/Dhwz0Rm4hUEdWrw333wcaNJjksWwbXXmsShvYOs0+xXUytWrVi8+bNxR7zBHUx\niVQdO3eahXdvvmkqyo4da6bQyqVzWxdT/fr1mT9/PgUFBeTn5/Pmm29qJbWIuF1YmEkQu3ebrVIH\nDTJbpC5aBAUFdkdXNRTbgsjMzGT06NGsW7cOgC5dujBjxgz+8Ic/eCTAs6kFIVJ15efD4sWmBlRO\njlmhff/9ptyHXFy5z2Jat24dnTp1KnNg5UkJQkTAVJOdMsWsq7jvPpMsrrvO7qi8V7l3MT3yyCPO\n5507dy5dVEWYNGkSzZs3p0WLFgwdOpRTp05x5MgRYmJiaNq0KT179iRXlb5EpAgdOsA778DmzWZ1\ndocOcMcdZp8K/Q1Zfko02/jkyZPldsHMzExee+01Nm7cyNatWykoKGDBggUkJiYSExNDeno6PXr0\nIDExsdyuKSKVU3AwJCbCnj0QEwMPPPB7Lai8PLujq/iKTBAFBQUcOXKEH3/80fn87EdpXXnllfj5\n+XHixAny8/M5ceIE11xzDUuWLCE+Ph6A+Ph4Fi9eXOpriEjVUrOmKd3x/ffw7LMwdy40bgx//zsc\nPmx3dBVXkWMQISEhzvIalmWdU2rD4XCwe/fuUl/01Vdf5f/+7/+oUaMGvXr1Yv78+dStW5ejR486\nr1evXj3n67OvqzEIESmJLVtg2jSzA15srNlLOyLC7qjsUWFKbezatYt+/frxxRdfcNVVVzFkyBAG\nDRrE6NGjz0kI9erVu6ClogQhIpfqf/+Dl182j9atzXqKnj2rVtlxt+wH4Q4bNmygS5cu1K9fH4CB\nAweSkpJCQEAABw4cICAggP3799OoUSOX358wYYLzeVRUFFFRUR6IWkQqqkaN4JlnYNw4WLAAnnwS\n/vhH06K4916oUcPuCMtfcnIyycnJZT6Px1sQmzdv5u6772b9+vVcfvnlDBs2jA4dOrBnzx7q16/P\nuHHjSExMJDc394KBarUgRKSsLAtWrTLVZNetgwcfhEcfhauvtjsy96kwXUwAkydPZt68efj4+NC2\nbVv+85//8PPPPxMbG8vevXsJCQnhvffeo06dOucGqwQhIuVoxw4zTvH223Drrab7qW1bu6Mqf25J\nEPn5+TRv3pzt27eXKbjyogQhIu5w9Ci89hrMnGlmP40dC/36QbVqdkdWPtxSi8nX15fw8HD27NlT\n6sBERLxd3bpmbGLXLjNdNjERmjY1rYuff7Y7OvsU28XUrVs3Nm3aRIcOHahZs6b5ksPBkiVLPBLg\n2dSCEBFPWbfOlPP47DMYNgxGj4aQELujKh23jUEUNRJux+whJQgR8bS9e03X0+zZEBVlup+6dKlY\n02Qr1CB1aSlBiIhdjh83K7SnTYM6dUyiGDIE/Pzsjqx4btsPIiUlhfbt21OrVi38/Pzw8fHhStXX\nFZEqplYtGDUKtm+Hp5+G//zHDGgnJkIZqg95tWITxKhRo3j77bdp0qQJJ0+e5PXXX2fkyJGeiE1E\nxOv4+JgZTitXwkcfmYQRFgaPPAI//GB3dOWrRNVcmzRpQkFBAdWqVWP48OEsW7bM3XGJiHi91q1h\nzhxISzMrtrt3h759YcWKylF2vNgEUbNmTU6dOkWrVq148skn+de//qVxABGRswQEwMSJpuz4oEGm\nlEfLlvD661COuyV4XIm2HPX39ycvL48pU6Zw7NgxRo4cSVhYmKdidNIgtYhUBJYFn39upslu2AAP\nPWTWVwQE2BOPW2cxnThxgqysLK6//vpSBVdelCBEpKLZvt3MfFqwAPr3hzFjTNeUJ7ltFtOSJUto\n06YNvXr1AmDTpk3079//0iMUEamCrr8eZs2CnTshPBxuuw2io2HJEigstDu6iyu2BdG2bVtWrlxJ\ndHQ0mzZtAiAyMpLvvvvOIwGeTS0IEanoTp+GhQtN99PRo/DYYzB8uJlG6y5ua0H4+fldUFXVx6dE\nk59EROQ8fn4QFwdff20W3q1ZY0p4PPGEWbXtTYr9pW/evDlvvfUW+fn57Nixg9GjR9OlSxdPxCYi\nUmk5HNC1K7z/vhnILiyENm3M9qgpKXZHZxSbIGbMmMG2bduoXr06cXFxXHnllUydOtUTsYmIVAkh\nIfDii5CZCTfeCPfcA506wbvvmi4pu6gWk4iIlykogA8/NLve7d5tSnw88IApS14abpvmun37dv75\nz3+SmZlJfn6+82IrV64sXaRAbm4uI0aMYNu2bTgcDubMmUOTJk2488472bNnj3aUExH5zcaNJlF8\n9JEZu3j8cbNXxaVwW4Jo2bIljzzyCG3btqXab9srORwO2rVrd8kXOyM+Pp7u3buTkJBAfn4+v/zy\nC3//+99p0KABTz75JC+88AJHjx7VntQiIr/JyYGXX4ZXXoGOHU012ejokpUdd1uCaNeuHd98880l\nn7goP/30E23atGH37t3nHA8PD2f16tX4+/tz4MABoqKi+OG8yldKECJS1f36K7z5pmlV+PqahXdx\ncXD55UV/p9wTxJEjR7AsixkzZtCwYUMGDhxI9erVne/Xq1fvki8G8O233/LQQw8RERHB5s2badeu\nHVOnTiUoKIijR48CYFkW9erVc752BqsEISICmHIeK1aY9RSbNplqsg8/DP7+F3623BNESEgIjiLa\nLg6H44IWQElt2LCBzp07s3btWtq3b8+YMWOoXbs2M2fOPCch1KtXjyPnFVl3OBw888wzztdRUVG2\n7GwnIuJN0tJg+nQz6+mOO6Br12SyspKd70+cOLFi7Ch34MABOnfuTEZGBgBffvklkyZNYvfu3axa\ntYqAgAD2799PdHS0uphERC7Bjz+aMYqXXjJlPcaONeXHq1Ur55XU69evZ//+/c7X8+bNo3///jz2\n2GMX/GXZTB7FAAANz0lEQVR/KQICAggODiY9PR2Azz77jObNm9OvXz/mzZvnvNaAAQNKfQ0Rkaqo\nfn146inIyDDlO555Bpo1K/35imxBtGnThs8//5x69eqxZs0a7rzzTmbOnMmmTZv44YcfWLhwYakv\nunnzZkaMGEFeXh6hoaHMmTOHgoICYmNj2bt3r6a5ioiUA8uC2bNhxIhyHoNo1aoVmzdvBuDRRx+l\nYcOGTJgw4YL3PEkJQkTk0iQnQ3R0OXcxFRQUcPq3Nd6fffYZ0dHRzvfOLJgTEZHKy7eoN+Li4uje\nvTsNGjTgiiuuoFu3bgDs2LHjgq4fERGpfC46iyklJYUDBw7Qs2dPatasCUB6ejrHjx+nbdu2Hgvy\nDHUxiYhcmrJ0MalYn4hIJeaWMQgREanalCBERMQlJQgREXFJCUJERFxSghAREZeUIERExCUlCBER\ncUkJQkREXFKCEBERl5QgRETEJSUIERFxSQlCRERcsi1BFBQU0KZNG/r16wfAkSNHiImJoWnTpvTs\n2ZPc3Fy7QhMREWxMENOmTSMiIgKHwwFAYmIiMTExpKen06NHDxITE+0KTUREsClB7Nu3j6VLlzJi\nxAhnCdolS5YQHx8PQHx8PIsXL7YjNBER+Y0tCWLs2LH84x//wMfn98sfPHgQf39/APz9/Tl48KAd\noYmIyG+K3HLUXT766CMaNWpEmzZtSE5OdvkZh8Ph7Ho634QJE5zPo6KiiIqKKv8gRUQqsOTkZOfv\na2Zm6c/j8R3lnnrqKebPn4+vry8nT57k2LFjDBw4kPXr15OcnExAQAD79+8nOjqaH3744dxgtaOc\niMglqVA7yj3//PNkZWWRkZHBggULuPnmm5k/fz79+/dn3rx5AMybN48BAwZ4OjQRETmL7esgznQl\njR8/nhUrVtC0aVNWrlzJ+PHjbY5MRKRq83gXU1moi0lE5NJUqC4mERGpGJQgRETEJSUIERFxSQlC\nRERcUoIQERGXlCBERMQlJQgREXFJCUJERFxSghAREZeUIERExCUlCBERcUkJQkREXFKCEBERl5Qg\nRETEJSUIERFxSQlCRERc8niCyMrKIjo6mubNmxMZGcn06dMBOHLkCDExMTRt2pSePXuSm5vr6dBE\nROQsHk8Qfn5+TJkyhW3btrFu3Tpeeuklvv/+exITE4mJiSE9PZ0ePXqQmJjo6dBEROQsHk8QAQEB\ntG7dGoBatWrRrFkzsrOzWbJkCfHx8QDEx8ezePFiT4cmIiJnsXUMIjMzk02bNtGxY0cOHjyIv78/\nAP7+/hw8eNDO0EREqjxfuy58/PhxBg0axLRp06hdu/Y57zkcDhwOh8vvTZgwwfk8KiqKqKgoN0Yp\nIlLxJCcnk5ycDEBmZunP47AsyyqXiC7B6dOnue222+jTpw9jxowBIDw8nOTkZAICAti/fz/R0dH8\n8MMP5wbrcGBDuCIiFVZyMkRHl+630+NdTJZlcf/99xMREeFMDgD9+/dn3rx5AMybN48BAwZ4OjQR\nETmLx1sQX375JTfddBMtW7Z0diNNmjSJDh06EBsby969ewkJCeG9996jTp065warFoSIyCUpSwvC\nli6m0lKCEBG5NBWqi0lERCoGJQgREXFJCUJERFxSghAREZeUIERExCUlCBERcUkJQkREXFKCEBER\nl5QgRETEJSUIERFxSQlCRERcUoIQERGXlCBERMQlJQgREXFJCUJERFzyqgSxbNkywsPDadKkCS+8\n8ILd4YiIVGlekyAKCgoYNWoUy5YtIy0tjXfeeYfvv//e7rC81pkNyUX34my6F7/TvSg7r0kQqamp\nhIWFERISgp+fH3fddRdJSUl2h+W19I//d7oXv9O9+J3uRdl5TYLIzs4mODjY+TooKIjs7GwbIxIR\nqdq8JkE4HA67QxARkbNZXiIlJcXq1auX8/Xzzz9vJSYmnvOZ0NBQC9BDDz300OMSHqGhoaX6XXZY\nlmXhBfLz87n++uv5/PPPueaaa+jQoQPvvPMOzZo1szs0EZEqydfuAM7w9fVl5syZ9OrVi4KCAu6/\n/34lBxERG3lNC0JERLyL1wxSn60kC+Yee+wxmjRpQqtWrdi0aZOHI/Sc4u7FW2+9RatWrWjZsiVd\nu3Zly5YtNkTpGSVdSLl+/Xp8fX354IMPPBidZ5XkXiQnJ9OmTRsiIyOJiorybIAeVNy9OHz4ML17\n96Z169ZERkYyd+5czwfpAQkJCfj7+9OiRYsiP3PJv5ulHlV2k/z8fCs0NNTKyMiw8vLyrFatWllp\naWnnfObjjz+2+vTpY1mWZa1bt87q2LGjHaG6XUnuxdq1a63c3FzLsizrk08+qdL34sznoqOjrVtv\nvdVauHChDZG6X0nuxdGjR62IiAgrKyvLsizLOnTokB2hul1J7sUzzzxjjR8/3rIscx/q1atnnT59\n2o5w3WrNmjXWxo0brcjISJfvl+Z30+taECVZMLdkyRLi4+MB6NixI7m5uRw8eNCOcN2qJPeic+fO\nXHXVVYC5F/v27bMjVLcr6ULKGTNmMHjwYBo2bGhDlJ5Rknvx9ttvM2jQIIKCggBo0KCBHaG6XUnu\nxdVXX82xY8cAOHbsGPXr18fX12uGX8tNt27dqFu3bpHvl+Z30+sSREkWzLn6TGX8YbzUxYOvv/46\nffv29URoHlfSfxdJSUk88sgjQOVdW1OSe7Fjxw6OHDlCdHQ0N9xwA/Pnz/d0mB5RknvxwAMPsG3b\nNq655hpatWrFtGnTPB2mVyjN76bXpdGS/k9tnTe2Xhl/DC7lv2nVqlXMnj2br776yo0R2ack92LM\nmDEkJibicDiwLOuCfyOVRUnuxenTp9m4cSOff/45J06coHPnznTq1IkmTZp4IELPKcm9eP7552nd\nujXJycns2rWLmJgYNm/eTO3atT0QoXe51N9Nr0sQgYGBZGVlOV9nZWU5m8lFfWbfvn0EBgZ6LEZP\nKcm9ANiyZQsPPPAAy5Ytu2gTsyIryb345ptvuOuuuwAzMPnJJ5/g5+dH//79PRqru5XkXgQHB9Og\nQQNq1KhBjRo1uOmmm9i8eXOlSxAluRdr167lL3/5CwChoaE0btyY7du3c8MNN3g0VruV6nez3EZI\nysnp06et6667zsrIyLBOnTpV7CB1SkpKpR2YLcm92LNnjxUaGmqlpKTYFKVnlORenG3YsGHWokWL\nPBih55TkXnz//fdWjx49rPz8fOuXX36xIiMjrW3bttkUsfuU5F6MHTvWmjBhgmVZlnXgwAErMDDQ\n+vHHH+0I1+0yMjJKNEhd0t9Nr2tBFLVg7pVXXgHgoYceom/fvixdupSwsDBq1qzJnDlzbI7aPUpy\nL5599lmOHj3q7Hf38/MjNTXVzrDdoiT3oqooyb0IDw+nd+/etGzZEh8fHx544AEiIiJsjrz8leRe\nPPXUUwwfPpxWrVpRWFjI5MmTqVevns2Rl7+4uDhWr17N4cOHCQ4OZuLEiZw+fRoo/e+mFsqJiIhL\nXjeLSUREvIMShIiIuKQEISIiLilBiIiIS0oQIiLikhKEiIi4pAQhlUKtWrXcev6pU6fy66+/lvv1\nPvzww4uWLhexk9ZBSKVQu3Ztfv75Z7edv3HjxmzYsIH69et75Hoi3kAtCKm0du3aRZ8+fbjhhhu4\n6aab2L59OwDDhg3j8ccfp2vXroSGhrJo0SIACgsLGTlyJM2aNaNnz57ceuutLFq0iBkzZpCTk0N0\ndDQ9evRwnv+vf/0rrVu3pnPnzvzvf/+74PpjxozhueeeA+DTTz+le/fuF3xm7ty5jB49+qJxnS0z\nM5Pw8HCGDx/O9ddfz913383y5cvp2rUrTZs2Zf369WW/cSJnlFsREBEb1apV64JjN998s7Vjxw7L\nsswGKTfffLNlWZYVHx9vxcbGWpZlWWlpaVZYWJhlWZb1/vvvW3379rUsy9TsqVu3rrOeU0hIyDn1\nexwOh/XRRx9ZlmVZTz75pPW3v/3tguufOHHCat68ubVy5Urr+uuvt3bv3n3BZ+bOnWuNGjXqonGd\nLSMjw/L19bW+++47q7Cw0GrXrp2VkJBgWZZlJSUlWQMGDCj2XomUlNfVYhIpD8ePHyclJYUhQ4Y4\nj+Xl5QGmxPGAAQMAaNasmXPTlC+//JLY2FgA/P39iY6OLvL8l112GbfeeisA7dq1Y8WKFRd8pkaN\nGrz22mt069aNadOm0bhx44vGXFRc52vcuDHNmzcHoHnz5txyyy0AREZGkpmZedFriFwKJQiplAoL\nC6lTp06R++5edtllzufWb8NwZ/aROP+4K35+fs7nPj4+5Ofnu/zcli1baNiw4UU3eiourvNVr179\nnGuf+c7F4hApDY1BSKV05ZVX0rhxYxYuXAiYH9stW7Zc9Dtdu3Zl0aJFWJbFwYMHWb16tfO92rVr\nO7etLKk9e/bwr3/9i02bNvHJJ5+4rLJ7sSQkYjclCKkUTpw4QXBwsPMxdepU3nrrLV5//XVat25N\nZGQkS5YscX7+7J20zjw/s4dzREQE9957L23btnXu9/3ggw/Su3dv5yD1+d8/f2cuy7IYMWIEL774\nIgEBAbz++uuMGDHC2c1V1HeLen7+d4p6XRl3VhT7aJqryFl++eUXatasyY8//kjHjh1Zu3YtjRo1\nsjssEVtoDELkLLfddhu5ubnk5eXx9NNPKzlIlaYWhIiIuKQxCBERcUkJQkREXFKCEBERl5QgRETE\nJSUIERFxSQlCRERc+v9brQ7wu4yTKgAAAABJRU5ErkJggg==\n",
- "text": [
- "<matplotlib.figure.Figure at 0x54faf90>"
- ]
- }
- ],
- "prompt_number": 86
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 14.12,Page No.340"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "%matplotlib inline\n",
- "\n",
- "#Initilization of variables\n",
- "H=6 #m #height of dam\n",
- "a=1.5 #m #top width\n",
- "b=3.5 #m #Bottom width\n",
- "rho_s=16 #KN/m**3 #density of soil\n",
- "rho_mason=22.5 #KN/m**3 #density of mason\n",
- "phi=30 #Degree #angle of repose\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#Let Length of dam ,L=1 m\n",
- "L=1 #m\n",
- "\n",
- "#weight of dam\n",
- "W=(a+b)*2**-1*L*H*rho_mason\n",
- "\n",
- "#Rankine's coeff earth pressure\n",
- "K=((1-sin(30*pi*180**-1))*(1+sin(phi*pi*180**-1))**-1)\n",
- "\n",
- "#Lateral thrust\n",
- "P=rho_s*H**2*L*2**-1*K\n",
- "\n",
- "#Distance of Line of action from vertical base\n",
- "x_bar=(b**2+b*a+a**2)*(3*(b+a))**-1\n",
- "\n",
- "#distance of pt where resultant cuts the base\n",
- "x=P*W**-1*H*3**-1\n",
- "\n",
- "#Eccentricity\n",
- "e=x_bar+x-b*2**-1\n",
- "\n",
- "#Pressure at heel B\n",
- "sigma1=W*b**-1*(1-6*round(e,3)*b**-1)\n",
- "\n",
- "#Pressure at heel C\n",
- "sigma2=W*b**-1*(1+6*round(e,3)*b**-1)\n",
- "\n",
- "#Result\n",
- "print\"The Max Intensities of soil at the wall is\",round(sigma2,2),\"KN/m**2\"\n",
- "print\"The Min Intensities of soil at the wall is\",round(sigma1,2),\"KN/m**2\"\n",
- "\n",
- "#Plotting the Shear Force Diagram\n",
- "\n",
- "X1=[0,L,L]\n",
- "Y1=[sigma2,sigma1,0]\n",
- "Z1=[0,0,0]\n",
- "plt.plot(X1,Y1,X1,Z1)\n",
- "plt.xlabel(\"Length x in m\")\n",
- "plt.ylabel(\"Shear Force in kN\")\n",
- "plt.show()\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Max Intensities of soil at the wall is 118.91 KN/m**2\n",
- "The Min Intensities of soil at the wall is 73.95 KN/m**2\n"
- ]
- },
- {
- "metadata": {},
- "output_type": "display_data",
- "png": "iVBORw0KGgoAAAANSUhEUgAAAYgAAAEPCAYAAABY9lNGAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
- "text": [
- "<matplotlib.figure.Figure at 0x555a0f0>"
- ]
- }
- ],
- "prompt_number": 113
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 14.13,Page No.341"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "%matplotlib inline\n",
- "\n",
- "#Initilization of variables\n",
- "H=6 #m #height of dam\n",
- "a=1 #m #top width\n",
- "b=3 #m #Bottom width\n",
- "rho_s=18 #KN/m**3 #density of soil\n",
- "rho_mason=24 #KN/m**3 #density of mason\n",
- "alpha=20\n",
- "phi=30\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#Let Length of dam ,L=1 m\n",
- "L=1 #m\n",
- "\n",
- "a2=cos(alpha*pi*180**-1)\n",
- "b2=(cos(alpha*pi*180**-1)-((cos(alpha*pi*180**-1)**2-cos(phi*pi*180**-1)**2))**0.5)\n",
- "c2=(cos(alpha*pi*180**-1)+((cos(alpha*pi*180**-1)**2-cos(phi*pi*180**-1)**2)**0.5))\n",
- "\n",
- "X=a2*b2*c2**-1\n",
- "\n",
- "#Total Pressue on the wall\n",
- "P=rho_s*H**2*2**-1*X\n",
- "\n",
- "#The Horizontal component of pressure\n",
- "P_H=P*cos(20*pi*180**-1)\n",
- "\n",
- "#The Vertical component of pressure\n",
- "P_V=P*sin(20*pi*180**-1)\n",
- "\n",
- "#weight of wall\n",
- "W=(a+b)*H*rho_mason*2**-1\n",
- "\n",
- "#TotaL Weight \n",
- "W1=W+P_V\n",
- "\n",
- "#Taking moment of vertical Loads about B,M_B=0\n",
- "x_bar=(rho_mason*a*H*0.5+rho_mason*H*2)*W1**-1\n",
- "\n",
- "x=P_H*W1**-1*H*3**-1\n",
- "\n",
- "#eccentricity\n",
- "e=x_bar+x-b*2**-1\n",
- "\n",
- "#Stress at the toe at C\n",
- "sigma_max=W1*b**-1*(1+6*round(e,2)*b**-1)\n",
- "\n",
- "#Stress at the heel at B\n",
- "sigma_min=W1*b**-1*(1-6*round(e,2)*b**-1)\n",
- "\n",
- "#Result\n",
- "print\"Pressure at the base of the wall:Pressure at the heel\",round(sigma_min,2),\"KN/m**2\"\n",
- "print\" :Pressure at the toe\",round(sigma_max,2),\"KN/m**2\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Pressure at the base of the wall:Pressure at the heel 37.84 KN/m**2\n",
- " :Pressure at the toe 184.76 KN/m**2\n"
- ]
- }
- ],
- "prompt_number": 155
- }
- ],
- "metadata": {}
- }
- ]
-}
\ No newline at end of file diff --git a/Strength_Of_Materials_by_B_K_Sarkar/chapter_15_som.ipynb b/Strength_Of_Materials_by_B_K_Sarkar/chapter_15_som.ipynb deleted file mode 100755 index 8ae049c0..00000000 --- a/Strength_Of_Materials_by_B_K_Sarkar/chapter_15_som.ipynb +++ /dev/null @@ -1,657 +0,0 @@ -{
- "metadata": {
- "name": "chapter 15.ipynb"
- },
- "nbformat": 3,
- "nbformat_minor": 0,
- "worksheets": [
- {
- "cells": [
- {
- "cell_type": "heading",
- "level": 1,
- "metadata": {},
- "source": [
- "Chapter no.15:Thin Cyclindrical Shell"
- ]
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 15.1,Page no.351"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "D=0.8 #m #Diameter of Shell\n",
- "L=3 #m #Length of shell\n",
- "t=0.01 #m #thickness of metal\n",
- "E=200*10**9 #Pa \n",
- "p=2.5*10**6 #Pa #Internal Pressure\n",
- "m=4 #Poisson's ratio\n",
- "\n",
- "#Calculation\n",
- "\n",
- "sigma_1=p*D*(2*t)**-1 #N/m**2 #Hoop stress\n",
- "sigma_2=p*D*(4*t)**-1 #N/m**2 #Longitudinal stress\n",
- "\n",
- "e_1=1*E**-1*(sigma_1-sigma_2*m**-1) #Hoop strain\n",
- "e_2=1*E**-1*(sigma_2-sigma_1*m**-1) #Hoop strain\n",
- "\n",
- "d=e_1*D*100 #cm #Increase in Diameter\n",
- "l=e_2*L*100 #cm #Increase in Length\n",
- "\n",
- "dell_v=2*e_1+e_2 #Volumetric strain\n",
- "V=dell_v*pi*4**-1*D**2*L*10**6 #cm**3 #Increase in Volume\n",
- "\n",
- "#Result\n",
- "print\"Change in Diameter is\",round(d,3),\"cm\"\n",
- "print\"Change in Length is\",round(l,3),\"cm\"\n",
- "print\"Change in Volume is\",round(V,2),\"cm**3\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Change in Diameter is 0.035 cm\n",
- "Change in Length is 0.037 cm\n",
- "Change in Volume is 1507.96 cm**3\n"
- ]
- }
- ],
- "prompt_number": 13
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 15.2,Page no.352"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "D=0.8 #m #iameter of water main\n",
- "h=100 #m #Pressure head\n",
- "w=10*10**3 #N/m**3 #Weight of Water\n",
- "sigma_t=20*10**6 #MPa #Permissible stress\n",
- "\n",
- "#Calculation\n",
- "\n",
- "p=w*h #N/m**2 #Pressure of inside the main\n",
- "t=p*D*(2*sigma_t)**-1*100 #m #Thcikness of metal\n",
- "\n",
- "#Result\n",
- "print\"The Thickness of metal is\",round(t,2),\"cm\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Thickness of metal is 2.0 cm\n"
- ]
- }
- ],
- "prompt_number": 21
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 15.3,Page no.352"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "p=2*10**6 #MPa #Steam Pressure\n",
- "t=0.02 #m #thickness of boiler plate\n",
- "sigma_t=120*10**6 #MPa #Tensile stress\n",
- "sigma_l=120*10**6 #MPa #Longitudinal stress\n",
- "rho=0.90 #% #Efficiency of Longitudinal joint\n",
- "rho_e=0.40 #% #Efficiency of circumferential joint\n",
- "\n",
- "#Calculations\n",
- "\n",
- "D_1=sigma_t*2*t*rho*p**-1 #Diameter of boiler \n",
- "D_2=sigma_l*4*t*rho_e*p**-1 #Diameter of boiler \n",
- "\n",
- "#Max diameter of boiler is equal to minimum value of diameter\n",
- "\n",
- "#Result\n",
- "print\"Maximum diameter of boiler is\",round(D_2,2),\"m\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Maximum diameter of boiler is 1.92 m\n"
- ]
- }
- ],
- "prompt_number": 29
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 15.4,Page no.352"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "L=0.9 #m #Length of cyclindrical shell\n",
- "D=0.2 #m #Internal Diameter\n",
- "t=0.008 #m #thickness of metal\n",
- "dV=20*10**-6 #m**3 #Additional volume\n",
- "E=200*10**9 #Pa \n",
- "m=1*0.3**-1 #Poissoin's ratio\n",
- "\n",
- "#Calculations\n",
- "\n",
- "V=pi*4**-1*D**2*L #Volume of cyclinder\n",
- "\n",
- "#Let X=2*e_1+e_2\n",
- "X=dV*V**-1 #Volumetric strain (Equation 1)\n",
- "\n",
- "#e_1=p*D*(2*E*t)**-1*(1-1*(2*m)**-1) #Circumferential strain\n",
- "#e_2=p*D*(2*E*t)**-1*(1*2**-1-1*(2*m)**-1) #Circumferential strain\n",
- "\n",
- "#substituting above values in equation 1 we get\n",
- "p=X*E*t*(D*((1-1*(2*m)**-1)+(1*4**-1-1*(2*m)**-1)))**-1*10**-3 #KN/m**2 #Pressure exerted by fluid\n",
- "sigma_t=p*D*(2*t)**-1 #KN/m**2 #hoop stress\n",
- "\n",
- "#Result\n",
- "print\"Pressure Exerted by Fluid on the cyclinder is\",round(p,2),\"KN/m**2\"\n",
- "print\"Hoop stress is\",round(sigma_t,2),\"KN/m**2\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Pressure Exerted by Fluid on the cyclinder is 5956.68 KN/m**2\n",
- "Hoop stress is 74458.45 KN/m**2\n"
- ]
- }
- ],
- "prompt_number": 41
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 15.5,Page no.353"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "t=0.015 #m #Thickness of plate\n",
- "sigma_t=120*10**6 #Pa #tensile stress\n",
- "sigma_l=120*10**6 #Pa #Longitudinal stress\n",
- "rho=0.7 #% #Efficiency of longitudinal joints\n",
- "rho_l=0.3 #% #Efficiency of circumferential joints\n",
- "p=2*10**6 #Pa #Internal pressure\n",
- "D=1.5 #m #shell diameter\n",
- "\n",
- "#Calculations (Part-1)\n",
- "\n",
- "D_1=sigma_t*2*t*rho*p**-1 #m \n",
- "D_2=sigma_l*4*t*rho_l*p**-1 #m \n",
- "\n",
- "#Thus max diameter of shell is min of above two cases\n",
- "\n",
- "#Calculations (Part-2)\n",
- "\n",
- "p_1=sigma_t*2*t*rho*D**-1*10**-6 #MPa\n",
- "p_2=sigma_l*4*t*rho_l*D**-1*10**-6 #MPa\n",
- "\n",
- "#Thus Internal pressure is min of above two cases\n",
- "\n",
- "#Result\n",
- "print\"Max Permissible Diameter of shell is\",round(D_2,2),\"m\"\n",
- "print\"Max Permissible Internal Pressure is\",round(p_2,2),\"MPa\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Max Permissible Diameter of shell is 1.08 m\n",
- "Max Permissible Internal Pressure is 1.44 MPa\n"
- ]
- }
- ],
- "prompt_number": 8
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 15.6,Page no.354"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "L=3 #m #Length\n",
- "D=1 #m #Internal Diameter\n",
- "t=0.015 #m #thickness\n",
- "p=1.5*10**6 #Pa #Internal pressure\n",
- "E=200*10**9 #Pa \n",
- "m=1*0.3**-1 #Poissoin's ratio\n",
- "\n",
- "#Calculations\n",
- "\n",
- "sigma_t=p*D*(2*t)**-1*10**-6 #MPa #Hoop stress\n",
- "sigma_l=p*D*(4*t)**-1*10**-6 #MPa #Longitudinal stress\n",
- "\n",
- "dD=(p*D**2*(2*t*E)**-1*(1-1*(2*m)**-1))*10**2 #cm #Change in Diameter\n",
- "dL=p*D*L*(2*t*E)**-1*(1*2**-1-1*m**-1)*10**2 #cm #Change in Length\n",
- "\n",
- "V=pi*4**-1*D**2*L #Volume \n",
- "dV=p*D*(2*t*E)**-1*(5*2**-1-2*(m)**-1)*V*10**6 #cm #Change in Volume\n",
- "\n",
- "#Result\n",
- "print\"The circumferential stresses induced is\",round(sigma_t,2),\"MPa\"\n",
- "print\"The Longitudinal stresses induced is\",round(sigma_l,2),\"MPa\"\n",
- "print\"The change in dimension are:D is\",round(dD,3),\"cm\"\n",
- "print\" :L is\",round(dL,4),\"cm\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "0.02125\n",
- "The circumferential stresses induced is 50.0 MPa\n",
- "The Longitudinal stresses induced is 25.0 MPa\n",
- "The change in dimension are:D is 0.021 cm\n",
- " :L is 0.015 cm\n"
- ]
- }
- ],
- "prompt_number": 26
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 15.7,Page no.355"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "L=0.9 #m #Length of cyclinder\n",
- "D=0.4 #m #Diameter \n",
- "t=0.006 #m #thickness\n",
- "p=5*10**6 #Pa #Pressure\n",
- "E=100*10**9\n",
- "m=3 #Poissoin's ratio\n",
- "k=2.6*10**9 #Pa #Bulk modulus\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#Let X=dV_1*V_1**-1\n",
- "X=p*(0.4-2*0.006)*(2*t*E)**-1*(5*2**-1-2*m**-1) #Volumetric strain\n",
- "dV_1=round(X,5)*pi*4**-1*0.388**2*L #cm**3 #Increase in volume of cyclinder\n",
- "V_1=pi*4**-1*0.388**2*L #VOlume\n",
- "dV_2=p*k**-1*V_1 #DEcrease in volume of oil due to increase in pressure\n",
- "\n",
- "dV=(dV_1+dV_2)*10**6 #Resultant additional space \n",
- "\n",
- "#Result\n",
- "print\"additional quantity of oil to be pumped is\",round(dV,2),\"cm**3\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "additional quantity of oil to be pumped is 519.62 cm**3\n"
- ]
- }
- ],
- "prompt_number": 23
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 15.8,Page no.356"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "A=1600*(3600)**-1 #Kg/sec #Amount of steam generated\n",
- "v=0.24 #m**3/kg #specific volume of steam\n",
- "sigma_t=4*10**6 #MPa #Tensile stress\n",
- "V_1=30 #m/s #Velocity of steam\n",
- "p=1*10**6 #Pa #Steam pressure\n",
- "\n",
- "#Calculation\n",
- "\n",
- "V=A*v #m**3/s #volume of steam \n",
- "D=(V*(pi*4**-1*V_1)**-1)**0.5*100 #Diameter of pipe\n",
- "t=p*D*(2*sigma_t)**-1 #Thicknes of pipe\n",
- "\n",
- "#Result\n",
- "print\"Diameter of boiler is\",round(D,2),\"cm\"\n",
- "print\"Thickness of steel plpe is\",round(t,2),\"cm\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Diameter of boiler is 6.73 cm\n",
- "Thickness of steel plpe is 0.84 cm\n"
- ]
- }
- ],
- "prompt_number": 43
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 15.9,Page no.359"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "P=14*10**3 #N #Axial pull\n",
- "dL=0.0084 #cm #Elongation\n",
- "L=0.25 #m #Length\n",
- "p=7*10**6 #Internal pressure\n",
- "dL_2=0.0034 #cm #Longation\n",
- "d=0.0475 #m #Internal diameter \n",
- "D=0.05 #m #External Diameter\n",
- "m=0.25\n",
- "\n",
- "#Calculation\n",
- "\n",
- "t=(D-d)*2**-1 #thickness od tube\n",
- "A=pi*4**-1*(D**2-d**2) #Area of tube\n",
- "sigma=P*A**-1 #stress\n",
- "e=dL*(L)**-1 #strain\n",
- "E=sigma*e**-1 #Modulus of Elasticity\n",
- "sigma_1=p*d*(2*t)**-1 #Hoop stress\n",
- "sigma_2=p*d*(4*t)**-1 #Longitudinal stress\n",
- "\n",
- "m=-(sigma_1*(dL_2*L**-1*E-sigma_2)**-1) #POissoin's ratio\\\n",
- "\n",
- "#Let X=1*m**-1\n",
- "X=1*m**-1 #Poissoin's ratio\n",
- "\n",
- "#Result\n",
- "print\"The value of Poissoin's ratio is\",round(X,3)\n",
- " "
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The value of Poissoin's ratio is 0.277\n"
- ]
- }
- ],
- "prompt_number": 28
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 15.10,Page no.357"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "D=0.8 #m #Diameter\n",
- "t=0.01 #m #Thickness \n",
- "p=5*10**6 #Pa #Pressure\n",
- "m=1*0.25**-1\n",
- "E=200*10**9 #Pa\n",
- "\n",
- "#Calculations\n",
- "\n",
- "sigma_1=5*10**6*0.8*(4*0.01)**-1 #stress\n",
- "sigma_2=sigma_1\n",
- "e_1=sigma_1*E**-1-sigma_2*(m*E)**-1 #strain\n",
- "e_v=3*e_1\n",
- "V=4*3**-1*pi*(D*2**-1)**3 #m**3 tress\n",
- "dell_v=e_v*V*10**6 #cm**3\n",
- "\n",
- "#Result\n",
- "print\"Volume of additional Fluid\",round(dell_v,3),\"cm**3\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Volume of additional Fluid 301.593 cm**3\n"
- ]
- }
- ],
- "prompt_number": 37
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 15.11,Page no.358"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\n",
- "d=0.3 #m #Diameter\n",
- "D=0.003 #m #Diameter of steel wire\n",
- "t=0.006 #m #thickness\n",
- "sigma_w=8*10**6 #Pa #Stress\n",
- "p=1*10**6 #Pa #Internal pressure\n",
- "E_s=200*10**9 #Pa #Modulus of Elasticity for steel\n",
- "E_c=100*10**9 #Pa #Modulus of Elasticity for cast iron\n",
- "m=1*0.3**-1\n",
- "\n",
- "#Calculations\n",
- "\n",
- "sigma_p=(sigma_w*pi*2**-1*d)*(2*t)**-1 #compressive hoop stress\n",
- "sigma_l=p*d*(4*t)**-1 #Longitudinal stress\n",
- "\n",
- "#when internal presure is apllied Let sigma_w_1=Tensile in wire and sigma_p_1=tensile hoop in wire\n",
- "#sigma_p_1*2*t+sigma_w_1*2*d**-1*pi*4**-1*d**2=p*D\n",
- "\n",
- "#After substituting values and further simplifying we get\n",
- "#1.2*sigma_p_1+0.471*sigma_w_1=3000 Equation 1\n",
- "\n",
- "#1*E_c**-1(sigma_p_1-sigma_1*m**-1+sigma_p)=1*E_s**-1(sigma_w_1-sigma_w)\n",
- "\n",
- "#After substituting values and further simplifying we get\n",
- "#sigma_p_1-0.5*sigma_w_1=1.36*10**6 \n",
- "#sigma_p_1=0.5*sigma_w_1-3.39*10**6 Equation 2\n",
- "\n",
- "#From Equation 2 substituting value of sigma_p_1 in Equation 1\n",
- "\n",
- "\n",
- "sigma_w_1=(40.68*10**3+0.3*10**6)*(10.71238*10**-3)**-1\n",
- "sigma_p_1=0.5*sigma_w_1-3.39*10**6\n",
- "\n",
- "#Let X=sigma_p_1 and Y=sigma_w_1\n",
- "X=sigma_p_1*10**-6 #MPa #Stresses in pipe\n",
- "Y=sigma_w_1*10**-6 #MPa #Stresses in wire\n",
- "\n",
- "#Result\n",
- "print\"Stress in the pipe is\",round(X,2),\"MN/m**2\"\n",
- "print\"Stress in the wire is\",round(Y,2),\"MN/m**2\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Stress in the pipe is 12.51 MN/m**2\n",
- "Stress in the wire is 31.8 MN/m**2\n"
- ]
- }
- ],
- "prompt_number": 29
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 15.12,Page no.359"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "D=0.038 #m #External Diameter\n",
- "d=0.035 #m #Internal Diameter\n",
- "d_1=0.0008 #m #Steel wire diameter\n",
- "p=2*10**6 #pa #Pa #Internal Pressure\n",
- "sigma_t_1=7*10**6 #Pa #Circumferential stress\n",
- "#E_s=1.6*E_s\n",
- "m=0.3\n",
- "\n",
- "#Calculation\n",
- "\n",
- "t=(D-d)*2**-1 #m Thickness \n",
- "\n",
- "#sigma_t*2*t=pi*d*2**-1*sigma_w\n",
- "#From Above equation we get\n",
- "\n",
- "#sigma_t=0.419*sigma_w (Equation 1)\n",
- "\n",
- "sigma_w_1=(p*d-sigma_t_1*2*t)*(2*d_1**-1*pi*4**-1*d_1**2)**-1 #stress in wire\n",
- "sigma_l=p*d*(4*t)**-1 #Longitudinal stress in tube\n",
- "\n",
- "#Now Equating equations of strain in tube and wire we get\n",
- "sigma_w=-(1.6*(sigma_t_1-sigma_l*m)-sigma_w_1)*1.67**-1*10**-6\n",
- "\n",
- "#Result\n",
- "print\"The Tension at which wire must have been wound is\",round(sigma_w,2),\"MPa\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Tension at which wire must have been wound is 20.0 MPa\n"
- ]
- }
- ],
- "prompt_number": 30
- }
- ],
- "metadata": {}
- }
- ]
-}
\ No newline at end of file diff --git a/Strength_Of_Materials_by_B_K_Sarkar/chapter_16_som.ipynb b/Strength_Of_Materials_by_B_K_Sarkar/chapter_16_som.ipynb deleted file mode 100755 index 177d5ab6..00000000 --- a/Strength_Of_Materials_by_B_K_Sarkar/chapter_16_som.ipynb +++ /dev/null @@ -1,524 +0,0 @@ -{
- "metadata": {
- "name": "chapter 16 som.ipynb"
- },
- "nbformat": 3,
- "nbformat_minor": 0,
- "worksheets": [
- {
- "cells": [
- {
- "cell_type": "heading",
- "level": 1,
- "metadata": {},
- "source": [
- "Chapter 16:Riveted Joints"
- ]
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 16.1,Page no.366"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "t=1 #cm #thickness of plates\n",
- "sigma_t=150 #MPa #Working stress\n",
- "sigma_c=212.5 #MPa #crushing stress\n",
- "sigma_s=94.5 #MPa #shearing stress\n",
- "\n",
- "#Calculation (Part-1)\n",
- "\n",
- "#P_s=pi*4**-1*d**2*sigma_s #N #Shearing strength\n",
- "#After substituting values and further simplifying we get\n",
- "#P_s=pi*4**-1*d**2*94.5*10**6 #N \n",
- "\n",
- "#P_c=d*t*sigma_c #N #crushing strength\n",
- "#After substituting values and further simplifying we get\n",
- "#P_c=d*1*10**-2*212.5*10**6 #N \n",
- "\n",
- "#P_t=(p-d)*t*sigma_t #N #Strength of plate in tearing\n",
- "#After substituting values and further simplifying we get\n",
- "#P_t=(p-d)*1*10**-2*150*10**6\n",
- "\n",
- "#Now comparing strengths \n",
- "#P_s=P_c \n",
- "#pi*4**-1*d**2*94.5*10**6=d*1*10**-2*212.5*10**6\n",
- "d=1*10**-2*212.5*10**6*(pi*4**-1*94.5*10**6)**-1 #m #Diameter of rivet\n",
- "\n",
- "#Now comparing strengths \n",
- "#P_t=P_c\n",
- "#(p-d)*1*10**-2*150*10**6=d*1*10**-2*212.5*10**6\n",
- "#Afte further simplifying equation we get\n",
- "#(p-d)=1.4166*d\n",
- "p=(1.4166*d+d) #m #Pitch length of rivet\n",
- "\n",
- "P=p*sigma_t*10**6*t*10**-2 #N #Strength of solid plate #Answer for strength of solid plate is incorrect in textbook \n",
- "\n",
- "rho=(p-d)*p**-1*100 #Efficiency of the joint #Notification has been changed\n",
- "\n",
- "#Calculation (Part-2)\n",
- "\n",
- "#P_s=2*pi*4**-1*d**2*sigma_s #N #Shearing strength\n",
- "#After substituting values and further simplifying we get\n",
- "#P_s=2*pi*4**-1*d**2*94.5*10**6 #N \n",
- "\n",
- "#P_c=2*d*t*sigma_c #N #crushing strength\n",
- "#After substituting values and further simplifying we get\n",
- "#P_c=2*d*1*10**-2*212.5*10**6 #N \n",
- "\n",
- "#P_t=(p-d)*t*sigma_t #N #Strength of plate in tearing\n",
- "#After substituting values and further simplifying we get\n",
- "#P_t=(p-d)*1*10**-2*150*10**6\n",
- "\n",
- "#Now comparing strengths \n",
- "#P_s=P_c \n",
- "#2*pi*4**-1*d**2*94.5*10**6=2*d*1*10**-2*212.5*10**6\n",
- "d=1*10**-2*212.5*10**6*(pi*4**-1*94.5*10**6)**-1 #m #Diameter of rivet\n",
- "\n",
- "#Now comparing strengths \n",
- "#P_t=P_c\n",
- "#(p-d)*1*10**-2*150*10**6=2*d*1*10**-2*212.5*10**6\n",
- "#Afte further simplifying equation we get\n",
- "#(p-d)=2.833*d\n",
- "p_1=(2.833*d+d) #m #Pitch length of rivets in shearing strength of plate #Notification for pitch length has been changed\n",
- "\n",
- "rho_2=(p_1-d)*p_1**-1*100 #Efficiency of the joint #Notification has been changed\n",
- "\n",
- "#Result \n",
- "print\"The Efficiency of joint in single rivet is\",round(rho,2),\"%\"\n",
- "print\"The Efficiency of joint in double rivet is\",round(rho_2,2),\"%\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Efficiency of joint in single rivet is 58.62 %\n",
- "The Efficiency of joint in double rivet is 73.91 %\n"
- ]
- }
- ],
- "prompt_number": 29
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 16.2,Page no.367"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "p=7.5 #cm #Pitch of rivets\n",
- "t=1.5 #cm #Thickness of plate\n",
- "d=2.5 #cm #diameter of rivets\n",
- "sigma_t=400 #MPa #Working stress\n",
- "sigma_c=640 #MPa #crushing stress\n",
- "sigma_s=320 #MPa #shearing stress\n",
- "n=2 #No. of rivets\n",
- "\n",
- "#Calculation\n",
- "\n",
- "P_t=(p-d)*t*10**-4*sigma_t*10**6*10**-3 #N #Strength of plate in tearing\n",
- "P_s=n*pi*4**-1*d**2*10**-4*sigma_s*10**6*10**-3 #N #Shearing strength\n",
- "P_c=n*d*t*10**-4*sigma_c*10**6*10**-3 #N #crushing strength\n",
- "\n",
- "#Thus Minimum force that will rapture the joint is least of P_t,P_s,P_c i.e P_t\n",
- "\n",
- "#Result\n",
- "print\"Minimum force that will rapture the joint is\",round(P_t,2),\"N\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Minimum force that will rapture the joint is 300.0 N\n"
- ]
- }
- ],
- "prompt_number": 39
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 16.3,Page no.367"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "d_1=2 #cm #Diameter of rivets\n",
- "p_1=6 #cm #Pitch of rivet\n",
- "d_2=3 #cm #Diameter of rivet\n",
- "p_2=8 #cm #Pitch of rivet\n",
- "sigma_t=120 #MPa #Working stress\n",
- "sigma_c=160 #MPa #crushing stress\n",
- "sigma_s=90 #MPa #shearing stress\n",
- "t=1.2 #cm #thickness of plate\n",
- "n=2 #No. of rivets\n",
- "\n",
- "#Calculation (part-1)\n",
- "\n",
- "P_t=(p_1-d_1)*t*10**-4*sigma_t*10**6 #N #Strength of plate in tearing\n",
- "P_s=n*pi*4**-1*d_1**2*10**-4*sigma_s*10**6 #N #Shearing strength\n",
- "P_c=n*d_1*t*10**-4*sigma_c*10**6 #N #crushing strength\n",
- "P=p_1*t*10**-4*sigma_t*10**6 #N #Strength of solid per pitch length\n",
- "\n",
- "rho_1=P_s*(P)**-1*100 #% #Efficiency of the joint\n",
- "\n",
- "#Calculation (part-2)\n",
- "\n",
- "P_t_2=(p_2-d_2)*t*10**-4*sigma_t*10**6 #N #Strength of plate in tearing\n",
- "P_s_2=n*pi*4**-1*d_2**2*10**-4*sigma_s*10**6 #N #Shearing strength\n",
- "P_c_2=n*d_2*t*10**-4*sigma_c*10**6 #N #crushing strength\n",
- "P_2=p_2*t*10**-4*sigma_t*10**6 #N #Strength of solid per pitch length\n",
- "\n",
- "rho_2=P_t_2*(P_2)**-1*100 #% #Efficiency of the joint\n",
- "\n",
- "#Result\n",
- "print\"First joint has higher Efficiency i.e\",round(rho_1,2),\"% than second joint\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "First joint has higher Efficiency i.e 65.45 % than second joint\n"
- ]
- }
- ],
- "prompt_number": 60
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 16.4,Page no.368"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "t=18 #mm #thickness of plates\n",
- "sigma_t=100 #MPa #Tensile stress #Notification has been changed\n",
- "sigma_s=70 #MPa #Shearing stress #Notification has been changed\n",
- "\n",
- "#Calculations\n",
- "\n",
- "d=6*t**0.5 #mm #Diameter of rivet #Answer is in correct in textbook\n",
- "s=pi*4**-1*d**2*10**-6*sigma_s*10**6 #N #Strength of one rivet in single shear #Answer is in correct in textbook\n",
- "\n",
- "#Consider strip of joint equal to pitch p\n",
- "\n",
- "#S_1=(p-d)*t*10**-3*sigma_t*10**6 #Strength of plate against tearing along 1-1\n",
- "#After substituting values and further simplifying we get\n",
- "#S_1=1800*p-45900 (Equation 1)\n",
- " \n",
- "#S_2=(p-d)*t*10**-3*sigma_t*10**6+s #Strength of plate against tearing along 1-1\n",
- "#After substituting values and further simplifying we get\n",
- "#S_1=1800*p-56050.64 (Equation 2)\n",
- "\n",
- "#But the value of Equation 2 is smaller than Equation 1\n",
- "\n",
- "#Strength of rivets in single shear is\n",
- "S=4*s\n",
- "\n",
- "#Equating Equation 2 to shearing value\n",
- "#1800*p-56050.64=S\n",
- "p=(S+56050.64)*18000**-1 #cm #Pitch of rivet\n",
- "\n",
- "#Result\n",
- "print\"Diameter of rivets is\",round(d,2),\"mm\"\n",
- "print\"Pitch of rivet is\",round(p,2),\"cm\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "35625.6606917\n",
- "Diameter of rivets is 25.46 mm\n",
- "Pitch of rivet is 11.03 cm\n"
- ]
- }
- ],
- "prompt_number": 77
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 16.5,Page no.369"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "t=12 #mm #Thickness of plate\n",
- "d=24 #mm #Diameter of rivets\n",
- "sigma_t=120 #MPa #stress in tension\n",
- "sigma_s=200 #MPa #stress in double shear\n",
- "sigma_b=200 #MPa #stress in Bearing\n",
- "n=1 #No. of rivet\n",
- "\n",
- "#Calculation\n",
- "\n",
- "#P_t=(p-d)*t*10**-4*sigma_t*10**6 #N #Strength of plate in tearing\n",
- "#After further simplifying we get\n",
- "#P_t=(p-24)*14400 #N \n",
- "\n",
- "P_s=n*pi*4**-1*d**2*10**-6*sigma_s*10**6 #N #Shearing strength of rivet in double shear\n",
- "\n",
- "P_b=n*d*10**-3*t*10**-3*sigma_b*10**6 #N #Bearing strength per pitch length\n",
- "\n",
- "#Now Equating P_t to P_s or P_b whichever is small\n",
- "#(p-24)*14400=P_b\n",
- "p=P_b*14400**-1+24*10**-1 #cm #Pitch of rivet\n",
- "p_min=2.5*d*10**-1 #cm #Minimum pitch\n",
- "\n",
- "#Now adopting 6.4 cm pitch\n",
- "\n",
- "rho=(p-d*10**-1)*p**-1*100\n",
- "\n",
- "#Result\n",
- "print\"Pitch of rivet is\",round(p,2),\"cm\"\n",
- "print\"Efficiency of joint is\",round(rho,2),\"%\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Pitch of rivet is 6.4 cm\n",
- "Efficiency of joint is 62.5 %\n"
- ]
- }
- ],
- "prompt_number": 90
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 16.6,Page no.370"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "t=12 #mm #thickness of plate\n",
- "d=18 #mm #Diameter of rivet\n",
- "p=8 #cm #pitch of rivet\n",
- "sigma_t=460 #MPa #Tensile stress\n",
- "sigma_s=320 #MPa #shearing stress\n",
- "sigma_b=640 #MPa #bearing stress\n",
- "n=2 #No. of rivet\n",
- "\n",
- "#Calculation\n",
- "\n",
- "P_t=(p-d*10**-1)*t*10**-1*10**-4*sigma_t*10**6 #N #Strength of plate in tearing\n",
- "P_s=n*2*pi*4**-1*d**2*10**-6*sigma_s*10**6 #N #Shearing strength of rivet pr pitch length\n",
- "P_b=n*d*10**-3*t*10**-3*sigma_b*10**6 #N #Bearing strength per pitch length\n",
- "\n",
- "#The joint will fail at a pull of P_b\n",
- "\n",
- "S=p*t*sigma_t*10**6*10**-5 #N #strength of solid plate\n",
- "rho=P_b*S**-1*100 #Efficiency of joint\n",
- "\n",
- "#Result\n",
- "print\"Pull per pitch length at which joint will fail is\",round(P_b,2),\"N\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Pull per pitch lenght at which joint will fail is 276480.0 N\n"
- ]
- }
- ],
- "prompt_number": 102
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 16.7,Page no.370"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "W=270 #KN #Load \n",
- "t=14 #mm #thickness of plate\n",
- "b=20 #cm #width of plate\n",
- "d=20 #mm #diameter of rivet\n",
- "sigma_s=70 #MPa #shear stress\n",
- "sigma_b=190 #MPa #stress in bearing\n",
- "sigma_t=110 #MPa #stress in tensile\n",
- "\n",
- "#Calculation\n",
- "\n",
- "S_1=1.75*pi*4**-1*b**2*10**-4*sigma_s*10**6 #strength of one rivet in double shear\n",
- "S_2=20*10**-3*t*10**-3*sigma_b*10**6\n",
- "\n",
- "n=W*10**3*S_1**-1\n",
- "\n",
- "#Adopt 7 rivets\n",
- "\n",
- "#The plates may tear along section 1-1\n",
- "W_1=(20-4)*10**-2*t*10**-3*sigma_t*10**6 #N #Permissible Load\n",
- "\n",
- "#The plates may tear along section 2-2,at the same time shearing the 4 rivets along 1-1 \n",
- "W_2=(20-2*2)*10**-2*t*10**-3*sigma_t*10**6+2*S_1 #N #Permissible Load\n",
- "\n",
- "#The plates may tear along section 3-3,at the same time shearing the rivets along 1-1 and 2-2\n",
- "W_3=(20-3*2)*10**-2*t*10**-3*sigma_t*10**6+4*S_1 #N #Permissible Load\n",
- "\n",
- "W_s=7*S_1 #N #Load to shear all the rivets \n",
- "W_c=7*S_2 #N #Load to crush all the rivets\n",
- "\n",
- "W_4=b*10**-2*t*10**-3*sigma_t*10**6 #N #Load carried by solid plate\n",
- "\n",
- "rho=W_1*W_4**-1*100 #% #Efficiency of joint\n",
- " \n",
- "#Result\n",
- "print\"Efficiency of joint is\",round(rho,2),\"%\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Efficiency of joint is 80.0 %\n"
- ]
- }
- ],
- "prompt_number": 131
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 16.8,Page no.371"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "D=1.5 #cm #Diameter of boiler\n",
- "rho=75 #% #Efficiency of joint\n",
- "sigma_t=85 #MPa #stress in tension\n",
- "sigma_s=70 #MPa #stress in shear\n",
- "P=1 #MPa #Steam Pressure #Notification has been changed\n",
- "\n",
- "#Calculation\n",
- "\n",
- "t=P*10**6*D*(2*sigma_t*10**6*rho*10**-2)**-1*100\n",
- "\n",
- "#Adopt 12 mm thickness of plate\n",
- "t_1=12 #mm \n",
- "d=6*t_1**0.5\n",
- "\n",
- "#Adopt 21 mm diameter of rivet\n",
- "d_1=21 #mm\n",
- "\n",
- "#P_t=(p-d_1*10**-1)*t*10**-1*10**-4*sigma_t*10**6 #N #Strength of plate in tearing\n",
- "#After substituting values and further simplifying we get\n",
- "#P_t=(p-2.1)*10200 #N \n",
- "\n",
- "P_s=1.875*pi*4**-1*d_1**2*10**-6*2*sigma_s*10**6\n",
- "\n",
- "#(p-d_1*10**-1)*10200=P_s\n",
- "p=P_s*10200**-1+d_1*10**-1\n",
- "\n",
- "#Result\n",
- "print\"pitch of plate is\",round(p,2),\"cm\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "pitch of plate is 11.01 cm\n"
- ]
- }
- ],
- "prompt_number": 111
- }
- ],
- "metadata": {}
- }
- ]
-}
\ No newline at end of file diff --git a/Strength_Of_Materials_by_B_K_Sarkar/chapter_17_som.ipynb b/Strength_Of_Materials_by_B_K_Sarkar/chapter_17_som.ipynb deleted file mode 100755 index f99e1c75..00000000 --- a/Strength_Of_Materials_by_B_K_Sarkar/chapter_17_som.ipynb +++ /dev/null @@ -1,443 +0,0 @@ -{
- "metadata": {
- "name": "chapter 17 som.ipynb"
- },
- "nbformat": 3,
- "nbformat_minor": 0,
- "worksheets": [
- {
- "cells": [
- {
- "cell_type": "heading",
- "level": 1,
- "metadata": {},
- "source": [
- "Chapter 17:Welded Joints"
- ]
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no.17.1,Page no.379"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of Variables\n",
- "\n",
- "b=12 #cm #width of steel plates\n",
- "t=1 #cm #thickness of steel plates\n",
- "sigma=75 #MPa #stress\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#The maximum Load which the plate can carry\n",
- "P=b*t*10**-6*sigma*10**6 #N \n",
- "\n",
- "#Length of weld for static loading\n",
- "\n",
- "#size of weld is equal to thickness of plate\n",
- "S=t #cm\n",
- "\n",
- "#P=2**0.5*l*S*sigma\n",
- "\n",
- "#After substituting values and simplifying above equation, we get, \n",
- "l=((P)*(2**0.5*S*sigma)**-1) #cm\n",
- "\n",
- "#add 1.25 to allow start and stop of weld run\n",
- "L=l+1.25 #cm \n",
- "\n",
- "#Length of weld for Dynamic loading\n",
- "\n",
- "#The stress concentration factor for transverse fillet weld is 1.5\n",
- "\n",
- "sigma_2=sigma*1.5**-1 #MPa #Permissible tensile stress\n",
- "\n",
- "#P=2**0.5*l_2*S*sigma_2 \n",
- "\n",
- "#After substituting values and simplifying above equation, we get,\n",
- "l_2=((P)*(2**0.5*S*sigma_2)**-1) #cm\n",
- "\n",
- "#add 1.25 cm\n",
- "l_3=l_2+1.25 #cm \n",
- "\n",
- "#Result\n",
- "print\"Length of weld for static loading\",round(L,2),\"cm\"\n",
- "print\"Length of weld for Dynamic loading\",round(l_3,2),\"cm\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Length of weld for static loading 9.74 cm\n",
- "Length of weld for Dynamic loading 13.98 cm\n"
- ]
- }
- ],
- "prompt_number": 3
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no.17.2,Page no.380"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of Variables\n",
- "\n",
- "d=6 #cm #diameter of rod\n",
- "L=40 #cm #Length of steel plate\n",
- "P=12 #KN #Load\n",
- "sigma=180 #MPa #Allowable stress\n",
- "\n",
- "#Calculations\n",
- "\n",
- "A=pi*4**-1*d**2 #cm**2 #Area of rod\n",
- "M=P*10**3*L #Ncm\n",
- "\n",
- "F=M*A**-1 #N/cm #Force per unit cm of weld at top and bottom\n",
- "\n",
- "V_s=P*10**3*(pi*d)**-1 #N/cm #vertical shear\n",
- "\n",
- "R=(F**2+V_s**2)**0.5 #N/cm #resultant Load\n",
- "\n",
- "S=R*(sigma)**-1*10**-2 #cm #size of weld\n",
- "\n",
- "#Result\n",
- "print\"size of weld is\",round(S,2),\"cm\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "size of weld is 0.94 cm\n"
- ]
- }
- ],
- "prompt_number": 13
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no.17.3,Page no.380"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of Variables\n",
- "\n",
- "b=12 #cm #width of plate\n",
- "S=t=1 #cm #thickness of plate\n",
- "P=50 #KN #load\n",
- "sigma_s=60 #MPa #shear stress\n",
- "\n",
- "#Calculations (part-1)\n",
- "\n",
- "#Under static Loading\n",
- "\n",
- "#P=2**0.5*l*S*sigma_s\n",
- "\n",
- "l=((P*10**3)*(2**0.5*S*sigma_s*10**-4*10**6)**-1) #cm \n",
- "\n",
- "#add 1.25 cm to start and stop weld run\n",
- "\n",
- "L=l+1.25 #cm #length of weld\n",
- "\n",
- "#Calculations (part-2)\n",
- "\n",
- "#Under Fatigue load\n",
- "\n",
- "#stress concentration factor for parallel fillet weld is 2.7\n",
- "\n",
- "sigma_s_2=sigma_s*2.7**-1 #MPa #permissible shear stress\n",
- "\n",
- "#P=2**0.5*l_2*S*sigma_s_2\n",
- "\n",
- "l_2=((P*10**3)*(2**0.5*S*sigma_s_2*10**-4*10**6)**-1) #cm\n",
- "\n",
- "#add 1.25 cm \n",
- "\n",
- "l_3=l_2+1.25 #cm #length of weld\n",
- "\n",
- "#Result\n",
- "print\"Length of weld Under static Loading is\",round(L,3),\"cm\"\n",
- "print\"Length of weld Under Ftigue Loading is\",round(l_3,3),\"cm\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Length of weld Under static Loading is 7.143 cm\n",
- "Length of weld Under Ftigue Loading is 17.16 cm\n"
- ]
- }
- ],
- "prompt_number": 11
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no.17.4,Page no.381"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of Variables\n",
- "\n",
- "sigma_t=100 #MPa #tensile stress\n",
- "P=170 #KN #Load\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#For equal stress in the welds A and B, the load shared by the fillet welds will be proportional to size of weld\n",
- "\n",
- "#t_a=0.7*s #Effective throat thickness of weld A in upper plate\n",
- "#s=size of weld \n",
- "\n",
- "#t_b=1.05*s #Effective throat thickness of weld B in lower plate\n",
- "\n",
- "#For weld A\n",
- "#P_1=l*t*sigma_t \n",
- "\n",
- "#After substituting values and simplifying above equation, we get,\n",
- "#P_1=84000*s #N (equation 1)\n",
- "\n",
- "#P_2=l*t_2*sigma_t\n",
- "\n",
- "#After substituting values and simplifying above equation, we get,\n",
- "#P_2=126000*s #N (equation 2)\n",
- "\n",
- "#After adding equation 1 and 2, we get,\n",
- "#P=210000*s (equation 3)\n",
- "\n",
- "#Now equating total forces of the fillets to load on the plates\n",
- "s=P*10**3*210000**-1 #cm\n",
- "\n",
- "#Result\n",
- "print\"size of end fillet is\",round(s,2),\"cm\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "size of end fillet is 0.81 cm\n"
- ]
- }
- ],
- "prompt_number": 12
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no.17.5,Page no.381"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of Variables\n",
- "\n",
- "L_1=30 #cm #length of longitudinal weld\n",
- "L_2=16 #cm #length of transverse weld\n",
- "#t=0.7*s #Effective thickness of weld \n",
- "sigma_t_1=100 #MPa #working stress for transverse welds\n",
- "sigma_t_2=85 #MPa #working stress for longitudinal welds\n",
- "P=150 #KN #load\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#For transverse weld\n",
- "#P_1=L_1*t*10**-4*sigma_t_1*10**6 \n",
- "\n",
- "#After substituting values and simplifying above equation, we get,\n",
- "#P_1=112000*s #N\n",
- "\n",
- "#For longitudinal weld\n",
- "#P_2=L_2*t*10**-4*sigma_t_2*10**6\n",
- "\n",
- "#Total force of resistance of weld\n",
- "#P=P_1+P_2 #N\n",
- "\n",
- "#after adding we get,\n",
- "#P=290500*s #N\n",
- "\n",
- "#Now equating total forces of resistance to pull of the joint\n",
- "s=P*10**3*290500**-1 #cm\n",
- "\n",
- "#Result \n",
- "print\"size of weld is\",round(s,3),\"cm\"\n",
- "\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "size of weld is 0.516 cm\n"
- ]
- }
- ],
- "prompt_number": 16
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no.17.6,Page no.382"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of Variables\n",
- "\n",
- "P=200 #KN #Load carried by the angle \n",
- "S=0.6 #mm #size of weld\n",
- "b=4.46 #cm #Distance of centre of gravity of the angle from the top shorter leg\n",
- "a=10.54 #cm #Distance of centre of gravity of the angle from the top edge of the angle\n",
- "sigma_s=102.5 #MPa #shear stress\n",
- "#l_1=Length of the top weld\n",
- "#l_2=length of the bottom weld\n",
- "#L=l_1+l_2 #cm #total length weld\n",
- "\n",
- "#Using the relation\n",
- "#P=L*0.7*S*sigma_s\n",
- "\n",
- "#After substituting values and simplifying we get\n",
- "L=(P*10**3)*(0.7*S*sigma_s*10**-4*10**6)**-1 #cm (equation 1)\n",
- "\n",
- "#Using the relation\n",
- "l_1=(L*b)*(a+b)**-1 #cm\n",
- "\n",
- "#substituting this value in equation 1 we have,\n",
- "l_2=L-l_1 #cm \n",
- "\n",
- "#Result\n",
- "print\"Distance of centre of gravity of the angle from the top edge of the angle\",round(l_2,2),\"cm\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Distance of centre of gravity of the angle from the top edge of the angle 32.64 cm\n"
- ]
- }
- ],
- "prompt_number": 12
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no.17.7,Page no.383"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of Variables\n",
- "\n",
- "P=12 #KN #Load\n",
- "sigma_s=75 #N/mm**2 #shear stress\n",
- "e=12 #cm\n",
- "r_1=2.5 #cm\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#A=(2*S*l)*(2)**0.5\n",
- "#sigma_s=P*A**-1 #MPa #shear stress\n",
- "\n",
- "#After substituting values and simplifying we get\n",
- "#sigma_s=16.97*S**-1 #MPa\n",
- "\n",
- "#I_g=S*l*(3*b**2+l**2)*(6)**-1 #cm**4 #Polar moment of Inertia of weld\n",
- "\n",
- "#After substituting values and simplifying we get\n",
- "#I_g=180.833*S #cm**4\n",
- "r_2=((8*2**-1)**2)+((5*2**-1)**2)**0.5 #cm #max radius of weld\n",
- "\n",
- "#sigma_s_2=P*e*r_2*I_g**-1 #MPa #shear stress due to bending moment\n",
- "\n",
- "cos_theta=r_1*r_2**-1\n",
- "\n",
- "#Now using the relation\n",
- "#sigma_s=(sigma_s_1**2+sigma_s_2**2+2sigma_s_1*sigma_s_2*cos_theta\n",
- "\n",
- "S=(2363.8958*5625**-1)**0.5 #cm #size of the weld\n",
- "\n",
- "#Result\n",
- "print\"size of the weld\",round(S,3),\"cm\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "size of the weld 0.648 cm\n"
- ]
- }
- ],
- "prompt_number": 11
- }
- ],
- "metadata": {}
- }
- ]
-}
\ No newline at end of file diff --git a/Strength_Of_Materials_by_B_K_Sarkar/chapter_1_som.ipynb b/Strength_Of_Materials_by_B_K_Sarkar/chapter_1_som.ipynb deleted file mode 100755 index ff3fcb22..00000000 --- a/Strength_Of_Materials_by_B_K_Sarkar/chapter_1_som.ipynb +++ /dev/null @@ -1,438 +0,0 @@ -{
- "metadata": {
- "name": "chapter 1 som.ipynb"
- },
- "nbformat": 3,
- "nbformat_minor": 0,
- "worksheets": [
- {
- "cells": [
- {
- "cell_type": "heading",
- "level": 1,
- "metadata": {},
- "source": [
- "Chapter 1:Centre Of Gravity\n"
- ]
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 1.1,Page No.8"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of Variables\n",
- "\n",
- "#Rectangle-1\n",
- "a_1=37.5 #cm**2 \n",
- "y_1=26.25 #cm \n",
- "\n",
- "#Rectangle-2\n",
- "a_2=50 #cm**2 \n",
- "y_2=15 #cm \n",
- "\n",
- "#Rectangle-3\n",
- "a_3=150 #cm**2 \n",
- "y_3=2.5 #cm \n",
- "\n",
- "\n",
- "#Calculation\n",
- "\n",
- "\n",
- "Y_bar=(a_1*y_1+a_2*y_2+a_3*y_3)*(a_1+a_2+a_3)**-1 #cm \n",
- "\n",
- "#Result\n",
- "print\"The centroid of the section is\",round(Y_bar,2),\"cm\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The centroid of the section is 8.88 cm\n"
- ]
- }
- ],
- "prompt_number": 5
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 1.2,Page No.9"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "#Area-1\n",
- "a_1=6 #cm**2 \n",
- "x_1=3 #cm\n",
- "y_1=0.5 #cm\n",
- "\n",
- "#Area-2\n",
- "a_2=6 #cm**2\n",
- "x_2=2.671 #cm\n",
- "y_2=3 #cm\n",
- "\n",
- "#Area-3\n",
- "a_3=16 #cm**2\n",
- "x_3=1 #cm\n",
- "y_3=5 #cm\n",
- "\n",
- "\n",
- "#Calculation\n",
- "\n",
- "\n",
- "X_bar=(a_1*x_1+a_2*x_2+a_3*x_3)*(a_1+a_2+a_3)**-1 #cm\n",
- "Y_bar=(a_1*y_1+a_2*y_2+a_3*y_3)*(a_1+a_2+a_3)**-1 #cm\n",
- "\n",
- "\n",
- "#Result\n",
- "print\"The centre of gravity of section is\",round(X_bar,2),\"cm\"\n",
- "print\"The centre of gravity of section is\",round(Y_bar,2),\"cm\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The centre of gravity of section is 1.79 cm\n",
- "The centre of gravity of section is 3.61 cm\n"
- ]
- }
- ],
- "prompt_number": 7
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 1.3,Page no.10"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "#Area-1\n",
- "a_1=93.75 #cm**2 \n",
- "y_1=6.25 #cm\n",
- "\n",
- "#Area-2\n",
- "a_2=93.75 #cm**2 \n",
- "y_2=6.25 #cm\n",
- "\n",
- "#Area-3\n",
- "a_3=375 #cm**2 \n",
- "y_3=9.375 #cm\n",
- "\n",
- "#Area-4\n",
- "a_4=353.43 #cm**2\n",
- "y_4=6.366 #cm\n",
- "\n",
- "\n",
- "#Calculation\n",
- "\n",
- "Y_bar=(a_1*y_1+a_2*y_2+a_3*y_3-a_4*y_4)*(a_1+a_2+a_3-a_4)**-1 #cm\n",
- "\n",
- "\n",
- "#Result\n",
- "print\"The centre of gravity lies at a distance of \",round(Y_bar,2),\"cm\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The centre of gravity lies at a distance of 11.66 cm\n"
- ]
- }
- ],
- "prompt_number": 8
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 1.4,Page no.10\n",
- "\n"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "\n",
- "a_1=36*pi #cm**2 #Area of Quadrant of a circle\n",
- "x_1=16/pi #cm \n",
- "y_1=16*pi**-1 #cm\n",
- "\n",
- "\n",
- "a_2=18*pi #cm**2 #Area of the semicircle\n",
- "x_2=6 #cm\n",
- "y_2=8*pi**-1 #cm\n",
- "\n",
- "\n",
- "#Calculation-1\n",
- "\n",
- "X_bar=(a_1*x_1-a_2*x_2)*(a_1-a_2)**-1 #cm\n",
- "\n",
- "#Calculation-2\n",
- "#To calculate Y_bar,taking AB as the Reference line\n",
- "\n",
- "Y_bar=(a_1*y_1-a_2*y_2)*(a_1-a_2)**-1 #cm\n",
- "\n",
- "#Result\n",
- "\n",
- "print\"The centre of gravity is \",round(X_bar,2),\"cm\"\n",
- "print\"The centre of gravity is\",round(Y_bar,2),\"cm\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The centre of gravity is 4.19 cm\n",
- "The centre of gravity is 7.64 cm\n"
- ]
- }
- ],
- "prompt_number": 9
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 1.5,Page no.11"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "#Circle-1 \n",
- "a_1=100*pi #cm**2\n",
- "x_1=10 #cm\n",
- " \n",
- "#Square-2 \n",
- "a_2=50 #cm**2\n",
- "x_2=15 #cm\n",
- " \n",
- "#Calculation\n",
- "\n",
- "X_bar=(a_1*x_1-a_2*x_2)*(a_1-a_2)**-1 #cm\n",
- "\n",
- "\n",
- "#Result\n",
- "print\"The centre of gravity is\",round(X_bar,2),\"cm\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The centre of gravity is 9.05 cm\n"
- ]
- }
- ],
- "prompt_number": 10
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 1.6,Page no.12\n"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#intilization of variables \n",
- "\n",
- "#Rectangle-1\n",
- "a_1=51200 #mm**2 \n",
- "x_1=160 #mm\n",
- "y_1=80 #mm\n",
- "\n",
- "#Triangle-2\n",
- "a_2=6400 #mm**2\n",
- "x_2=80*3**-1 #mm\n",
- "y_2=320*3**-1 #mm\n",
- "\n",
- "#Semicircle-3\n",
- "a_3=1250*pi #mm**2\n",
- "x_3=210 #mm\n",
- "y_3=(160-(4*50-(3*pi)**-1)) #mm\n",
- "\n",
- "\n",
- "#Calculation\n",
- "\n",
- "X_bar=(a_1*x_1-a_2*x_2-a_3*x_3)*(a_1-a_2-a_3)**-1 #mm\n",
- "Y_bar=(a_1*y_1-a_2*y_2-a_3*y_3)*(a_1-a_2-a_3)**-1 #mm\n",
- "\n",
- "#Result\n",
- "print\"The centroid of the given area is\",round(X_bar,2),\"mm\"\n",
- "print\"The centroid of the given area is\",round(Y_bar,2),\"mm\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The centroid of the given area is 176.07 mm\n",
- "The centroid of the given area is 87.34 mm\n"
- ]
- }
- ],
- "prompt_number": 27
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 1.8,Page no.12"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "\n",
- "alpha=pi/2 #degree #In case of semicircle\n",
- "\n",
- "#Semicircle-1\n",
- "r_1=20 #cm #radius of semicircle \n",
- "y_1=4*r_1*(3*pi)**-1 #cm #distance from the base\n",
- "a_1=(pi*r_1**2)*2**-1 #cm**2 #area of semicircle\n",
- "\n",
- "#Semicircle-2\n",
- "r_2=16 #cm #radius of semicircle\n",
- "y_2=4*r_2*(3*pi)**-1 #cm #distance from the base\n",
- "a_2=(pi*r_2**2)*2**-1 #cm**2 #area of semicircle\n",
- "\n",
- "#Calculations\n",
- "\n",
- "\n",
- "Y_bar=(a_1*y_1-a_2*y_2)*(a_1-a_2)**-1 #cm #centroid\n",
- "\n",
- "\n",
- "#Result\n",
- "print\"The centroid of the area is \",round(Y_bar,2),\"cm\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The centroid of the area is 11.51 cm\n"
- ]
- }
- ],
- "prompt_number": 11
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no1.12,Page no.16"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "#Right Circular Cyclinder\n",
- "#m_1=(16*pi*h*rho_1) #gm \n",
- "#y_1=4+h*2**-1 #cm\n",
- "\n",
- "#Hemisphere\n",
- "#m_2=256*pi*rho_1 #gm \n",
- "y_2=2.5 #cm \n",
- "\n",
- "Y_bar=4 #cm\n",
- "r=4 #cm\n",
- "\n",
- "#Calculation\n",
- "\n",
- "#Y_bar=(m_1*y_1+m_2*y_2)*(m_1+m_2)**-1 #cm #Centroid\n",
- "h=(402.114*25.132**-1)**0.5\n",
- "\n",
- "#Result\n",
- "print\"The value of h is\",round(h,2),\"cm\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The value of h is 4.0 cm\n"
- ]
- }
- ],
- "prompt_number": 2
- }
- ],
- "metadata": {}
- }
- ]
-}
\ No newline at end of file diff --git a/Strength_Of_Materials_by_B_K_Sarkar/chapter_2_som.ipynb b/Strength_Of_Materials_by_B_K_Sarkar/chapter_2_som.ipynb deleted file mode 100755 index 16ba879f..00000000 --- a/Strength_Of_Materials_by_B_K_Sarkar/chapter_2_som.ipynb +++ /dev/null @@ -1,465 +0,0 @@ -{
- "metadata": {
- "name": "chapter 2 som.ipynb"
- },
- "nbformat": 3,
- "nbformat_minor": 0,
- "worksheets": [
- {
- "cells": [
- {
- "cell_type": "heading",
- "level": 1,
- "metadata": {},
- "source": [
- "Chapter 2:Moment Of Inertia"
- ]
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 2.1,Page no.29"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of Variables\n",
- " \n",
- "#Rectangle-1\n",
- "b_1=10 #cm #width of Rectangle-1\n",
- "d_1=2 #cm #breadth of Rectangle-1\n",
- "a_1=40 #cm**2 #Area of Rectangle-1\n",
- "y_1=1 #cm #Distance of centroid-1\n",
- "\n",
- "#Rectangle-2\n",
- "b_2=2 #cm #width of Rectangle-2\n",
- "d_2=10 #cm #breadth of Rectangle-2\n",
- "a_2=20 #cm**2 #Area of rectangle-2\n",
- "y_2=7 #cm #Distance of centroid-2\n",
- "\n",
- "#Rectangle-3\n",
- "b_3=20 #cm #width of Rectangle-3\n",
- "d_3=2 #cm #breadth of Rectangle-3\n",
- "a_3=20 #cm**2 #Area of rectangle-3\n",
- "y_3=13 #cm #Distance of centroid-3\n",
- "\n",
- "\n",
- "\n",
- "#Calculation\n",
- "Y_bar=((a_1*y_1+a_2*y_2+a_3*y_3)*(a_1+a_2+a_3)**-1) #cm #centre of gravity of section\n",
- "\n",
- "Y_1=4.5 #cm #Distance of centroid of rectangle 1 to C.G\n",
- "Y_2=1.5 #cm #Distance of centroid of rectangle 2 to C.G\n",
- "Y_3=7.5 #cm #Distance of centroid of rectangle 3 to C.G\n",
- "\n",
- "I_x_x_1=b_1*d_1**3*12**-1+a_1*Y_1**2 #moment of inertia of rectangle 1 about centroidal x-x axis of the section\n",
- "I_x_x_2=b_2*d_2**3*12**-1+a_2*Y_2**2 #moment of inertia of rectangle 2 about centroidal x-x axis of the section\n",
- "I_x_x_3=b_3*d_3**3*12**-1+a_3*Y_3**2 #moment of inertia of rectangle 3 about centroidal x-x axis of the section\n",
- "I_x_x=I_x_x_1+I_x_x_2+I_x_x_3 #cm**4 \n",
- "\n",
- "#Result\n",
- "print\"Moment of Inertia of the section is\",round(I_x_x,2),\"cm**4\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Moment of Inertia of the section is 2166.67 cm**4\n"
- ]
- }
- ],
- "prompt_number": 10
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 2.2,Page no.31"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of Variables\n",
- "\n",
- "#Rectangle-1\n",
- "b_1=2 #cm #width of Rectangle-1\n",
- "d_1=12 #cm #breadth of Rectangle-1\n",
- "a_1=24 #cm**2 #Area of Rectangle-1\n",
- "y_1=6 #cm #Distance of centroid-1\n",
- "\n",
- "#Rectangle-2\n",
- "b_2=6 #cm #width of Rectangle-2\n",
- "d_2=2 #cm #breadth of Rectangle-2\n",
- "a_2=12 #cm**2 #Area of rectangle-2\n",
- "y_2=1 #cm #Distance of centroid-2\n",
- "\n",
- "#Rectangle-3\n",
- "b_3=2 #cm #width of Rectangle-3\n",
- "d_3=12 #cm #breadth of Rectangle-3\n",
- "a_3=24 #cm**2 #Area of rectangle-3\n",
- "y_3=6 #cm #Distance of centroid-3\n",
- "\n",
- "#Calculation\n",
- "Y_bar=((a_1*y_1+a_2*y_2+a_3*y_3)*(a_1+a_2+a_3)**-1) #cm #centre of gravity of section\n",
- "\n",
- "Y_1=6 #cm #Distance of centroid of rectangle 1 to base \n",
- "Y_2=1 #cm #Distance of centroid of rectangle 2 to base\n",
- "Y_3=6 #cm #Distance of centroid of rectangle 3 to base\n",
- "\n",
- "I_x_x_1=b_1*d_1**3*12**-1+a_1*Y_1**2 #moment of inertia of rectangle 1 about centroidal x-x axis of the section\n",
- "I_x_x_2=b_2*d_2**3*12**-1+a_2*Y_2**2 #moment of inertia of rectangle 2 about centroidal x-x axis of the section\n",
- "I_x_x_3=b_3*d_3**3*12**-1+a_3*Y_3**2 #moment of inertia of rectangle 3 about centroidal x-x axis of the section\n",
- "I_x_x=I_x_x_1+I_x_x_2+I_x_x_3 #cm**4 \n",
- "\n",
- "\n",
- "#Result\n",
- "print\"Moment of Inertia of the section is\",round(I_x_x,2),\"cm**4\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Moment of Inertia of the section is 2320.0 cm**4\n"
- ]
- }
- ],
- "prompt_number": 11
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no2.3,Page no.32"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of Variables\n",
- "\n",
- "#Rectangle-1\n",
- "b_1=12 #cm #width of Rectangle-1\n",
- "d_1=2 #cm #breadth of Rectangle-1\n",
- "a_1=24 #cm**2 #Area of Rectangle-1\n",
- "y_1=1 #cm #Distance of centroid-1\n",
- "\n",
- "#Rectangle-2\n",
- "b_2=2 #cm #width of Rectangle-2\n",
- "d_2=6 #cm #breadthof Rectangle-2\n",
- "a_2=12 #cm**2 #Area of rectangle-2\n",
- "y_2=5 #cm #Distance of centroid-2\n",
- "\n",
- "#Rectangle-3\n",
- "b_3=5 #cm #width of Rectangle-3\n",
- "d_3=2 #cm #breadth of Rectangle-3\n",
- "a_3=10 #cm**2 #Area of rectangle-3\n",
- "y_3=9 #cm #Distance of centroid-3\n",
- "\n",
- "#Calculation\n",
- "Y_bar=((a_1*y_1+a_2*y_2+a_3*y_3)*(a_1+a_2+a_3)**-1) #cm #centre of gravity of section\n",
- "\n",
- "Y_1=2.78 #cm #Distance of centroid of rectangle 1 to C.G \n",
- "Y_2=1.22 #cm #Distance of centroid of rectangle 2 to C.G\n",
- "Y_3=5.22 #cm #Distance of centroid of rectangle 3 to C.G \n",
- "\n",
- "I_x_x_1=b_1*d_1**3*12**-1+a_1*Y_1**2 #moment of inertia of rectangle 1 about centroidal x-x axis of the section\n",
- "I_x_x_2=b_2*d_2**3*12**-1+a_2*Y_2**2 #moment of inertia of rectangle 2 about centroidal x-x axis of the section\n",
- "I_x_x_3=b_3*d_3**3*12**-1+a_3*Y_3**2 #moment of inertia of rectangle 3 about centroidal x-x axis of the section\n",
- "I_x_x=I_x_x_1+I_x_x_2+I_x_x_3 #cm**4 \n",
- "\n",
- "\n",
- "#Result\n",
- "print\"Moment of Inertia of the section is\",round(I_x_x,2),\"cm**4\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Moment of Inertia of the section is 523.16 cm**4\n"
- ]
- }
- ],
- "prompt_number": 12
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no2.4,Page no.33"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "D=10 #cm #diameter of circle\n",
- "b=4 #cm #width of rectangle \n",
- "d=4 #cm #breadth of rectangle\n",
- "Y=1 #cm #Distance of centroid of rectangle 1 to C.G\n",
- "a=16 #cm**2 #area of rectangle\n",
- "\n",
- "#Calculations\n",
- "\n",
- "I_x_x_1=pi*64**-1*(D**4) #cm**4 #moment of inertia of circle about x-x axis\n",
- "I_x_x_2=b*d**3*12**-1+a*Y**2 #cm**4 #moment of inertia of rectangle about x-x axis\n",
- "I_x_x=I_x_x_1-I_x_x_2 #cm**4 #Total moment of inertia of the section\n",
- "\n",
- "#Result\n",
- "print\"Total moment of inertia of the section is\",round(I_x_x,2),\"cm**4\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Total moment of inertia of the section is 453.54 cm**4\n"
- ]
- }
- ],
- "prompt_number": 23
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 2.5,Page no.33"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "b_1=10 #cm #Breadth of the triangle\n",
- "h=9 #cm #Height of triangle\n",
- "b_2=2 #cm #width of rectangle\n",
- "d=3 #cm #Depth of rectangle\n",
- "\n",
- "#Triangle ABC-1\n",
- "a_1=45 #cm**2 #Area of triangle\n",
- "y_1=3 #cm #C.G of triangle\n",
- "\n",
- "#Rectanglar hole-2\n",
- "a_2=6 #cm**2 #Area of rectangle\n",
- "y_2=4.5 #cm #C.G of rectangle\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#Using relations\n",
- "Y_bar=((a_1*y_1-a_2*y_2)*(a_1-a_2)**-1) #cm\n",
- "\n",
- "I_1=b_1*h**3*36**-1+a_1*(y_1-Y_bar)**2 #cm**4 #M.I of triangle ABC about x-x passing through C.G of section\n",
- "I_2=b_2*d**3*12**-1+a_2*(y_2-Y_bar)**2 #cm**4 #M.I of rectangular hole about x-x passing through C.G of section\n",
- "I=I_1-I_2 #cm**4 #M.I of whole section about x-x passing through the C.G \n",
- "\n",
- "I_3=b_1*h**3*12**-1 #cm**4 #M.I of triangle ABC about the base BC\n",
- "I_4=b_2*d**3*12**-1+a_2*y_2**2 #cm**4 #M.I of Rectangular hole about the base BC\n",
- "\n",
- "I_5=I_3-I_4 #cm**4 #M.I of the whole section about the base BC\n",
- "\n",
- "#Result\n",
- "print\"M.I of whole section about x-x passing through the C.G\",round(I,2),\"cm**4\"\n",
- "print\"M.I of the whole section about the base BC is\",round(I_5,2),\"cm**4\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "M.I of whole section about x-x passing through the C.G 182.42 cm**4\n",
- "M.I of the whole section about the base BC is 481.5 cm**4\n"
- ]
- }
- ],
- "prompt_number": 39
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no2.6,Page no.34"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "\n",
- "#Notifications has been changed as per requirement\n",
- "\n",
- "\n",
- "h=8 #cm #height of triangle\n",
- "b=8 #cm #breadth of triangle or diameter semicircle\n",
- "d=4 #cm #diameter of circle enclosed\n",
- "\n",
- "#Calculations\n",
- "\n",
- "I_1=b*h**3*12**-1 #cm #moment of inertia of the triangle ABC about the axis AB\n",
- "I_2=pi*b**4*128**-1 #cm ##moment of inertia of the semicircle about the axis AB\n",
- "I_3=pi*d**4*64**-1 #cm #moment of inertia of circle about the circle about the axis\n",
- "\n",
- "I=I_1+I_2-I_3 #cm #Moment of Inertia of the shaded area about the axia AB\n",
- "\n",
- "#Result\n",
- "print\"Moment of Inertia of the shaded area is\",round(I,2),\"cm\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Moment of Inertia of the shaded area is 429.3 cm\n"
- ]
- }
- ],
- "prompt_number": 30
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no.2.12,Page no.38"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "#Rectangle\n",
- "a_1=600 #cm**2 #Area of the Rectangle\n",
- "y_1=15 #cm #C.G of Rectangle\n",
- "b=20 #cm #width of rectangle\n",
- "d=30 #cm #depth of rectangle\n",
- "D=15 #cm #Diameter of circle\n",
- "\n",
- "#Circle\n",
- "a_2=176.7 #cm**2 #Area of the circle\n",
- "y_2=20 #cm #C.G of the circle\n",
- " \n",
- "#Calculation\n",
- "\n",
- "Y_bar=((a_1*y_1-a_2*y_2)*(a_1-a_2)**-1) #cm #Distance of C.G From the AB\n",
- "Y_bar_1=2.1 #cm\n",
- "Y_bar_2=7.1 #cm\n",
- "\n",
- "I_1=b*d**3*12**-1 #cm**4 #M.I of the rectangle about its C.G and parallel to x-x axis\n",
- "I_2=I_1+a_1*Y_bar_1**2\n",
- "I_3=pi*D**4*64**-1+a_2*Y_bar_2**2 #cm**4 #M.I of circular section about x-x axis\n",
- "\n",
- "I=I_2-I_3 #cm**4 #M.I of the section about x-x axis\n",
- "\n",
- "#Result\n",
- "print\"M.I of the section about x-x axis\",round(I,2),\"cm**4\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "M.I of the section about x-x axis 36253.5 cm**4\n"
- ]
- }
- ],
- "prompt_number": 50
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no.2.13,Page no.38"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "d=90 #cm #Diameter of grindstone\n",
- "t=10 #cm #thickness of grindstone\n",
- "rho=0.0026 #Kg/cm**3 #Density\n",
- "\n",
- "#calculations\n",
- "\n",
- "#M=Mass of grindstone=Volume *Density=Area*Thickness*Density\n",
- "M=pi*4**-1*d**2*t*rho #Kg \n",
- "R=d*2**-1 #cm #radius\n",
- "I_g=M*R**2*2**-1 #Kg*m**2\n",
- "\n",
- "k=R*(2**0.5)**-1 #cm #Radius of gyration\n",
- "\n",
- "#Result\n",
- "print\"Radius of gyration is\",round(k,2),\"cm\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Radius of gyration is 31.82 cm\n"
- ]
- }
- ],
- "prompt_number": 6
- }
- ],
- "metadata": {}
- }
- ]
-}
\ No newline at end of file diff --git a/Strength_Of_Materials_by_B_K_Sarkar/chapter_3_som.ipynb b/Strength_Of_Materials_by_B_K_Sarkar/chapter_3_som.ipynb deleted file mode 100755 index 8ecddb1d..00000000 --- a/Strength_Of_Materials_by_B_K_Sarkar/chapter_3_som.ipynb +++ /dev/null @@ -1,948 +0,0 @@ -{
- "metadata": {
- "name": "chapter 3 som.ipynb",
- "signature": "sha256:f204f91e23b9b059e7969e16bcc2c68fd35a3a7bdfec7a765456a9a04f17dab5"
- },
- "nbformat": 3,
- "nbformat_minor": 0,
- "worksheets": [
- {
- "cells": [
- {
- "cell_type": "heading",
- "level": 1,
- "metadata": {},
- "source": [
- "Chapter 3:Stresses And Strains"
- ]
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 3.1,Page no.54"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of Variables\n",
- "\n",
- "P=40 #mm #Force applied to stretch a tape\n",
- "L=30 #m #Length of steel tape\n",
- "A=6*1 #mm #Cross section area\n",
- "E=200*10**9*10**-6 #KN/m**2 #Modulus of Elasticity\n",
- "\n",
- "#Calculations\n",
- "\n",
- "sigma_L=(P*L*10**3)*(A*E)**-1 #mm \n",
- "\n",
- "#Result\n",
- "print\"The Elongation of steel tape is\",round(sigma_L,4),\"mm\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Elongation of steel tape is 1.0 mm\n"
- ]
- }
- ],
- "prompt_number": 65
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 3.2,Page no.54"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of VAriables\n",
- "\n",
- "\n",
- "#D=(D_0-2) #cm #Inside Diameter of cyclinder\n",
- "#A=(pi*(D_0-1)) #cm**2 #Area of cross-section\n",
- "#L=(pi*(D_0-1)*5400) #N #Crushing load for column\n",
- "F=6 #Factor of safety\n",
- "T=1 #cm #wall thickness of cyclinder\n",
- "\n",
- "#S=L*F**-1\n",
- "#After Simplifying,we get\n",
- "S=600*10**3\n",
- "\n",
- "#Calculations\n",
- "\n",
- "D_0=(S*F)*(pi*54000)**-1+1 #cm #Outside diameter of cyclinder\n",
- "\n",
- "#Result\n",
- "print\"The outside Diameter of cyclinder is\",round(D_0,2),\"cm\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The outside Diameter of cyclinder is 22.22 cm\n"
- ]
- }
- ],
- "prompt_number": 4
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 3.3,Page no.56"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math \n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "P=800 #N #force applied to steel wire\n",
- "L=150 #m #Length of steel wire\n",
- "E=200 #GN/m**2 #Modulus of Elasticity\n",
- "d=10 #mm #Diameter of steel wire\n",
- "W=7.8*10**4 #N/m**3 #Weight Density of steel\n",
- "#A=(pi*4**-1)*(d)**2 #m**2\n",
- "\n",
- "#After simplifying Area,we get\n",
- "A=7.85*10**-5 #m**2\n",
- "\n",
- "#calculation (Part-1)\n",
- "\n",
- "#Elongation Due to 800N Load \n",
- "dell_L_1=(P*L*10**-3)*(A*E*10**9*10**-6)**-1 #mm\n",
- "\n",
- "#calculation (Part-2)\n",
- "\n",
- "#Elongation due to Weight of wire \n",
- "dell_L_2=((pi*4**-1)*150*W*L*10**-3)*(2*A*E*10**7)**-1 #mm\n",
- "\n",
- "#calculation (Part-3)\n",
- "\n",
- "#Total Elongation of wire\n",
- "dell_L_3=dell_L_1+dell_L_2\n",
- "\n",
- "\n",
- "#Result\n",
- "print\"The Elongation due to 800N Load is\",round(dell_L_1,2),\"mm\"\n",
- "print\"The Elongation due to Weight of wire is\",round(dell_L_2,2),\"mm\"\n",
- "print\"Total Elongation of wire is\",round(dell_L_3,2),\"mm\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Elongation due to 800N Load is 7.64 mm\n",
- "The Elongation due to Weight of wire is 4.39 mm\n",
- "Total Elongation of wire is 12.03 mm\n"
- ]
- }
- ],
- "prompt_number": 25
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 3.4,Page no.55"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Intilization of variables\n",
- "\n",
- "d=10 #mm #Diameter of Punching Hole\n",
- "t=4 #mm #Thickness of Mild Steel Plate\n",
- "tou=320 #N/mm**2 #Shear Strength of mild Steel\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#Force Required for punching the hole\n",
- "P=tou*pi*d*t #N \n",
- "\n",
- "#Area of punch in contact with the plate surface\n",
- "A=(pi*4**-1*d**2) #mm*2\n",
- "\n",
- "#Compressive stress\n",
- "sigma_c=P*A**-1 #N/mm*2\n",
- "\n",
- "#Result\n",
- "print\"Force Required for punching the hole is\",round(P,2),\"N\"\n",
- "print\"Compressive stress is\",sigma_c,\"N/mm*2\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Force Required for punching the hole is 40212.39 N\n",
- "Compressive stress is 512.0 N/mm*2\n"
- ]
- }
- ],
- "prompt_number": 29
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 3.6,Page no.57"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "P=200*10**3 #N\n",
- "L_1=0.10 #mm #Length of of portin AB\n",
- "L_2=0.16 #mm #Length of of portin BC\n",
- "L_3=0.12 #mm #Length of of portin CD\n",
- "E=200*10**9 #N\n",
- "d_1=0.1 #cm\n",
- "d_2=0.08 #cm\n",
- "d_3=0.06 #cm\n",
- "A_1=(pi*4**-1)*(0.1)**2 #mm**2\n",
- "A_2=(pi*4**-1)*(0.08)**2 #mm**2\n",
- "A_3=(pi*4**-1)*(0.06)**2 #mm**2\n",
- "\n",
- "#Calculations\n",
- "\n",
- "dell_L_1=(P*L_1*10**3)*(A_1*E)**-1 #mm\n",
- "dell_L_2=(P*L_2*10**3)*(A_2*E)**-1 #mm\n",
- "dell_L_3=(P*L_3*10**3)*(A_3*E)**-1 #mm\n",
- "dell_L=dell_L_1+dell_L_2+dell_L_3 #mm\n",
- "\n",
- "#Result\n",
- "print\"Total Elongation of steel bar is\",round(dell_L,3),\"mm\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Total Elongation of steel bar is 0.087 mm\n"
- ]
- }
- ],
- "prompt_number": 67
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 3.7,Page no.57"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "#from F.B.D,we get\n",
- "P_1=50 #KN\n",
- "P_2=20 #KN\n",
- "P_3=40 #KN\n",
- "\n",
- "d=0.02 #mm #Diameter of steel bar\n",
- "L_1=0.4 #mm\n",
- "L_2=0.3 #mm\n",
- "L_3=0.2 #mm\n",
- "E=210*10**9 #N\n",
- "\n",
- "#After simplifying Area,we get\n",
- "A=pi*10**-4 #m**2 #Area of cross section\n",
- "\n",
- "#Calculations\n",
- "\n",
- "sigma_AB=P_1*1000*A #N/m**2\n",
- "sigma_BA=P_2*1000*A #N/m**2\n",
- "sigma_CD=P_3*1000*A #N/m**2\n",
- "dell_L=((P_1*L_1+P_2*L_2+P_3*L_3)*(A*E)**-1)*10**6 #mm\n",
- "\n",
- "#Result\n",
- "print\"Total Elongation of Steel bar is\",round(dell_L,3),\"mm\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Total Elongation of Steel bar is 0.515 mm\n"
- ]
- }
- ],
- "prompt_number": 44
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 3.8,Page no.58"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "import numpy as np\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "#R_a+R_c=25 #KN #R_a,R_b are reactions at supports A and C respectively\n",
- "L_ab=2 #m\n",
- "L_bc=3 #m\n",
- "\n",
- "#Calculation\n",
- "\n",
- "#From F.B.D,we get\n",
- "#dell_L_AB=(R_a*L_AB)*(A*E)**-1 #Elongation of portion AB\n",
- "#dell_L_BC=(R_c*L_BC)*(A*E)**-1 #Compression of portion BC\n",
- "\n",
- "#After simplifying above equations we get,\n",
- "#R_a=(1.5)*R_c #KN\n",
- "#R_a+R_c=25 #KN\n",
- "#Solving the above simultaneous equations using matrix method\n",
- "A=np.array([[1,-1.5],[1,1]]) #Here the coefficients of the first equations of unknowns are setup\n",
- "B=np.array([0,25]) #Here the RHS of both equations are setup\n",
- "C=np.linalg.solve(A,B)\n",
- "\n",
- "#print C[0] #Prints the first element in the vector C\n",
- "#print C[1] #Prints the second element in the vector C\n",
- "\n",
- "#Result\n",
- "print\"The reaction at support A is\",round(C[0],2),\"KN\"\n",
- "print\"The reaction at support C is\",round(C[1],2),\"KN\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The reaction at support A is 15.0 KN\n",
- "The reaction at support C is 10.0 KN\n"
- ]
- }
- ],
- "prompt_number": 26
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 3.9,Page no.59"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "#P is the force acting on the bar BC compressive in nature and force on AB is (100-P) Tensile in nature\n",
- "E=200*10*9 #N\n",
- "A_1=3*10**-4 #cm**2 #Area of AB\n",
- "A_2=4*10**-4 #cm**2 #Area of BC\n",
- "L=1.5 #cm #Length of bar\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#The total elongation of bar\n",
- "#(((100-P)*10**3*1.5)*(3*10**-4*E)**-1)-((P*10**3*1.5)*(4*10**-4*E)**-1)=0 \n",
- "\n",
- "#The total elongation of bar is limited to 1\n",
- "#(25-0.4375*P)*10**-4=1*10**-3\n",
- "\n",
- "#After simplifying above equation we get,\n",
- "P=-(10-25)*0.4375**-1 #KN #Total elongation of bar\n",
- "F_AB=100-P #KN #force in AB\n",
- "F_BC=P #KN #Force in BC\n",
- "sigma_AB=(((F_AB)*(3*10**-4)**-1)*10**-3) #KN #Stress in AB\n",
- "sigma_BC=((F_BC)*(4*10**-4)**-1*10**-3) #KN #Stress in Bc\n",
- "\n",
- "\n",
- "#Result\n",
- "print\"F_AB\",round(F_AB,2),\"KN\"\n",
- "print\"F_BC\",round(F_BC,2),\"KN\"\n",
- "print\"sigma_AB\",round(sigma_AB,2),\"KN\"\n",
- "print\"sigma_BC\",round(sigma_BC,2),\"KN\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "F_AB 65.71 KN\n",
- "F_BC 34.29 KN\n",
- "sigma_AB 219.05 KN\n",
- "sigma_BC 85.71 KN\n"
- ]
- }
- ],
- "prompt_number": 17
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 3.12,Page no.61"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "P=500 #KN #Safe Load\n",
- "d=20 #mm #steel rod diameter\n",
- "n=4 #number of steel rod\n",
- "sigma_c=4 #N/mm**2 #stress in concrete \n",
- "#E_S*E_c**-1=15\n",
- "\n",
- "\n",
- "#Calculations\n",
- "\n",
- "A_s=4*pi*4**-1*d**2 #mm**2 #Area os steel rod\n",
- "sigma_s=15*sigma_c #N/mm**2 #stress in steel\n",
- "\n",
- "#P=sigma_s*A_s+sigma_c*A_c \n",
- "\n",
- "#After substituting and simplifying above equation we get,\n",
- "\n",
- "A_c=(P*10**3-sigma_s*1256)*(sigma_c)**-1 #mm**2 #Area of the concrete\n",
- "X=(A_s+A_c)**0.5 #mm #Total cross sectional area\n",
- "P_s=A_s*sigma_s*10**-3 #KN #Load carried by steel\n",
- "\n",
- "#Result\n",
- "print\"Load carried by steel is\",round(P_s,2),\"KN\"\n",
- "print\"stress induced in steel is\",round(sigma_s,3),\"KN\"\n",
- "print\"cross sectional area of column is\",round(X,2),\"mm\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Load carried by steel is 75.4 KN\n",
- "stress induced in steel is 60.0 KN\n",
- "cross sectional area of column is 327.74 mm\n"
- ]
- }
- ],
- "prompt_number": 11
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 3.13,Page no.62"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "A_s=500 #mm**2\n",
- "E_s=200000\n",
- "E_al=80000\n",
- "A_al=1000\n",
- "\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#(P_al*L_al)*(A_al*E_al)**-1+(P_s*L_s)*(A_s*E_s)**-1=1*2**-1 \n",
- "\n",
- "P=1*1000**-1*((A_s*E_s*A_al*E_al)*(A_s*E_s+A_al*E_al)**-1) #N\n",
- "P_s=P_al=P #N\n",
- "sigma_t=P_s*A_s**-1 #N/mm**2 #Tensile stress in bolt\n",
- "sigma_c=P_al*A_al**-1 #N/mm**2 #Compressive stress in Aluminium tube\n",
- "\n",
- "#result\n",
- "print\"Tensile stress in bolt is\",round(sigma_t,2),\"N/mm**2\"\n",
- "print\"Compressive stress in Aluminium tube is\",round(sigma_c,2),\"N/mm**2\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Tensile stress in bolt is 88.89 N/mm**2\n",
- "Compressive stress in Aluminium tube is 44.44 N/mm**2\n"
- ]
- }
- ],
- "prompt_number": 1
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 3.14,Page no.63"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "A=1600 #mm**2 #Area of the Bar\n",
- "P=480*10**3 #N #Load\n",
- "dell_L=0.4 #mm #Contraction of metal bar\n",
- "L=200 #mm #Length of metal bar\n",
- "sigma_t=0.04 #mm #Guage Length\n",
- "t=40\n",
- "\n",
- "#Calculations\n",
- "\n",
- "sigma_L=dell_L*L**-1\n",
- "E=((P*L)*(A*dell_L)**-1*10**-3) #N/mm**2 #Young's Modulus \n",
- "m=t*sigma_t**-1*sigma_L\n",
- "\n",
- "\n",
- "#Result\n",
- "print\"The value of Young's Modulus is\",round(E,2),\"N/mm*2\"\n",
- "print\"The value of Poissoin's ratio is\",round(m,2)"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The value of Young's Modulus is 150.0 N/mm*2\n",
- "The value of Poissoin's ratio is 2.0\n"
- ]
- }
- ],
- "prompt_number": 1
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 3.15,Page no.63"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "A_s=0.003848 #m**2 #Area of steel bar\n",
- "A_al=0.003436 #m**2 #Area of Aluminium tube\n",
- "E=220*10*9 #N #Young's modulus of steel\n",
- "E=70*10*9 #N #Young's modulus of aluminium\n",
- "P=600*10**3 #N #Load applied to the bar\n",
- "#dell_L_al-dell_L_s=0.00015 #mm #difference between strain in aluminium bar and steel bar\n",
- "\n",
- "#Calculations\n",
- "\n",
- "\n",
- "#Let the aluminium tube be compressed by dell_L_al and steel bar by by dellL_s\n",
- "#dell_L_al=sigma_al*E_al**-1*L_al\n",
- "#dell_L_s=sigma_s*E_s**-1*L_s\n",
- "\n",
- "#After substituting and simplifying above equation we get,\n",
- "#((sigma_al*70**-1)-(sigma_s*220**-1))=300000 #(equation 1)\n",
- "\n",
- "#After simplifying above equation we get,\n",
- "#sigma_al=17462.165*10**4-1.1199*sigma_s #(equation 2)\n",
- "\n",
- "#Now substituting sigma_al in equation(1)\n",
- "#((17462.165*10**4-1.1199*sigma_s)*(70)**-1)-(sigma_s*220**-1)=300000\n",
- "\n",
- "#After simplifying above equation we get,\n",
- "\n",
- "sigma_s=-((300000-249.4594*10**4)*0.0205444**-1)*10**-6 #MN/m**2 #stress developed in steel bar\n",
- "#sigma_al=17462.165*10**4-1.1199*sigma_s\n",
- "sigma_al=(17462.165*10**4-1.1199*106822005.02)*10**-6\n",
- "\n",
- "\n",
- "#Result\n",
- "print\"stress developed in steel bar is\",round(sigma_s,2),\"MN/m**2\"\n",
- "print\"stress developed in aluminium bar is\",round(sigma_al,2),\"MN/m**2\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "stress developed in steel bar is 106.82 MN/m**2\n",
- "stress developed in aluminium bar is 54.99 MN/m**2\n"
- ]
- }
- ],
- "prompt_number": 21
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 3.16,Page no.64"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "E=200 #GN/m**2 #Modulus of elasticity\n",
- "alpha=11*10**-6 #per degree celsius #coeffecient o flinear expansion of steel bar\n",
- "L=6 #m #Length of rod\n",
- "\n",
- "\n",
- "#Calculations \n",
- "\n",
- "#(Part-1) #IF the walls do not yield\n",
- "\n",
- "t=58 #degree celsius #Fall in temperature #(t=80-22)\n",
- "dell=alpha*t #strain\n",
- "sigma=E*10**9*dell*10**-6 #MN/m**2 #Stress\n",
- "A=pi*4**-1*6.25*10**-4 #mm**2 #Area of wall and rod\n",
- "P=sigma*10**6*A*10**-3 #KN #Pull Exerted\n",
- "\n",
- "#(Part-2) #IF the walls yield together at the two ends is 1.15 mm\n",
- "\n",
- "L_2=L*(1-alpha*t) #m #Length of rod at 22 degree celsius\n",
- "L_3=L-L_2 #m #Decrease in Length \n",
- "\n",
- "#As the walls yield by 1.5 mm, actual decrease in length is\n",
- "L_4=L_3-0.0015 #m \n",
- "dell_2=L_4*L**-1 #strain \n",
- "P_2=E*10**9*dell_2*A*10**-3 #KN\n",
- "\n",
- "#Result\n",
- "print\"Pull Exerted by the rod:when walls do not yield\",round(P,2),\"KN\"\n",
- "print\" :when total yield together at two ends is 1.5 mm\",round(P_2,2),\"KN\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Pull Exerted by the rod:when walls do not yield 62.64 KN\n",
- " :when total yield together at two ends is 1.5 mm 38.09 KN\n"
- ]
- }
- ],
- "prompt_number": 43
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 3.17,Page no.65"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "D=4.5 #cm #External Diameter of tube\n",
- "d=3 #cm #Internal diameter of tube\n",
- "t=3 #mm #thickness of tube\n",
- "t_1=30 #degree celsius\n",
- "t_2=180 #degree celsius #when metal heated\n",
- "L=30 #cm #Original LEngth\n",
- "alpha_s=1.08*10**-5 #Per degree celsius #coefficient of Linear expansion of steel tube\n",
- "alpha_c=1.7*10**-5 #Per degree celsius #coefficient of Linear expansion of copper tube\n",
- "E_s=210 #GPa #Modulus of Elasticity of steel \n",
- "E_c=110 #GPA #Modulus of Elasticity of copper\n",
- "\n",
- "#Calculation\n",
- "\n",
- "#For Equilibrium of the system, Total tension in steel=Total tension in copper\n",
- "\n",
- "#sigma_s*A_s=sigma_c*A_c (equation 1)\n",
- "\n",
- "A_c=pi*4**-1*d**2 #cm**2 #Area of copper\n",
- "A_s=pi*4**-1*(D**2-d**2) #cm**2 #Area of steel\n",
- "\n",
- "#simplifying equation 1\n",
- "#sigma_s=1.785*sigma_c\n",
- "\n",
- "T=t_2-t_1 #change in temperature\n",
- "\n",
- "#Actual expansion of steel=Actual expansion of copper\n",
- "#alpha_s*T*L+sigma_s*E_s**-1*L=alpha_c*T*L-sigma_c*E_c**-1*L\n",
- "\n",
- "#After substituting values in above equation and simplifying we get\n",
- "\n",
- "sigma_c=(930*10**5*1.7591**-1)*10**-6 #MN/m**2 #Stress in copper\n",
- "sigma_s=1.785*sigma_c #MN/m**2 #Stress in steel\n",
- "\n",
- "#Increase in Length of either component\n",
- "L_2=(alpha_s*T+sigma_s*10**6*(E_s*10**9)**-1)*L\n",
- "\n",
- "#Result\n",
- "print\"stress in copper bar is\",round(sigma_c,2),\"MN/m**2\"\n",
- "print\"stress in steel bar is\",round(sigma_s,2),\"MN/m**2\"\n",
- "print\"Increase in Length is\",round(L_2,3),\"cm\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "stress in copper bar is 52.87 MN/m**2\n",
- "stress in steel bar is 94.37 MN/m**2\n",
- "Increase in Length is 0.062 cm\n"
- ]
- }
- ],
- "prompt_number": 54
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 3.18,Page no.66"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "t_1=15 #degree celsius #temperature of steel bar\n",
- "t_2=315 #degree celsius #raised temperature \n",
- "E_s=210 #GPa #Modulus of Elasticity of steel bar\n",
- "E_c=100 #GPa #Modulus of Elasticity of copper bar\n",
- "dell_L=0.15 #cm #Increase in Length of bar\n",
- "\n",
- "#Calculation\n",
- "\n",
- "#For Equilibrium of the system, Tension in steel bar = Tension in copper bar\n",
- "#sigma_s*A_s = sigma_c*2*A_c\n",
- "#sigma_S=2*sigma_c\n",
- "\n",
- "#Actual expansion of steel = Actual expansion of copper\n",
- "#L*alpha_s*T+sigma_s*E_s**-1*L = L*alpha_c*T-sigma_c*E_c**-1*L (Equation 1)\n",
- "\n",
- "T=t_2-t_1 #per degree celsius #change in temperature\n",
- "\n",
- "#After substituting values in above equation and simplifying we get\n",
- "sigma_c=(1650*10**5*1.9524**-1)*10**-6 #MN/m**2 #Stress in copper\n",
- "sigma_s=2*sigma_c #MN/m**2 #Stress in steel\n",
- "\n",
- "#Actual Expansion of steel bar \n",
- "#L*alpha_s*T+sigma_s*E_s**-1*L = L*alpha_c*T-sigma_c*E_c**-1*L \n",
- "#After substituting values in above equation and simplifying we get\n",
- "L=0.15*10**-2*0.0044048**-1 #m\n",
- "\n",
- "#Result\n",
- "print\"Stress in copper bar is\",round(sigma_c,2),\"MN/m**2\"\n",
- "print\"Stress in steel bar is\",round(sigma_s,2),\"MN/m**2\"\n",
- "print\"Original Length of bar is\",round(L,2),\"m\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Stress in copper bar is 84.51 MN/m**2\n",
- "Stress in steel bar is 169.02 MN/m**2\n",
- "Original Length of bar is 0.34 m\n"
- ]
- }
- ],
- "prompt_number": 60
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 3.19,Page no.67"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "L=100 #m #Length of rod\n",
- "A=2 #cm**2 #cross sectional area\n",
- "rho=80 #KN/m**3\n",
- "\n",
- "#Calculatiom\n",
- "W=A*10**-4*L*rho #KN\n",
- "\n",
- "sigma_s=10+1.6 #KN #Rod experiencing max tensile stress when it is at top performing upstroke\n",
- "sigma_s_2=sigma_s*10**3*200**-1 #N/mm**2 #corresponding stress at this moment\n",
- "\n",
- "sigma_c=1 #KN ##Rod experiencing max compressive stress at its lower end,free from its own weight\n",
- "sigma_c_2=sigma_c*10**3*200**-1 #corresponding stress at this moment\n",
- "\n",
- "#Result\n",
- "print\"Tensile stress in bar\",round(sigma_s_2,2),\"N/mm**2\"\n",
- "print\"Compressive stress in bar\",round(sigma_c_2,2),\"N/mm**2\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Tensile stress in bar 58.0 N/mm**2\n",
- "Compressive stress in bar 5.0 N/mm**2\n"
- ]
- }
- ],
- "prompt_number": 64
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 3.20,Page no.68"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "sigma=0.012 #strain\n",
- "P=150 #KN #Total Load on the Post\n",
- "E=1.4*10**4 #N/mm**2 #modulus of elasticity\n",
- "#b be the width of the post in mm\n",
- "#2b is the longer dimension of the post in mm\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#We know,\n",
- "#sigma=(P*(A*E)**-1) \n",
- "\n",
- "#After substituting values and simplifying, we get\n",
- "b=((150*10**3)*(0.012*1.4*2*10**4)**-1)**0.5\n",
- "q=2*b #mm #Longer dimension of post\n",
- "\n",
- "#Result\n",
- "print\"Width of post is\",round(b,2),\"mm\"\n",
- "print\"Longer dimension of post is\",round(q,2),\"mm\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Width of post is 21.13 mm\n",
- "Longer dimension of post is 42.26 mm\n"
- ]
- }
- ],
- "prompt_number": 6
- }
- ],
- "metadata": {}
- }
- ]
-}
\ No newline at end of file diff --git a/Strength_Of_Materials_by_B_K_Sarkar/chapter_4_som.ipynb b/Strength_Of_Materials_by_B_K_Sarkar/chapter_4_som.ipynb deleted file mode 100755 index 87824640..00000000 --- a/Strength_Of_Materials_by_B_K_Sarkar/chapter_4_som.ipynb +++ /dev/null @@ -1,2019 +0,0 @@ -{
- "metadata": {
- "name": "chapter 4 som.ipynb"
- },
- "nbformat": 3,
- "nbformat_minor": 0,
- "worksheets": [
- {
- "cells": [
- {
- "cell_type": "heading",
- "level": 1,
- "metadata": {},
- "source": [
- "Chapter No.4:Shearing Force And Bending Moment"
- ]
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 4.4.1,Page No.89"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "%matplotlib inline\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "F_B=-10 #KN #Force at pt B\n",
- "F_D=-20 #KN #Force at pt D\n",
- "w_CB=5 #KN/m #u.d.l at CB\n",
- "w_AE=40 #KN/m #u.d.l at AE\n",
- "L_ED=L_CB=2 #m #Length of ED & CB\n",
- "L_CD=1 #m #Length of CD\n",
- "L_AE=3 #m #Length of AE\n",
- "L=8 #m #span of beam\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#Shear Force Calculations\n",
- "\n",
- "#Shear Force at B\n",
- "V_B=F_B #KN\n",
- "\n",
- "#Shear Force at C\n",
- "V_C=F_B-(w_CB*L_CB)\n",
- "\n",
- "#Shear Force at D\n",
- "V_D1=V_C\n",
- "V_D2=V_C+F_D\n",
- "\n",
- "#Shear Force at E\n",
- "V_E=V_D2\n",
- "\n",
- "#Shear Force at A\n",
- "V_A=V_D-(w_AE*L_AE)\n",
- "\n",
- "#Bending Moment Calculations\n",
- "\n",
- "#Bending Moment at B\n",
- "M_B=0\n",
- "\n",
- "#Bending Moment at C\n",
- "M_C=F_B*L_CB-w_CB*L_CB**2*2**-1\n",
- "\n",
- "#Bending Moment at D\n",
- "M_D=F_B*(L_CB+L_CD)-w_CB*L_CB*(L_CB*2**-1+L_CD)\n",
- "\n",
- "#Bending Moment at E\n",
- "M_E=F_B*(L_CB+L_CD+L_ED)-w_CB*L_CB*(L_CB*2**-1+L_CD+L_ED)+F_D*L_ED\n",
- "\n",
- "#Bending Moment at A\n",
- "M_A=F_B*L-w_CB*L_CB*(L_CB*2**-1+L_CD+L_ED+L_AE)+F_D*(L_AE+L_ED)-w_AE*(L_AE**2*2**-1)\n",
- "\n",
- "#Result\n",
- "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
- "\n",
- "#Plotting the Shear Force Diagram\n",
- "\n",
- "X1=[0,L_CB,L_CB+L_DC,L_CB+L_DC,L_CB+L_DC+L_ED,L_CB+L_DC+L_ED+L_AE,L_CB+L_DC+L_ED+L_AE]\n",
- "Y1=[V_B,V_C,V_D1,V_D2,V_E,V_A,0]\n",
- "Z1=[0,0,0,0,0,0,0]\n",
- "plt.plot(X1,Y1,X1,Z1)\n",
- "plt.xlabel(\"Length x in m\")\n",
- "plt.ylabel(\"Shear Force in kN\")\n",
- "plt.show()\n",
- "\n",
- "#Plotting the Bendimg Moment Diagram\n",
- "\n",
- "Y2=[M_B,M_C,M_D,M_E,M_A]\n",
- "X2=[0,L_CB,L_CB+L_DC,L_CB+L_DC+L_ED,L_CB+L_DC+L_ED+L_AE]\n",
- "Z2=[0,0,0,0,0]\n",
- "plt.plot(X2,Y2)\n",
- "plt.xlabel(\"Lenght in m\")\n",
- "plt.ylabel(\"Bending Moment in kN.m\")\n",
- "plt.show()"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Shear Force and Bending Moment Diagrams are the results\n"
- ]
- },
- {
- "metadata": {},
- "output_type": "display_data",
- "png": "iVBORw0KGgoAAAANSUhEUgAAAYwAAAEPCAYAAABRHfM8AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRK5CYII=\n",
- "text": [
- "<matplotlib.figure.Figure at 0x59f9130>"
- ]
- },
- {
- "metadata": {},
- "output_type": "display_data",
- "png": "iVBORw0KGgoAAAANSUhEUgAAAYwAAAEPCAYAAABRHfM8AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
- "text": [
- "<matplotlib.figure.Figure at 0x5549230>"
- ]
- }
- ],
- "prompt_number": 86
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 4.4.2,Page No.90"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "%matplotlib inline\n",
- "\n",
- "#Initilization of variables\n",
- "w_CB=1 #KN/m #u.d.l on Length CB\n",
- "F_D=2 #KN #Pt Load at D\n",
- "L_AD=L_DC=1 #m #Length of AD & DC\n",
- "L_CB=2 #m #Length of CB\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#Shear Force at B\n",
- "V_B=0 #KN\n",
- "\n",
- "#Shear Force at C\n",
- "V_C=-(w_CB*L_CB)\n",
- "\n",
- "#Shear Force at D\n",
- "V_D1=V_C\n",
- "V_D2=V_C-F_D\n",
- "\n",
- "#Shear Force at A\n",
- "V_A=V_D2 \n",
- "\n",
- "#Bending Moment Calculations\n",
- "\n",
- "#Bending Moment at B\n",
- "M_B=0\n",
- "\n",
- "#Bending Moment at C\n",
- "M_C=-w_CB*L_CB**2*2**-1\n",
- "\n",
- "#Bending Moment at D\n",
- "M_D=-w_CB*L_CB*(L_CB*2**-1+L_DC)\n",
- "\n",
- "#Bending Moment at A\n",
- "M_A=-w_CB*L_CB*(L_CB*2**-1+L_DC+L_AD)-F_D*L_AD\n",
- "\n",
- "#Result\n",
- "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
- "\n",
- "#Plotting the Shear Force Diagram\n",
- "\n",
- "X1=[0,L_CB,L_CB+L_DC,L_CB+L_DC,L_CB+L_DC+L_AD,L_CB+L_DC+L_AD]\n",
- "Y1=[0,V_C,V_D1,V_D2,V_A,0]\n",
- "Z1=[0,0,0,0,0,0]\n",
- "plt.plot(X1,Y1,X1,Z1)\n",
- "plt.xlabel(\"Length x in m\")\n",
- "plt.ylabel(\"Shear Force in kN\")\n",
- "plt.show()\n",
- "\n",
- "#Plotting the Bendimg Moment Diagram\n",
- "\n",
- "Y2=[M_B,M_C,M_D,M_A]\n",
- "X2=[0,L_CB,L_CB+L_DC,L_CB+L_DC+L_AD]\n",
- "Z2=[0,0,0,0]\n",
- "plt.plot(X2,Y2)\n",
- "plt.xlabel(\"Length in m\")\n",
- "plt.ylabel(\"Bending Moment in kN.m\")\n",
- "plt.show()"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Shear Force and Bending Moment Diagrams are the results\n"
- ]
- },
- {
- "metadata": {},
- "output_type": "display_data",
- "png": "iVBORw0KGgoAAAANSUhEUgAAAY4AAAEPCAYAAABV6CMBAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nEZEkTBxERCQJEwcREUnCxEFERJL8P6KhBCKbfJ61AAAAAElFTkSuQmCC\n",
- "text": [
- "<matplotlib.figure.Figure at 0x59c7d50>"
- ]
- },
- {
- "metadata": {},
- "output_type": "display_data",
- "png": "iVBORw0KGgoAAAANSUhEUgAAAYQAAAEPCAYAAABCyrPIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nGgYCEREBAP4f5wfdcfm2/kAAAAAASUVORK5CYII=\n",
- "text": [
- "<matplotlib.figure.Figure at 0x5549cb0>"
- ]
- }
- ],
- "prompt_number": 85
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 4.4.3,Page No.91"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "%matplotlib inline\n",
- "\n",
- "#Initilization of variables\n",
- "AC=5000 #N/m #u.v.l\n",
- "L_AB=4 #m #Length of AB\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#Consider a section at Distance x from B\n",
- "#DB=x\n",
- "#By similar triangles (triangle ABC and BDE) we get\n",
- "\n",
- "#Shear Force at x\n",
- "#F_x=-DB*DE*2**-1\n",
- "#After substituting values in above equation we get\n",
- "#F_x=625*x**2\n",
- "\n",
- "#shear Force at B where x=0\n",
- "V_B=0\n",
- "\n",
- "#shear Force at A where x=L_AB=4\n",
- "V_A=625*L_AB**2\n",
- "\n",
- "#Bending Moment Calculation\n",
- "\n",
- "#M_x=DB*DE*DB*3**-1*2**-1\n",
- "#Substituting values in above equation we get\n",
- "#M_x=-625*x**3*3**-1\n",
- "\n",
- "#Bending Moment at B where x=0\n",
- "M_B=0\n",
- "\n",
- "#Bending Moment at A where x=L_AB=4\n",
- "M_A=-625*L_AB**3*3**-1\n",
- "\n",
- "#Result\n",
- "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
- "\n",
- "#Plotting the Shear Force Diagram\n",
- "\n",
- "X1=[0,L_AB]\n",
- "Y1=[V_B,V_A]\n",
- "Z1=[0,0]\n",
- "plt.plot(X1,Y1,X1,Z1)\n",
- "plt.xlabel(\"Length x in m\")\n",
- "plt.ylabel(\"Shear Force in kN\")\n",
- "plt.show()\n",
- "\n",
- "#Plotting the Bendimg Moment Diagram\n",
- "\n",
- "Y2=[M_B,M_A]\n",
- "X2=[0,L_AB]\n",
- "Z2=[0,0]\n",
- "plt.plot(X2,Y2)\n",
- "plt.xlabel(\"Length in m\")\n",
- "plt.ylabel(\"Bending Moment in kN.m\")\n",
- "plt.show()"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Shear Force and Bending Moment Diagrams are the results\n"
- ]
- },
- {
- "metadata": {},
- "output_type": "display_data",
- "png": "iVBORw0KGgoAAAANSUhEUgAAAZUAAAEPCAYAAACKplkeAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nchl2KkRE5DL/D4FiVgDUzkokAAAAAElFTkSuQmCC\n",
- "text": [
- "<matplotlib.figure.Figure at 0x59a61f0>"
- ]
- },
- {
- "metadata": {},
- "output_type": "display_data",
- "png": "iVBORw0KGgoAAAANSUhEUgAAAZ0AAAEPCAYAAACZcRnqAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nwm7+H/JugJQ8mxQzAAAAAElFTkSuQmCC\n",
- "text": [
- "<matplotlib.figure.Figure at 0x557b350>"
- ]
- }
- ],
- "prompt_number": 84
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 4.4.4,Page No.92"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "%matplotlib inline\n",
- "\n",
- "#Initilization of variables\n",
- "F_C=F_D=F_E=30 #KN #Pt Load at C,D,E respectively\n",
- "L_AE=L_ED=L_DC=1.5 #m #Length of AE,ED,DC respectively\n",
- "L_CB=0.5 #m #Length of CB\n",
- "L_AC=4.5 #m #Length of AC\n",
- "L_AD=3 #m #Length of AD\n",
- "w=10 #KN/m #u.d.l\n",
- "L=5 #m #Length of beam\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#Shear Force Calculations\n",
- "\n",
- "#Shear Force at B\n",
- "V_B=0 #KN\n",
- "\n",
- "#Shear Force at C\n",
- "V_C1=-w_CB*L_CB\n",
- "V_C2=-w*L_CB-F_C #KN\n",
- "\n",
- "#Shear Force at D\n",
- "V_D1=-w*(L_DC+L_CB)-F_C*L_DC\n",
- "V_D2=-w*(L_DC+L_CB)-F_C-F_D #KN\n",
- "\n",
- "#Shear Force at E\n",
- "V_E1=-w*(L_DC+L_CB+L_ED)-F_C*(L_DC+L_ED)\n",
- "V_E2=-F_C-F_D-F_E-w*(2*L_ED+L_CB)\n",
- "\n",
- "#Shear Force at A\n",
- "V_A=-w*L-F_C-F_D-F_E\n",
- "\n",
- "#Bending Moment Calculations\n",
- "\n",
- "#Bending Moment at B\n",
- "M_B=0\n",
- "\n",
- "#Bending Moment at C\n",
- "M_C=-w*L_CB**2*2**-1\n",
- "\n",
- "#Bending Moment at D\n",
- "M_D=-w*(L_DC+L_CB)**2*2**-1-F_C*L_DC\n",
- "\n",
- "#Bending Moment at E\n",
- "M_E=-w*(L_DC+L_CB+L_ED)**2*2**-1-F_C*(L_ED+L_DC)-F_D*L_ED\n",
- "\n",
- "#Bending Moment at A\n",
- "M_A=-w*L**2*2**-1-F_C*L_AC-F_D*L_AD-F_E*L_AE\n",
- "\n",
- "#Result\n",
- "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
- "\n",
- "#Plotting the Shear Force Diagram\n",
- "\n",
- "X1=[0,L_CB,L_CB,L_CB+L_DC,L_CB+L_DC,L_CB+L_DC+L_ED,L_CB+L_DC+L_ED,L_CB+L_DC+L_ED+L_AE,L_CB+L_DC+L_ED+L_AE]\n",
- "Y1=[V_B,V_C1,V_C2,V_D1,V_D2,V_E1,V_E2,V_A,0]\n",
- "Z1=[0,0,0,0,0,0,0,0,0]\n",
- "plt.plot(X1,Y1,X1,Z1)\n",
- "plt.xlabel(\"Length x in m\")\n",
- "plt.ylabel(\"Shear Force in kN\")\n",
- "plt.show()\n",
- "\n",
- "#Plotting the Bendimg Moment Diagram\n",
- "\n",
- "X2=[0,L_CB,L_CB+L_DC,L_CB+L_DC+L_ED,L_CB+L_DC+L_ED+L_AE,L_CB+L_DC+L_ED+L_AE]\n",
- "Y2=[M_B,M_C,M_D,M_E,M_A,0]\n",
- "Z2=[0,0,0,0,0,0]\n",
- "plt.plot(X2,Y2)\n",
- "plt.xlabel(\"Length in m\")\n",
- "plt.ylabel(\"Bending Moment in kN.m\")\n",
- "plt.show()"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Shear Force and Bending Moment Diagrams are the results\n"
- ]
- },
- {
- "metadata": {},
- "output_type": "display_data",
- "png": "iVBORw0KGgoAAAANSUhEUgAAAYwAAAEPCAYAAABRHfM8AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAAAElFTkSuQmCC\n",
- "text": [
- "<matplotlib.figure.Figure at 0x59f97d0>"
- ]
- },
- {
- "metadata": {},
- "output_type": "display_data",
- "png": "iVBORw0KGgoAAAANSUhEUgAAAYwAAAEPCAYAAABRHfM8AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nigAAAABJRU5ErkJggg==\n",
- "text": [
- "<matplotlib.figure.Figure at 0x59a25b0>"
- ]
- }
- ],
- "prompt_number": 88
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 4.4.5,Page No.93"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "%matplotlib inline\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "w1=30 #KN/m #u.d.l on L_CB\n",
- "F_C=120 #KN #Pt Load at C\n",
- "w2=50 #KN/m #u.d.l on L_AD\n",
- "L_DC=L_CB=2 #m #Length of DC and CB respectively\n",
- "L_AD=4 #m #Length of AD\n",
- "L_AB=L=8 #m #Length of beam\n",
- "\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#Let R_A & R_B be the reactions at A & B\n",
- "#R_A+R_B=380\n",
- "\n",
- "#Taking Moment at A\n",
- "#M_A=-R_B*L+F_C(L_DC+L_AD)+w1*L_CB*(L_CB*2**-1+L_DC+L_AD)+w2*L_AD**2*2**-1=0\n",
- "\n",
- "#After Rearranging the terms we get\n",
- "R_B=(F_C*(L_DC+L_AD)+w1*L_CB*(L_CB*2**-1+L_DC+L_AD)+w2*L_AD**2*2**-1)*L**-1\n",
- "R_A=380-R_B\n",
- "\n",
- "#Shear Force Calculations\n",
- "\n",
- "#Shear Force at B\n",
- "V_B=R_B\n",
- "\n",
- "#Shear Force at C\n",
- "V_C1=-w1*L_CB+R_B\n",
- "V_C2=R_B-w1*L_CB-F_C\n",
- "\n",
- "#Shear Force at D\n",
- "V_D=V_C2\n",
- "\n",
- "#Shear Force at A\n",
- "V_A=V_D-w2*L_AD\n",
- "\n",
- "#Point of contraflexure \n",
- "#Let E be the point EB=x\n",
- "#Shear Force at E\n",
- "#V_E=0=R_B-F_C-w1*L_CB-w2*(L_EB-L_DC-L_CB)\n",
- "L_EB=-((-R_B+F_C+w1*L_CB)*w2**-1-L_DC-L_CB)\n",
- "V_E=0\n",
- "\n",
- "#Bending Moment Calculations\n",
- "\n",
- "#Bending Moment at B\n",
- "M_B=0\n",
- "\n",
- "#Bending Moment at C\n",
- "M_C=R_B*L_CB-w1*L_CB**2*2**-1\n",
- "\n",
- "#Bending Moment at D\n",
- "M_D=R_B*(L_CB+L_DC)-w1*L_CB*(L_CB*2**-1+L_DC)-F_C*L_DC\n",
- "\n",
- "#Bending Moment at A\n",
- "M_A=0\n",
- "\n",
- "#Bending Moment at E\n",
- "L_ED=L_EB-(L_DC+L_CB) #m #Length of ED\n",
- "M_E=-w1*L_CB*(L_ED+L_DC+L_CB*2**-1)-F_C*(L_DC+L_ED)+R_B*L_EB\n",
- "\n",
- "#Result\n",
- "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
- "\n",
- "#Plotting the Shear Force Diagram\n",
- "\n",
- "X1=[0,L_CB,L_CB,L_CB+L_DC,L_CB+L_DC+L_AD,L_CB+L_DC+L_AD]\n",
- "Y1=[V_B,V_C1,V_C2,V_D,V_A,0]\n",
- "Z1=[0,0,0,0,0,0]\n",
- "plt.plot(X1,Y1,X1,Z1)\n",
- "plt.xlabel(\"Length x in m\")\n",
- "plt.ylabel(\"Shear Force in kN\")\n",
- "plt.show()\n",
- "\n",
- "#Plotting the Bendimg Moment Diagram\n",
- "\n",
- "X2=[0,L_CB,L_CB+L_DC,L_CB+L_DC+L_ED,L_CB+L_DC+L_AD]\n",
- "Y2=[M_B,M_C,M_D,M_E,M_A]\n",
- "Z2=[0,0,0,0,0]\n",
- "plt.plot(X2,Y2)\n",
- "plt.xlabel(\"Length in m\")\n",
- "plt.ylabel(\"Bending Moment in kN.m\")\n",
- "plt.show()"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Shear Force and Bending Moment Diagrams are the results\n"
- ]
- },
- {
- "metadata": {},
- "output_type": "display_data",
- "png": "iVBORw0KGgoAAAANSUhEUgAAAYwAAAEPCAYAAABRHfM8AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQmCC\n",
- "text": [
- "<matplotlib.figure.Figure at 0x59f5d30>"
- ]
- },
- {
- "metadata": {},
- "output_type": "display_data",
- "png": "iVBORw0KGgoAAAANSUhEUgAAAYQAAAEPCAYAAABCyrPIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\npCAIIYQA4P8B6xCgR/uRzl4AAAAASUVORK5CYII=\n",
- "text": [
- "<matplotlib.figure.Figure at 0x5a39bd0>"
- ]
- }
- ],
- "prompt_number": 79
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 4.4.6,Page No.95"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "%matplotlib inline\n",
- "\n",
- "#Initilization of variables\n",
- "F_C=100 #KN #Pt Load at C\n",
- "F_E=50 #KN #Pt Load at E\n",
- "w=20 #KN/m\n",
- "L_AE=L_ED=L_DC=L_CB=2 #m #Length of AE,ED,DC,CB respectively\n",
- "L=8 #m #Length of Beam\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#Let R_A & R_B be the reactions at A & B\n",
- "#R_A+R_B=190\n",
- "\n",
- "#Taking Moment at A\n",
- "#M_A=-R_B*L+F_C*(3*L_AE)+w*L_DC*(L_DC*2**-1+2*L_ED)+F_E*L_AE=0\n",
- "R_B=(F_C*(3*L_AE)+w*L_DC*(L_DC*2**-1+2*L_ED)+F_E*L_AE)*L**-1\n",
- "R_A=190-R_B\n",
- "\n",
- "#Shear Force Calculations\n",
- "\n",
- "#Shear Force at B\n",
- "V_B=R_B\n",
- "\n",
- "#Shear Force at C\n",
- "V_C1=R_B\n",
- "V_C2=R_B-F_C\n",
- "\n",
- "#Shear Force at D\n",
- "V_D=V_C2-w*L_DC\n",
- "\n",
- "#Shear Force at E\n",
- "V_E1=V_D\n",
- "V_E2=V_D-F_E\n",
- "\n",
- "#Shear Force at A\n",
- "V_A=V_E2\n",
- "\n",
- "#Point of contraflexure \n",
- "#Let F be the point BF=x\n",
- "#Shear Force at F\n",
- "#V_F=R_B-F_C-w*(L_BF-L_CB)\n",
- "L_FB=-((-R_B+F_C)*w**-1-L_CB)\n",
- "V_F=0\n",
- "\n",
- "#Bending Moment Calculations\n",
- "\n",
- "#Bending Moment at B\n",
- "M_B=0\n",
- "\n",
- "#Bending Moment at C\n",
- "M_C=R_B*L_CB\n",
- "\n",
- "#Bending Moment at D\n",
- "M_D=R_B*(L_CB+L_DC)-F_C*L_DC-w*L_DC**2*2**-1\n",
- "\n",
- "#Bending Moment at E\n",
- "M_E=R_B*(L_CB+L_DC+L_ED)-F_C*(L_ED+L_DC)-w*L_DC*(L_DC*2**-1+L_ED)\n",
- "\n",
- "#Bending Moment at A\n",
- "M_A=R_B*(L_ED+L_DC+L_AE+L_CB)-F_C*(L_ED+L_DC+L_AE)-w*L_DC*(L_DC*2**-1+L_ED+L_AE)-F_E*L_AE\n",
- "\n",
- "#Bending Moment at F\n",
- "L_FC=L_BF-L_CB\n",
- "M_F=R_B*L_FB-F_C*L_FC-w*L_FC**2*2**-1\n",
- "L_DF=L_DC-L_FC\n",
- "\n",
- "#Result\n",
- "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
- "\n",
- "#Plotting the Shear Force Diagram\n",
- "\n",
- "X1=[0,L_CB,L_CB,L_CB+L_DC,L_CB+L_DC+L_ED,L_CB+L_DC+L_ED,L_CB+L_DC+L_ED+L_AE]\n",
- "Y1=[V_B,V_C1,V_C2,V_D,V_E1,V_E2,V_A]\n",
- "Z1=[0,0,0,0,0,0,0,]\n",
- "plt.plot(X1,Y1,X1,Z1)\n",
- "plt.xlabel(\"Length x in m\")\n",
- "plt.ylabel(\"Shear Force in kN\")\n",
- "plt.show()\n",
- "\n",
- "#Plotting the Bendimg Moment Diagram\n",
- "\n",
- "X2=[0,L_CB,L_CB+L_FC,L_CB+L_DC,L_CB+L_DC+L_ED,L_CB+L_DC+L_AD]\n",
- "Y2=[M_B,M_C,M_F,M_D,M_E,M_A]\n",
- "Z2=[0,0,0,0,0,0]\n",
- "plt.plot(X2,Y2)\n",
- "plt.xlabel(\"Length in m\")\n",
- "plt.ylabel(\"Bending Moment in kN.m\")\n",
- "plt.show()"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Shear Force and Bending Moment Diagrams are the results\n"
- ]
- },
- {
- "metadata": {},
- "output_type": "display_data",
- "png": "iVBORw0KGgoAAAANSUhEUgAAAYwAAAEPCAYAAABRHfM8AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSBYWBhERyfL/OMwEVaZmLAEAAAAASUVORK5CYII=\n",
- "text": [
- "<matplotlib.figure.Figure at 0x59f37d0>"
- ]
- },
- {
- "metadata": {},
- "output_type": "display_data",
- "png": "iVBORw0KGgoAAAANSUhEUgAAAYQAAAEPCAYAAABCyrPIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRU5ErkJggg==\n",
- "text": [
- "<matplotlib.figure.Figure at 0x552a590>"
- ]
- }
- ],
- "prompt_number": 74
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 4.4.7,Page No.96"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "%matplotlib inline\n",
- "\n",
- "#Initilization of variables\n",
- "w=20 #KN/m #u.d.l on Length CB\n",
- "F_D= 50 #KN #Pt Load at D\n",
- "L_CB=5 #m #Length of CB\n",
- "L_DC=3 #M #Length of DC\n",
- "L_AD=2 #m #Length of AD\n",
- "L=10 #m #Length of Beam\n",
- "\n",
- "#Calculations\n",
- "\n",
- "theta=arctan(4*3**-1)*(180*pi**-1)\n",
- "F_DV=F_D*sin(theta*pi*180**-1) #Force at Pt D vertically\n",
- "F_DH=F_D*cos(theta*pi*180**-1) #Force at pt D horizontally\n",
- "\n",
- "#Let R_A & R_B be the reactions at A & B\n",
- "#R_A+R_B=140\n",
- "\n",
- "#Taking Moment at A\n",
- "#M_A=0=-R_B*L+w*L_CB*(L_CB*2**-1+L_DC+L_AD)+F_DV*L_AD\n",
- "R_B=(w*L_CB*(L_CB*2**-1+L_DC+L_AD)+F_DV*L_AD)*L**-1\n",
- "R_A=140-R_B\n",
- "\n",
- "#Shear Force Calculations\n",
- "\n",
- "#Shear Force at B\n",
- "V_B=R_B\n",
- "\n",
- "#Shear Force at C\n",
- "V_C=V_B-w*L_CB\n",
- "\n",
- "#Shear Force at D\n",
- "V_D1=V_C\n",
- "V_D2=V_C-F_DV\n",
- "\n",
- "#Shear Force at A\n",
- "V_A=V_D\n",
- "\n",
- "#Pt of Contraflexure\n",
- "#Let E be the pt And BE=x\n",
- "#V_E=0=R_B-w*x\n",
- "x=L_BE=R_B*w**-1\n",
- "\n",
- "#Bending Moment Calculations\n",
- "\n",
- "#Bending Moment at B\n",
- "M_B=0\n",
- "\n",
- "#Bending Moment at C\n",
- "M_C=R_B*L_CB-w*L_CB**2*2**-1\n",
- "\n",
- "#Bending Moment at D\n",
- "M_D=R_B*(L_CB+L_DC)-w*L_CB*(L_CB*2**-1+L_DC)\n",
- "\n",
- "#Bending Moment at A\n",
- "M_A=R_B*L-w*L_CB*(L_CB*2**-1+L_DC+L_AD)-F_DV*L_AD\n",
- "\n",
- "#Bending Moment at E\n",
- "M_E=R_B*L_BE-w*L_BE**2*2**-1\n",
- "\n",
- "#Result\n",
- "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
- "\n",
- "#Plotting the Shear Force Diagram\n",
- "\n",
- "X1=[0,L_CB,L_CB+L_DC,L_CB+L_DC,L_CB+L_DC+L_AD] \n",
- "Y1=[V_B,V_C,V_D1,V_D2,V_A]\n",
- "Z1=[0,0,0,0,0]\n",
- "plt.plot(X1,Y1,X1,Z1)\n",
- "plt.xlabel(\"Length x in m\")\n",
- "plt.ylabel(\"Shear Force in kN\")\n",
- "plt.show()\n",
- "\n",
- "#Plotting the Bendimg Moment Diagram\n",
- "\n",
- "X2=[0,L_BE,L_CB,L_CB+L_DC,L_CB+L_DC+L_AD]\n",
- "Y2=[M_B,M_E,M_C,M_D,M_A] \n",
- "Z2=[0,0,0,0,0,0]\n",
- "plt.plot(X2,Y2)\n",
- "plt.xlabel(\"Length in m\")\n",
- "plt.ylabel(\"Bending Moment in kN.m\")\n",
- "plt.show()"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Shear Force and Bending Moment Diagrams are the results\n"
- ]
- },
- {
- "metadata": {},
- "output_type": "display_data",
- "png": "iVBORw0KGgoAAAANSUhEUgAAAYgAAAEPCAYAAABY9lNGAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzt3XtclHXe//HXKGibh8wTbGALt6gweD6VtiamaFmaeaC0\nNdTMLe80O6nbtkW1CpaZZmv33cFiy19q6yMh7+RWbxvXNglPaYYJKhiCUImkhobg9ftj1lF0kNPM\nXAzzfj4e82jm4jp8mEdeH77fz/X9fi2GYRiIiIhcpoHZAYiISN2kBCEiIk4pQYiIiFNKECIi4pQS\nhIiIOKUEISIiTrk9QUyZMoWAgAC6dOni2FZYWEh0dDQdO3Zk6NChFBUVOX4WHx9Phw4dCA8PZ8OG\nDe4OT0REKuD2BDF58mRSUlLKbUtISCA6OpqMjAwGDx5MQkICAOnp6axatYr09HRSUlKYPn0658+f\nd3eIIiLihNsTxIABA7j++uvLbUtOTiY2NhaA2NhY1q5dC0BSUhLjx4/H39+fkJAQwsLCSEtLc3eI\nIiLihCk1iIKCAgICAgAICAigoKAAgLy8PIKDgx37BQcHk5uba0aIIiI+z/QitcViwWKxXPXnIiLi\neX5mXDQgIID8/HwCAwM5duwYbdu2BSAoKIicnBzHfkePHiUoKOiK48PCwjh06JDH4hURqQ/at2/P\nwYMHq7y/KS2IkSNHkpiYCEBiYiKjRo1ybF+5ciUlJSVkZWWRmZlJ3759rzj+0KFDGIahl2Hw/PPP\nmx5DXXnpu9B3oe/i6q/q/mHt9hbE+PHj2bJlCz/99BPt2rXjxRdfZO7cucTExPDuu+8SEhLC6tWr\nAbBarcTExGC1WvHz82PZsmXqYhIRMYnbE8RHH33kdPumTZucbn/mmWd45pln3BmSiIhUgelFaqmd\nqKgos0OoM/RdXKTv4iJ9FzVnMQzD6xYMslgseGHYIiKmqu69Uy0IERFxSglCREScUoIQERGnlCBE\nRMQpJQgREXFKCUJERJxSghAREaeUIERExCklCBERcUoJQkREnFKCEBERp5QgRETEKSUIERFxSglC\nREScUoIQERGnlCBERMQpJQgREXHK1AQRHx9PZGQkXbp0YcKECfz6668UFhYSHR1Nx44dGTp0KEVF\nRU6PnT8ftKiciIj7mJYgsrOzefvtt9m1axfffPMNZWVlrFy5koSEBKKjo8nIyGDw4MEkJCQ4Pf6T\nT2DiRDh71sOBi4j4CNMSRPPmzfH396e4uJjS0lKKi4u54YYbSE5OJjY2FoDY2FjWrl3r9PgtW+Dc\nOYiKgvx8DwYuIuIjTEsQLVu25Mknn+TGG2/khhtuoEWLFkRHR1NQUEBAQAAAAQEBFBQUOD3+2mth\n5Uq44w646Sb4+mtPRi8iUv+ZliAOHTrE4sWLyc7OJi8vj9OnT/Phhx+W28disWCxWCo8h8UCzz8P\nCxdCdLS920lERFzDz6wL79ixg/79+9OqVSsARo8ezbZt2wgMDCQ/P5/AwECOHTtG27ZtnR4fFxfn\neB8VFcX69VHccw/s3w9/+pM9eYiI+DKbzYbNZqvx8RbDMOdZoD179nD//fezfft2rrnmGiZNmkTf\nvn05cuQIrVq1Ys6cOSQkJFBUVHRFodpiseAs7NxcGDUKOnWCd96Ba67x1G8jIlL3VXTvrHB/sxIE\nwMsvv0xiYiINGjSgZ8+evPPOO5w6dYqYmBi+//57QkJCWL16NS1atCh33NV+yeJimDwZjhyBtWsh\nMNATv4mISN3nVQmipir7JQ0DXnwRli+HpCTo3t2DwYmI1FFKEJf4+GOYPh3eegvuuccDgYmI1GHV\nTRCmFak9Ydw4CA1FxWsRkRqo1y2IC1S8FhGp/r3TJybrCwrSyGsRkeryiQQBGnktIlJdPtHFdDkV\nr0XEF6lIXQUqXouIVM4nWxAXqHgtIr5ERepqUPFaRKRiPp0gQMVrEZGK+HQX0+VUvBaR+kxF6lpQ\n8VpE5CK1IJxQ8VpE6iMVqV1AxWsRESWICql4LSK+Tl1MVaDitYjUBypSu4GK1yLii9SCqAYVr0XE\nm6lI7UYqXouILzE1QRQVFTF27FgiIiKwWq189dVXFBYWEh0dTceOHRk6dChFRUVmhngFFa9FxFeY\nmiAee+wxhg8fzv79+9m7dy/h4eEkJCQQHR1NRkYGgwcPJiEhwcwQnbJY4PnnYeFCiI6GTz4xOyIR\nEdczrQbx888/06NHDw4fPlxue3h4OFu2bCEgIID8/HyioqL47rvvyu1jVg3CmR077MXrRx5R8VpE\n6javqUFkZWXRpk0bJk+eTM+ePXnooYf45ZdfKCgoICAgAICAgAAKCgrMCrFKeveG1FR7K2LiRDh7\n1uyIRERcw7THXEtLS9m1axdvvPEGffr0YdasWVd0J1ksFiwV/EkeFxfneB8VFUVUVJQbo726C8Xr\nyZPtxeu1ayEw0LRwREQAsNls2Gy2Gh9vWhdTfn4+/fr1IysrC4AvvviC+Ph4Dh8+zOeff05gYCDH\njh1j0KBBdbqL6VKGAS++CMuXQ1ISdO9udkQiIhd5TRdTYGAg7dq1IyMjA4BNmzYRGRnJiBEjSExM\nBCAxMZFRo0aZFWK1qXgtIvWJqQPl9uzZw9SpUykpKaF9+/a89957lJWVERMTw/fff09ISAirV6+m\nRYsW5Y6rqy2IS6l4LSJ1TXXvnRpJ7UYaeS0idYnXdDH5Ao28FhFvpgThZhp5LSLeSl1MHqRpw0XE\nTJruuw7TtOEi4k3UgjCBitciYgYVqb2Aitci4g2UIEyi4rWI1HXqYqoDVLwWEU9QkdoLqXgtInVR\nhS2IQYMGOT/g33euzZs3uy+qStS3FsQFKl6LiDu5bKqNHTt2lDspQGpqKgsWLKBt27blfu5p9TVB\nABQX26cNP3JE04aLiGu5ZS4mm83GX//6V86cOcOzzz7LHXfcUasga6s+JwjQtOEi4h4uTRApKSnM\nmzePRo0a8eyzz1bY7eRp9T1BXKDitYi4kssSRJ8+ffjxxx956qmn6Nevn+PkF/Ts2bOWodacryQI\n0LThIuI6LksQF5bwrGjJz88//7z60bmILyUIUPFaRFzD5TWI8+fP06BB+fF0Z8+e5RoT71K+liBA\nxWsRqT2XT7UxderUcp9Pnz7N8OHDqx+Z1IpGXouIp1WaIIKCgpg+fToAJ06cYOjQoUycONHtgcmV\ntOa1iHhSlR5zffrppzl58iQ7d+5k7ty5jB071hOxVcgXu5gup+K1iFSXy2oQa9asKXfCl156iT59\n+nD77bdjsVgYPXq0SwIuKyujd+/eBAcH8+mnn1JYWMi9997LkSNHCAkJYfXq1bRo0aJ80EoQgIrX\nIlI9LksQkyZNKvcEk2EY5T6/9957tQjzokWLFrFz505OnTpFcnIys2fPpnXr1syePZsFCxZw4sQJ\nEhISygetBOFwoXj9/ff2LicVr0WkIm4ZSe0uR48eZdKkSfz5z39m0aJFfPrpp4SHh7NlyxYCAgLI\nz88nKiqK7777rtxxShDlaeS1iFSFVy0Y9Pjjj/PKK6+Ue4y2oKCAgIAAAAICAigoKDArPK+h4rWI\nuINp032vW7eOtm3b0qNHD2w2m9N9LBZLhQP14uLiHO+joqIcA/t8maYNF5FL2Wy2Cu+vVWFaF9Mz\nzzzDBx98gJ+fH2fPnuXkyZOMHj2a7du3Y7PZCAwM5NixYwwaNEhdTNWk4rWIOOPyGsTZs2dZs2YN\n2dnZlJaWOi7y3HPP1S7SS2zZsoWFCxfy6aefMnv2bFq1asWcOXNISEigqKhIReoaUPFaRC7n8hrE\n3XffTXJyMv7+/jRt2pSmTZvSpEmTWgXpzIWupLlz57Jx40Y6duzI5s2bmTt3rsuv5QsujLy+/XaN\nvBaRmqm0BdG5c2f27dvnqXiqRC2I6tG04SICbmhB9O/fn71799YqKDHXuHGwfj3MnAnz59sfixUR\nqUylLYiIiAgOHjxIaGgojRs3th9ksZiaNNSCqBkVr0V8m8uL1NnZ2U63h4SEVCcul1KCqDkVr0V8\nl8u6mE6ePAlA8+bNnb7EO6l4LSJVVWEL4s477+R//ud/CAkJuWKwmsVi4fDhwx4J0Bm1IFxDxWsR\n3+JVczHVlBKE62jacBHfoQQh1abitYhv8KrJ+qRuCAqCLVvg3DkYNAjy882OSETqAiUIAVS8FpEr\nVSlBbN261bFA0I8//khWVpZbgxJzaNpwEblUpTWIuLg4du7cyYEDB8jIyCA3N5eYmBj+9a9/eSrG\nK6gG4X4qXovUPy6vQXzyySckJSU5JugLCgri1KlTNY9QvELv3pCaam9FTJwIZ8+aHZGIeFqlCaJx\n48blVnz75Zdf3BqQ1B0qXov4tkoTxLhx4/jjH/9IUVERb731FoMHD2bq1KmeiE3qABWvRXxXlcZB\nbNiwgQ0bNgAwbNgwoqOj3R7Y1agGYQ6NvBbxbi4fKJeVlUVgYCC/+c1vADhz5gwFBQWarM9HqXgt\n4r1cXqQeO3YsDRs2vHhAgwaMHTu2ZtGJ11PxWsR3VJogysrKaNSokeNz48aNOXfunFuDkrpNxWsR\n31BpgmjdujVJSUmOz0lJSbRu3dqtQUndp+K1SP1XaQ3i4MGD3H///eTl5QEQHBzMBx98QFhYWK0u\nnJOTwwMPPMAPP/yAxWJh2rRpzJw5k8LCQu69916OHDlCSEgIq1evpkWLFuWDVg2iTlHxWsQ7uLRI\nXVZWxpw5c1i4cKFjcFyzZs1qHyWQn59Pfn4+3bt35/Tp0/Tq1Yu1a9fy3nvv0bp1a2bPns2CBQs4\nceIECQkJ5YNWgqhzVLwWqftcWqRu2LAhX3zxBYZh0KxZM5clB4DAwEC6d+8OQNOmTYmIiCA3N5fk\n5GRiY2MBiI2NZe3atS67priPitci9U+lXUwPP/wweXl5jBs3jmuvvdZ+kMXC6NGjXRZEdnY2AwcO\nZN++fdx4442cOHECAMMwaNmypeOzI2i1IOosrXktUjedOQPXXlu9e6dfZTucPXuWli1bsnnz5nLb\nXZUgTp8+zZgxY1iyZMkVLRSLxXLFcqcXxMXFOd5HRUURFRXlknikdi4Ur1980V68TkqCfzcURcTD\nbDYbNpsNgMtu4VVi6opy586d46677uKOO+5g1qxZAISHh2Oz2QgMDOTYsWMMGjSI7777rtxxakF4\nBxWvReqG9HQYOBB++snFA+VycnK45557aNOmDW3atGHMmDEcPXq0VsGCvfvowQcfxGq1OpIDwMiR\nI0lMTAQgMTGRUaNG1fpaYo5x42D9epg5E+bPB+V0Ec87fx4efhgu6XSpskpbEEOGDOH+++/nD3/4\nAwArVqxgxYoVbNy4sSaxOnzxxRfceuutdO3a1dGNFB8fT9++fYmJieH777/XY671hNa8FjHP8uXw\nX/8F27aBn5+L52Lq1q0be/bsqXSbJylBeB8Vr0U874cfoHNn2LDBXgt0+VxMrVq14oMPPqCsrIzS\n0lI+/PBDjaSWatPIaxHPe+op+2PnNX1QpNIWRHZ2NjNmzCA1NRWA/v37s3TpUm688caaXdEF1ILw\nbipei7jf5s32Vvu330LTpvZtLhtJnZqays033+ySQF1NCcL7aeS1iPucPQtdu8Krr8KIERe3u6yL\n6ZFHHnG879evX82iFKmARl6LuE9Cgr32cGlyqIlKaxBgHywn4mqaNlzE9Q4cgDfegNdfr/25KkwQ\nZWVlFBYWcvz4ccf7S18irqDitYjrGIZ9zMNf/gLBwbU/X4U1iJCQEMf4BMMwyk15YbFYOHz4cO2v\nXkOqQdRPKl6L1E5iIixdCl99BZcsBOrg8jWp6yIliPpLxWuRmvnpJ4iMhM8+g169nO+jBCFeTyOv\nRapvyhRo3hwWL654H5cPlBPxNBWvRapnyxbYuBFeesm151WCkDpJxWuRqvn1V3th+vXXwYVrugGV\nJIjS0lI6derk2iuKVJHFAs8/DwsXQnS0fcyEiJT38svQsaO9W9bVrrpgkJ+fH+Hh4Rw5coTf/e53\nrr+6SBWMGwehofbi9f79Kl6LXJCZCUuWwK5d7vk3UWmResCAAezevZu+ffvSpEkT+0EWC8nJya6P\npopUpPZNKl6LXGQY9pb18OHwxBNVO8blTzFdWK7ucmYu8akE4bs0bbiI3Ycf2uda2r4d/CpdPNpO\nj7lKvWcY9jWvly/XmtfimwoL7WMekpKgb9+qH+fyx1y3bdtGnz59aNq0Kf7+/jRo0IDmzZtXPSIR\nF1PxWnzdnDkwdmz1kkNNVNowefTRR1m5ciUxMTHs2LGDv//97xw4cMC9UYlUgYrX4ou2brWv9f7t\nt+6/VpXGQXTo0IGysjIaNmzI5MmTSUlJcXdcIlWiacPFl5SU2Mc8LF4M113n/utVmiCaNGnCr7/+\nSrdu3Zg9ezaLFi1ye/9/SkoK4eHhdOjQgQULFrj1WuL9NPJafMXChRASAmPGeOZ6VVpyNCAggJKS\nEl577TVOnjzJ9OnTCQsLc0tAZWVldOrUiU2bNhEUFESfPn346KOPiIiIuBi0itTihIrXUp8dOmSf\nVWDHDnuSqInq3jsrrUGEhIRQXFxMfn4+cXFxNYuqGtLS0ggLCyPk39/AfffdR1JSUrkEIeLMheK1\n1WovXmvacKkvDMM+Ff6cOTVPDjVRaRdTcnIyPXr0YNiwYQDs3r2bkSNHui2g3Nxc2rVr5/gcHBxM\nbm6u264n9c+4cfYi3syZMH++/R+XiDdbtQqOHYNZszx73UpbEHFxcXz11VcMGjQIgB49erh1sSBL\nFR9DsURdsl8IEOqWcMSbTYU/n4M/v2h2ICIuMAYaza/mMVlAds0vWWmC8Pf3p0WLFuW2NWjgvklg\ng4KCyMnJcXzOyckh2MnaeYZNfxZK5TTyWrzdww/bu0/ffLP256rqH+AXVHqnj4yMZMWKFZSWlpKZ\nmcmMGTPo379/jQOsTO/evcnMzCQ7O5uSkhJWrVrl1i4tqd80bbh4s23bIDkZ4uPNuX6lCWLp0qV8\n++23NG7cmPHjx9O8eXMWX23Jolry8/PjjTfeYNiwYVitVu69914VqKVWNPJavNG5czBtGrz2GlzW\nieMxmotJfIrWvBZv8fLLsHmz/YELV/1/6vLJ+g4cOMDChQvJzs6mtLTUcZHNmzfXLtJaUIKQ2tC0\n4VLXZWVBnz6Qlgb/8R+uO6/LE0TXrl155JFH6NmzJw0bNnRcpFevXrWLtBaUIKS2VLyWusow4M47\nYcAAeyvXlVyeIHr16sXOnTtrHZgrKUGIK2jktdRFH38ML7xgXyWuUSPXnttlCaKwsBDDMFi6dClt\n2rRh9OjRNG7c2PHzli1b1j7aGlKCEFf6+GP7KFWNvBaz/fyzfSaA1avhlltcf36XJYiQkJAKn5m1\nWCxuHSxXGSUIcTUVr6UuePRR+4ytb73lnvNrRTmRGlLxWsyUlgZ3321f58FdHTQuW1Fu+/btHDt2\nzPE5MTGRkSNHMnPmTAoLC2sXpUgdpGnDxSylpfYxDwsXui851ESFCWLatGmOmsM///lP5s6dS2xs\nLM2bN2fatGkeC1DEkzTyWsywZAm0aQMTJpgdSXkVdjF169aNPXv2APCf//mftGnTxjHd96U/M4O6\nmMQTVLwWTzhyBHr1sq+M6KZldhxc1sVUVlbGuXPnANi0aZNjNlfAMWBOpD7TtOHiboZhL0zPmuX+\n5FATFc7mOn78eAYOHEjr1q259tprGTBgAACZmZlXzO4qUl9dWPN61ChIT1fxWlzrk0/sK8X94x9m\nR+LcVZ9i2rZtG/n5+QwdOpQmTZoAkJGRwenTp+nZs6fHgrycupjE0zTyWlzt5EmIjIQVK+DWWz1z\nTT3mKuImGnktrvTYY3D6NLz7rueuqQQh4mYqXktt7dgBd91lH/PQqpXnrlvde2elK8qJSHnjxkFo\nqD057N+vkddSPaWl8Mc/2qfz9mRyqAn3rR0qUo9dKF5/8glMnAhnz5odkXiLN96A666z/39T16mL\nSaQWVLyW6sjJgR494F//sk/p4mkuGwchIpXTyGupjpkzYcYMc5JDTagGIVJLF9a8tlrta17fcotq\nEnVJ797w5z+bHYX9ybf0dPsfFN7ClC6mp59+mnXr1tGoUSPat2/Pe++9x3XXXQdAfHw8y5cvp2HD\nhrz++usMHTr0yqDVxSR11IED9puA1A2HDsH/+3/2xXfMdOqUfcxDYqJ9IkizeMVjrhs3bmTw4ME0\naNCAuXPnApCQkEB6ejoTJkxg+/bt5ObmMmTIEDIyMmjQoHxPmBKEiFTFrl0wdar5CeKJJ+D4cXuC\nMJNX1CCio6MdN/2bbrqJo0ePApCUlMT48ePx9/cnJCSEsLAw0tLSzAhRRMQldu+2j5ZeuNDsSKrP\n9CL18uXLGT58OAB5eXkEBwc7fhYcHExubq5ZoYmI1EpZmX2dh4QE+3Te3sZtRero6Gjynay4Mn/+\nfEaMGAHAvHnzaNSoEROuMgl6RcueXph6HCAqKoqoqKhaxSsi4mpvvml/0m3SJHOub7PZsNlsNT7e\nbQli48aNV/35+++/z2effcb//d//ObYFBQWRk5Pj+Hz06FGCgoKcHn9pghARqWtycyEuDrZuNe+p\ntsv/eH7hhReqdbwpXUwpKSm88sorJCUlcc0lcyePHDmSlStXUlJSQlZWFpmZmfTt29eMEEVEauWx\nx+CRRyAiwuxIas6UcRAzZsygpKSE6OhoAPr168eyZcuwWq3ExMRgtVrx8/Nj2bJlFXYxiYjUVevW\nwZ498MEHZkdSO5pqQ0TqLTMec/3lF/uYh3fegSFDPHfdqvCKx1xFROqrF16A3/++7iWHmtBUGyIi\nLrJnD7z/PuzbZ3YkrqEWhIiIC5SV2dd5mDcP2rY1OxrXUIIQEXGBt94CPz948EGzI3EddTGJiNTS\nsWPw3HNgs0GDevRndz36VUREzPH44/DQQ/anl+oTtSBERGohJQW2b4fly82OxPWUIEREaqi4GKZP\nvzjnUn2jLiYRkRp66SX7UrPDhpkdiXuoBSEiUgP79tlHS3/zjdmRuI9aECIi1XT+vH3Mw0svQWCg\n2dG4jxKEiEg1vfOOPUlMm2Z2JO6lLiYRkWooKIBnn4VNm+rXmAdn6vmvJyLiWk88AZMnQ9euZkfi\nfmpBiIhU0YYN8OWX9WcyvsqoBSEiUgVnztjHPPztb9CkidnReIYShIhIFcybBz16wPDhZkfiOepi\nEhGpRHo6/Pd/29d78CVqQYiIXMX58/DwwxAXBzfcYHY0nmVqgnj11Vdp0KABhYWFjm3x8fF06NCB\n8PBwNmzYYGJ0IiL2FeLOnrUnCV9jWhdTTk4OGzdu5He/+51jW3p6OqtWrSI9PZ3c3FyGDBlCRkYG\nDer7w8YiUif98APMnWt/eqlhQ7Oj8TzT7rxPPPEEL7/8crltSUlJjB8/Hn9/f0JCQggLCyMtLc2k\nCEXE1z31FEycCN27mx2JOUxpQSQlJREcHEzXy0aa5OXlcfPNNzs+BwcHk5ub6+nwRETYvBm2bIFv\nvzU7EvO4LUFER0eTn59/xfZ58+YRHx9frr5gGEaF57FYLE63x8XFOd5HRUURFRVV41hFRC51oeaw\ndCk0bWp2NDVns9mw2Ww1Pt5tCWLjxo1Ot+/bt4+srCy6desGwNGjR+nVqxdfffUVQUFB5OTkOPY9\nevQoQUFBTs9zaYIQEXGlhATo3BlGjjQ7ktq5/I/nF154oVrHW4yr/fnuAaGhoezcuZOWLVuSnp7O\nhAkTSEtLcxSpDx48eEUrwmKxXLXVISICsGsXTJ1q/29Vffcd/P738PXXEBzsvtjMUN17p+kD5S69\n+VutVmJiYrBarfj5+bFs2bIKu5hERFzNMOxdS3/5S/1LDjVheguiJtSCEJGqqG4LIjHRXnf46qv6\n+Vir17UgRETqgp9+gtmz4bPP6mdyqAmNQBMRwZ4cxo+HXr3MjqTuUAtCRHzeli2wcaN9Uj65SC0I\nEfFpv/5qL0y//jo0a2Z2NHWLEoSI+LSXX4aOHWHUKLMjqXvUxSQiPiszE5YssT/lpCfqr6QWhIj4\nJMOARx6BZ56BG280O5q6SQlCRHzSihVw/DjMnGl2JHWXuphExOcUFsLTT0NSEvjpLlghtSBExOfM\nmQNjx0LfvmZHUrcpd4qIT9m6Fdav9+11HqpKLQgR8RklJfYxD4sXw3XXmR1N3acEISI+Y+FCCAmB\nMWPMjsQ7qItJRHzCoUOwaBHs2KExD1WlFoSI1HuGAdOn2yfkCwkxOxrvoQQhIvXeypVw7Bg8/rjZ\nkXgXdTGJSL3288/w5JOwZg34+5sdjXdRC0JE6rXDh+Huu6FfP7Mj8T6mJYilS5cSERFB586dmTNn\njmN7fHw8HTp0IDw8nA0bNpgVnojUA9dcA7/9LcTHmx2JdzIlQXz++eckJyezd+9e9u3bx1NPPQVA\neno6q1atIj09nZSUFKZPn8758+fNCNFr2Gw2s0OoM/RdXKTvws5qhffft9GihdmReCdTEsSbb77J\nn/70J/z/3SHYpk0bAJKSkhg/fjz+/v6EhIQQFhZGWlqaGSF6Dd0ILtJ3cZG+i4u+/NJmcgTey5QE\nkZmZyT//+U9uvvlmoqKi2LFjBwB5eXkEBwc79gsODiY3N9eMEEVEfJ7bnmKKjo4mPz//iu3z5s2j\ntLSUEydOkJqayvbt24mJieHw4cNOz2PRiBYREXMYJrj99tsNm83m+Ny+fXvjxx9/NOLj4434+HjH\n9mHDhhmpqalXHN++fXsD0EsvvfTSqxqv9u3bV+tebco4iFGjRrF582YGDhxIRkYGJSUltG7dmpEj\nRzJhwgSeeOIJcnNzyczMpK+T+XgPHjxoQtQiIr7FlAQxZcoUpkyZQpcuXWjUqBF///vfAbBarcTE\nxGC1WvHz82PZsmXqYhIRMYnFMAzD7CBERKTu8bqR1CkpKYSHh9OhQwcWLFhgdjimycnJYdCgQURG\nRtK5c2def/11s0MyXVlZGT169GDEiBFmh2KqoqIixo4dS0REBFarldTUVLNDMk18fDyRkZF06dKF\nCRMm8Ot5EVwlAAAHS0lEQVSvv5odksdMmTKFgIAAunTp4thWWFhIdHQ0HTt2ZOjQoRQVFV31HF6V\nIMrKynj00UdJSUkhPT2djz76iP3795sdlin8/f157bXX+Pbbb0lNTeVvf/ubz34XFyxZsgSr1erz\n3ZKPPfYYw4cPZ//+/ezdu5eIiAizQzJFdnY2b7/9Nrt27eKbb76hrKyMlStXmh2Wx0yePJmUlJRy\n2xISEoiOjiYjI4PBgweTkJBw1XN4VYJIS0sjLCyMkJAQ/P39ue+++0hKSjI7LFMEBgbSvXt3AJo2\nbUpERAR5eXkmR2Weo0eP8tlnnzF16lR8udf0559/ZuvWrUyZMgUAPz8/rvPRpdOaN2+Ov78/xcXF\nlJaWUlxcTFBQkNlhecyAAQO4/vrry21LTk4mNjYWgNjYWNauXXvVc3hVgsjNzaVdu3aOzxpIZ5ed\nnc3u3bu56aabzA7FNI8//jivvPIKDRp41f/SLpeVlUWbNm2YPHkyPXv25KGHHqK4uNjssEzRsmVL\nnnzySW688UZuuOEGWrRowZAhQ8wOy1QFBQUEBAQAEBAQQEFBwVX396p/Tb7edeDM6dOnGTt2LEuW\nLKFp06Zmh2OKdevW0bZtW3r06OHTrQeA0tJSdu3axfTp09m1axdNmjSptBuhvjp06BCLFy8mOzub\nvLw8Tp8+zYoVK8wOq86wWCyV3lO9KkEEBQWRk5Pj+JyTk1Nuag5fc+7cOcaMGcMf/vAHRo0aZXY4\npvnyyy9JTk4mNDSU8ePHs3nzZh544AGzwzJFcHAwwcHB9OnTB4CxY8eya9cuk6Myx44dO+jfvz+t\nWrXCz8+P0aNH8+WXX5odlqkCAgIcM1wcO3aMtm3bXnV/r0oQvXv3JjMzk+zsbEpKSli1ahUjR440\nOyxTGIbBgw8+iNVqZdasWWaHY6r58+eTk5NDVlYWK1eu5LbbbnOMrfE1gYGBtGvXjoyMDAA2bdpE\nZGSkyVGZIzw8nNTUVM6cOYNhGGzatAmr1Wp2WKYaOXIkiYmJACQmJlb+h2VNpsow02effWZ07NjR\naN++vTF//nyzwzHN1q1bDYvFYnTr1s3o3r270b17d2P9+vVmh2U6m81mjBgxwuwwTPX1118bvXv3\nNrp27Wrcc889RlFRkdkhmWbBggWG1Wo1OnfubDzwwANGSUmJ2SF5zH333Wf89re/Nfz9/Y3g4GBj\n+fLlxvHjx43BgwcbHTp0MKKjo40TJ05c9RwaKCciIk55VReTiIh4jhKEiIg4pQQhIiJOKUGIiIhT\nShAiIuKUEoSIiDilBCH1irunG1m8eDFnzpxx+fU+/fRTn56+XuomjYOQeqVZs2acOnXKbecPDQ1l\nx44dtGrVyiPXEzGTWhBS7x06dIg77riD3r17c+utt3LgwAEAJk2axGOPPcYtt9xC+/btWbNmDQDn\nz59n+vTpREREMHToUO68807WrFnD0qVLycvLY9CgQQwePNhx/meffZbu3bvTr18/fvjhhyuuP2vW\nLF566SUA/vd//5eBAwdesc/777/PjBkzrhrXpbKzswkPD2fy5Ml06tSJ+++/nw0bNnDLLbfQsWNH\ntm/fXvsvTsQDI75FPKZp06ZXbLvtttuMzMxMwzAMIzU11bjtttsMwzCM2NhYIyYmxjAMw0hPTzfC\nwsIMwzCMjz/+2Bg+fLhhGIaRn59vXH/99caaNWsMwzCMkJAQ4/jx445zWywWY926dYZhGMbs2bON\nv/71r1dcv7i42IiMjDQ2b95sdOrUyTh8+PAV+7z//vvGo48+etW4LpWVlWX4+fkZ+/btM86fP2/0\n6tXLmDJlimEYhpGUlGSMGjWq0u9KpDJ+ZicoEXc6ffo027ZtY9y4cY5tJSUlgH264wuTlUVERDjm\nxv/iiy+IiYkB7LNfDho0qMLzN2rUiDvvvBOAXr16sXHjxiv2+c1vfsPbb7/NgAEDWLJkCaGhoVeN\nuaK4LhcaGuqYiC8yMtKx1kHnzp3Jzs6+6jVEqkIJQuq18+fP06JFC3bv3u30540aNXK8N/5djrNY\nLOXWlTCuUqbz9/d3vG/QoAGlpaVO99u7dy9t2rSp8gJXzuK6XOPGjctd+8IxV4tDpDpUg5B6rXnz\n5oSGhvKPf/wDsN9s9+7de9VjbrnlFtasWYNhGBQUFLBlyxbHz5o1a8bJkyerFcORI0dYtGgRu3fv\nZv369aSlpV2xz9WSkIhZlCCkXikuLqZdu3aO1+LFi1mxYgXvvvsu3bt3p3PnziQnJzv2v3RFrQvv\nx4wZQ3BwMFarlYkTJ9KzZ0/Hus7Tpk3j9ttvdxSpLz/+8hW6DMNg6tSpvPrqqwQGBvLuu+8ydepU\nRzdXRcdW9P7yYyr6rNUXxRX0mKuIE7/88gtNmjTh+PHj3HTTTXz55ZeVrr4lUt+oBiHixF133UVR\nURElJSU899xzSg7ik9SCEBERp1SDEBERp5QgRETEKSUIERFxSglCREScUoIQERGnlCBERMSp/w/s\n1dP2DjKdkgAAAABJRU5ErkJggg==\n",
- "text": [
- "<matplotlib.figure.Figure at 0x5692870>"
- ]
- },
- {
- "metadata": {},
- "output_type": "display_data",
- "png": "iVBORw0KGgoAAAANSUhEUgAAAYYAAAEPCAYAAABGP2P1AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nNZ/McBW52dsAAAAASUVORK5CYII=\n",
- "text": [
- "<matplotlib.figure.Figure at 0x5687310>"
- ]
- }
- ],
- "prompt_number": 37
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 4.4.8,Page No.97"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "%matplotlib inline\n",
- "\n",
- "#Initilization of variables\n",
- "F_C=150 #KN #Pt LOad at C\n",
- "w=300 #KN #u.v.l\n",
- "L=6 #m #Length of beam\n",
- "L_AE=L_DC=L_CB=1 #m #Lengthof AE,DC,CB\n",
- "L_ED=3 #m #Length of ED\n",
- "L_Ed=2 #m\n",
- "L_dD=1 #m\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#Let R_A & R_B be the reactions at A & B\n",
- "#R_A+R_B=450\n",
- "\n",
- "#Taking Moment at A\n",
- "#M_A=0=R_B*L-F_C*(L_CD+L_ED+L_AE)-w*(2*3**-1*L_ED+L_AE)\n",
- "R_B=(F_C*(L_DC+L_ED+L_AE)+w*(2*3**-1*L_ED+L_AE))*L**-1\n",
- "R_A=450-R_B\n",
- "\n",
- "#Shear Force Calculations\n",
- "\n",
- "#Shear Force at B\n",
- "V_B=R_B\n",
- "\n",
- "#Shear Force at C\n",
- "V_C1=R_B\n",
- "V_C2=R_B-F_C\n",
- "\n",
- "#Shear Force at D\n",
- "V_D=V_C2\n",
- "\n",
- "#Shear Force at E\n",
- "V_E=V_D-w\n",
- "\n",
- "#Shear Force at A\n",
- "V_A=V_E\n",
- "\n",
- "#Pt of contraflexure\n",
- "#Let F be the pt and EF=x\n",
- "#Let w1 be the rate of Loading at D we get\n",
- "w1=w*2*3**-1\n",
- "#The rate of Loading at distance x is200*x*3**-1\n",
- "\n",
- "#V_F=0=-R_B+200*x*3**-1*x*2**-1\n",
- "#After substituting values and simplifying further we get\n",
- "L_EF=x=(R_A*3*100**-1)**0.5\n",
- "\n",
- "#Bending Moment Calculations\n",
- "\n",
- "#Bending Moment at B\n",
- "M_B=0\n",
- "\n",
- "#Bending Moment at C\n",
- "M_C=R_B*L_CB\n",
- "\n",
- "#Bending Moment at D\n",
- "M_D=R_B*(L_CB+L_DC)-F_C*L_DC\n",
- "\n",
- "#Bending Moment at E\n",
- "M_E=R_B*(L_CB+L_DC+L_ED)-F_C*(L_DC+L_ED)-w*L_Ed\n",
- "\n",
- "#Bending Moment at A\n",
- "M_A=0\n",
- "\n",
- "#Bending Moment at F\n",
- "M_F=R_A*(L_AE+L_EF)-200*x*3**-1*x*2**-1*x*3**-1\n",
- "\n",
- "L_FD=L_ED-L_EF\n",
- "\n",
- "\n",
- "#Result\n",
- "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
- "\n",
- "#Plotting the Shear Force Diagram\n",
- "\n",
- "X1=[0,L_CB,L_CB,L_CB+L_CD,L_CB+L_CD+L_ED,L_CB+L_CD+L_ED+L_AE,L_CB+L_CD+L_ED+L_AE] \n",
- "Y1=[V_B,V_C1,V_C2,V_D,V_E,V_A,0]\n",
- "Z1=[0,0,0,0,0,0,0]\n",
- "plt.plot(X1,Y1,X1,Z1)\n",
- "plt.xlabel(\"Length x in m\")\n",
- "plt.ylabel(\"Shear Force in kN\")\n",
- "plt.show()\n",
- "\n",
- "#Plotting the Bendimg Moment Diagram\n",
- "\n",
- "X2=[0,L_CB,L_CB+L_DC,L_FD+L_DC+L_CB,L_CB+L_DC+L_ED,L_CB+L_DC+L_ED+L_AE]\n",
- "Y2=[M_B,M_C,M_D,M_F,M_E,M_A] \n",
- "Z2=[0,0,0,0,0,0]\n",
- "plt.plot(X2,Y2)\n",
- "plt.xlabel(\"Length in m\")\n",
- "plt.ylabel(\"Bending Moment in kN.m\")\n",
- "plt.show()"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Shear Force and Bending Moment Diagrams are the results\n"
- ]
- },
- {
- "metadata": {},
- "output_type": "display_data",
- "png": "iVBORw0KGgoAAAANSUhEUgAAAY8AAAEPCAYAAAC6Kkg/AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nTkSuQmCC\n",
- "text": [
- "<matplotlib.figure.Figure at 0x5a94790>"
- ]
- },
- {
- "metadata": {},
- "output_type": "display_data",
- "png": "iVBORw0KGgoAAAANSUhEUgAAAYQAAAEPCAYAAABCyrPIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQmCC\n",
- "text": [
- "<matplotlib.figure.Figure at 0x561c550>"
- ]
- }
- ],
- "prompt_number": 132
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 4.4.9,Page No.99"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "%matplotlib inline\n",
- "\n",
- "#Initilization of variables\n",
- "M_C=40 #KNM #Moment at Pt C\n",
- "w=20 #KNm #u.d.l on L_AD\n",
- "L=10 #m #Length of beam\n",
- "L_CB=5 #m #Length of CB\n",
- "L_DC=1 #m #Length of DC\n",
- "L_AD=4 #m #Length of AD\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#Let R_A & R_B be the reactions at A & B\n",
- "#R_A+R_B=80\n",
- "\n",
- "#Taking Moment at A\n",
- "#M_A=0=R_B*L-M-w*L_AD**2*2**-1\n",
- "R_B=(w*L_AD**2*2**-1+M_C)*L**-1\n",
- "R_A=80-R_B\n",
- "\n",
- "#Shear Force Calculations\n",
- "\n",
- "#Shear Force at B\n",
- "V_B=R_B\n",
- "\n",
- "#Shear Force at C\n",
- "V_C=V_B\n",
- "\n",
- "#Shear Force at D\n",
- "V_D=V_C\n",
- "\n",
- "#Shear Force at A\n",
- "V_A=V_D-w*L_AD\n",
- "\n",
- "#Pt of contraflexure\n",
- "#Let E be the pt and BE=x\n",
- "#V_E=0=R_B-w*(L_BE-L_DC-L_CB)\n",
- "L_BE=x=R_B*w**-1+L_DC+L_CB\n",
- "\n",
- "#Bending Moment Calculations\n",
- "\n",
- "#Bending Moment at B\n",
- "M_B=0\n",
- "\n",
- "#Bending Moment at C\n",
- "M_C1=R_B*L_CB\n",
- "M_C2=M_C1-M_C\n",
- "\n",
- "#Bending Moment at D\n",
- "M_D=R_B*(L_CB+L_DC)-M_C\n",
- "\n",
- "#Bending Moment at A\n",
- "M_A=R_B*L-M_C-w*L_AD**2*2**-1\n",
- "\n",
- "#Bending Moment at E\n",
- "L_ED=L_BE-(L_DC+L_CB)\n",
- "M_E=R_B*L_BE-M_C-w*L_ED**2*2**-1\n",
- "\n",
- "#Result\n",
- "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
- "\n",
- "#Plotting the Shear Force Diagram\n",
- "\n",
- "X1=[0,L_CB,L_CB+L_DC,L_CB+L_DC+L_AD,L_CB+L_DC+L_AD] \n",
- "Y1=[V_B,V_C,V_D,V_A,0]\n",
- "Z1=[0,0,0,0,0]\n",
- "plt.plot(X1,Y1,X1,Z1)\n",
- "plt.xlabel(\"Length x in m\")\n",
- "plt.ylabel(\"Shear Force in kN\")\n",
- "plt.show()\n",
- "\n",
- "#Plotting the Bendimg Moment Diagram\n",
- "\n",
- "X2=[0,L_CB,L_CB,L_CB+L_DC,L_CB+L_DC+L_ED,L_CB+L_DC+L_AD]\n",
- "Y2=[M_B,M_C1,M_C2,M_D,M_E,M_A] \n",
- "Z2=[0,0,0,0,0,0]\n",
- "plt.plot(X2,Y2,X2,Z2)\n",
- "plt.xlabel(\"Length in m\")\n",
- "plt.ylabel(\"Bending Moment in kN.m\")\n",
- "plt.show()"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Shear Force and Bending Moment Diagrams are the results\n"
- ]
- },
- {
- "metadata": {},
- "output_type": "display_data",
- "png": "iVBORw0KGgoAAAANSUhEUgAAAYgAAAEPCAYAAABY9lNGAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nCCIiMosJgoiIzPp/LAeVCX7IXVUAAAAASUVORK5CYII=\n",
- "text": [
- "<matplotlib.figure.Figure at 0x5687390>"
- ]
- },
- {
- "metadata": {},
- "output_type": "display_data",
- "png": "iVBORw0KGgoAAAANSUhEUgAAAYYAAAEPCAYAAABGP2P1AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nhwsDERHZ4cJARER2/h8J2LstD77CmgAAAABJRU5ErkJggg==\n",
- "text": [
- "<matplotlib.figure.Figure at 0x5565a90>"
- ]
- }
- ],
- "prompt_number": 35
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 4.4.10,Page No.100"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "%matplotlib inline\n",
- "\n",
- "#Initilization of variables\n",
- "w=10 #KNm #u.d.l on L_AD\n",
- "F_D=20 #KN #Pt Load at D\n",
- "M_C=240 #KNm #moment at Pt C\n",
- "L_DC=L_CB=2 #m #Length of DC and CB\n",
- "L_AD=4 #m #Length of AD\n",
- "L=8 #m #Length of Beam\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#Let R_A & R_B be the reactions at A & B\n",
- "#R_A+R_B=60\n",
- "\n",
- "#Taking Moment at A\n",
- "#M_A=0=-R_B*L-M_C+F_D*L_AD+w*L_AD**2*2**-1\n",
- "R_B=-(M_C-F_D*L_AD-w*L_AD**2*2**-1)*L**-1\n",
- "R_A=60-R_B\n",
- "\n",
- "#Shear Force Calculations\n",
- "\n",
- "#Shear Force at B\n",
- "V_B=R_B\n",
- "\n",
- "#Shear Force at C\n",
- "V_C=V_B\n",
- "\n",
- "#Shear Force at D\n",
- "V_D1=V_B\n",
- "V_D2=V_D1-F_D\n",
- "\n",
- "#Shear Force at A\n",
- "V_A=V_D2-w*L_AD\n",
- "\n",
- "#Bending Moment Calculations\n",
- "\n",
- "#Bending Moment at B\n",
- "M_B=0\n",
- "\n",
- "#Bending Moment at C\n",
- "M_C1=R_B*L_CB\n",
- "M_C2=M_C+R_B*L_CB\n",
- "\n",
- "#Bending Moment at D\n",
- "M_D=R_B*(L_DC+L_CB)+M_C\n",
- "\n",
- "#Bending Moment at A\n",
- "M_A=R_B*L+M_C-w*L_AD**2*2**-1-F_D*L_AD\n",
- "\n",
- "#Result\n",
- "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
- "\n",
- "#Plotting the Shear Force Diagram\n",
- "\n",
- "X1=[0,L_CB,L_CB+L_DC,L_CB+L_DC,L_CB+L_DC+L_AD] \n",
- "Y1=[V_B,V_C,V_D1,V_D2,V_A]\n",
- "Z1=[0,0,0,0,0]\n",
- "plt.plot(X1,Y1,X1,Z1)\n",
- "plt.xlabel(\"Length x in m\")\n",
- "plt.ylabel(\"Shear Force in kN\")\n",
- "plt.show()\n",
- "\n",
- "#Plotting the Bendimg Moment Diagram\n",
- "\n",
- "X2=[0,L_CB,L_CB,L_CB+L_DC,L_CB+L_DC+L_AD,L_CB+L_DC+L_AD]\n",
- "Y2=[M_B,M_C1,M_C2,M_D,M_A,0] \n",
- "Z2=[0,0,0,0,0,0]\n",
- "plt.plot(X2,Y2,X2,Z2)\n",
- "plt.xlabel(\"Length in m\")\n",
- "plt.ylabel(\"Bending Moment in kN.m\")\n",
- "plt.show()"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Shear Force and Bending Moment Diagrams are the results\n"
- ]
- },
- {
- "metadata": {},
- "output_type": "display_data",
- "png": "iVBORw0KGgoAAAANSUhEUgAAAYUAAAEPCAYAAACtCNj2AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nrAAAAABJRU5ErkJggg==\n",
- "text": [
- "<matplotlib.figure.Figure at 0x5684b90>"
- ]
- },
- {
- "metadata": {},
- "output_type": "display_data",
- "png": "iVBORw0KGgoAAAANSUhEUgAAAYUAAAEPCAYAAACtCNj2AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nIiIZQ4GIiGQMBSIikjEUiIhI9v+ebmxA5oKUQQAAAABJRU5ErkJggg==\n",
- "text": [
- "<matplotlib.figure.Figure at 0x54a1290>"
- ]
- }
- ],
- "prompt_number": 34
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 4.4.11,Page No.101"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "%matplotlib inline\n",
- "\n",
- "#Initilization of variables\n",
- "F_C=5 #KN #Force at C\n",
- "w=2 #KNm #u.d.l on beam\n",
- "L_BC=3 #m #Length of BC\n",
- "L_AB=6 #m #Length of AB\n",
- "L=9 #m #Length of Beam\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#Let R_A & R_B be the reactions at A & B\n",
- "#R_A+R_B=23\n",
- "\n",
- "#Taking Moment at A\n",
- "#M_A=0=F_C*L-R_B*L_AB+w*L**2*2**-1\n",
- "R_B=-(-F_C*L-w*L**2*2**-1)*L_AB**-1\n",
- "R_A=23-R_B\n",
- "\n",
- "#Shear Force Calculations\n",
- "\n",
- "#Shear Force at C\n",
- "V_C1=0\n",
- "V_C2=-F_C\n",
- "\n",
- "#Shear Force at B\n",
- "V_B=V_C2-w*L_BC**2*2**-1\n",
- "\n",
- "#Shear Force at A\n",
- "V_A=F_C*L+R_B*L_AB-w*L**2*2**-1\n",
- "\n",
- "#Pt of contraflexure\n",
- "#Let D be the pt And L_AD=x\n",
- "#V_D=0=R_A+w*L_AD\n",
- "L_AD=x=R_A*w**-1\n",
- "\n",
- "#Bending Moment Calculations\n",
- "\n",
- "#Bending Moment at C\n",
- "M_C=0\n",
- "\n",
- "#Bending Moment at B\n",
- "M_B=-F_C*L_BC-w*L_BC**2*2**-1\n",
- "\n",
- "#Bending Moment at A\n",
- "M_A=-F_C*L-w*L**2*2**-1+R_B*L_AB\n",
- "\n",
- "#Bending Moment at D\n",
- "L_DC=L-L_AD\n",
- "L_DB=L_DC-L_BC\n",
- "M_D=-R_A*L_AD+w*L_AD**2*2**-1\n",
- "\n",
- "#Result\n",
- "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
- "\n",
- "#Plotting the Shear Force Diagram\n",
- "\n",
- "X1=[0,L_BC,L_BC+L_AB,L_BC+L_AB] \n",
- "Y1=[V_C,V_B,V_A,0]\n",
- "Z1=[0,0,0,0]\n",
- "plt.plot(X1,Y1,X1,Z1)\n",
- "plt.xlabel(\"Length x in m\")\n",
- "plt.ylabel(\"Shear Force in kN\")\n",
- "plt.show()\n",
- "\n",
- "#Plotting the Bendimg Moment Diagram\n",
- "\n",
- "X2=[0,L_BC,L_BC+L_DB,L_BC+L_AB]\n",
- "Y2=[M_C,M_B,M_D,M_A] \n",
- "Z2=[0,0,0,0]\n",
- "plt.plot(X2,Y2,X2,Z2)\n",
- "plt.xlabel(\"Length in m\")\n",
- "plt.ylabel(\"Bending Moment in kN.m\")\n",
- "plt.show()\n",
- "\n",
- "#The Bending moment in book is incorrect"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Shear Force and Bending Moment Diagrams are the results\n"
- ]
- },
- {
- "metadata": {},
- "output_type": "display_data",
- "png": "iVBORw0KGgoAAAANSUhEUgAAAYUAAAEPCAYAAACtCNj2AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
- "text": [
- "<matplotlib.figure.Figure at 0x5a802b0>"
- ]
- },
- {
- "metadata": {},
- "output_type": "display_data",
- "png": "iVBORw0KGgoAAAANSUhEUgAAAYUAAAEPCAYAAACtCNj2AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQggrKQpCCCGs/j/tX4O/byA0EgAAAABJRU5ErkJggg==\n",
- "text": [
- "<matplotlib.figure.Figure at 0x587df90>"
- ]
- }
- ],
- "prompt_number": 56
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 4.4.12,Page No.102"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "%matplotlib inline\n",
- "\n",
- "#Initilization of variables\n",
- "F_C=5 #KN #Pt Load at C\n",
- "F_D=4 #KN #Pt Load at D\n",
- "L_BC=1.25 #m #Length of BC\n",
- "L_DB=1 #m #Length of DB\n",
- "L_AD=3 #m #Length of AD\n",
- "w=2 #KN/m #u.d.l\n",
- "L=5.25 #m #Length of beam\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#Let R_A & R_B be the reactions at A & B\n",
- "#R_A+R_B=15\n",
- "\n",
- "#Taking Moment at A\n",
- "#M_A=0=F_C*L-R_B*(L_DB+L_AD)+F_D*L_AD+w*L_AD**2*2**-1\n",
- "R_B=-(-F_C*L-F_D*L_AD-w*L_AD**2*2**-1)*(L_DB+L_AD)**-1\n",
- "R_A=15-R_B\n",
- "\n",
- "#Shear Force Calculations\n",
- "\n",
- "#Shear Force at C\n",
- "V_C=-F_C\n",
- "\n",
- "#Shear Force at B\n",
- "V_B1=V_C\n",
- "V_B2=V_C+R_B\n",
- "\n",
- "#Shear Force at D\n",
- "V_D1=V_B2\n",
- "V_D2=V_B2-F_D\n",
- "\n",
- "#Shear Force at A\n",
- "V_A=-(w*L_AD)-F_D-F_C+R_B\n",
- "\n",
- "#Pt of contraflexure\n",
- "#Let E be the pt and BE=x\n",
- "#V_E=0=-F_C+R_B-F_D-w*(L_BE-L_DB)\n",
- "L_BE=x=-((F_C-R_B+F_D)*w**-1-L_DB)\n",
- "\n",
- "#Bending Moment Calculations\n",
- "\n",
- "#Bending Moment at C\n",
- "M_C=0\n",
- "\n",
- "#Bending Moment at B\n",
- "M_B=-F_C*L_BC\n",
- "\n",
- "#Bending Moment at D\n",
- "M_D=-F_C*(L_DB+L_BC)-R_B*L_DB\n",
- "\n",
- "#Bending Moment at A\n",
- "M_A=-F_C*L+R_B*(L_DB+L_AD)-F_D*L_AD-w*L_AD**2*2**-1\n",
- "\n",
- "#Bending Moment at E\n",
- "L_ED=L_BE-L_DB\n",
- "M_E=-F_C*(L_BC+L_BE)+R_B*L_BE-F_D*(L_BE-L_DB)-w*(L_BE-L_DB)**2*2**-1\n",
- "\n",
- "#Result\n",
- "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
- "\n",
- "#Plotting the Shear Force Diagram\n",
- "\n",
- "X1=[0,L_BC,L_BC,L_BC+L_DB,L_BC+L_DB,L_BC+L_DB+L_AD,L_BC+L_DB+L_AD] \n",
- "Y1=[V_C,V_B1,V_B2,V_D1,V_D2,V_A,0]\n",
- "Z1=[0,0,0,0,0,0,0]\n",
- "plt.plot(X1,Y1,X1,Z1)\n",
- "plt.xlabel(\"Length x in m\")\n",
- "plt.ylabel(\"Shear Force in kN\")\n",
- "plt.show()\n",
- "\n",
- "#Plotting the Bendimg Moment Diagram\n",
- "\n",
- "X2=[0,L_BC,L_BC+L_DB,L_BC+L_DB+L_ED,L_BC+L_DB+L_AD]\n",
- "Y2=[M_C,M_B,M_D,M_E,M_A] \n",
- "Z2=[0,0,0,0,0]\n",
- "plt.plot(X2,Y2,X2,Z2)\n",
- "plt.xlabel(\"Length in m\")\n",
- "plt.ylabel(\"Bending Moment in kN.m\")\n",
- "plt.show()\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Shear Force and Bending Moment Diagrams are the results\n"
- ]
- },
- {
- "metadata": {},
- "output_type": "display_data",
- "png": "iVBORw0KGgoAAAANSUhEUgAAAX8AAAEPCAYAAACqZsSmAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSEEsfyIiBf0XvygBcwiqmzQAAAAASUVORK5CYII=\n",
- "text": [
- "<matplotlib.figure.Figure at 0x57a1c30>"
- ]
- },
- {
- "metadata": {},
- "output_type": "display_data",
- "png": "iVBORw0KGgoAAAANSUhEUgAAAYUAAAEPCAYAAACtCNj2AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nZiLiAAAAAElFTkSuQmCC\n",
- "text": [
- "<matplotlib.figure.Figure at 0x567dff0>"
- ]
- }
- ],
- "prompt_number": 39
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 4.4.13,Page No.103"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "%matplotlib inline\n",
- "\n",
- "#Initilization of variables\n",
- "F_E=20 #KN #Pt Load at E\n",
- "F_C=30 #KN #Pt Load at C\n",
- "F_B=60 #KN #Pt Load at B\n",
- "L_AB=L_BC=L_CD=1.5 #m #Length of AB,BC,CD respectively\n",
- "L_DE=2.5 #m #Length od DE\n",
- "L_AD=4.5 #m #Length of AD\n",
- "L=7 #m #Length of beam\n",
- "w=30 #KN/m\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#LEt R_A and R_D be the reactions at A and D\n",
- "#R_A+R_D=245\n",
- "\n",
- "#Taking moment at A\n",
- "#M_A=0=-R_D*(L_BC+L_AB+L_CD)+F_E*L+w*L_Ad**2*2**-1+F_C*(L_AB+L_BC)+F_B*L_AB\n",
- "R_D=-(-(F_E*L)-(w*L_AD**2*2**-1)-F_C*(L_AB+L_BC)-F_B*L_AB)*(L_BC+L_AB+L_CD)**-1\n",
- "R_A=245-R_D\n",
- "\n",
- "#Shear Force Calculations\n",
- "\n",
- "#Shear Force at C\n",
- "V_E1=0\n",
- "V_E2=-F_E\n",
- "\n",
- "#Shear Force at D\n",
- "V_D1=V_E2\n",
- "V_D2=V_E2+R_D\n",
- "\n",
- "#Shear Force at C\n",
- "V_C1=V_D2\n",
- "V_C2=V_D2-F_C-w*L_CD\n",
- "\n",
- "#Shear Force at B\n",
- "V_B1=V_C2\n",
- "V_B2=-F_E+R_D-F_C-w*(L_BC+L_CD)-F_B\n",
- "\n",
- "#Shear Force at A\n",
- "V_A=-F_E-F_C-F_B-w*L_AD+R_D\n",
- "\n",
- "#Pt of contraflexure\n",
- "#Let F be the pt and EF=x\n",
- "#V_F=-F_E-F_C+R_D-w*L_FE+w*L_DE\n",
- "L_FE=-(F_E+F_C-R_D-w*L_DE)*w**-1\n",
- "L_FD=L_FE-L_DE\n",
- "L_FC=L_FE-L_CD-L_DE\n",
- "\n",
- "#Bending Moment Calculations\n",
- "\n",
- "#Bending Moment at E\n",
- "M_E=0\n",
- "\n",
- "#Bending Moment at D\n",
- "M_D=-F_E*L_DE\n",
- "\n",
- "#Bending Moment at C\n",
- "M_C=-F_E*(L_CD+L_DE)+R_D*L_CD-w*L_CD**2*2**-1\n",
- "\n",
- "#Bending Moment at F\n",
- "M_F=-w*L_FD**2*2**-1-F_C*L_FC+R_D*L_FD-F_E*L_FE\n",
- "\n",
- "#Bending Moment at B\n",
- "M_B=-F_E*(L_DE+L_CD+L_BC)-F_C*L_BC+R_D*(L_CD+L_BC)-w*(L_BC+L_CD)**2*2**-1\n",
- "\n",
- "#Bending Moment at A\n",
- "M_A=-F_E*L+R_D*(L_AD)-F_C*(L_BC+L_AB)-F_B*L_AB-w*(L_AD)**2*2**-1\n",
- "\n",
- "#Bending Moment at F\n",
- "M_F=-F_E*L_FE+R_D*L_FD-F_C*L_FC-w*L_FD**2*2**-1\n",
- "\n",
- "#Pt of contraflexure\n",
- "#Let G be the pt and GE=y\n",
- "#M_G=-F_E*L_GE+R_D*(L_GE-L_DE)-F_C*(L_GE-L_DE)**2*2**-1\n",
- "#After substituting values and further simplifying we get\n",
- "#y**2-12.9+29.35=0\n",
- "a=1\n",
- "b=-12.9\n",
- "c=29.35\n",
- "\n",
- "X=b**2-4*a*c\n",
- "\n",
- "y1=(-b+X**0.5)*(2*a)**-1\n",
- "y2=(-b-X**0.5)*(2*a)**-1\n",
- "\n",
- "#Result\n",
- "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
- "\n",
- "#Plotting the Shear Force Diagram\n",
- "\n",
- "X1=[0,0,L_DE,L_DE,L_DE+L_CD,L_DE+L_CD,L_DE+L_CD+L_BC,L_DE+L_CD+L_BC,L_DE+L_CD+L_BC+L_AB,L_DE+L_CD+L_BC+L_AB] \n",
- "Y1=[V_E1,V_E2,V_D1,V_D2,V_C1,V_C2,V_B1,V_B2,V_A,0]\n",
- "Z1=[0,0,0,0,0,0,0,0,0,0]\n",
- "plt.plot(X1,Y1,X1,Z1)\n",
- "plt.xlabel(\"Length x in m\")\n",
- "plt.ylabel(\"Shear Force in kN\")\n",
- "plt.show()\n",
- "\n",
- "#Plotting the Bendimg Moment Diagram\n",
- "\n",
- "X2=[0,L_DE,L_DE+L_CD,L_DE+L_CD+L_FC,L_DE+L_CD+L_BC,L_DE+L_CD+L_BC+L_AB]\n",
- "Y2=[M_E,M_D,M_C,M_F,M_B,M_A] \n",
- "Z2=[0,0,0,0,0,0]\n",
- "plt.plot(X2,Y2,X2,Z2)\n",
- "plt.xlabel(\"Length in m\")\n",
- "plt.ylabel(\"Bending Moment in kN.m\")\n",
- "plt.show()\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Shear Force and Bending Moment Diagrams are the results\n"
- ]
- },
- {
- "metadata": {},
- "output_type": "display_data",
- "png": "iVBORw0KGgoAAAANSUhEUgAAAYwAAAEPCAYAAABRHfM8AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nf8LLU3A+j4vPAAAAAElFTkSuQmCC\n",
- "text": [
- "<matplotlib.figure.Figure at 0x588f3b0>"
- ]
- },
- {
- "metadata": {},
- "output_type": "display_data",
- "png": "iVBORw0KGgoAAAANSUhEUgAAAYUAAAEPCAYAAACtCNj2AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRHr/DzMnCmec/cF2AAAAAElFTkSuQmCC\n",
- "text": [
- "<matplotlib.figure.Figure at 0x54f18f0>"
- ]
- }
- ],
- "prompt_number": 71
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 4.4.14,Page No.105"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "%matplotlib inline\n",
- "\n",
- "#Initilization of variables\n",
- "L_DE=L_BC=2.5 #m #Length of DE & BC\n",
- "L_CD=L_AB=5 #m #Length of CD & AB\n",
- "F_C=F_B=80 #KN #Pt Load at C & B\n",
- "w1=16 #KN/m #u.d.l on L_DE\n",
- "w2=10 #KN/m #u.d.l on L_AB\n",
- "L=10 #m #Length of beam\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#LEt R_A and R_D be the reactions at A and D\n",
- "#R_A+R_D=250\n",
- "\n",
- "#Taking moment at A\n",
- "#M_A=0=w1*L_DE*(L_DE*2**-1+L_CD+L_BC+L_AB)-R_D*(L_CD+L_BC+L_AB)+F_C*(L_BC+L_AB)+F_C*(L_BC+L_AB)+F_B*L_AB+w2*L_AB**2*2**-1\n",
- "R_D=-(-w1*L_DE*(L_DE*2**-1+L_CD+L_BC+L_AB)-F_C*(L_BC+L_AB)-F_B*(L_AB)-w2*L_AB**2*2**-1)*(L_CD+L_BC+L_AB)**-1\n",
- "R_A=250-R_D\n",
- "\n",
- "#Shear Force Calculations\n",
- "\n",
- "#Shear Force at E\n",
- "V_E=0\n",
- "\n",
- "#Shear Force at D\n",
- "V_D1=-w1*L_DE\n",
- "V_D2=-w1*L_DE+R_D\n",
- "\n",
- "#Shear Force at C\n",
- "V_C1=V_D2\n",
- "V_C2=V_D2-F_C\n",
- "\n",
- "#Shear Force at B\n",
- "V_B1=V_C2\n",
- "V_B2=V_C2-F_B\n",
- "\n",
- "#Shear Force at A\n",
- "V_A1=V_B2-w2*L_AB\n",
- "V_A2=0\n",
- "\n",
- "#Bending Moment Calculations\n",
- "\n",
- "#Bending Moment at E\n",
- "M_E=0\n",
- "\n",
- "#Bending Moment at D\n",
- "M_D=-w1*L_DE**2*2**-1\n",
- "\n",
- "#Bending Moment at C\n",
- "M_C=R_D*L_CD-w1*L_DE*(L_DE*2**-1+L_CD)\n",
- "\n",
- "#Bending Moment at B\n",
- "M_B=-w1*L_DE*(L_DE*2**-1+L_CD+L_BC)+R_D*(L_CD+L_BC)-F_C*L_BC\n",
- "\n",
- "#Bending Moment at A\n",
- "M_A=-w1*L_DE*(L_DE*2**-1+L_CD+L_BC+L_AB)+R_D*(L_CD+L_BC+L_AB)-F_C*(L_BC+L_AB)-F_B*L_AB-w2*L_AB**2*2**-1\n",
- "\n",
- "#Result\n",
- "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
- "\n",
- "#Plotting the Shear Force Diagram\n",
- "\n",
- "X1=[0,L_FE,L_FE,L_DE+L_CD,L_DE+L_CD,L_DE+L_CD+L_BC,L_DE+L_CD+L_BC,L_DE+L_CD+L_BC+L_AB,L_DE+L_CD+L_BC+L_AB] \n",
- "Y1=[V_E,V_D1,V_D2,V_C1,V_C2,V_B1,V_B2,V_A1,V_A2]\n",
- "Z1=[0,0,0,0,0,0,0,0,0]\n",
- "plt.plot(X1,Y1,X1,Z1)\n",
- "plt.xlabel(\"Length x in m\")\n",
- "plt.ylabel(\"Shear Force in kN\")\n",
- "plt.show()\n",
- "\n",
- "#Plotting the Bendimg Moment Diagram\n",
- "\n",
- "X2=[0,L_DE,L_DE+L_CD,L_DE+L_CD+L_BC,L]\n",
- "Y2=[M_E,M_D,M_C,M_B,M_A] \n",
- "Z2=[0,0,0,0,0]\n",
- "plt.plot(X2,Y2,X2,Z2)\n",
- "plt.xlabel(\"Length in m\")\n",
- "plt.ylabel(\"Bending Moment in kN.m\")\n",
- "plt.show()"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Shear Force and Bending Moment Diagrams are the results\n"
- ]
- },
- {
- "metadata": {},
- "output_type": "display_data",
- "png": "iVBORw0KGgoAAAANSUhEUgAAAY8AAAEPCAYAAAC6Kkg/AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nrkJggg==\n",
- "text": [
- "<matplotlib.figure.Figure at 0x5639ad0>"
- ]
- },
- {
- "metadata": {},
- "output_type": "display_data",
- "png": "iVBORw0KGgoAAAANSUhEUgAAAY8AAAEPCAYAAAC6Kkg/AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nKtDsF20iLgAAAABJRU5ErkJggg==\n",
- "text": [
- "<matplotlib.figure.Figure at 0x58b75b0>"
- ]
- }
- ],
- "prompt_number": 95
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 4.4.15,Page No.105"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "%matplotlib inline\n",
- "\n",
- "#Initilization of variables\n",
- "L=8 #m #Length of beam\n",
- "L_AD=4 #m #Length of AD\n",
- "w=300 #KN #u.d.l\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#Let R_A and R_C be the reactions at A and C\n",
- "#R_A+R_C=300\n",
- "\n",
- "#Taking moment at A\n",
- "#LEt x be the distance from Pt B L_CB=x\n",
- "#R_C*(L-L_CB)=300*L*2**-1\n",
- "#R_C=1200*(8-x)**-1\n",
- "#After substituting values and further simplifying we get\n",
- "#R_A=300-R_C\n",
- "#R_A=1200-300*x*(8-x)**-1\n",
- "\n",
- "#B.M at D\n",
- "#M_D=R_A*L_AD-w*2**-1*2=0\n",
- "\n",
- "#Now substituting value of R_A we get\n",
- "#M_D=4*1200-300*x*(8-x)**-1-300=0\n",
- "\n",
- "#Further on simplification we get\n",
- "L_CB=x=600*225**-1\n",
- "\n",
- "R_C=1200*(8-x)**-1\n",
- "R_A=(1200-300*x)*(8-x)**-1\n",
- "\n",
- "#Pt of contraflexure\n",
- "#Let E be the pt and BE=y\n",
- "#V_E=0=-R_A*2**-1*L_BE+R_C\n",
- "L_BE=R_C*(R_A*2**-1)**-1\n",
- "L_AE=L-L_BE\n",
- "L_AC=L-L_CB\n",
- "L_EC=L_BE-L_CB\n",
- "\n",
- "#Shear Force at B\n",
- "V_B=0\n",
- "\n",
- "#Shear Force at C\n",
- "V_C1=-w\n",
- "V_C2=-V_C1+R_C\n",
- "\n",
- "#Shear Force at A\n",
- "V_A=-w+R_C\n",
- "\n",
- "#B.M at C\n",
- "M_C=-w*L_CB\n",
- "\n",
- "#B.M at E\n",
- "M_E=-R_A*L_AE+w*L_AE\n",
- "\n",
- "#B.M at A\n",
- "M_A=0\n",
- "\n",
- "#Result\n",
- "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
- "\n",
- "#Plotting the Shear Force Diagram\n",
- "\n",
- "X1=[0,L_CB,L_CB,L_CB+L_AC,L_CB+L_AC] \n",
- "Y1=[V_B,V_C1,V_C2,V_A,0]\n",
- "Z1=[0,0,0,0,0]\n",
- "plt.plot(X1,Y1,X1,Z1)\n",
- "plt.xlabel(\"Length x in m\")\n",
- "plt.ylabel(\"Shear Force in kN\")\n",
- "plt.show()\n",
- "\n",
- "#Plotting the Bendimg Moment Diagram\n",
- "\n",
- "X2=[0,L_CB,L_CB+L_EC,L_CB+L_AC]\n",
- "Y2=[M_B,M_C,M_E,M_A] \n",
- "Z2=[0,0,0,0]\n",
- "plt.plot(X2,Y2,X2,Z2)\n",
- "plt.xlabel(\"Length in m\")\n",
- "plt.ylabel(\"Bending Moment in kN.m\")\n",
- "plt.show()"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Shear Force and Bending Moment Diagrams are the results\n"
- ]
- },
- {
- "metadata": {},
- "output_type": "display_data",
- "png": "iVBORw0KGgoAAAANSUhEUgAAAYwAAAEPCAYAAABRHfM8AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
- "text": [
- "<matplotlib.figure.Figure at 0x541cd90>"
- ]
- },
- {
- "metadata": {},
- "output_type": "display_data",
- "png": "iVBORw0KGgoAAAANSUhEUgAAAYwAAAEPCAYAAABRHfM8AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzt3XtYlHXaB/DvEKiVaOYBakaFCzAYIUEU3dxNTPCAq6Ep\nBSao2bavtera28He3VbbNbCyFFtq7fKsb1gvV6J5CFxDzQOgYFa4CgYuDAfdXFQEdwJ+7x8TkwjD\nDMwz8zwz8/1cF5fwMM/Mjdnc/A7371YJIQSIiIjMcJM7ACIicgxMGEREZBEmDCIisggTBhERWYQJ\ng4iILMKEQUREFpE1YdTW1mLmzJkICgqCVqtFbm4url69iujoaAwZMgQTJkxAbW2t8fHJyckICAhA\nYGAgsrKyZIyciMj1yJowFi9ejJiYGJw7dw5nz55FYGAgUlJSEB0djQsXLmD8+PFISUkBABQVFWHn\nzp0oKirCgQMHsHDhQjQ3N8sZPhGRS5EtYVy7dg1Hjx7F/PnzAQDu7u7o3bs3du/ejaSkJABAUlIS\ndu3aBQDIzMxEfHw8PDw84OPjA39/f+Tl5ckVPhGRy5EtYZSWlqJ///6YN28ehg8fjmeffRY3b95E\nTU0NvLy8AABeXl6oqakBAFRWVkKj0Rjv12g00Ol0ssROROSKZEsYjY2NKCgowMKFC1FQUIB7773X\nOP3UQqVSQaVSmXyOjr5HRETScpfrhTUaDTQaDUaOHAkAmDlzJpKTk+Ht7Y3q6mp4e3ujqqoKAwYM\nAACo1WqUl5cb76+oqIBarW7zvP7+/rh48aJ9fggiIifh5+eHkpKSDh8j2wjD29sbAwcOxIULFwAA\nBw8exNChQzF16lRs2bIFALBlyxbExsYCAKZNm4b09HTo9XqUlpaiuLgYERERbZ734sWLEEIo/uNP\nf/qT7DE4S5yOECPjZJxK/7DkF23ZRhgAsG7dOsyePRt6vR5+fn7YtGkTmpqaEBcXhw0bNsDHxwef\nfPIJAECr1SIuLg5arRbu7u5IS0vjlBQRkR3JmjCGDRuG/Pz8NtcPHjzY7uNfe+01vPbaa7YOi4iI\n2sFKb5lERkbKHYJFHCFOR4gRYJxSY5z2pxJCOFUDJZVKBSf7kYiIbM6S906OMIiIyCJMGEREZBEm\nDCIisggTBhERWYQJg4iILMKEQUREFmHCICIiizBhEBGRRZgwiIjIIkwYRERkESYMIiKyCBMGERFZ\nhAmDiIgswoRBREQWYcIgIiKLMGEQEZFFmDCIiMgiTBhE5FCEABITgYQEoKFB7mhcCxMGETmU7duB\n06cNieOxx4DLl+WOyHUwYRCRw7h0CVi6FNixw/ARFQWMHg2cOyd3ZK5BJcx1/XYwljQyJyLH09Rk\nGFFMmQK8/PLP17dsAV56Cfj4Y2D8ePnic3SWvHfKPsJoampCWFgYpk6dCgC4evUqoqOjMWTIEEyY\nMAG1tbXGxyYnJyMgIACBgYHIysqSK2QiksE77xj+fPHF1teTkoBPPjGsaWzcaP+4XInsCWPt2rXQ\narVQqVQAgJSUFERHR+PChQsYP348UlJSAABFRUXYuXMnioqKcODAASxcuBDNzc1yhk5EdlJYaEgY\nW7cCd93V9vuRkcCRI8CbbwKvvQbwrcE2ZE0YFRUV2LdvHxYsWGAcCu3evRtJSUkAgKSkJOzatQsA\nkJmZifj4eHh4eMDHxwf+/v7Iy8uTLXYiso+GBuDpp4F33wUGDzb9uIceAk6cAA4fBp56ijuobEHW\nhPH73/8eb7/9Ntzcfg6jpqYGXl5eAAAvLy/U1NQAACorK6HRaIyP02g00Ol09g2YiOxu2TJg6FBD\n0jCnf3/g7383jEK4g0p67nK98Oeff44BAwYgLCwMOTk57T5GpVIZp6pMfb89y5cvN34eGRmJyMhI\nKyIlIrlkZwMZGcDXXwMdvBW00qOHYQfVn/5k2EG1dy8QFGTbOB1RTk6OyfdeU2RLGMePH8fu3bux\nb98+3Lp1C9evX8ecOXPg5eWF6upqeHt7o6qqCgMGDAAAqNVqlJeXG++vqKiAWq1u97lvTxhE5Jiu\nXgXmzQM2bwbuv79z97q5AX/+M+DvD4wdyx1U7bnzl+kVK1aYvUcR22oPHz6Md955B3v27MHLL7+M\nvn374pVXXkFKSgpqa2uRkpKCoqIiJCQkIC8vDzqdDlFRUSgpKWkzyuC2WiLHJwTw5JPAgw8Ca9ZY\n91w5OYbnSk4G5s+XJDynZMl7p2wjjDu1vPG/+uqriIuLw4YNG+Dj44NPPvkEAKDVahEXFwetVgt3\nd3ekpaV1OF1FRI5r+3bgu+8MNRbWatlBNWUKUFIC/OUvhhEIdZ4iRhhS4giDyLFdugSMGGFYvwgN\nle55r1wBYmMBtdqQiO6+W7rndgYOUbhHRNSiqclwsOBLL0mbLADuoJICEwYRKYapam6ptOyg4hlU\nXcMpKSJShMJCYMIE4NSpjgv0pMIzqFrjlBQROQRLq7mlxDOoOo8jDCKS3ZIlQGUlsHOn5QV6Ujl/\n3rCDKi7OtXdQWfLeyYRBRLLKzjbUR3z9decL9KTCHVSckiIihWup5t60Sb5kAXAHlaWYMIhIFkIA\nv/0tMHOmYdeS3LiDyjzFVHoTkWuRsppbKjyDqmNcwyAiu7NVNbeUXO0MKi56E5HimOrNrUSutIOK\ni95EpDi2ruaWErv4tcaEQUR2Y643txK17KByd+cOKiYMIrILOaq5pdKygyo62rV3UJlNGHv27EFY\nWBj69OkDT09PeHp6olevXvaIjYicSGd6cyuRSgW88Yah9evYsYZRh6sxu+jt5+eHzz77DMHBwXBz\ngBUfLnoTKY8Sqrml5Iw7qCTpuKfRaDB06FCHSBZEpDzW9OZWKlft4md2hHHy5Em8/vrrGDduHLp1\n62a4SaXC0qVL7RJgZ3GEQaQcUvbmViJnOoNKkm21f/zjH9GzZ0/cunULdXV1qKurw40bNyQLkoic\nV0s1d3Ky3JHYhqvtoDI7wggODsa3335rr3isxhEGkTI4QjW3VIQwLIZv3w7s3QsEBckdUedJMsKI\niYnBF198IVlQROT8bNmbW4lcZQeV2RFGz549UV9fj27dusHDw8Nwk0qF69ev2yXAzuIIg0h+q1YB\n+/YBhw45ToGeVBx1BxXPkiIiu7N3b24lcsQzqBR9llR5eTnGjRuHoUOHIjg4GKmpqQCAq1evIjo6\nGkOGDMGECRNQW1trvCc5ORkBAQEIDAxEVlaWXKETkQmOXM0tJWc9g6pLI4ywsDAUFhZa9cLV1dWo\nrq5GaGgo6urqEB4ejl27dmHTpk3o168fXn75ZaxatQr//ve/kZKSgqKiIiQkJCA/Px86nQ5RUVG4\ncOFCm/oQjjCI5LNkCVBVBaSn2783txLdumWYliotBTIzgQED5I7INJuNMKxNFgDg7e2N0J9Ww3r2\n7ImgoCDodDrs3r0bSUlJAICkpCTs2rULAJCZmYn4+Hh4eHjAx8cH/v7+yMvLszoOIpJGdjaQkQF8\n8AGTRQtnO4NKETNrZWVlKCwsxKhRo1BTUwMvLy8AgJeXF2pqagAAlZWV0Gg0xns0Gg10Op0s8RJR\na0rpza1EzrSDyuTRIL6+viZvUqlU+P777yUJoK6uDk888QTWrl0LT0/PNq+j6uBXFVPfW758ufHz\nyMhIREZGShEqEbVDab25lSopybCuo5QdVDk5OcjJyenUPSYTRn5+vvFzlUqF5uZm7Ny5E++88w6G\nDx/e5SBv9+OPP+KJJ57AnDlzEBsbC8Awqqiuroa3tzeqqqow4KdJP7VajfLycuO9FRUVUKvV7T7v\n7QmDiGxLib25lUpJZ1Dd+cv0ihUrzN5jMtR+/fqhX79+uP/++7Fnzx5ERkbixIkT2LdvHzIyMqwO\nVgiBZ555BlqtFkuWLDFenzZtGrb89C9vy5YtxkQybdo0pKenQ6/Xo7S0FMXFxYiIiLA6DiLqukuX\ngKVLDfP0jnyOkj058g4qk7uk9Ho9Nm7ciPfeew+//OUvsWzZMvj7+0v2wl999RUeffRRPPzww8ap\npeTkZERERCAuLg7//Oc/4ePjg08++QT33XcfAODNN9/Exo0b4e7ujrVr12LixIltfyDukiKyC0fq\nza1ESttBZVXhnkajgbu7OxYvXoxBgwYZ39SFEFCpVJgxY4b0EUuACYPIPly5mlsqSjqDyqqEMXfu\nXOOTtGfTpk3WRWcjTBhEtsdqbmlt2WI4d+vjj4Hx4+WJQZKjQW7duoUePXq0uvbDDz+gb9++1kdo\nA0wYRLbV0GA4hfbVV4E5c+SOxnnIfQaVJIV7M2bMwI8//mj8uqqqCtHR0dZHR0QOadkyIDjYcXtz\nK1XLDqo33wReew1obpY7orbMJozp06cjLi4OTU1NKCsrw8SJE5GSkmKP2IhIYVjNbVtK30Fl0VlS\n77//Pg4cOIBLly7hww8/xJgxY+wRW5dwSorINq5eBR5+2NCbmwV6tiXHDiqr1jBWr17d6km2bt2K\nkJAQhIWFsac3kYtx9t7cSmTvHVSWvHearPS+ceNGqx1S06dPh0qlQl1dnXQREpFDYDW3/bWcQeXn\nZziDSs4dVMaY2ECJiDriSr25lcoeO6jYcY+IrMJqbuWwdRc/RXfcIyLle+cdw58vvihvHKSMHVRM\nGETUrsJCQ8LYupVHfyhF//6Gfhru7oaR3+XL9n19s1NSly9fxkcffYSysjI0NjYablKpsHHjRrsE\n2FmckiKyHqu5lc0WO6is2iXV4vHHH8ejjz6K6OhoY//sjpoaEZHjYzW3ssm1g8rsCCM0NBRnzpyx\nfSQS4QiDyDrZ2YadOF9/zXarjkCqHVSSLHr/+te/xt69e7seBRE5DPbmdjz2PIPK7AijZ8+eqK+v\nR7du3eDh4WG4SaXC9evXbReVFTjCIOoaVnM7titXgNhYQK02FFh2tgMi6zCIyGLbtgEpKYYeF2y3\n6pisOYPKqoRx7tw5BAUFoaCgoN0bhw8fbnkkdsSEQdR5rOZ2Hl3dQWVVwnj22Wfx0UcfITIyst1d\nUV9++aVlUdgZEwZR57Ca2zl1tosfp6SIyCz25nZendlBxYRBRB1ib27nZ+kZVDxLiohMamgwFOa9\n+y6ThTOT8gwqJgwiF8Vqbtch1RlUZhPG+HZWS9q7Zi8HDhxAYGAgAgICsGrVKtniIHJk7M3tenr0\nAHbsAKKjgdGjgXPnOv8cJs+SamhoQH19Pa5cuYKrV68ar1+/fh06na5LAVurqakJL7zwAg4ePAi1\nWo2RI0di2rRpCLJ170IiJ9JSzb15M6u5XY21Z1CZTBh/+9vfsHbtWlRWViI8PNx43dPTEy+88IJV\nQXdVXl4e/P394ePjAwB46qmnkJmZyYRBZCEhgN/+Fpg5E4iKkjsakktSkmHdqrNnUJlMGEuWLMGS\nJUuQmpqKRYsWSRWnVXQ6HQYOHGj8WqPRIDc3V8aIiBwLe3NTi5YzqKZMAUpKLLvH7PHmixYtwvHj\nx1v1wwCAxMTErsbZZZYeq66KvO1xPgB8bRIOkWOKA+55S+4gSHalAMoAaIDk45bdYjZhPP300/j+\n++8RGhqKu26r6pEjYajVapSXlxu/Li8vh0ajafM4kcM6DKLbsZqbzLHkF3KzCeP06dMoKipSRNOk\nESNGoLi4GGVlZXjwwQexc+dOfPzxx3KHRaR47M1NUjCbMIKDg1FVVYUHH3zQHvF0yN3dHe+//z4m\nTpyIpqYmPPPMM1zwJjKjpTf3qVM8+oOsY/ZokMjISJw5cwYRERHo3r274SaVCrt377ZLgJ3Fo0GI\nfsbe3GQpSc6SysnJafNkKpUKY8eOlSZKiTFhEP1syRKgqgpIT2eBHnVMssMHy8rKUFJSgqioKNTX\n16OxsRG9evWSLFApMWEQGbA3N3WGJIcPrl+/HrNmzcJzzz0HAKioqMD06dOliZCIbIK9uckWzCaM\nv/71r/jqq6+MI4ohQ4bgcldPriIim2M1N9mK2V1S3bt3Ny52A0BjY6MittgSUftYzU22YnaEMXbs\nWKxcuRL19fXIzs7GrFmzMHXqVHvERkSddOkSsHSp4VTSu++WOxpyNmYXvZuamrBhwwZkZWUBACZO\nnIgFCxYodpTBRW9yVazmJmuwRSuRC2FvbrKGJLuk9uzZg7CwMPTp0weenp7w9PRU7JZaIlfVUs29\ndSuTBdmO2RGGn58fPvvsMwQHB8PNVPdwBeEIg1xNSzX3smVst0pdJ8kIQ6PRYOjQoQ6RLIhcUUtv\n7tmz5Y6EnJ3ZbbWrVq3C5MmTMW7cOHTr1g2AIRMtXbrU5sERUcdaenN//TWP/iDbM5sw/vjHP8LT\n0xO3bt2CXq+3R0xEZAH25iZ7M7uGERwcjG+//dZe8ViNaxjkCoQw9GN+8EFgzRq5oyFnIMkaRkxM\nDL744gvJgiIi623fDhQVAcnJckdCrsTsCKNnz56or69Ht27d4OHhYbhJpcL169ftEmBncYRBzu7S\nJcOuqIMHgWHD5I6GnAUL94icDKu5yVYsee80u+gNAJmZmThy5IixcRLPkiKSB3tzk5zMjjBeffVV\n5OfnY/bs2RBCID09HSNGjECyQidPOcIgZ1VYCEyYYOjNPXiw3NGQs5FkSiokJARnzpzBXT+dN9DU\n1ITQ0FB888030kUqISYMckas5iZbk2SXlEqlQm1trfHr2tpaxZ5US+SsWM1NSmB2DWPZsmUYPnw4\nIiMjAQCHDx9GSkqKreMiop+wmpuUwqJdUpWVlcjPz4dKpUJERAS8vb3tEVuXcEqKnMnVq8DDDxuq\nudlulWzJqimpgoIC40d1dTU0Gg3UajUqKytRUFBgVWAvvfQSgoKCMGzYMMyYMQPXrl0zfi85ORkB\nAQEIDAw0Nm0CgNOnTyMkJAQBAQFYvHixVa9P5AjYm5uUxuQIw83NDcHBwejbt2+7N3755ZddftHs\n7GyMHz8ebm5uePXVVwEAKSkpKCoqQkJCAvLz86HT6RAVFYXi4mLjyOb9999HREQEYmJisGjRIkya\nNKntD8QRBjmJbdsMTZHy89lulWzPqjqMd999F59++inuuecePPnkk5g+fTo8PT0lCSw6Otr4+ahR\no5CRkQHAUO8RHx8PDw8P+Pj4wN/fH7m5uRg8eDBu3LiBiIgIAEBiYiJ27drVbsIgcgYtvbkPHmSy\nIOUwOSW1ZMkSHDt2DKmpqaioqMD48eMxa9YsnDlzRtIANm7ciJiYGACGtRKNRmP8nkajgU6na3Nd\nrVZDp9NJGgeRUjQ1AYmJwEsv8egPUhazu6T8/Pzw+OOPo76+Htu3b8f58+cRGhpq9omjo6NRXV3d\n5vqbb75prBRfuXIlunXrhoSEhC6Ebtry5cuNn0dGRhp3eBE5gtWrDX+ymptsKScnBzk5OZ26x2TC\nuHjxItLT05GZmYlBgwbhySefxP/8z//gbgvHx9nZ2R1+f/Pmzdi3bx/+/ve/G6+p1WqUl5cbv66o\nqDAutldUVLS6rlarTT737QmDyJEUFgJvv22o5mZvbrKlO3+ZXrFihdl7Olz0DgkJQWxsLHr16mV4\n8E+LItZ23Dtw4ABefPFFHD58GP369TNeb1n0zsvLMy56l5SUQKVSYdSoUUhNTUVERASmTJnCRW9y\nOqzmJjlZtej9+uuvGyu66+rqJA3sd7/7HfR6vXHx+xe/+AXS0tKg1WoRFxcHrVYLd3d3pKWlGWNI\nS0vD3Llz0dDQgJiYGC54k9NhNTcpHY83J1KA7Gxg/nxDNTfbrZIcJDlLiohs6+pVQ7LYtInJgpSN\nIwwiGbE3NymFZA2UiMg2Wnpzb9kidyRE5pkdYaxevbpV5lGpVOjduzfCw8MtqsewN44wyFGwNzcp\niSQNlBISEnDq1ClMnToVQgjs3bsXISEhuHTpEmbOnIlXXnlF0qCtxYRBjoC9uUlpJEkYv/rVr7B/\n/3707NkTgGGLbUxMDA4cOIDw8HCcO3dOuoglwIRBjuCtt4C9e4FDh1igR8ogyRrGlStX0K1bN+PX\nHh4eqKmpwT333IMePXpYHyWRi2E1Nzkqswlj9uzZGDVqFGJjYyGEwJ49e5CQkICbN29Cq9XaI0Yi\np9HQYKjifu89YPBguaMh6hyLttXm5+fj2LFjUKlUGDNmDEaMGGGP2LqEU1KkZEuWAFVVQHo6262S\nskiyhgEATU1NqK6uRmNjo/GojkGDBkkTpcSYMEipWM1NSibJGsa6deuwYsUKDBgwAHfdNuH6zTff\nWB8hkYtgNTc5A7MjDD8/P+Tl5Zls1ao0HGGQ0rCamxyBJCOMQYMGGY83J6LOYzU3OQuzCcPX1xfj\nxo3DlClTjNtrre2HQeQq2JubnIlFI4xBgwZBr9dDr9cbGygRUcfYm5ucDU+rJbIRVnOTI7FqW+3i\nxYuxdu1aTJ06td0n3r17tzRRSowJg5SgsBCYMMFQzc0CPXIEVi16z5kzBwDw4osvShsVkZNjNTc5\nK05JEUmM1dzkiKwaYYSEhHT4xGfPnu16ZEROKjsbyMgwVHMzWZCzMZkw9uzZAwBIS0sDYJiiEkJg\nx44d9omMyMGwmpucndkpqdDQUJw5c6bVtbCwMBQWFto0sK7ilBTJgdXc5Ogsee90M/ckQgh89dVX\nxq+PHTvGN2SiO7RUcycnyx0Jke2YTRgbN27EwoULMXjwYAwePBgLFy7Exo0bJXnx1atXw83NDVev\nXjVeS05ORkBAAAIDA5GVlWW8fvr0aYSEhCAgIACLFy+W5PWJpNBSzb1jB6u5ybmZrfQODw/H2bNn\nce3aNQBA7969JXnh8vJyZGdnY/Bt+w6Lioqwc+dOFBUVQafTISoqCsXFxVCpVPiv//ovbNiwARER\nEcYWsZMmTZIkFqKuYjU3uRKzCePWrVvIyMhAWVkZGhsbARjmul5//XWrXnjp0qV466238Pjjjxuv\nZWZmIj4+Hh4eHvDx8YG/vz9yc3MxePBg3LhxAxEREQCAxMRE7Nq1iwmDZLd6teFPliuRKzCbMB5/\n/HHcd999CA8Pl6yHd2ZmJjQaDR5++OFW1ysrKzF69Gjj1xqNBjqdDh4eHtBoNMbrarUaOp1OkliI\nuoq9ucnVmE0YOp0OX3zxRaefODo6GtXV1W2ur1y5EsnJya3WJ6ReRF++fLnx88jISERGRkr6/ESs\n5iZHl5OTg5ycnE7dYzZhPPLIIzh79myb0YA52dnZ7V7/9ttvUVpaimE/TfhWVFQgPDwcubm5UKvV\nKC8vNz62oqICGo0GarUaFRUVra6r1WqTr317wiCyhWXLgOBgYPZsuSMh6po7f5lesWKF2XvM1mEE\nBQWhpKQEvr6+6N69u+EmCSu9fX19cfr0adx///0oKipCQkIC8vLyjIveJSUlUKlUGDVqFFJTUxER\nEYEpU6Zg0aJF7a5hsA6DbI29uckZSdJxb//+/ZIF1J7be2totVrExcVBq9XC3d0daWlpxu+npaVh\n7ty5aGhoQExMDBe8SRas5iZXZtHhg0ePHkVJSQnmzZuHK1euoK6uDr6+vvaIr9M4wiBbYTU3OTOr\n+mG0WL58OU6fPo3z58/jwoUL0Ol0iIuLw7FjxyQNVipMGGQr27YBq1YB+fks0CPnI8mU1GeffYbC\nwkKEh4cDMGxpvXHjhjQREjkI9uYmsuBokO7du8PN7eeH3bx506YBESkNq7mJDMwmjFmzZuG5555D\nbW0t1q9fj/Hjx2PBggX2iI1IEVjNTWRg0aJ3VlaWsdBu4sSJiI6OtnlgXcU1DJJSYSEwcaJh3YIF\neuTMJFn0vt2VK1fQr1+/VlthlYYJg6TS0ACMGGEo0nv6abmjIbItq/phnDhxApGRkZgxYwYKCwsR\nHByMkJAQeHl52bw2g0gJWM1N1JrJEUZ4eDiSk5Nx7do1PPvsszhw4ABGjx6Nf/zjH3jqqafadOFT\nCo4wSAqs5iZXY9UIo6mpCRMmTMCsWbPwwAMPGE+RDQwMVPSUFJG1WM1N1D6TCeP2pCDVseZESicE\n8NvfAjNnAlFRckdDpCwmp6Tuuusu3HPPPQCAhoYG3H1btVJDQ4OxmZLSqFQqNDUJuJndMEzUVks1\n96lTAH9PIlci+S4pR6BSqeDvL/DCC8DcuYBEHWXJBVy6ZNgVdfAgC/TI9Vi1huHItmwBTp4EfH2B\nF14A/vEPuSMipWM1N5F5TpkwHnkE+Phj4JtvgD59gMhIYNIkYO9eoLlZ7uhIiVjNTWSeU05J3fkj\n3boFfPIJkJoKXLsGTldRK6zmJnLhKak79ehhmG7Iz+d0FbXW0pv73XeZLIjMcYmE0UKl4nQVtcZq\nbiLLucSUVEc4XeW6WM1N9DOX3VbblR9JCODECWDdOuCLL4CEBEPyCAy0QZAku6tXDbuhNm1igR4R\nwDWMTuF0letgNTdR13CE0QFOVzknVnMTtcUpKYlwusp5sJqbqH2ckpIIp6ucA6u5iawjW8JYt24d\ngoKCEBwcjFdeecV4PTk5GQEBAQgMDDS2hQWA06dPIyQkBAEBAVi8eLEcIQMA1Grgz38GysoMI40/\n/Ql46CFg7VrDtBUpF6u5iawkZHDo0CERFRUl9Hq9EEKIy5cvCyGE+O6778SwYcOEXq8XpaWlws/P\nTzQ3NwshhBg5cqTIzc0VQggxefJksX///naf294/UnOzEMeOCfHUU0L06SPE888Lce6cXUMgCxQU\nCNG/vxBlZXJHQqRMlrx3yjLC+OCDD7Bs2TJ4eHgAAPr37w8AyMzMRHx8PDw8PODj4wN/f3/k5uai\nqqoKN27cQEREBAAgMTERu3btkiP0Ntqbrho7ltNVSsJqbiJpyJIwiouLceTIEYwePRqRkZE4deoU\nAKCyshIajcb4OI1GA51O1+a6Wq2GTqeze9zmtExXXbrE6SolYTU3kTTcbfXE0dHRqK6ubnN95cqV\naGxsxL///W+cPHkS+fn5iIuLw/fffy/Zay9fvtz4eWRkJCIjIyV7bku0nF01Z87Pu6tWrODuKjlk\nZwMZGYZqbnYWJvpZTk4OcnJyOnWPzRJGdna2ye998MEHmDFjBgBg5MiRcHNzw7/+9S+o1WqUl5cb\nH1dRUQEdstxfAAANV0lEQVSNRgO1Wo2KiopW19Vqtcnnvz1hyKlluuqRRwCdDvjwQ8N0VWgosGgR\nMHky2BnQhtibm8i0O3+ZXrFihdl7ZHm7io2NxaFDhwAAFy5cgF6vR79+/TBt2jSkp6dDr9ejtLQU\nxcXFiIiIgLe3N3r16oXc3FwIIbBt2zbExsbKEXqX3T5dNXs2p6tsjdXcRNKTJWHMnz8f33//PUJC\nQhAfH4+tW7cCALRaLeLi4qDVajF58mSkpaVB9dM8QlpaGhYsWICAgAD4+/tj0qRJcoRuNR61bh/b\ntwNFRUBystyREDkPVnorQMt01fr1nK6SAqu5iTqPR4M4GJ5dZb2mJuCxx4ApU4CXX5Y7GiLHwaNB\nHAynq6zHam4i2+EIQ+E4XWU59uYm6jpOSTmRlumqtWuB69c5XXWnhgbDusWyZYaqbiLqHCYMJ9Ry\n1HpqKpCVxWLAFkuWAFVVQHo6C/SIuoJrGE6opRgwPb312VUTJ7ru2VUt1dwffMBkQWRLHGE4AVee\nrmJvbiJpcErKxbjadJUQwJNPGqro33tP7miIHBunpFyMq01XsZqbyL44wnByzjpdxWpuImlxSoqM\nnGm6itXcRNLjlBQZOdN0Fau5ieTBEYYLu3O66vnngXnzlD1dxWpuItvgCIM61HJ21alTjnF2FXtz\nE8mLCYMcZrqKvbmJ5MUpKWqX0qarsrMN7Va//prtVolsgbukyGpK2F3Fam4i2+MaBllN7ukq9uYm\nUg6OMKjT7DldtW0bsGqVYWG+Rw/pn5+IDDglRTZl6+kqVnMT2Q+npMimbDld1dRk2PL70ktMFkRK\nwREGSUqq6aq33jIknUOHgLvusk2sRPQzxY4w8vLyEBERgbCwMIwcORL5+fnG7yUnJyMgIACBgYHI\nysoyXj99+jRCQkIQEBCAxYsXyxE2WUCKYsDCQuCdd4CtW5ksiBRFyGDs2LHiwIEDQggh9u3bJyIj\nI4UQQnz33Xdi2LBhQq/Xi9LSUuHn5yeam5uFEEKMHDlS5ObmCiGEmDx5sti/f3+7zy3Tj9RpX375\npdwhWESKOCsqhPjDH4QYMECICROE+PxzIZqa2n9sfb0QWq0Q27bZN0Z7YJzSYpzSsuS9U5YRxgMP\nPIBr164BAGpra6FWqwEAmZmZiI+Ph4eHB3x8fODv74/c3FxUVVXhxo0biIiIAAAkJiZi165dcoQu\nmZycHLlDsIgUcarVwJ//bFjEnj0beP114KGHgDVrgJ/+GRh1pZrblf4u7YFxSstR4rSEuxwvmpKS\ngl/+8pf47//+bzQ3N+PEiRMAgMrKSowePdr4OI1GA51OBw8PD2g0GuN1tVoNnU5n97jJOi3TVXPm\n/Ly76o03ft5dVV5u6M399dfszU2kRDZLGNHR0aiurm5zfeXKlUhNTUVqaiqmT5+OTz/9FPPnz0d2\ndratQiGFadld9cgjgE4HfPihYXfVzZvArl08+oNIsewwNdaGp6en8fPm5mbRq1cvIYQQycnJIjk5\n2fi9iRMnipMnT4qqqioRGBhovP6///u/4rnnnmv3uf38/AQAfvCDH/zgRyc+/Pz8zL53yzIl5e/v\nj8OHD2Ps2LE4dOgQhgwZAgCYNm0aEhISsHTpUuh0OhQXFyMiIgIqlQq9evVCbm4uIiIisG3bNixa\ntKjd5y4pKbHnj0JE5DJkSRjr16/H888/j//85z+4++67sX79egCAVqtFXFwctFot3N3dkZaWBtVP\nk9lpaWmYO3cuGhoaEBMTg0mTJskROhGRy3K6wj0iIrINpzka5MCBAwgMDERAQABWrVoldzgmzZ8/\nH15eXggJCZE7FJPKy8sxbtw4DB06FMHBwUhNTZU7pHbdunULo0aNQmhoKLRaLZYtWyZ3SB1qampC\nWFgYpk6dKncoJvn4+ODhhx9GWFiYcRu70tTW1mLmzJkICgqCVqvFyZMn5Q6pjfPnzyMsLMz40bt3\nb8X+f5ScnIyhQ4ciJCQECQkJ+M9//mP6wV1btlaWxsZG4efnJ0pLS4VerxfDhg0TRUVFcofVriNH\njoiCggIRHBwsdygmVVVVicLCQiGEEDdu3BBDhgxR7N/nzZs3hRBC/Pjjj2LUqFHi6NGjMkdk2urV\nq0VCQoKYOnWq3KGY5OPjI3744Qe5w+hQYmKi2LBhgxDC8N+9trZW5og61tTUJLy9vcU///lPuUNp\no7S0VPj6+opbt24JIYSIi4sTmzdvNvl4pxhh5OXlwd/fHz4+PvDw8MBTTz2FzMxMucNq169+9Sv0\n6dNH7jA65O3tjdDQUABAz549ERQUhMrKSpmjat8999wDANDr9WhqasL9Ct2TW1FRgX379mHBggWK\nP+tMyfFdu3YNR48exfz58wEA7u7u6C1XG0gLHTx4EH5+fhg4cKDcobTRq1cveHh4oL6+Ho2Njaiv\nrzcWUrfHKRKGTqdr9R+jpeCPrFdWVobCwkKMGjVK7lDa1dzcjNDQUHh5eWHcuHHQarVyh9Su3//+\n93j77bfh5qbs/+VUKhWioqIwYsQIfPTRR3KH00ZpaSn69++PefPmYfjw4Xj22WdRX18vd1gdSk9P\nR0JCgtxhtOv+++/Hiy++iEGDBuHBBx/Efffdh6gOOpUp+1+vhVQsC7aJuro6zJw5E2vXrkXPnj3l\nDqddbm5uOHPmDCoqKnDkyBFFHsPw+eefY8CAAQgLC1P0b+8AcOzYMRQWFmL//v3461//iqNHj8od\nUiuNjY0oKCjAwoULUVBQgHvvvRcpKSlyh2WSXq/Hnj17MGvWLLlDadfFixexZs0alJWVobKyEnV1\nddixY4fJxztFwlCr1SgvLzd+XV5e3uooEeq8H3/8EU888QSefvppxMbGyh2OWb1798aUKVNw6tQp\nuUNp4/jx49i9ezd8fX0RHx+PQ4cOITExUe6w2vXAAw8AAPr374/p06cjLy9P5oha02g00Gg0GDly\nJABg5syZKCgokDkq0/bv34/w8HD0799f7lDaderUKTzyyCPo27cv3N3dMWPGDBw/ftzk450iYYwY\nMQLFxcUoKyuDXq/Hzp07MW3aNLnDclhCCDzzzDPQarVYsmSJ3OGY9K9//Qu1tbUAgIaGBmRnZyMs\nLEzmqNp68803UV5ejtLSUqSnp+Oxxx7D1q1b5Q6rjfr6ety4cQMAcPPmTWRlZSluN5+3tzcGDhyI\nCxcuADCsDwwdOlTmqEz7+OOPER8fL3cYJgUGBuLkyZNoaGiAEAIHDx7scFpXlsI9qbm7u+P999/H\nxIkT0dTUhGeeeQZBQUFyh9Wu+Ph4HD58GD/88AMGDhyIN954A/PmzZM7rFaOHTuG7du3G7dXAoat\nd0orlqyqqkJSUhKam5vR3NyMOXPmYPz48XKHZZZSp1Bramowffp0AIapn9mzZ2PChAkyR9XWunXr\nMHv2bOj1evj5+WHTpk1yh9Sumzdv4uDBg4pcC2oxbNgwJCYmYsSIEXBzc8Pw4cPxm9/8xuTjWbhH\nREQWcYopKSIisj0mDCIisggTBhERWYQJg4iILMKEQUREFmHCICIiizBhkMuy9XEna9asQUNDQ6de\nb8+ePYo+np9cG+swyGV5enoaK5ttwdfXF6dOnULfvn3t8npEtsYRBtFtLl68iMmTJ2PEiBF49NFH\ncf78eQDA3LlzsXjxYowZMwZ+fn7IyMgAYDgtd+HChQgKCsKECRMwZcoUZGRkYN26daisrMS4ceNa\nVZ//4Q9/QGhoKH7xi1/g8uXLbV5/8+bN+N3vftfha96urKwMgYGBmDdvHh566CHMnj0bWVlZGDNm\nDIYMGYL8/Hxb/DWRq7Jxfw4ixerZs2eba4899pgoLi4WQghx8uRJ8dhjjwkhhEhKShJxcXFCCCGK\nioqEv7+/EEKITz/9VMTExAghhKiurhZ9+vQRGRkZQoi2zYhUKpX4/PPPhRBCvPzyy+Ivf/lLm9ff\nvHmzeOGFFzp8zduVlpYKd3d38e2334rm5mYRHh4u5s+fL4QQIjMzU8TGxnb2r4XIJKc4S4pICnV1\ndThx4kSro6j1ej0Aw/lPLaf2BgUFoaamBgDw1VdfIS4uDgCMPTlM6datG6ZMmQIACA8PR3Z2dofx\nmHrNO/n6+hoP4Bs6dKixn0FwcDDKyso6fA2izmDCIPpJc3Mz7rvvPhQWFrb7/W7duhk/Fz8t/alU\nqlY9LkQHS4IeHh7Gz93c3NDY2Gg2pvZe807du3dv9bwt91j6GkSW4hoG0U969eoFX19f/N///R8A\nwxv02bNnO7xnzJgxyMjIgBACNTU1OHz4sPF7np6euH79eqdi6CjhEMmNCYNcVn19PQYOHGj8WLNm\nDXbs2IENGzYgNDQUwcHB2L17t/Hxtx9L3vL5E088AY1GA61Wizlz5mD48OHGHtO/+c1vMGnSJOOi\n9533t3fM+Z3XTX1+5z2mvlbqUerkmLitlshKN2/exL333osffvgBo0aNwvHjxzFgwAC5wyKSHNcw\niKz061//GrW1tdDr9Xj99deZLMhpcYRBREQW4RoGERFZhAmDiIgswoRBREQWYcIgIiKLMGEQEZFF\nmDCIiMgi/w/S42ZzlwktGgAAAABJRU5ErkJggg==\n",
- "text": [
- "<matplotlib.figure.Figure at 0x5513cb0>"
- ]
- }
- ],
- "prompt_number": 3
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 4.4.16,Page No.107"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "%matplotlib inline\n",
- "\n",
- "#Initilization of variables\n",
- "F_C=250 #KN #Pt LOad at C\n",
- "M_D=120 #KNM #moment at Pt D\n",
- "w=50 #KN/m #u.d.l 0n L_AD\n",
- "L_DB=L_BC=2 #m #Length of DB & BC\n",
- "L_AD=4 #m #Length of AD\n",
- "L=8 #m #Length of beam\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#LEt R_A and R_D be the reactions at A and D\n",
- "#R_A+R_D=450\n",
- "\n",
- "#Taking moment at A\n",
- "#M_A=0=-R_B*(L_DB+L_AD)+M_D+F_C*L+w*L_AD**2*2**-1\n",
- "R_B=-(-M_D-F_C*L-w*L_AD**2*2**-1)*(L_DB+L_AD)**-1\n",
- "R_D=450-R_B\n",
- "\n",
- "#Shear Force Calculations\n",
- "\n",
- "#Shear Force at C\n",
- "V_C=-F_C\n",
- "\n",
- "#Shear Force at B\n",
- "V_B1=V_C\n",
- "V_B2=R_B-F_C\n",
- "\n",
- "#Shear Force at D\n",
- "V_D=V_B2\n",
- "\n",
- "#Shear Force at A\n",
- "V_A=-F_C+R_B-w*L_AD\n",
- "\n",
- "#Pt of contralfexure\n",
- "#Let E be the pt and CE=x\n",
- "#V_E=0=-F_C+R_B-w*(L_EC-L_DB-L_BC)\n",
- "L_EC=-((+F_C-R_B)*w**-1-L_DB- L_BC)\n",
- "L_ED=L_EC-L_DB-L_BC\n",
- "\n",
- "#Bending Moment Calculations\n",
- "\n",
- "#Bending Moment at C\n",
- "M_C=0\n",
- "\n",
- "#Bending Moment at B\n",
- "M_B=-F_C*L_BC\n",
- "\n",
- "#Bending Moment at D\n",
- "M_D1=-F_C*(L_BC+L_DB)+R_B*L_DB\n",
- "M_D2=M_D1-M_D\n",
- "\n",
- "#Bending Moment at E\n",
- "M_E=-F_C*L_EC+R_B*(L_ED+L_DB)-w*L_ED**2*2**-1-M_D\n",
- "\n",
- "#Bending Moment at A\n",
- "M_A=0\n",
- "\n",
- "#Pt of contraflexure\n",
- "#Let F be the pt and CF=y\n",
- "#M_F=0=- F_C*L_FC+R_B*(L_FC-L_BC)-M_D-w*(L_FC-L_DB-L_BC)\n",
- "#After substituting values and further simplifying we get equation as\n",
- "#y**2-14.8*y+54.5=0\n",
- "\n",
- "a=1\n",
- "b=-14.8\n",
- "c=54.4\n",
- "\n",
- "X=b**2-4*a*c\n",
- "\n",
- "y1=(-b+X**0.5)*(2*a)**-1\n",
- "y2=(-b-X**0.5)*(2*a)**-1\n",
- "\n",
- "#From above two equations y2 is taken into consideration\n",
- "\n",
- "#Result\n",
- "print \"The Shear Force and Bending Moment Diagrams are the results\"\n",
- "\n",
- "#Plotting the Shear Force Diagram\n",
- "\n",
- "X1=[0,L_BC,L_BC,L_BC+L_DB,L_BC+L_DB+L_AD,L_BC+L_DB+L_AD] \n",
- "Y1=[V_C,V_B1,V_B2,V_D,V_A,0]\n",
- "Z1=[0,0,0,0,0,0]\n",
- "plt.plot(X1,Y1,X1,Z1)\n",
- "plt.xlabel(\"Length x in m\")\n",
- "plt.ylabel(\"Shear Force in kN\")\n",
- "plt.show()\n",
- "\n",
- "#Plotting the Bendimg Moment Diagram\n",
- "\n",
- "X2=[0,L_BC,L_BC+L_DB,L_BC+L_DB,L_BC+L_DB+L_ED,L_BC+L_DB+L_AD,]\n",
- "Y2=[M_C,M_B,M_D1,M_D2,M_E,M_A] \n",
- "Z2=[0,0,0,0,0,0]\n",
- "plt.plot(X2,Y2,X2,Z2)\n",
- "plt.xlabel(\"Length in m\")\n",
- "plt.ylabel(\"Bending Moment in kN.m\")\n",
- "plt.show()"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Shear Force and Bending Moment Diagrams are the results\n"
- ]
- },
- {
- "metadata": {},
- "output_type": "display_data",
- "png": "iVBORw0KGgoAAAANSUhEUgAAAYwAAAEPCAYAAABRHfM8AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQ0REPPL/AYCLPN0YseBLAAAAAElFTkSuQmCC\n",
- "text": [
- "<matplotlib.figure.Figure at 0x55131f0>"
- ]
- },
- {
- "metadata": {},
- "output_type": "display_data",
- "png": "iVBORw0KGgoAAAANSUhEUgAAAYwAAAEPCAYAAABRHfM8AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\niIjILP8Py78BVKsS0nAAAAAASUVORK5CYII=\n",
- "text": [
- "<matplotlib.figure.Figure at 0x540da10>"
- ]
- }
- ],
- "prompt_number": 2
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [],
- "language": "python",
- "metadata": {},
- "outputs": [],
- "prompt_number": 2
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [],
- "language": "python",
- "metadata": {},
- "outputs": []
- }
- ],
- "metadata": {}
- }
- ]
-}
\ No newline at end of file diff --git a/Strength_Of_Materials_by_B_K_Sarkar/chapter_5_som.ipynb b/Strength_Of_Materials_by_B_K_Sarkar/chapter_5_som.ipynb deleted file mode 100755 index f706786e..00000000 --- a/Strength_Of_Materials_by_B_K_Sarkar/chapter_5_som.ipynb +++ /dev/null @@ -1,740 +0,0 @@ -{
- "metadata": {
- "name": "chapter 5 som.ipynb"
- },
- "nbformat": 3,
- "nbformat_minor": 0,
- "worksheets": [
- {
- "cells": [
- {
- "cell_type": "heading",
- "level": 1,
- "metadata": {},
- "source": [
- "Chapter 5:Bending Stresses in Beams"
- ]
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 5.1,Page no.121"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "b=100 #mm #width of timber joist\n",
- "d=200 #mm #depth of joist\n",
- "L=3 #m #Length of beam\n",
- "sigma=7 #KN/mm**2 #bending stress\n",
- "w_1=5 #KN/mm**2 #unit weight of timber\n",
- "\n",
- "#Calculations\n",
- "w=0.1*0.2*1*5*100 #N/m #self weight of the joist\n",
- "I_xx=1*12**-1*100*200**3 #mm**4 #M.I of section about N.A\n",
- "\n",
- "#M=W*L+w*L**2*2**-1 #Max Bending moment\n",
- "#Therefore,M=(3*W+450)\n",
- "\n",
- "#using the relation M*I**-1=sigma*y**-1,we get\n",
- "W=(((7*2*10**8)*(100*10**3*3)**-1)-450)*3**-1 #N #Max Load applied\n",
- "\n",
- "#Result\n",
- "print\"The Max value of Load applied is\",round(W,2)\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Max value of Load applied is 1405.56\n"
- ]
- }
- ],
- "prompt_number": 1
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 5.2,Page no.122"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "D=160 #mm #Overall Depth\n",
- "B=150 #mm #Width of Flange\n",
- "f_t=40 #mm #Flange thickness\n",
- "W_t=50 #mm #Web thickness\n",
- "sigma_t=20 #N/mm**2 #tension stress\n",
- "sigma_c=75 #N/mm**2 #compression stress\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#Rectangle-1\n",
- "a_1=150*40 #mm**2 #Area of Rectangle-1\n",
- "y_1=40*2**-1 #mm #C.G of Rectangle-1\n",
- "\n",
- "#Rectangle-2\n",
- "a_2=120*50 #mm**2 #Area of Rectangle-2\n",
- "y_2=40+120*2**-1 #mm #C.G of Rectangle-2\n",
- "\n",
- "Y_bar=(a_1*y_1+a_2*y_2)*(a_1+a_2)**-1 #mm #Distance of C.G from the bottom flange\n",
- "I=1*12**-1*150*40**3+150*40*(60-40)**2+1*12**-1*50*120**3+50*120*(100-60)**2 #mm**4 #M.I of section about N.A\n",
- "y_t=60 #mm #Permissible tensile stress at the bottom face of flange from N.A\n",
- "y_c=100 #mm #Permissible tensile stress at the top face of flange from N.A\n",
- "\n",
- "#M=W*L*4**-1 #Max bending mooment at the centre\n",
- "\n",
- "#Using the relation M*I**-1=sigma_t*y_t**-1 we get\n",
- "W=(0.333*4*272*10**5)*(2.5*1000)**-1 #N #MAx central load\n",
- "\n",
- "#Result\n",
- "print\"The Max Bending Moment at the centre is\",round(W,2),\"N\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Max Bending Moment at the centre is 14492.16 N\n"
- ]
- }
- ],
- "prompt_number": 4
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 5.3,Page no.123"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "b=10 #cm #width of beam\n",
- "d=20 #cm depth of beam\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#R_a and R_b are the reactions at A and B respectively.\n",
- "#Moment of all forces about A\n",
- "\n",
- "R_b=(4*4*4*2**-1-2*1.5)*(2)**-1 #KN \n",
- "#R_a+R_b=18 \n",
- "R_a=18-R_b\n",
- "\n",
- "#Consider a section at a distance x from A\n",
- "#M_x=9.25*x-2(x-1.5)-4*x*x*2**-1=7.25*x+3-2*x**2 \n",
- "\n",
- "#Taking derivative of above equation to find max value of M_x we get\n",
- "x=1.81 #m\n",
- "\n",
- "M=7.25*x+3-2*x**2 #kN*m \n",
- "I=b*d**3*12**-1 #cm**4 #M.I of the section\n",
- "y=10 \n",
- "sigma=M*I**-1*y*10**8*(10**2)**-1 #Max bending stress\n",
- "\n",
- "#Result\n",
- "print\"The Max Bending stress is\",round(sigma,2),\"KN/m**2\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Max Bending stress is 14355.45 KN/m**2\n"
- ]
- }
- ],
- "prompt_number": 7
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 5.4,Page no.124"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "sigma=8 #N/mm**2 #Max bending stress\n",
- "W=5000 #N/m**2 #Load of floor\n",
- "A=450 #cm**2 #Area of joist\n",
- "L=5 #m #span of floor\n",
- "\n",
- "#Calculations\n",
- "#Let x be the centre to centre spacingof the joists\n",
- "\n",
- "#A_1=5*x**2 #m**2 #Area of floor between any two joists\n",
- "#W_1=5*x*W #N #total load supported by one interior joist\n",
- "#M=W_1*L*8**-1 #Max bending moment \n",
- "I=1*12**-1*b*(d*10**-2)**3*10**-2 #m**4 #M.I of joist\n",
- "y=0.15 #cm #Distance of of farthest fibre\n",
- "M=I*y**-1*sigma #N*m\n",
- "\n",
- "#Now equating to max bending moment we get\n",
- "x=(18000*8)*(25000*5)**-1\n",
- "\n",
- "#Result\n",
- "print\"The Max Bending Moment is\",round(x,2),\"m\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Max Bending Moment is 1.15 m\n"
- ]
- }
- ],
- "prompt_number": 9
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 5.7,Page no.126"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "d=12 #m #depth of mast\n",
- "D_1=20 #cm #diameter at the base \n",
- "D_2=10 #cm #diameter at the top\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#Consider section at a distance x cm below top of mast and y be the diameter at this section\n",
- "\n",
- "#triangle OAB and ODC are similar,we get\n",
- "#2*AB=x*120**-1\n",
- "#EB=y=10+x*120**-1\n",
- "#after simplifying we get, x=120*(y-10)\n",
- "\n",
- "#Z=pi*64**-1*y**4)*(y*32**-1)**-1 #Section modulus\n",
- "#After simplifying we get\n",
- "#Z=(pi*y**3)*(32)**-1\n",
- "\n",
- "#M=120*P(y-10) #bending moment at that section\n",
- "\n",
- "#From flexural formula we get,\n",
- "#sigma=M*Z**-1\n",
- "#After substituting and simplifying above equation we get,\n",
- "#sigma=3840*P*pi**-1*(1*y**2-1-10*y**3-1)\n",
- "\n",
- "#To find max value of sigma taking derivative of above equation we get\n",
- "y=15 #cm\n",
- "\n",
- "#Now substituting value of y in all equations with variable y\n",
- "x=120*(y-10)\n",
- "#sigma=3840*P*(15-10)*(pi*15**3)**-1 \n",
- "\n",
- "#After implifying above equation we get\n",
- "\n",
- "P=(3500*pi*15**3)*(3840*5)**-1 #N #Magnitude of load causing failure\n",
- "\n",
- "#Result\n",
- "print\"The Magnitude of Load is\",round(P,2),\"N\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Magnitude of Load is 1932.82 N\n"
- ]
- }
- ],
- "prompt_number": 10
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 5.8,Page no.127"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "L=3 #m #span of beam\n",
- "t=20 #mm #Thickness of steel\n",
- "D=200 #mm #overall depth \n",
- "B=140 #mm #overall width\n",
- "b=100 #mm #width of inner rectangle\n",
- "d=160 #mm #depth of inner rectangle\n",
- "w=77 #KN/mm**2\n",
- "sigma=100 #N/mm**2 #Bending stress\n",
- "#Calculations\n",
- "V=((D*10**-3*B*10**-3)-(d*10**-3*b*10**-3)) #m**3 #Volume of rectangular box\n",
- "W=V*3*w #KN #Weight of Beam\n",
- "I=(B*D**3-b*d**3)*12**-1 #mm**4 #M.I of beam section\n",
- "\n",
- "#Now using the relation,M*I**-1=sigma*y**-1\n",
- "\n",
- "y=200 #mm #distance from farthest fibre\n",
- "M=I*sigma*2*y**-1 #N*mm\n",
- "\n",
- "#M=3000*W+2772*3000*2**-1\n",
- "#After sub values in above equation we get\n",
- "\n",
- "W=((59.2*10**6-2772*3000*2**-1)*(3000)**-1)*10**-3 #KN #Max concentrated Load at free end\n",
- "\n",
- "F=W+2.772*2**-1 #KN #shear force at half length\n",
- "\n",
- "#Result\n",
- "print\"The shear force at half length is\",round(F,2),\"KN\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The shear force at half length is 19.73 KN\n"
- ]
- }
- ],
- "prompt_number": 15
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 5.9,Page no.128"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "B=24 #mm #width of beam section\n",
- "D=21.7 #mm #depth of beam section\n",
- "E_1=11440 #MN/m**2 #Modulus of Elasticity parallel grain\n",
- "E_2=2860 #MN/m**2 ##Modulus of Elasticity perpendicular grain\n",
- "sigma_1=8.57 #MN/m**2\n",
- "sigma_2=2.14 #MN/m**2\n",
- "L=1.2 #m #span of beam\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#Ratio of smaller modulus to larger modulus is E_2:E_1=1:4\n",
- "#Dimension of transformed Beam section\n",
- "b=18 #mm #width of Beam section\n",
- "d=3.1 #mm #depth of beam section\n",
- "\n",
- "I=(1*12**-1*B*10**-3*(D*10**-3)**3)-(3*(1*12**-1*b*10**-3*(d*10**-3)**3)) #m**4 #M.I of transformed section\n",
- "y=21.7*10**-3*2**-1 \n",
- "M=I*sigma_1*10**6*y**-1 #N*m #Safe B.M\n",
- "P=4*M*L**-1 #N\n",
- "\n",
- "#Result\n",
- "print\"Safe value of Load is\",round(P,2),\"N\" "
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Safe value of Load is 53.45 N\n"
- ]
- }
- ],
- "prompt_number": 28
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 5.11,Page no.131"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "D=4 #cm #Outside diameter\n",
- "d=3 #cm #inside diamter\n",
- "L=2 #m #span of beam\n",
- "W=1000 #N #Max safe Load\n",
- "\n",
- "#Calculations\n",
- "\n",
- "I=pi*64**-1*(D**4-d**4) #cm**4 #M.I\n",
- "A=pi*4**-1*(D**2-d**2) #cm**2 #Area \n",
- "y=2 \n",
- "Z=I*y**-1 #cm**3 #Section modulus\n",
- "\n",
- "M=W*L*4**-1 #N*cm #Max bending moment\n",
- "\n",
- "#From Flexural Formula\n",
- "sigma=M*Z**-1 #N/cm**2\n",
- "\n",
- "#For Tubes\n",
- "#M.I about x-x axis\n",
- "I_1=4*(8.59+5.492*2**2) #cm**4 \n",
- "\n",
- "Z_1=122.32*4**-1 #cm**3 \n",
- "\n",
- "#M=W_1*200*4**-1 #N*cm\n",
- "#After substituting values we get\n",
- "#M=50*W_1 (equation 1)\n",
- "\n",
- "#Again from Flexural Formula\n",
- "M=sigma*Z_1\n",
- "\n",
- "#substitute value of M in equation 1\n",
- "\n",
- "W=11640*30.58*50**-1 #N\n",
- "\n",
- "#Result\n",
- "print\"Max central load is\",round(W,2),\"N\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Max central load is 7119.02 N\n"
- ]
- }
- ],
- "prompt_number": 33
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 5.12,Page no.133"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "b=200 #mm #width of beam\n",
- "d=300 #mm #depth of beam\n",
- "t=12 #mm #thickness of beam\n",
- "E_s=220 #KN/m**2 #modulus of elasticity of steel\n",
- "E_w=11 #KN/m**2 #modulus of elasticity of timber\n",
- "sigma_s=115 #MN/m**2 #stress of steel\n",
- "sigma_w=9.2 #MN/m**2 #stress of timber\n",
- "L=2 #m #Span of beam\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#E_w*E_s**-1=1*20**-1 #ratio of Modulus of elasticity of timber to steel\n",
- "\n",
- "\n",
- "#(Part-1)\n",
- "b_1=b*20**-1 #mm #web thickness of transformed section\n",
- "stress=20*sigma_w #MN/m**2 #Allowable stress in web of equivalen beam\n",
- "#But allowable stress in flanges is sigma_s is 115 KN/m**2 and therefore taken into consideration\n",
- "\n",
- "\n",
- "d_1=324 #mm #depth of beam with thickness in consideration\n",
- "I=1*12**-1*0.2*0.324**3-2*1*12**-1*0.095*0.3**3 #m**4 #M.I of transformed section\n",
- "\n",
- "#Using Relation, M*I**-1=sigma*y**-1 we get\n",
- "\n",
- "#Part-2\n",
- "M_max=I*(324*10**-3*2**-1)**-1*sigma_s*10**6 #N*m #Max allowable Bending moment for steel section\n",
- "\n",
- "#Part-3\n",
- "#As beam is simply supported at the ends and the load is applied at the centre of beam\n",
- "#M_max=W*L*4**-1 #Max Bending moment \n",
- "W=M_max*4*L**-1 #N #Allowable stress Load\n",
- "\n",
- "#Result\n",
- "print\"Web thickness of Equivalent steel section is\",round(b_1,2),\"mm\"\n",
- "print\"Max Allowable bending moment for section is\",round(M_max,2),\"N*m\"\n",
- "print\"Allowable safe Load is\",round(W,2),\"N\"\n",
- " "
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Web thickness of Equivalent steel section is 10.0 mm\n",
- "Max Allowable bending moment for section is 98935.78 N*m\n",
- "Allowable safe Load is 197871.56 N\n"
- ]
- }
- ],
- "prompt_number": 6
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 5.13,Page no.135"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "d=10 #cm #distance between joists\n",
- "t=2 #cm #thickness of steel plate \n",
- "d_2=20 #cm #depth of beam\n",
- "sigma_t=8.5 #N/mm**2 #stress in timber \n",
- "E_s=2*10**5 #N/mm**2 #Modulus of elasticity of steel\n",
- "E_t=10**4 #N/mm**2 ##Modulus of elasticity of timber\n",
- "L=5 #cm #span of beam\n",
- "\n",
- "#calculation\n",
- "sigma=10*15**-1*sigma_t #stress in timber at distance of 10 cm from XX\n",
- "\n",
- "dell=sigma*E_t**-1 #strain in timber at 10 cm from XX\n",
- "\n",
- "sigma_s=dell*E_s #N/mm**2 #Max stress\n",
- "\n",
- "#For Timber\n",
- "Z_w=1*6**-1*10*30**2*2 #cm**3 #section modulus of timber\n",
- "M_w=sigma_t*100*Z_w #moment of resistance of timber\n",
- "\n",
- "#For steel\n",
- "Z_s=1*6**-1*2*20**2 #cm**3 #section modulus of steel\n",
- "M_s=sigma_s*Z_s*100 #moment of resistance of steel\n",
- "\n",
- "M=(M_w+M_s)*10**-5 #total moment of resistance\n",
- "\n",
- "#M=w*L**2*8**-1 #N*m #Max bending moment\n",
- "w=8*M*(L**2)**-1 #N/m #Max uniform distributed Load\n",
- "\n",
- "#Result\n",
- "print\"Moment of resistance is\",round(M,3),\"N*cm\"\n",
- "print\"Max uniform distributed Load\",round(w,3),\"N/m\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Moment of resistance is 40.611 N*cm\n",
- "Max uniform distributed Load 12.996 N/m\n"
- ]
- }
- ],
- "prompt_number": 25
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 5.14,Page no.136"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "B=10 #cm #width of timber section\n",
- "D=15 #cm #depth of timber section\n",
- "b=10 #cm #width of steel plate\n",
- "t=12 #mm #thickness \n",
- "w=3 #KN/m #Uniformly distributed Load\n",
- "L=4 #m #Span of beam\n",
- "m=20 #Ratio of modulus of elasticity of steel to timber \n",
- "W=3 #KN/m #Load\n",
- "\n",
- "#Calculations\n",
- "\n",
- "y_1=15*2**-1 #C.G of timber \n",
- "y_2=1.2*2**-1 #C.G of steel plate\n",
- "b_s=10*m**-1 #cm #Equivalent width of steel\n",
- "Y_bar=(10*1.2*0.6+15*0.5*8.7)*(10*1.2+15*0.5)**-1 #cm #distance of C.G from bottom edge\n",
- "\n",
- "I=1*12**-1*10*(1.2)**3+10*1.2*(3.72-0.6)**2+1*12**-1*0.5*(15)**3+0.5*15*(7.5-3.72)**2\n",
- "M=W*10**5*L**2*8**-1 #N*m\n",
- "\n",
- "Y_bar_1=3.72 #cm #C.G from bottom edge\n",
- "Y_bar_2=16.2-Y_bar #cm #C.G from top edge\n",
- "\n",
- "sigma_1=(M*I**-1*Y_bar_1)*10**-2 #N/mm**2 #stress at bottom\n",
- "\n",
- "sigma_2=(M*I**-1*Y_bar_2)*10**-2 #N/mm**2 #stress at top\n",
- "\n",
- "sigma_max=sigma_2*m**-1 \n",
- "\n",
- "#The Answers in book for Moment of Inertia about x-x axis onwards are incorrect\n",
- "\n",
- "#Result\n",
- "print M\n",
- "print\"The Max Stress in steel is\",round(sigma_1,2),\"N/mm**2\"\n",
- "print\"The Max Stress in timber is\",round(sigma_max,2),\"N/mm**2\"\n",
- "\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "600000.0\n",
- "The Max Stress in steel is 60.98 N/mm**2\n",
- "The Max Stress in timber is 10.23 N/mm**2\n"
- ]
- }
- ],
- "prompt_number": 8
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 5.15,Page no.137"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "B=20 #cm #width of timber\n",
- "D=30 #cm #depth of timber\n",
- "d=25 #cm #depth of steel plate\n",
- "b=1.2 #cm #width of steel plate\n",
- "sigma_s=90 #N/mm**2 #Bending stress in steel\n",
- "sigma_t=6 #N/mm**2 #Bending stress in timber\n",
- "m=20 #Ratio of modulus of elasticity of of steel to timber\n",
- "\n",
- "#Calculation\n",
- "\n",
- "#Equivalent width of wood section,when 1.2 cm wide steel plate is replaced by steel plate is\n",
- "b_1=1.2*20 #cm\n",
- "d_1=25 #cm #depth of wood section\n",
- "y_1=d*2**-1 #cm #C.G of timber section\n",
- "y_2=D*2**-1 #cm #C.G of steel section\n",
- "\n",
- "Y_bar=(2*d*b_1*y_1+D*B*y_2)*(2*d*b_1+D*B)**-1 #cm #Distance of C.G from Bottom edge\n",
- "I=B*D**3*12**-1+B*D*(y_2-Y_bar)**2+2*(b_1*d_1**3*12**-1+b_1*d_1*(Y_bar-y_1)**2) #M.I of equivalent timber section about N.A\n",
- "Y=30-Y_bar #distance of C.G from top of equivalent wood section\n",
- "\n",
- "#Thus max stress will occur at top and that in steel will occur at bottom\n",
- "#sigma_s=m*Y_bar*Y**-1*sigma_t \n",
- "\n",
- "#After simplifying we get\n",
- "#sigma_s=15.99*sigma_t\n",
- "\n",
- "sigma_t=sigma_s*15.99**-1 #N/mm**2 #Max stress in Equivalent timber section\n",
- "\n",
- "Z_t=I*Y**-1 #Section modulus of equivalent section\n",
- "M=sigma_t*Z_t*10**-5*100 #Moment of resistance of beam\n",
- "\n",
- "#Result\n",
- "print\"Position of N.A is\",round(Y_bar,2),\"cm\"\n",
- "print\"Moment of Resistance of beam is\",round(M,2),\"KN*m\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Position of N.A is 13.33 cm\n",
- "Moment of Resistance of beam is 37.15 KN*m\n"
- ]
- }
- ],
- "prompt_number": 13
- }
- ],
- "metadata": {}
- }
- ]
-}
\ No newline at end of file diff --git a/Strength_Of_Materials_by_B_K_Sarkar/chapter_6_som.ipynb b/Strength_Of_Materials_by_B_K_Sarkar/chapter_6_som.ipynb deleted file mode 100755 index 7960d97b..00000000 --- a/Strength_Of_Materials_by_B_K_Sarkar/chapter_6_som.ipynb +++ /dev/null @@ -1,914 +0,0 @@ -{
- "metadata": {
- "name": "chapter 6.ipynb"
- },
- "nbformat": 3,
- "nbformat_minor": 0,
- "worksheets": [
- {
- "cells": [
- {
- "cell_type": "heading",
- "level": 1,
- "metadata": {},
- "source": [
- "Chapter 6:Slope and Deflection"
- ]
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 6.1,Page No.154"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "b=0.12 #m #Width of beam\n",
- "d=0.2 #m #Depth of beam\n",
- "dell=0.005 #m #Deflection\n",
- "E=2*10**5*10**6 #N/m**2 \n",
- "L=2.5 #m #Length of beam\n",
- "\n",
- "#Calculations\n",
- "\n",
- "I=b*d**3*12**-1 #m**4 #M.I of rectangular section\n",
- "w=8*E*I*dell*(L**4)**-1 #N/m #U.d.l\n",
- "\n",
- "#Let slope at free end be theta\n",
- "theta=w*L**3*(6*E*I)**-1 #Radian \n",
- "\n",
- "W=dell*3*E*I*(L**3)**-1*10**-3 #kN #Concentrated Load \n",
- "\n",
- "theta_2=W*L**2*(2*E*I)**-1 #Slope at free end\n",
- "\n",
- "#Result\n",
- "print\"Uniformly distributed Load beam should carry is\",round(w,2),\"N/m\"\n",
- "print\"Concentrated Load at free end is\",round(W,2),\"KN\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Uniformly distributed Load beam should carry is 16384.0 N/m\n",
- "Concentrated Load at free end is 15.36 KN\n"
- ]
- }
- ],
- "prompt_number": 73
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 6.2,Page No.155"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "L=6 #m #Length of beam\n",
- "y_b=1.5*10**-2 #m #Deflection\n",
- "E=2*10**7*10**4\n",
- "sigma=10*10**3*10**4\n",
- "#d=2*b\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#Let w*I**-1=X #From Deflection at the free end Equation \n",
- "X=y_b*8*E*(L**4)**-1*10**-3 #Equation 1\n",
- "\n",
- "#Let w*b*I**-1=Y #From Max bending stress at the extreme fibre From N.A\n",
- "Y=sigma*2*(L**2)**-1 #Equation 2\n",
- " \n",
- "b=Y*X**-1 #width of beam #mm\n",
- "d=2*b #depth of beam #mm\n",
- " \n",
- "#Result\n",
- "print\"The Dimension of Beam are:b\",round(b,2),\"mm (width)\"\n",
- "print\" :d\",round(d,2),\"mm (depth)\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Dimension of Beam are:b 300.0 mm (width)\n",
- " :d 600.0 mm (depth)\n"
- ]
- }
- ],
- "prompt_number": 25
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 6.3,Page No.156"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "L=3 #m #Length of beam\n",
- "L_1=1.2 #m #Distance from fixed end\n",
- "d=0.25 #m #Depth of beam\n",
- "w=15*10**3 #N #U.d.L\n",
- "W=40*10**3 #N #Point Load\n",
- "E=2*10*10**4 #N/m**2 \n",
- "I=13500*10**-4 #M.I\n",
- "\n",
- "#Calculations\n",
- "\n",
- "y_b=W*L_1**3*(3*E*I)**-1+W*L_1**2*(2*E*I)**-1*(L-L_1)+w*L**4*(8*E*I)**-1 #Deflection at free end\n",
- "\n",
- "M=W*L_1+w*L*L*2**-1 #Max Bending moment at the fixed end A #Nm\n",
- "y=d*2**-1\n",
- "sigma_max=M*y*I**-1 #N/cm**2 #Max Bending stress at extreme fibre \n",
- "\n",
- "#Result\n",
- "print\"Deflection at the free end is\",round(y_b,4),\"cm\"\n",
- "print\"Max stress due to bending is\",round(sigma_max,2),\"N/cm**2\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Deflection at the free end is 0.8398 cm\n",
- "Max stress due to bending is 10694.44 N/cm**2\n"
- ]
- }
- ],
- "prompt_number": 35
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 6.4,Page No.156"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "M=100*10**3 #N #Moment\n",
- "L=3 #m #Length\n",
- "d=0.15 #m #Width\n",
- "b=0.1 #m #width\n",
- "E=2.1*10**7*10**4 #N/cm**2 \n",
- "\n",
- "#Calculations\n",
- "\n",
- "I=b*d**3*12**-1 #cm**4 #M.I of beam section\n",
- "B_1=M*L*(E*I)**-1 #radian #Slope at B\n",
- "B_2=M*L**2*(2*E*I)**-1*10**2 #cm #Deflection at point B\n",
- "\n",
- "#Result\n",
- "print\"The slope at Point B is\",round(B_1,2),\"radian\"\n",
- "print\"The Deflection at point B is\",round(B_2,2),\"cm\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The slope at Point B is 0.05 radian\n",
- "The Deflection at point B is 7.62 cm\n"
- ]
- }
- ],
- "prompt_number": 81
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 6.5,Page No.157"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "b=0.1 #m #width \n",
- "d=0.2 #m #depth\n",
- "L=2 #m #Length of beam\n",
- "L_1=1 #m #Length from free end\n",
- "E=210*10**9 \n",
- "W=1*10**3 #N #Concentrated Load\n",
- "w=2*10**3 #N/m\n",
- "\n",
- "#Calculations\n",
- "\n",
- "I=b*d**3*12**-1 #m**4 #M.I of the beam section\n",
- "\n",
- "#Slope at free end\n",
- "theta=W*L**2*(2*E*I)**-1+w*L**3*(6*E*I)**-1-w*(L-L_1)**3*(6*E*I)**-1 \n",
- "\n",
- "#Deflection at free end\n",
- "y_b=(W*L**3*(3*E*I)**-1+w*L**4*(8*E*I)**-1-w*(L-L_1)**4*(8*E*I)**-1-w*(L-L_1)**3*L_1*(6*E*I)**-1)*10**3 \n",
- "\n",
- "#Result\n",
- "print\"Slope at free end is\",round(theta,5),\"radian\"\n",
- "print\"Deflection at free end is\",round(y_b,2),\"mm\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Slope at free end is 0.00031 radian\n",
- "Deflection at free end is 0.43 mm\n"
- ]
- }
- ],
- "prompt_number": 59
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 6.6,Page No.158"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "L=10 #m #span of beam\n",
- "W=10*10**3 #N #Point Load\n",
- "a=6 #m #Distance from left end of beam to point Load\n",
- "b=4 #m ##Distance from right end of beam to point Load\n",
- "E=210*10**9 \n",
- "I=10**-4 #m #M.I of beam\n",
- "\n",
- "#Calculation \n",
- "\n",
- "#slope at left end is given by\n",
- "theta_A=W*b*(L**2-b**2)*(6*E*I*L)**-1 #radian\n",
- "\n",
- "#Deflection under Load is\n",
- "y_c=W*a*b*(L**2-a**2-b**2)*(6*E*I*L)**-1*10**3 #m\n",
- "\n",
- "#Maximum Deflection of the beam is\n",
- "y_max=W*a*(L**2-a**2)**1.5*(15.588457*E*I*L)**-1*10**3 #m\n",
- "\n",
- "#Result\n",
- "print\"slope at left end is\",round(theta_A,5),\"radian\"\n",
- "print\"Deflection under Load is\",round(y_c,2),\"m\"\n",
- "print\"#Maximum Deflection of the beam is\",round(y_max,2),\"m\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "slope at left end is 0.00267 radian\n",
- "Deflection under Load is 9.14 m\n",
- "#Maximum Deflection of the beam is 9.38 m\n"
- ]
- }
- ],
- "prompt_number": 72
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 6.7,Page No.158"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "L=5 #m #Length of beam\n",
- "w=40*10**3 #N #U.d.L \n",
- "y_max=0.01 #Deflection\n",
- "sigma_s=7*10**6 #Bending stress\n",
- "E=10.5*10**9\n",
- "\n",
- "#Calculation\n",
- "\n",
- "M=w*L*8**-1 #N*m #Max Bending moment \n",
- "\n",
- "#From equation of max deflection\n",
- "I=5*w*L**3*(y_max*384*E)**-1 #m**4 \n",
- "\n",
- "d=sigma_s*2*I*M**-1*10**2 #cm\n",
- "b=12*I*((d*10**-2)**3)**-1*10**2 #cm #Breadth\n",
- "\n",
- "#Result\n",
- "print\"Minimum value of breadth is\",round(b,2),\"cm\"\n",
- "print\"Minimum value of Depth is\",round(d,2),\"cm\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Minimum value of breadth is 17.77 cm\n",
- "Minimum value of Depth is 34.72 cm\n"
- ]
- }
- ],
- "prompt_number": 94
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 6.8,Page No.159"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "L=6 #m #Length of beam\n",
- "d=0.15 #m #diameter\n",
- "y_max=1.035*10**-2 #m #Deflection\n",
- "E=210*10**9 \n",
- "\n",
- "#Calculations\n",
- "\n",
- "I=pi*64**-1*d**4 #M.I of Beam\n",
- "W=y_max*48*E*(L**3)**-1 #Point Load\n",
- "theta_A=3*y_max*L**-1\n",
- "theta_B=-theta_A\n",
- "\n",
- "#Result\n",
- "print\"The Heaviest central Point Load placed is\",round(W,2),\"N\"\n",
- "print\"Slope at supports are:theta_A\",round(theta_A,5),\"radian\"\n",
- "print\" :theta_B\",round(theta_B,5),\"radian\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Heaviest central Point Load placed is 483000000.0 N\n",
- "Slope at supports are:theta_A 0.00517 radian\n",
- " :theta_B -0.00517 radian\n"
- ]
- }
- ],
- "prompt_number": 103
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 6.9,Page No.160"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "L=14 #m #Lenth of steel girder\n",
- "E=210*10**9 #modulus of Elasticity of steel\n",
- "I=16*10**4*10**-8 #M.I of girder section\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#R_a+R_b=200 #R_a & R_b are the Reactions at supports A & B respectively\n",
- "\n",
- "#After taking moment at B We get\n",
- "R_a=(120*11+80*4.5)*14**-1 #KN\n",
- "R_b=200-R_a\n",
- "\n",
- "#After considering section at X-X at a distance x from left end A and taking B.M at X-X\n",
- "#M=120*x-120(x-3)-80*(x-9.5)\n",
- "\n",
- "#After Integrating twice we get\n",
- "#EI*dy*dx**-1=-60*x**2*+60(x-3)**2+40(x-9.5)**2+C_1 #slope \n",
- "\n",
- "#Again on Integrating we get\n",
- "#EI*y=-20*x**3+20(x-3)**3+40*3**-1*(x-9.5)**3+C_1*x+C_2 #Deflection\n",
- "\n",
- "#At A deflection is zero,i.e at x=0,y=0 \n",
- "#At B deflection is zero,i.e at x=14,y=0 So C_2=0\n",
- "\n",
- "C_1=-(-20*(14)**3+20*(11)**3+40*3**-1*(14-9.5)**3)*14**-1 #constant \n",
- "\n",
- "#Now Deflection at D i.e at x=3 m\n",
- "x=3\n",
- "y_D=1*(E*I)**-1*(-20*x**3+20*(x-3)**3+C_1*x)*10**3\n",
- "\n",
- "#Now Deflection at D i.e at x=9.5 m\n",
- "x=9.5\n",
- "y_C=1*(E*I)**-1*(-20*x**3+20*(x-3)**3+40*3**-1*(x-9.5)**3+C_1*x)*10**3\n",
- "\n",
- "#Result\n",
- "print\"Deflection under points of two Loads are i.e: at pt D\",round(y_D,4),\"m\"\n",
- "print\" : at pt C\",round(y_C,4),\"m\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Deflection under points of two Loads are i.e: at pt D 0.0156 m\n",
- " : at pt C 0.0199 m\n"
- ]
- }
- ],
- "prompt_number": 17
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 6.10,Page No.161"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "E=200*10**9 #Pa \n",
- "I=20000*10**-8 #m**4\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#Now Taking moment at B\n",
- "R_a=(1000*3*4.5+1000*2)*6**-1 #Reaction Force at pt A\n",
- "\n",
- "#On part BC u.d.l of 1KN/m is introduced both above and below \n",
- "#consider section at distance x i.e X-X and considering moment at section X-X\n",
- "\n",
- "#M=15500*x*6**-1-1000*x**2*2**-1-1000(x-4)+1000*2**-1*(x-3)**2\n",
- "#EI*d**2y*d**x=-M=15500*x*6**-1-1000*x**2*2**-1-1000(x-4)+1000*2**-1*(x-3)**2\n",
- "\n",
- "#Now Integrating above Equation we get Equation of slope\n",
- "#EI*dy*dx**-1=-15500*x**2*12**-1+1000*x**3*6**-1+1000*(x-4)**2*2**-1+1000*6**-1*(x-3)**3+C_1\n",
- "\n",
- "#Now Integrating above Equation we get Equation of Deflection\n",
- "#EI*y=-15500*x**3*36**-1+1000*x**4*24**-1+1000*(x-4)**3*6**-1+1000*24**-1*(x-3)**3+C_1*x+C_2\n",
- "\n",
- "#At x=0,deflection is zero,i.e y=0 C_2=0\n",
- "#At x=6,deflection is zero,i.e y=0 \n",
- "x=6\n",
- "C_1=-(-15500*x**3*36**-1+1000*x**4*24**-1+1000*(x-4)**3*6**-1+1000*(x-3)**4*24**-1)*x**-1 #Constant\n",
- "\n",
- "#Answer for constant C_1 is incorrect in Book\n",
- "\n",
- "#Now Deflection at C,put x=3 m\n",
- "x=3\n",
- "y_C=1*(E*I)**-1*(-15500*x**3*36**-1+1000*x**4*24**-1+1000*(x-4)**3*6**-1+1000*24**-1*(x-3)**3+C_1*x)*10**3\n",
- "\n",
- "#Now Deflection at D,put x=4 m\n",
- "x=4\n",
- "y_D=1*(E*I)**-1*(-15500*x**3*36**-1+1000*x**4*24**-1+1000*(x-4)**3*6**-1+1000*24**-1*(x-3)**3+C_1*x)*10**3\n",
- "\n",
- "#Answers for y_C & y_D are incorrect in book\n",
- "\n",
- "#Result\n",
- "print\"Deflection at pt C is\",round(y_C,2),\"mm\"\n",
- "print\"Deflection at pt D is\",round(y_D,2),\"mm\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Deflection at pt C is 0.22 mm\n",
- "Deflection at pt D is 0.15 mm\n"
- ]
- }
- ],
- "prompt_number": 29
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 6.11,Page No.162"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "L=2.5 #m #Length of beam\n",
- "L_1=1.5 #m #Length from Fixed end\n",
- "W=50*10**3 #N #Load\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#Case-1\n",
- "y=W*L**3*3**-1 #Deflection of the cantilever at free end\n",
- "\n",
- "#Case-2\n",
- "#Deflection of cantilever at free end is\n",
- "#y_1=W_1*L**3*3**-1+W_1*L_1**3*3**-1+W_1*L_1**3*3**-1*(L-L_1)\n",
- "#After substituting values in above equation and simplifying further we get\n",
- "\n",
- "#y_1=22.375*W_1*3**-1\n",
- "\n",
- "W_1=y*3*22.375**-1*10**-3 #Magnitude of equal Loads\n",
- "M_1=W*L*10**-3\n",
- "M_2=W_1*L+W_1*L_1\n",
- "\n",
- "#Let M_1=sigma_1*z and M_2=sigma_2*z\n",
- "#Dividing above two equations we get\n",
- "\n",
- "#Let X=sigma_1*sigma_2**-1\n",
- "X=M_2*M_1**-1*100\n",
- "\n",
- "#Result\n",
- "print\"Magnitude of equal Loads is\",round(W_1,2),\"KN\"\n",
- "print\"Max Bending stress is\",round(X,2),\"%\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Magnitude of equal Loads is 34.92 N\n",
- "Max Bending stress is 111.73 %\n"
- ]
- }
- ],
- "prompt_number": 113
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 6.12,Page No.163"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "L=4 #m #Length of Beam\n",
- "\n",
- "#calculations\n",
- "\n",
- "#Consider a section at distance x from A and B.M at this section is\n",
- "#M=P*(3-x)-10*x**2+90*x-195 \n",
- "\n",
- "#Now #EI*d**2*y*d**2*x=-P*(3-x)+10*x**2-90*x+195\n",
- "\n",
- "#On Integrating above equation we get \n",
- "#E*I*dy*dx**-1=-P*(3*x-x**2*2**-1)+10*x**3*2**-1-45*x**2+195*x+C_1\n",
- "\n",
- "#Again On Integrating above equation we get \n",
- "#E*I*y=-P*(3*x**2*2**-1-x**3*6**-1)+10*x**4*12**-1-15*x**3+195*x**2*2**-1+C_1*x+C_2\n",
- "\n",
- "#But at x=0,dy*dx**-1=0 we get ,C_1=0\n",
- "# x=0,y=0 we get ,C_2=0\n",
- "#At x=3 m,y=0\n",
- "x=3\n",
- "C_1=0\n",
- "C_2=0\n",
- "P=(10*x**4*12**-1-15*x**3+195*x**2*2**-1+C_1*x+C_2)*(3*x**2*2**-1-x**3*6**-1)**-1\n",
- "\n",
- "#Result\n",
- "print\"Load taken by prop is\",round(P,2),\"KN\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Load taken by prop is 60.0 KN\n"
- ]
- }
- ],
- "prompt_number": 33
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 6.13,Page No.163"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "L=6 #m #Span of Beam\n",
- "sigma=100*10**6 #Pa #Bending stress\n",
- "E=210*10**9\n",
- "y=0.45 #m #Depth\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#Taking moment at B\n",
- "R_a=20*6*3+6*40*2*2**-1\n",
- "\n",
- "#At a section x from A the rate of Loading=20+2*3**-1*x #KN/m\n",
- "#S.F=100-20*x-x**2*3**-1\n",
- "#M=100*x-10*x**2-x**3*9**-1 \n",
- "\n",
- "#Thus B.M will be max where S.F is zero,we get equation as\n",
- "#x**2+60*x-300=0\n",
- "a=1\n",
- "b=60\n",
- "c=-300\n",
- "\n",
- "X=b**2-4*a*c\n",
- "x_1=(-b+X**0.5)*(2*a)**-1\n",
- "x_2=(-b-X**0.5)*(2*a)**-1\n",
- "\n",
- "x=4.641\n",
- "M=100*x-10*x**2-x**3*9**-1 #KN*m #Max bending moment\n",
- "I=M*sigma**-1*y*1000*2**-1 #m**4 #M.I\n",
- "\n",
- "#E*I*d**2*y*(d*x**2)**-1=-100*x+10*x**2+x**3*9**-1\n",
- "\n",
- "#AFter Integrating above EquATION WE get\n",
- "#E*I*dy*(dx)**-1=-50*x**2+10*3**-1*x**3+x**4*36**-1+C_1\n",
- "#Again Integrating above EquATION WE get\n",
- "#E*I*y=-50*x**3*3**-1+10*12**-1*x**4+x**5*180**-1+C_1*x+C_2\n",
- "\n",
- "#At x=0,y=0 ,C_2=0\n",
- "#At x=6,y=0 \n",
- "x=6\n",
- "C_2=0\n",
- "C_1=-(-50*x**3*3**-1+10*12**-1*x**4+x**5*180**-1)*x**-1\n",
- "\n",
- "x=3 #m\n",
- "y=1*(E*I)**-1*(-50*x**3*3**-1+10*12**-1*x**4+x**5*180**-1+C_1*x+C_2)*1000*100\n",
- "\n",
- "#Result\n",
- "print\"The central Deflection is\",round(y,2),\"m\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The central Deflection is 0.76 m\n"
- ]
- }
- ],
- "prompt_number": 58
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 6.14,Page No.168"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "L=10 #m #Lenght of cantilever beam\n",
- "P_1=20*10**3 #N #Load at free end\n",
- "P_2=20*10**3 #N #Load at middle of beam\n",
- "E=200*10**9 #Pa \n",
- "I=20000*10**-8 #m**4\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#Taking moment at pt B we get\n",
- "R_a=20*5*10**-1 #Force at pt A\n",
- "\n",
- "#Now B.M at b=0,at C=-100,at A=-300 KN*m\n",
- "\n",
- "#Now Area of B.M \n",
- "A_1=2**-1*5*100 #KN*m**2\n",
- "A_2=5*100 #KN*m**2\n",
- "A_3=2**-1*5*200 #KN*m**2\n",
- "\n",
- "#Total Area of B.M diagram is given by A\n",
- "A=A_1+A_2+A_3\n",
- "\n",
- "theta=A*10**3*(E*I)**-1 #radian\n",
- "\n",
- "x_1=2*3**-1*5\n",
- "x_2=3*2**-1*5\n",
- "x_3=5*3**-1*5\n",
- "M_1=A_1*x_1\n",
- "M_2=A_2*x_2\n",
- "M_3=A_3*x_3\n",
- "\n",
- "M=M_1+M_2+M_3 #Total moments of B.M about B\n",
- "\n",
- "y_B=M*10**3*(E*I)**-1 #Deflection a tfree end\n",
- "\n",
- "#REsult\n",
- "print\"Slope of cantilever at free end is\",round(theta,2),\"radian\"\n",
- "print\"Deflection of cantilever at free end is\",round(y_B,2),\"m\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Slope of cantilever at free end is 0.03 radian\n",
- "Deflection of cantilever at free end is 0.22 m\n"
- ]
- }
- ],
- "prompt_number": 65
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no.6.15,Page no.169"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#Slope at A is Zero and deflection at C is zero According to Mohr's second theorem\n",
- "#Let A_1*x_1=Y\n",
- "Y=1*30**-1*80*4*(3*4**-1*4+2)\n",
- "P=200*27**-1 #Reaction at ens D\n",
- "\n",
- "#Result\n",
- "print\"The reaction at end C is\",round(P,2),\"KN\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The reaction at end C is 7.41 KN\n"
- ]
- }
- ],
- "prompt_number": 72
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 6.16,Page No.171"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "E=200*10**9 #Pa\n",
- "I=2500*10**-8 #m**4\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#Taking moment about A we get\n",
- "R_a=(30*5+30*1)*6**-1 #Reaction at pt A\n",
- "R_b=60-R_a #Reaction at pt B\n",
- "\n",
- "M_c=30*1 #B.M at C\n",
- "M_d=30*1 #B.M at D\n",
- "M_a=0 #B.M at a\n",
- "M_b=0 #B.M at b\n",
- "\n",
- "#For conjugate beam taking moment about B_dash\n",
- "R_a_dash=(30*2**-1*(5+1*3**-1)+30*4*3+30*2*3**-1*2**-1)*6**-1\n",
- "R_b_dash=150-R_a_dash\n",
- "\n",
- "y_e=1*(E*I)**-1*(R_a_dash*3-30*2*1-2**-1*1*30*(2+1*3**-1))*1000\n",
- "\n",
- "#Result\n",
- "print\"Deflection at the centre is\",round(y_e,2),\"m\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Deflection at the centre is 0.03 m\n"
- ]
- }
- ],
- "prompt_number": 69
- }
- ],
- "metadata": {}
- }
- ]
-}
\ No newline at end of file diff --git a/Strength_Of_Materials_by_B_K_Sarkar/chapter_7_som.ipynb b/Strength_Of_Materials_by_B_K_Sarkar/chapter_7_som.ipynb deleted file mode 100755 index 7c6e418f..00000000 --- a/Strength_Of_Materials_by_B_K_Sarkar/chapter_7_som.ipynb +++ /dev/null @@ -1,642 +0,0 @@ -{
- "metadata": {
- "name": "chapter 7 som.ipynb"
- },
- "nbformat": 3,
- "nbformat_minor": 0,
- "worksheets": [
- {
- "cells": [
- {
- "cell_type": "heading",
- "level": 1,
- "metadata": {},
- "source": [
- "Chapter 7:Torsion"
- ]
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 7.1,Page no.183"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "G=84 #Gpa #Modulus of Rigidity\n",
- "N=110 #no. of revolution\n",
- "#d*D**-1=0.6 #Ratio of inner diameter to outer diameter\n",
- "sigma_s=63 #MPa #shear stress\n",
- "L=3 #m #Length of shaft\n",
- "P=590 #KW #Power\n",
- "\n",
- "#Calculation\n",
- "\n",
- "#P=2*pi*N*T_mean*60000**-1 #KW #Power\n",
- "T_mean=P*60000*(2*pi*N)**-1 #N*m #Mean Torque\n",
- "\n",
- "#I_p=p*32**-1*(D**4-d**4)\n",
- "\n",
- "#After substituting value of d in above equation we get\n",
- "#I_p=0.0272*pi*D**4 #m**4 #Polar moment of Inertia\n",
- "\n",
- "T_max=1.2*T_mean #N*m #Max torque\n",
- "\n",
- "#Using Relation\n",
- "#T_max*T_p**-1=sigma_s*R**-1=G*theta*L**-1 \n",
- "\n",
- "#After substituting values and simplifying we get\n",
- "\n",
- "D=(5.7085*10**-3)**0.3333 #m #Diameter of shaft\n",
- "\n",
- "theta=1.4*pi*180**-1 #radians\n",
- "\n",
- "#theta=((T_max*L)*(G*10**9*I_p)) #radians\n",
- "\n",
- "#After substituting values and simplifying we get\n",
- "D_1=(1.0513*10**-3)**0.25\n",
- "\n",
- "#Result\n",
- "print\"The Minimum external diameter is\",round(D_1,2),\"m\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Minimum external diameter is 0.18 m\n"
- ]
- }
- ],
- "prompt_number": 17
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 7.2,Page no.184"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "P=295 #KW #Power\n",
- "N=100 #R.p.m \n",
- "sigma_s=80 #MPa #shear stress\n",
- "\n",
- "\n",
- "#Calculations\n",
- "\n",
- "T_mean=((P*60000)*(2*pi*N)**-1) #N*m\n",
- "\n",
- "#T_max=T_mean=(pi*D**3*sigma_s)*16**-1\n",
- "D=((T_mean*16)*(pi*sigma_s*10**6)**-1)**0.333 #m #Diameter of solid shaft\n",
- "\n",
- "#For hollow shaft\n",
- "#I_p_h=pi*32**-1*(D_1**4-d_1**4) (equation 1)\n",
- "\n",
- "#Now d_1=0.6*D_1\n",
- "#substituting above value in equation 1,we get,\n",
- "\n",
- "#I_p_h=0.0272*pi*D_1**4\n",
- "\n",
- "#For solid shaft\n",
- "#I_p_s=pi*32**-1*D**4\n",
- "\n",
- "#T and sigma_s being the same then I_p*R**-1 will be the same for the two shafts\n",
- "#Using relation I_p_h*R_1**-1=I_p_s*R**-1\n",
- "\n",
- "#Substituting values and simplifying we get\n",
- "\n",
- "D_1=(D**3*0.8704**-1)**0.3333333 #m #External diameter of hollow shaft\n",
- "d_1=0.6*D_1 #cm #Internal diameter of hollow shaft\n",
- "\n",
- "A_s=pi*4**-1*(D*10**2)**2 #cm**2 #Area of solid shaft\n",
- "A_h=pi*4**-1*(((D_1*10**2)**2)-((d_1*10**2)**2))\n",
- "\n",
- "W=(A_s-A_h)*A_s**-1*100 #Percentage #Percentage saving in weight\n",
- "\n",
- "\n",
- "#Result\n",
- "print\"Diameter of solid shaft is \",D,\"m\"\n",
- "print\"Percentage saving in weight is\",round(W,2),\"%\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Diameter of solid shaft is 0.121751208998 m\n",
- "Percentage saving in weight is 29.8 %\n"
- ]
- }
- ],
- "prompt_number": 54
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 7.7,Page no.188"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "P_C=45 #KW Power aplled at C\n",
- "P_B=15 #KW Power taken off at B\n",
- "P_BA=30 #KW #Power transmitted across BA\n",
- "G=85 #GPa\n",
- "\n",
- "#Calculations (Part-1)\n",
- "\n",
- "#For BC\n",
- "P_1=45 #KW #Power across BC\n",
- "N_1=200 #r.p.m\n",
- "d_1=0.075 #m #diameter of shaft BC\n",
- "L_BC=2 #m #Length of shaft BC\n",
- "\n",
- "\n",
- "T_BC=60000*P_1*(2*pi*N_1)**-1 #N*m #Torque transmitted across BC\n",
- "sigma_s_BC=16*T_BC*((pi*(d_1)**3)**-1)*10**-6 #N/m**2 #max shear stress in BC\n",
- "I_p_BC=pi*32**-1*d_1**4 #m**4 #Polar M.I of BC\n",
- "theta_1=T_BC*L_BC*(G*10**9*I_p_BC)**-1 #Radian #Max angle of twist theta_1 in BC of B relative to C\n",
- "\n",
- "#For AB\n",
- "P_2=30 #KW #Power across AB\n",
- "N_2=200 #r.p.m\n",
- "d_2=0.05 #m #diameter of shaft AB\n",
- "L_BC=4 #m #Length of shaft AB\n",
- "\n",
- "\n",
- "T_AB=60000*P_2*(2*pi*N_2)**-1 #N*m #Torque transmitted across AB\n",
- "sigma_s_AB=16*T_AB*(pi*(d_2)**3)**-1*10**-6 #N/m**2 #max shear stress in AB\n",
- "I_p_AB=pi*32**-1*d_2**4 #m**4 #Polar M.I of AB\n",
- "theta_2=T_AB*L_BC*(G*10**9*I_p_AB)**-1 #Radian #Max angle of twist theta_1 in AB of A relative to B\n",
- "C=(theta_1+theta_2)*180*pi**-1 #radian #Angle of Twist of gear\n",
- "\n",
- "\n",
- "#Result\n",
- "print\"Angle of Twist of gear is\",round(C,2),\"Degree\"\n",
- "print\"The maximum shear stress developed in the shaft AB is\",round(sigma_s_AB,2)\n",
- "\n",
- " "
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Angle of Twist of gear is 7.23 Degree\n",
- "The maximum shear stress developed in the shaft AB is 58.36\n"
- ]
- }
- ],
- "prompt_number": 1
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 7.8,Page no.189"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "L_BC=1.8 #m #Length of BC\n",
- "L_AB=1.2 #m #Length of AB\n",
- "sigma_s=70 #MPa #shear stress\n",
- "d_1=0.05 #m #diameter of BC\n",
- "d_2=0.1 #m #diameter of AB\n",
- "r_BC=0.025 #cm #Radius of BC\n",
- "\n",
- "#Calculations\n",
- "\n",
- "I_p_BC=pi*32**-1*d_1**4 #m**4 #Polar M.I of BC\n",
- "I_p_AB=pi*32**-1*d_2**4 #m**4 #Polar M.I od AB\n",
- "\n",
- "#For BC\n",
- "#theta_1=T*L_BC*(G*10**9*I_p_BC)**-1 #Angle of Twist of C relative to B\n",
- "#After substituting and simplifying value, we get\n",
- "\n",
- "#theta_1=3.4923*10**-5*T\n",
- "\n",
- "#For AB\n",
- "#theta_2=T*L_AB*(G*10**9*I_p_AB)**-1 #Angle of Twist of B relative to A\n",
- "#After substituting and simplifying value, we get\n",
- "\n",
- "#theta_2=1.45513*T\n",
- "\n",
- "#sigma_s=T*R*(I_P)**-1 #The max shear stress in BC\n",
- "\n",
- "#After substituting and simplifying value in above equation, we get\n",
- "\n",
- "T=sigma_s*10**6*I_p_BC*r_BC**-1 \n",
- "theta_1=3.4923*10**-5*T\n",
- "theta_2=1.45513*10**-6*T\n",
- "theta_c=theta_1-theta_2 #radian #total angle of twist\n",
- "\n",
- "#Result\n",
- "print\"Total angle of Twist is\",round(theta_c,3),\"radian\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Total angle of Twist is 0.057 radian\n"
- ]
- }
- ],
- "prompt_number": 16
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 7.9,Page no.190"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "D=0.05 #m #Diameter of shaft\n",
- "sigma_s_a=55 #MPa #shear stress of alloy\n",
- "sigma_s_s=80 #MPa #shear stress of steel\n",
- "P=185 #KW #Power \n",
- "\n",
- "#Calculations\n",
- "\n",
- "#For alloy shaft,\n",
- "#theta*L**-1=T*(G_A*I_p_A)**-1\n",
- "\n",
- "#For steel shaft,\n",
- "#theta*L*-1=I*(G_S*I_p_S)**-1\n",
- "\n",
- "#After substituting and simplifying we get\n",
- "d=(246.2*10**-8)**0.25 #m #Internal diameter of steel shaft\n",
- "\n",
- "T_1=pi*16**-1*D**3*sigma_s_s*10**6 #N*m #For alloy shaft max torque\n",
- "T_2=pi*16**-1*((D**4-d**4)*D**-1)*sigma_s_s*10**6 #N*m #For steel shaft max torque\n",
- "\n",
- "#Permissible torque,T_2\n",
- "\n",
- "#P=2*pi*N*T_2*(60000)**-1 \n",
- "\n",
- "#After substituting we get\n",
- "N=P*60000*(2*pi*T_2)**-1 #r.p.m #Speed\n",
- "\n",
- "#Result\n",
- "print\"The speed at which the shafts to be driven is\",round(N,0),\"r.p.m\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The speed at which the shafts to be driven is 1485.0 r.p.m\n"
- ]
- }
- ],
- "prompt_number": 6
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 7.10,Page no.190"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "sigma_s=90 #MPa #shear stress of steel\n",
- "sigma_d=60 #MPa #shear stress of duralumin\n",
- "G_d=28 #GPa #modulus of rigidity of duralumin\n",
- "G_s=84 #GPa #modulus of rigidity of steel\n",
- "L=1 #m #Length of shaft\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#theta*L**-1=sigma_s*(G_s*R_s)**-1=sigma_d*(G_d*R_d)**-1\n",
- "\n",
- "#After substituting and simplifying,we get,\n",
- "#D=2*d\n",
- "\n",
- "#T_s=pi*16**-1*d**3*sigma_s #N*m #torque of steel\n",
- "#T_d=pi*16*(((D**4-d**4)*D**4)**-1)*sigma_d #N*m #torque of duralumin\n",
- "\n",
- "#After substituting and simplifying above two equations,we get,\n",
- "\n",
- "#T_s=17.6714*10**6*d**3 #N*m\n",
- "#T_d=88.3572*d**3 #N*m\n",
- "\n",
- "#T=T_s+T_d #Total torque\n",
- "\n",
- "#T=106.02875*10**6*d**3 \n",
- "\n",
- "d=(700*(106.02875*10**6)**-1)**0.333 #m \n",
- "D=2*d #m\n",
- "R_s=d*2**-1 #m\n",
- "\n",
- "theta=(sigma_s*10**6*L*(G_s*10**9*R_s)**-1)*180*pi**-1 #degree #Angle of twist\n",
- "\n",
- "#Result\n",
- "print\"The Angle of Twist is\",round(theta,2),\"Degree\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Angle of Twist is 6.52 Degree\n"
- ]
- }
- ],
- "prompt_number": 36
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 7.11,Page no.191"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "P=4415 #KW #Power transmitted\n",
- "N=110 #r.p.m\n",
- "sigma_s=75 #MPs #shear stress\n",
- "G=85 #GPa\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#D=2*d \n",
- "\n",
- "T=P*60000*(2*pi*N)**-1 #N*m #Torque Transmitted\n",
- "\n",
- "#T=pi*16**-1*(D**4-d**4)*D**-1*sigma_s #N*m\n",
- "\n",
- "#After substituting and simplifying above equations,we get,\n",
- "\n",
- "D=(T*16*pi**-1*(sigma_s*10**6)**-1)**(1*3**-1)\n",
- "d=D*2**-1\n",
- "X=5*(sigma_s*10**6)**2*(16*G*10**9)**-1\n",
- "\n",
- "#U*V**-1 #Energy stored\n",
- "#X=U*V**-1 #Energy stored #Notations has been changed\n",
- "\n",
- "#Result\n",
- "print\"Diameter of shaft is:D\",round(D,2),\"cm\"\n",
- "print\" :d\",round(d,2),\"cm\"\n",
- "print\"Energy stored per cubic meter is\",round(X,2),\"N/m**2\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Diameter of shaft is:D 0.3 cm\n",
- " :d 0.15 cm\n",
- "Energy stored per cubic meter is 20680.15 N/m**2\n"
- ]
- }
- ],
- "prompt_number": 65
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 7.12,Page no.192"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "P=3680 #KW #Power transmitted\n",
- "N=110 #r.p.m \n",
- "X=20000 #N*m #Energy stored\n",
- "G=85 #GPa\n",
- "\n",
- "#Calculations\n",
- "\n",
- "\n",
- "#U*V**-1=X #Strain Energy per unit volume #Notification has been changed\n",
- "#X=sigma_s**2*(4*G)**-1*((D**2+d**2)*(D**2)**-1)\n",
- "\n",
- "T=P*60000*(2*pi*N)**-1 #N*m #Torque transmitted by shaft\n",
- "sigma_s=(20000*3*G*10**9)**(1*2**-1) #MPa #shear stress of shaft\n",
- "\n",
- "#T=pi*16**-1*((D**4-d**4)*D**-1)*sigma_s \n",
- "\n",
- "#After substituting and simplifying above equations,we get,\n",
- "\n",
- "d=((T*16*3**0.5)*(pi*8*sigma_s)**-1)**(1*3**-1)\n",
- "D=3**0.5*d \n",
- "\n",
- "#Result\n",
- "print\"Diameter of shaft is D=\",round(D,2),\"m\"\n",
- "print\" d=\",round(d,2),\"m\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Diameter of shaft is D= 0.29 m\n",
- " d= 0.17 m\n"
- ]
- }
- ],
- "prompt_number": 83
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 7.13,Page no.193"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "D=8 #cm #Diameter of bronze\n",
- "d=5 #cm #diameter of steel shaft\n",
- "R_b=4 #cm #Radius of bronze\n",
- "R_s=2.5 #cm #Radius of steel shaft\n",
- "sigma_b=40 #MPa #shear stress of bronze\n",
- "sigma_s=65 #MPa #shear stress of steel shaft\n",
- "N=500 #r.p.m\n",
- "G_s=85 #GPa #Modulus of rigidity of steel\n",
- "G_b=45 #GPa #Modulus of rigidity of bronze\n",
- "\n",
- "#Calculations\n",
- "\n",
- "I_p_s=pi*32**-1*(5*10**-2)**4 #m**4 #Polar M.I of Steel shaft\n",
- "I_p_b=pi*32**-1*((8*10**-2)**4-(5*10**-2)**4) #m**4 #Polar M.I of Bronze shaft\n",
- "\n",
- "#T*(G_b*I_p_b)**-1=T_s*(G_s*I_s)**-1\n",
- "\n",
- "#After substituting and simplifying above equations,we get\n",
- "\n",
- "#T_b=2.94*T_s\n",
- "\n",
- "T_b=I_p_b*sigma_b*10**6*(R_b*10**-2)**-1 #N*m #Torque carried by bronze\n",
- "T_s=I_p_s*sigma_s*10**6*(R_s*10**-2)**-1 #N*m #Torque carried by steel shaft\n",
- "T_s_1=T_b*2.94**-1 #N*m \n",
- "\n",
- "T=T_b+T_s_1 #N*m #Total Torque\n",
- "P=(2*pi*N*T*(60000)**-1) #KW #Power transmitted\n",
- "\n",
- "#Result\n",
- "print\"Power transmitted by compound shaft is\",round(P,2),\"KW\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Power transmitted by compound shaft is 239.11 KW\n"
- ]
- }
- ],
- "prompt_number": 78
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 7.14,Page no.194"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "d=10 #cm #Diameter of shaft\n",
- "r=5 #cm #radius of shaft\n",
- "P=100 #KW #Power \n",
- "N=120 #r.p.m \n",
- "n=6 \n",
- "L_k=14 #cm #Length of key\n",
- "B_k=2.5 #cm #width of key\n",
- "n=6 \n",
- "d_b=2 #cm #Diameter of bolt\n",
- "D_b=30 #cm #Diameter of bolt circle\n",
- "R_b=15 #cm #radius \n",
- "\n",
- "#Calculations\n",
- "\n",
- "T=(P*60000*(2*pi*N)**-1)*10**2 #N*m #Torque\n",
- "I_p=pi*32**-1*d**4 #Polar M.I of shaft\n",
- "sigma_s=T*r*(I_p)**-1 #N/cm**2\n",
- "sigma_k=T*(L_k*B_k*r)**-1 #N/cm**2\n",
- "sigma_b=T*4*(n*pi*d_b**2*R_b)**-1 #N/cm**2\n",
- "\n",
- "#Result\n",
- "print\"shear stress in shaft\",round(sigma_s,2),\"N/cmm**2\"\n",
- "print\" Key\",round(sigma_k,2),\"N/cm**2\"\n",
- "print\" bolts\",round(sigma_b,2),\"N/cm**2\" "
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "shear stress in shaft 4052.85 N/cmm**2\n",
- " Key 4547.28 N/cm**2\n",
- " bolts 2814.48 N/cm**2\n"
- ]
- }
- ],
- "prompt_number": 90
- }
- ],
- "metadata": {}
- }
- ]
-}
\ No newline at end of file diff --git a/Strength_Of_Materials_by_B_K_Sarkar/chapter_8_som.ipynb b/Strength_Of_Materials_by_B_K_Sarkar/chapter_8_som.ipynb deleted file mode 100755 index 08e71ab5..00000000 --- a/Strength_Of_Materials_by_B_K_Sarkar/chapter_8_som.ipynb +++ /dev/null @@ -1,1251 +0,0 @@ -{
- "metadata": {
- "name": "chapter 8 som.ipynb"
- },
- "nbformat": 3,
- "nbformat_minor": 0,
- "worksheets": [
- {
- "cells": [
- {
- "cell_type": "heading",
- "level": 1,
- "metadata": {},
- "source": [
- "Chapter 8:Springs"
- ]
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 8.1,Page no.206"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "k=1 #KN/m #stiffness of spring\n",
- "P=45 #N #Maximum Load\n",
- "sigma_s=126 #MPa #Max shear stress\n",
- "L=4.5 #cm #Lenght of spring\n",
- "G=42 #GPa #Modulus of rigidity\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#sigma_s_max=16*P*R*(pi*d**3)**-1 #Max shear stress\n",
- "\n",
- "#After substituting values in above equation and simolifying we get\n",
- "#1000=42*10**9*d**4*(64*R**3*n)**-1 (#Equation 1)\n",
- "\n",
- "#R=0.175*10**6*pi*d**3 #Radius of spring (Equation 2)\n",
- "\n",
- "#L=n*d #solid length of spring\n",
- "#Thus simplifying above equation, n=L*d**-1\n",
- "\n",
- "#substituting value of n and R in (equation 1) we get,\n",
- "\n",
- "d=(42*10**9*(1000*64*4.5*10**-2*(0.175*pi)**3*(10**6)**3)**-1)**0.25*10**2 #cm #diameter of helical spring\n",
- "\n",
- "#substituting value d in (equation 2) we get,\n",
- "R=0.175*10**6*pi*(d)**3*10**-6*100 #cm #Radius of coil\n",
- "D=2*R #cm #Mean diameter of coil\n",
- "n=0.045*0.00306**-1 #Number of turns\n",
- "\n",
- "\n",
- "#Result\n",
- "print\"The Diameter of wire is\",round(d,3),\"cm\"\n",
- "print\"The Mean Diameter of coil is\",round(D,2),\"cm\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Diameter of coil is 0.306 cm\n",
- "The Mean Diameter of coil is 3.15 cm\n"
- ]
- }
- ],
- "prompt_number": 16
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 8.2,Page no.207"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "import numpy as np\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "L=15 #cm #Length of close coiled helical spring\n",
- "U=50 #N*m #Strain energy\n",
- "sigma_s=140 #MPa #Shear stress\n",
- "D=10 #cm #Mean coil diameter\n",
- "G=80 #GPa #Modulus of rigidity\n",
- "\n",
- "R=D*2**-1 #cm #Mean coil Radius\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#Let dell be the deflection of the spring when fully compressed\n",
- "# 0.15-dell=n*d (Equation 1)\n",
- " \n",
- "#U=(sigma_s)**2*V*(4*G)**-1 #Strain energy\n",
- "\n",
- "#After substituting values in above equation and simolifying we get\n",
- "V=50*4*80*10**9*((140*10**6)**2)**-1 #m**3 #Volume of spring\n",
- "\n",
- "#But V=pi*4**-1*d**2*2*pi*R*n\n",
- "#After substituting values in above equation and simolifying we get\n",
- "#n=3.308*10**-3*(d**2)**-1 #Number of turns\n",
- "\n",
- "#We know, T=P*R \n",
- "#Now substituting values in T and simolifying we get\n",
- "#P=549.7787*10**6*d**3 #Load\n",
- "\n",
- "#U=P*dell*2**-1\n",
- "#After substituting values in above equation and simolifying we get\n",
- "#dell=0.18189*10**-6*d**3 #Deflection \n",
- "\n",
- "#After substituting values in above equation and simolifying we get\n",
- "\n",
- "#d**3-22.0533*10**-3*d**2-1.21261*10**-6=0\n",
- "\n",
- "coeff=[1,-22.0533*10**-3,0,-1.21261*10**-6]\n",
- "d=np.roots(coeff) #Diameter of steel wire\n",
- "n=3.308*10**-3*((d[0])**2)**-1 #no.of coils\n",
- "\n",
- "#Result\n",
- "print\"Diameter of steel wire is\",d[0],\"m\"\n",
- "print\"number of coils\",n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Diameter of steel wire is (0.0241350343273+0j) m\n",
- "number of coils (5.67897110767+0j)\n"
- ]
- }
- ],
- "prompt_number": 9
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 8.3,Page no.208"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "k=10 #KN/m #stiffness\n",
- "L=40 #cm #Length of coil when adjascent coil touch each other\n",
- "G=80 #GPa #Modulus of rigidity\n",
- "#dell=0.002*n #Max compression\n",
- "\n",
- "#Calculation\n",
- "\n",
- "#k=G*d**4*(8*D**3*n)**-1 #Stiffness\n",
- "#After substituting values in above equation and simolifying we get\n",
- "#d**4=D**3*n*10**-6 (Equation 1)\n",
- "\n",
- "#L=n*d, #After substituting values we get\n",
- "#n=0.4*d**-1 (Equation 2)\n",
- "\n",
- "#Again, d*D**-1=1*10**-1\n",
- "#After solving above ratios we get,D=10*d\n",
- "\n",
- "#After substituting values in Equation 1 And Equation 2 we get\n",
- "d=(10**3*0.4*10**-6)**0.5*100 #cm\n",
- "D=10*d #cm #Mean Diameter \n",
- "R=D*2**-1 #cm #Mean Radius\n",
- "n=0.4*(d*10**-2)**-1 #Number of turns\n",
- "dell=0.002*n*100 #Deflection\n",
- "\n",
- "#k=P*dell**-1 \n",
- "#after solving above equation we get\n",
- "P=k*10**3*dell*10**-2 #N #Load\n",
- "\n",
- "sigma_s_max=16*P*R*10**-2*(pi*(d*10**-2)**3)**-1 #N/m**2 #Max shear stress\n",
- "\n",
- "#Result\n",
- "print\"The wire diameter is\",round(d,2),\"cm\"\n",
- "print\"The Mean diameter is\",round(D,2),\"cm\"\n",
- "print\"Max Load applied is\",round(P,2),\"N\"\n",
- "print\"Max shear stress is\",round(sigma_s_max,0),\"N/m**2\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The wire diameter is 2.0 cm\n",
- "The Mean diameter is 20.0 cm\n",
- "Max Load applied is 400.0 N\n",
- "Max shear stress is 25464791.0 N/m**2\n"
- ]
- }
- ],
- "prompt_number": 39
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 8.4,Page no.209"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "G=80 #GPa #Modulus of rigidity\n",
- "P=1 #KN #Load\n",
- "dell=10 #cm #Deflection\n",
- "sigma_s=350 #MPa #Max shear stress\n",
- "rho=78000 #N/m**3 #Density of materials\n",
- "\n",
- "#Calculations\n",
- "\n",
- "U=P*1000*dell*10**-2*2**-1 #N*m #Energy stored\n",
- "\n",
- "#Again U=sigma_s**2*V*(4*G)**-1 \n",
- "#After substituting values in above equation and further simplifying we get\n",
- "V=50*4*80*10**9*((350*10**6)**2)**-1 #m**3 #Volume\n",
- "\n",
- "W=V*rho #N #Weight\n",
- "\n",
- "#Now T=P*R=pi*d**3*sigma_s*16**-1\n",
- "#After substituting values in above equation and further simplifying\n",
- "D=(10**6*16*(2*pi*350*10**6)**-1)**0.5*10**2 #cm #Mean diameter of coil\n",
- "\n",
- "k=P*10**3*(dell*10**-2)**-1 #stiffness\n",
- "\n",
- "#Also k=D*n**-1*10**6\n",
- "#After substituting values in above equation and further simplifying\n",
- "n=10**6*D*10**-2*k**-1 #number of turns\n",
- "\n",
- "#Result\n",
- "print\"The Value of weight is\",round(W,3),\"N\"\n",
- "print\"Mean coil diameter is\",round(D,2),\"cm\"\n",
- "print\"The number of Turns is\",round(n,4)"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Value of weight is 10.188 N\n",
- "Mean coil diameter is 8.53 cm\n",
- "The number of Turns is 8.5297\n"
- ]
- }
- ],
- "prompt_number": 19
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 8.5,Page no.210"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "d=6 #mm #Diameter of steel wire\n",
- "n=50 #number of turns\n",
- "D=5 #cm #Mean Diameter\n",
- "R=D*2**-1 #cm #Radius of coil\n",
- "G=80 #GPa #Modulus of Rigidity\n",
- "P=150 #KN #Load\n",
- "\n",
- "#Calculation\n",
- "\n",
- "#Dell=64*P*R**3*n*(G*d**4)**-1 #Deflection\n",
- "#After substituting values in above equation and simplifying we get\n",
- "#P=2073.6*dell #Gradually applied equivalent Load\n",
- "\n",
- "#loss of potential Energy of the weight=Gain of strain Energy of the spring\n",
- "#150*(0.05+dell)=P*dell*2**-1\n",
- "#After substituting values in above equation we get\n",
- "\n",
- "#dell**2-0.1446*dell-0.00723=0\n",
- "#Above Equation is in the form of ax^2+bx+c=0\n",
- "\n",
- "a=1\n",
- "b=-0.1446\n",
- "c=-0.00723\n",
- "\n",
- "#First computing value of b^2-4ac and store it in a variable say X\n",
- "X=b**2-(4*a*c)\n",
- "#now roots are given as x=(-b+X**0.5)/(2*a) and second root is negative sign before X\n",
- "\n",
- "\n",
- "dell_1=(-b+X**0.5)*(2*a)**-1*10**2\n",
- "dell_2=(-b-X**0.5)*(2*a)**-1*10**2\n",
- "\n",
- "P=2073.6*dell_1*10**-2 #N \n",
- "\n",
- "sigma=16*P*R*10**-2*(pi*(d*10**-3)**3)**-1 #N/m**2 #Max stress\n",
- "\n",
- "#Result\n",
- "print\"The Max Extension of the Spring is\",round(dell_1,2),\"cm\"\n",
- "print\"The Max stress is\",sigma,\"N/m**2\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Max Extension of the Spring is 18.39 cm\n",
- "The Max stress is 224797751.663 N/m**2\n"
- ]
- }
- ],
- "prompt_number": 46
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 8.6,Page no.209"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "W=200 #N #weight \n",
- "v=4 #m/s #velocity of spring\n",
- "sigma=600 #MPa #max allowable stress in spring\n",
- "G=80 #GPa #Modulus of rigidity\n",
- "rho=78000 #N/m**3 #density\n",
- "d=8 #mm #diameter of spring\n",
- "D=5 #cm #Mean Diameter of coil\n",
- "\n",
- "\n",
- "#Calculation \n",
- "\n",
- "E=W*v**2*(2*9.81)**-1 #N*m #Kinetic Energy #Notification has been changed\n",
- "\n",
- "#U=sigma_s**2*V*(4*G)**-1 #Strain Energy stored inthe spring\n",
- "\n",
- "#After substituting values in above equation and simplifying we get\n",
- "V=163.1*4*80*10**9*((600*10**6)**2)**-1 #Volume \n",
- "\n",
- "W=rho*V #N #Weight of spring\n",
- "\n",
- "#Now V=pi*4**-1*d**2*pi*D*n\n",
- "#After substituting values in above equation and simplifying we get\n",
- "n=0.000145*4*(pi**2*0.008**2*0.05)**-1 #number of turns of spring\n",
- "\n",
- "#T=P*R=pi*16**-1*d**3*sigma_s #Torsion\n",
- "#After substituting values in above equation and simplifying we get\n",
- "P=pi*0.008**3*600*10**6*(0.025*16)**-1 #N\n",
- "\n",
- "#Now U=P*dell*2**-1 \n",
- "#Again,After substituting values in above equation and simplifying we get\n",
- "dell=163.1*2*(2412.743)**-1*10**2 #cm\n",
- "\n",
- "#Result\n",
- "print\"The Max Deflection Produced is\",round(dell,2),\"cm\"\n",
- "print\"Number of coil are\",round(n,2),"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Max Deflection Produced is 13.52 cm\n",
- "Number of coil are 18.36\n"
- ]
- }
- ],
- "prompt_number": 28
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 8.7,Page no.211"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "n=12 #number of coils\n",
- "d=3 #cm #mean diameter\n",
- "k=720 #N/m #stiffness of spring\n",
- "sigma_s=190 #MPa #Max shear stress\n",
- "G=80 #GPa #Modulus of rigidity\n",
- "D=3 #mm #Diameter of outer spring\n",
- "\n",
- "#Calculations\n",
- "R=D*2**-1 #mm #Radius of outer spring\n",
- "\n",
- "#Dell_1=64*P*(R*10**-3**3*n*(G*10**9*(d*10**-3)**4)**-1 #m #Extension of first spring\n",
- "#After substituting values and further simplifying we get\n",
- "#Dell_1=0.0004*P #m\n",
- "\n",
- "#Dell_2=64*P*(R*10**-3**3*n*(G*10**9*(d_1)**4)**-1 #m #Extension of first spring\n",
- "#After substituting values and further simplifying we get\n",
- "#Dell_2=3.24*10**-14*P*(d_1**4)**-1 #m #where d_1 is diameter of inner spring\n",
- "\n",
- "#Dell=Dell_1+Dell_2\n",
- "#After substituting values and further simplifying we get\n",
- "#dell=0.0004*P+3.24*10**-14*P*((d)**4)**-1\n",
- "\n",
- "#But dell=P*k**-1=P*720**-1\n",
- "\n",
- "#Now substituting value of dell in above equation we get\n",
- "d_1=(3.24*10**-14*(1*720**-1-0.0004)**-1)**0.25 #cm #diameter of inner spring\n",
- "\n",
- "#Now T=P*R=pi*d_1**3*dell_s*sigma_s*16**-1\n",
- "#simplifying above equation further \n",
- "#P=pi*d**3*sigma_s*(16*R)**-1 \n",
- "#Now substituting values and further simplifying we get\n",
- "P=pi*d_1**3*sigma_s*10**6*(16*R*10**-2)**-1 #N #Limiting Load\n",
- "\n",
- "dell=P*k**-1*10**2 #cm #Total Elongation\n",
- "\n",
- "#Result\n",
- "print\"Greatest Load that can be carried by composite spring is\",round(P,0),\"N\"\n",
- "print\"Extension in spring is\",round(dell,2),\"cm\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Greatest Load that can be carried by composite spring is 34.0 N\n",
- "Extension in spring is 4.73 cm\n"
- ]
- }
- ],
- "prompt_number": 20
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 8.8,Page no.212"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "#Outer spring\n",
- "n_1=10 #number of coils\n",
- "D_1=3 #cm #Diameter of coil\n",
- "d_1=3 #mm #diameter of wire\n",
- "dell_1=2 #cm #deflection of spring\n",
- "\n",
- "#Inner spring\n",
- "n_2=8 #number of coils\n",
- "\n",
- "G=80 #GPa #Modulus of rigidity\n",
- "\n",
- "#Calculation\n",
- "\n",
- "R_1=D_1*2**-1\n",
- "P_1=G*10**9*dell_1*10**-2*(d_1*10**-3)**4*(64*(R_1*10**-2)**3*n_1)**-1 #Load carried outer spring for compression of 2 cm\n",
- "\n",
- "P_2=100-P_1 #N #Load carried by inner spring\n",
- "k_2=P_2*0.01**-1 #N/m #stiffness of inner spring\n",
- "\n",
- "#D_2=D_1*10**-2-d_1*10**-3-2*dell_1*10**-2-d_2 #Diameter of inner spring\n",
- "#Further simplifying above equation we get\n",
- "#D_2=0.023-d_2\n",
- "\n",
- "#Now from stiffness equation of inner spring\n",
- "#k=G*d_2**4*(8*D_2**3*n_2)**-1\n",
- "#Now substituting values and further simplifying we get\n",
- "#d**4=(0.023-d)**3*312500**-1\n",
- "\n",
- "#As d is small compared with 0.023,as a first appromixation\n",
- "d_2_1=(0.023**3*312500**-1)**0.25 #m\n",
- "\n",
- "#Second Approximation\n",
- "d_2_2=((0.023-d_2_1)**3*312500**-1)**0.25 #m\n",
- "\n",
- "#Final approximation\n",
- "d_2_3=((0.023-d_2_2)**3*312500**-1)**0.25*100 #cm\n",
- "\n",
- "#Result\n",
- "print P_1\n",
- "print\"Stiffness of inner spring is\",round(k_2,2),\"N/m\"\n",
- "print\"Wire Diameter of inner spring is\",round(d_2_3,3),\"cm\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "60.0\n",
- "Stiffness of inner spring is 4000.0 N/m\n",
- "Wire Diameter of inner spring is 0.231 cm\n"
- ]
- }
- ],
- "prompt_number": 12
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 8.9,Page no.212"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "L= 3 #m #Length of rod\n",
- "d_1=25*10**-3 #m #Diameter of rod\n",
- "n= 5 #no. of coils\n",
- "sigma=70*10**6 #MPa #instantaneous stress\n",
- "E=70*10**9 #Pa \n",
- "G=80*10**9 #Pa\n",
- "D=24*10**-2 #Spring diameter\n",
- "R=d_2*2**-1 #spring radius\n",
- "d=4*10**-2 #diameter of steel\n",
- "\n",
- "#Calculations\n",
- "\n",
- "dell_1=sigma*L*(E)**-1\n",
- "\n",
- "#Let P be the equivalent applied Load which will produce same stress of 70 MPa\n",
- "P=pi*4**-1*(d_1)**2*E*10**-3 #KN\n",
- "\n",
- "#deflection of the spring is given by\n",
- "dell_2=P*64*R**3*n*(G*d**4)**-1 \n",
- "\n",
- "#Now Loss of Potential Energy of the weight=strain energy stored in the rod and the spring\n",
- "#Height measured from top of uncompressed spring\n",
- "h=((P*dell_1*2**-1+P*dell_2*2**-1)*(5.5*10**3)**-1-(dell_1+dell_2))*10**2\n",
- "\n",
- "#Shear stress in the spring is given by\n",
- "sigma_s=16*P*R*(pi*d**3)**-1*10**-6 #MPa \n",
- "\n",
- "#Result\n",
- "print\"Height measured from top of uncompressed spring\",round(h,2),\"cm\"\n",
- "print\"max shearing stress is\",round(sigma_s,2),\"MPa\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Height measured from top of uncompressed spring 20.34 cm\n",
- "max shearing stress is 328.13 MPa\n"
- ]
- }
- ],
- "prompt_number": 18
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 8.10,Page no.213"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "L=75 #cm #Legth of Leaf spring\n",
- "P=8 #KN #Load\n",
- "y_c=20 #mm #Deflection\n",
- "sigma=200 #MPa #Bending stress \n",
- "E=200 #GPa #modulus of Elasticity\n",
- "#b=12*t\n",
- "\n",
- "#Calculation\n",
- "\n",
- "#y_c=sigma*L**2*(4*E*t)**-1 \n",
- "#After substituting values and further simplifying we get\n",
- "t=200*10**6*(75*10**-2)**2*(4*200*10**9*0.02)**-1*10**2 #Thickness of plate\n",
- "\n",
- "b=12*t #width of plate\n",
- "\n",
- "#Now using relation we get\n",
- "#sigma=3*P*L*(2*n*b*t**2)**-1 \n",
- "#After substituting values and further simplifying we get\n",
- "n=3*8*10**3*0.75*(2*200*10**6*0.084*0.007**2)**-1\n",
- "\n",
- "#Y_c=L**2*(8*R)**-1\n",
- "R=(L*10**-2)**2*(8*y_c*10**-3)**-1 #m #Radius of spring\n",
- "\n",
- "#Result\n",
- "print\"The thickness of plate is\",round(t,2),\"cm\"\n",
- "print\"The width of plate is\",round(b,2),\"cm\"\n",
- "print\"The number of plate is\",round(n,2)\n",
- "print\"The Radius of plate is\",round(R,2)"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The thickness of plate is 0.7 cm\n",
- "The width of plate is 8.44 cm\n",
- "The number of plate is 10.93\n",
- "The Radius of plate is 3.52\n"
- ]
- }
- ],
- "prompt_number": 4
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 8.11,Page no.214"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "L=75 #cm #span of laminated steel spring\n",
- "P=7.5 #KN #Load\n",
- "y_c=5 #cm #Central Deflection\n",
- "sigma=400 #MPa #Bending stress\n",
- "E=200 #GPa #Modulus of Elasticity\n",
- "#b=12*t\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#y_c=3*P*L**3*(8*E*n*b*t**3)**-1 #Deflection\n",
- "#After substituting values and further simplifying we get\n",
- "#nt**4=9.887*10**-9 (Equation 1)\n",
- "\n",
- "#We Know sigma=3*P*L*(2*n*b*t**3)**-1 #bending stress\n",
- "#Again after substituting values and further simplifying we get\n",
- "#nt**3=1.757*10**-6 (Equation 2)\n",
- "\n",
- "#After Divviding (Equation 1) by (Equation 2) we have\n",
- "t=9.887*10**-9*(1.757*10**-6)**-1*10**2 #cm \n",
- "\n",
- "#substituting value of t in Equation 2) we get\n",
- "n=1.757*10**-6*((t*10**-2)**3)**-1 #Number of plates\n",
- "R=(L*10**-2)**2*(8*y_c*10**-2)**-1 #Radius of curvature\n",
- "\n",
- "#Result\n",
- "print\"The thickness of Plates is\",round(t,2),\"cm\"\n",
- "print\"The Number of Plates is\",round(n,2)\n",
- "print\"The Radius of Curvature of Plates is\",round(R,2),\"m\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The thickness of Plates is 0.56 cm\n",
- "The Number of Plates is 9.86\n",
- "The Radius of Curvature of Plates is 1.41 m\n"
- ]
- }
- ],
- "prompt_number": 2
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 8.12,Page no.214"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "L=1.3 #m #Length of carriage spring\n",
- "b=10 #cm #width of spring\n",
- "t=12 #mm #thickness of spring\n",
- "sigma=150 #MPa #Bending stresses\n",
- "E=200 #GPa #Modulus of Elasticity\n",
- "U=120 #N*m #Strain Energy\n",
- "\n",
- "#Calculation\n",
- "\n",
- "#V=n*b*t*L #Volume of carriage spring\n",
- "#U=sigma**2*(6*E)**-1*V\n",
- "#After substituting values in above equation and further simplifying we get\n",
- "n=120*6*200*10**9*2*((150*10**6)**2*10*10**-2*12*10**-3*1.3)**-1\n",
- "\n",
- "sigma_1=(120*6*200*10**9*2*(9*0.1*0.012*1.3)**-1)**0.5*10**-6 #MPa #Actual Bending stress\n",
- "\n",
- "R=E*t*(2*sigma_1)**-1 #m \n",
- "\n",
- "#Result\n",
- "print\"The number of plates is\",round(n,2)\n",
- "print\"Radius of curvature is\",round(R,3)"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The number of plates is 8.21\n",
- "Radius of curvature is 8.379\n"
- ]
- }
- ],
- "prompt_number": 10
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 8.13,Page no.215"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "P=200 #N #Load\n",
- "h=10 #cm #Height of Load dropped\n",
- "n=10 #Number of turns\n",
- "b_1=5 #cm #width of plates\n",
- "t=6 #mm #thickness of plates\n",
- "L=75 #cm #Length of plates\n",
- "E=200 #GPa #Modulus of Elasticity\n",
- "\n",
- "#Calculaion\n",
- "\n",
- "#Let P be the equivalent gradually applied load whuch would cause the same stress as is caused by the impact Load\n",
- "#200(0.1+dell)=P*dell*2**-1 (Equation 1)\n",
- "\n",
- "#dell=3*P*L**3*(8*E*n*b*t**3)**-1 #Deflection\n",
- "#After substituting values in above equation and further simplifying we get\n",
- "#P=136533.33*dell\n",
- "\n",
- "#After substituting values of P in (equation 1) and further simplifying we get\n",
- "#200(0.1+dell)=136533.33*dell**2*2**-1\n",
- "\n",
- "#simplifying above equation we get\n",
- "#dell**2-2.93*10**-3*dell-2.93*10**-4=0\n",
- "#The Above Equation is in the form of ax**2+bx+c=0\n",
- "a=1\n",
- "b=-2.93*10**-3\n",
- "c=-2.93*10**-4\n",
- "\n",
- "#First computing value of b^2-4ac and store it in a variable say X\n",
- "X=b**2-(4*a*c)\n",
- "#now roots are given as x=(-b+X**0.5)/(2*a) and second root is negative sign before X\n",
- "\n",
- "dell_1=(-b+X**0.5)*(2*a)**-1\n",
- "dell_2=(-b-X**0.5)*(2*a)**-1\n",
- "\n",
- "#Now deflection cannot be negative so consider value of dell_1\n",
- "\n",
- "P=136533.33*dell_1\n",
- "sigma=3*P*L*10**-2*(2*n*b_1*10**-2*(t*10**-3)**2)**-1*10**-6 #MPa #Max instantaneous stress\n",
- "R=(L*10**-2)**2*(8*dell_1)**-1 #Radius of curvature\n",
- " \n",
- "#Result\n",
- "print\"Max instantaneous stress in plates is\",round(sigma,2),\"MPa\"\n",
- "print\"Radius of curvature of spring is\",round(R,2),\"m\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Max instantaneous stress in plates is 159.1 MPa\n",
- "Radius of curvature of spring is 3.77 m\n"
- ]
- }
- ],
- "prompt_number": 5
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 8.14,Page no.215"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "L=70 #cm #Length of Longest plate\n",
- "P=3.5 #KN #central Load\n",
- "y_c=1.8 #cm #central deflection\n",
- "sigma=190 #MPa #allowable bending stress\n",
- "#b=12*t\n",
- "E=200 #GPa #Modulus of Elasticity\n",
- "\n",
- "#Calculation\n",
- "\n",
- "y_c=3*P*L**3*(8*n*E*b*t**3)**-1 #Deflection (#Equation 1)\n",
- "sigma=3*P*L*(2*n*b*t**2)**-1 #stress\n",
- "#Dividing Equation 1 by Equation 2 we get\n",
- "#y_c*sigma**-1=L**2*(4*E*t)**-1\n",
- "#After substituting values in above equation and further simplifying we get\n",
- "t=190*10**6*0.7**2*(1.8*10**-2*4*200*10**9)**-1*10**3 #thickness of plate\n",
- "b=12*t #Width of plates\n",
- "\n",
- "#sigma=3*2**-1*P*L*(n*b*t**2)**-1 #stress\n",
- "#After substituting values in above equation and further simplifying we get\n",
- "n=3*3.5*10**3*0.7*(2*190*10**6*0.077583*(6.465*10**-3)**2)**-1\n",
- "\n",
- "#Now sigma*y**-1=E*R**-1 \n",
- "#simplifying above equationwe get\n",
- "R=200*10**9*6.465*10**-3*(2*190*10**6)**-1 #Radius of Curvature\n",
- "a=L*10**-2*(2*n)**-1*10**3 #Overlap\n",
- "\n",
- "#Result\n",
- "print\"size of the plate is:\",round(b,2),\"mm\"\n",
- "print\" :\",round(t,2),\"mm\"\n",
- "print\"Overlap of plates is\",round(a,2),\"mm\"\n",
- "print\"Number of plates is\",round(n,2)\n",
- "print\"The Radius of curvature is\",round(R,3),\"m\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "size of the plate is: 77.58 mm\n",
- " : 6.47 mm\n",
- "Overlap of plates is 58.68 mm\n",
- "Number of plates is 5.96\n",
- "The Radius of curvature is 3.403 m\n"
- ]
- }
- ],
- "prompt_number": 39
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 8.15,Page no.216"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "alpha=30 #degree #helix angle\n",
- "dell=2.3*10**-2 #m #Vertical displacement\n",
- "W=40 #N #Axial Load\n",
- "d=6*10**-3 #steel rod diameter\n",
- "E=200*10**9 #Pa \n",
- "G=80*10**9 #Pa \n",
- "\n",
- "#Calculations\n",
- "\n",
- "#from equation of deflection of the spring under the Load we get\n",
- "#R**3*n=8.49*10**-4 \n",
- "\n",
- "#Let R**3*n=X\n",
- "X=8.49*10**-4 #Equation 1\n",
- "\n",
- "#from equation of angular rotation\n",
- "#R**2*n=8.1*10**-3\n",
- "\n",
- "#Let R**2*n=Y\n",
- "Y=8.1*10**-3 #Equation 2\n",
- "\n",
- "#After dividing equation 1 by equation 2 we get R \n",
- "#Let Z=R\n",
- "\n",
- "Z=X*Y**-1\n",
- "R=Z*10**2 #cm #Mean Radius\n",
- "\n",
- "#Result\n",
- "print\"Mean Radius of Open coiled spring of helix angle is\",round(R,2),\"cm\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Mean Radius of Open coiled spring of helix angle is 10.48 cm\n"
- ]
- }
- ],
- "prompt_number": 4
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 8.16,Page no.217"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "n=10 #Number of coils\n",
- "sigma=100 #MPa #Bending stress\n",
- "sigma_s=110 #MPa #Twisting stress\n",
- "#D=8*d\n",
- "dell=1.8 #cm #Max extension of of wire\n",
- "E=200 #GPa #Modulus of Elasticity\n",
- "G=80 #GPa #Modulus od Rigidity\n",
- "\n",
- "#Calculation\n",
- "\n",
- "#M=W*R*sin_alpha=pi*d**3*sigma_1*32**-1 #(Equation 1) #Bending moment\n",
- "#As D=8*d \n",
- "#then R=D*2**-1\n",
- "#Therefore, R=4*d\n",
- "\n",
- "#Now substituting values in equation 1 we get\n",
- "#W*sin_alpha=2454369.3*d**2 (Equation 2)\n",
- "\n",
- "#T=W*R*cos_alpha=pi*d**3*sigma_s #Torque (Equation 3) \n",
- "#Now substituting values in equation 3 we get\n",
- "#W*cos_alpha=5399612.4*d**2 (Equation 4)\n",
- "\n",
- "#Dividing Equation 2 by Equation 4 we get,\n",
- "#tan_alpha=0.4545\n",
- "alpha=arctan(0.4545)*180*pi**-1\n",
- "\n",
- "#From Equation 2 we get\n",
- "#W=2454369.3*d**2*(sin24.443)**-1\n",
- "#W=5931241.1*d**2 (Equation 5)\n",
- "\n",
- "#dell=64*W*R**3*n*sec_alpha*(d**4)**-1*((cos_alpha)**2*G**-1+2*sin_alpha**2*E**-1)\n",
- "#Now substituting values in above equation we get\n",
- "#W=33140.016*d (Equation 6)\n",
- "\n",
- "#From Equation 5 and Equation 6 we get\n",
- "#5931241.1*d**2=33140.016*d\n",
- "#After simplifying above equation we get\n",
- "d=33140.016*5931241.1**-1 #m #Diameter of wire\n",
- "W=33140.016*d #N #MAx Permissible Load\n",
- "\n",
- "#Result\n",
- "print\"The Max Permissible Load is\",round(W,2),\"N\"\n",
- "print\"Thw Wire Diameter is\",round(d,6),\"m\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Max Permissible Load is 185.17 N\n",
- "Thw Wire Diameter is 0.005587 m\n"
- ]
- }
- ],
- "prompt_number": 1
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 8.18,Page no.218"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "#Calculation\n",
- "\n",
- "n=10 #number of coils\n",
- "d=2*10**-2 #m #Diameter of wire\n",
- "D=12*10**-2 #m #Diameter of coiled spring\n",
- "R=0.06 #m #Radius of coiled spring\n",
- "dell=0.5*10**-2 #Deflection\n",
- "E=200*10**9 #Pa \n",
- "G=80*10**9 #Pa \n",
- "alpha=30 #degree\n",
- "\n",
- "#Calculations\n",
- "\n",
- "#beta=64*W*R**2*n*sinalpha*(d**4)**-1*(1*G**-1-2*E**-1)+64*T*R*n*secalpha*(d**4)**-1*(sin**2alpha*G**-1+2*cos**2alpha*E**-1)=0\n",
- "#From above equation anf simplifying we get\n",
- "\n",
- "#T=-6.11*10**-3*W\n",
- "\n",
- "#dell=64*W*R**3*n*sec(alpha)*(d**4)**-1*[(cos(alpha))**2*G**-1+2*(sin(alpha))**2*E**-1]+64*T*R**2*n*sin(alpha)*(d**4)**-1*[1*G**-1+2*E**-1]\n",
- "\n",
- "#After substituting Values and further simplifying we get\n",
- "#1.1847*10**-5*W+1.62*10**-4*T=0.005\n",
- "\n",
- "#Now substituting value of T in above equation we get\n",
- "#1.1847*10**-5*W-9.8982*10**-7*W=0.005\n",
- "W=0.005*(1.1847*10**-5-9.8982*10**-7)**-1 #N\n",
- "T=-6.11*10**-3*W #N*m\n",
- "\n",
- "#Result\n",
- "print\"The axial Load is\",round(W,2),\"N\"\n",
- "print\"Necesscary torque is\",round(T,2),\"N*m\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The axial Load is 460.52 N\n",
- "Necesscary torque is -2.81 N*m\n"
- ]
- }
- ],
- "prompt_number": 22
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 8.19,Page no.219"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "d=6 #mm #Diameter of steel wire\n",
- "n=1 #number of turns\n",
- "D=6.5 #cm #Mean of diameter\n",
- "G=80 #GPa #modulus of rigidity\n",
- "P_1=150 #Load\n",
- "p=1.5 #cm #Pitch of coil\n",
- "\n",
- "#Calculation \n",
- "\n",
- "R=D*2**-1\n",
- "#For one turn deflection is\n",
- "dell=p-d*10**-1 #cm \n",
- "\n",
- "#dell=64*P*R**3*n*(G*d**4)**-1 \n",
- "#Now, after simplifying further we get,\n",
- "P=dell*10**-2*G*10**9*(d*10**-3)**4*(64*(R*10**-2)**3*n)**-1 #N #Axial Load\n",
- "\n",
- "dell_2=dell*8 #cm #Total Displacement #Notification has been changed\n",
- "U=P*dell_2*10**-2*2**-1 #N-m #Strain Energy\n",
- "\n",
- "#Potential Energy given by 150N Load is\n",
- "#U=150*(h+0.072)\n",
- "\n",
- "#After simplifying above equation we get\n",
- "h=(U*P_1**-1-0.072)*10**2 #cm #Height from which 150 N load falls\n",
- "\n",
- "#Result\n",
- "print\"Axial Load is\",round(P,2),\"N\"\n",
- "print\"Height from which 150 N load falls is\",round(h,2),\"cm\" "
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Axial Load is 424.72 N\n",
- "Height from which 150 N load falls is 2.99 cm\n"
- ]
- }
- ],
- "prompt_number": 25
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem 8.20,Page no.219"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "alpha=30 #degree \n",
- "E=200*10**9 #Pa\n",
- "G=80*10**9 #pa \n",
- "\n",
- "#Calculations\n",
- "\n",
- "#For alpha=30 #Degree\n",
- "#dell=64*W*R**3*n*sec(alpha)*(d**4)**-1*(cos(alpha)**2*G**-1+2*sin(alpha)**2*E**-1)\n",
- "#Now substituting values in above equation we get\n",
- "\n",
- "#dell_1=64*W*R**3*n*(d**4)**-1*1330*(10**9)**-1 (equation 1)\n",
- "\n",
- "#For alpha=0 #Degree\n",
- "#dell=64*W*R**3*n*sec(alpha)*(d**4)**-1*(cos(alpha)**2*G**-1+2*sin(alpha)**2*E**-1)\n",
- "#Now substituting values in above equation we get\n",
- "\n",
- "#dell_2=64*W*R**3*n*(d**4)**-1*1250*(10**9)**-1 (equation 2)\n",
- "\n",
- "#subtracting equation 1 and equation 2 we get\n",
- "#Let dell_1-dell_2=X\n",
- "#X=64*W*R**3*n*(d**4)**-1*80*(10**9)\n",
- "\n",
- "#Let Y=X*dell_1**-1*100\n",
- "Y=80*1330**-1*100 #% under estimation of axial extension\n",
- "\n",
- "#Result\n",
- "print\"% under estimation of axial extension is\",round(Y,2)"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "% under estimation of axial extension is 6.02\n"
- ]
- }
- ],
- "prompt_number": 12
- }
- ],
- "metadata": {}
- }
- ]
-}
\ No newline at end of file diff --git a/Strength_Of_Materials_by_B_K_Sarkar/chapter_9_som.ipynb b/Strength_Of_Materials_by_B_K_Sarkar/chapter_9_som.ipynb deleted file mode 100755 index 318df44c..00000000 --- a/Strength_Of_Materials_by_B_K_Sarkar/chapter_9_som.ipynb +++ /dev/null @@ -1,502 +0,0 @@ -{
- "metadata": {
- "name": "chapter 9 som.ipynb"
- },
- "nbformat": 3,
- "nbformat_minor": 0,
- "worksheets": [
- {
- "cells": [
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Chapter No.9:Columns And Struts"
- ]
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 9.1,Page no.232"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "D=15 #cm #External Diameter\n",
- "t=2 #cm #Thickness\n",
- "L=6 #m #Length of cyclinder\n",
- "E=80*10**9 #Pa\n",
- "alpha=1*1600**-1 \n",
- "sigma_c=550*10**6 #Pa #compressive stress\n",
- "\n",
- "#Calculations\n",
- "\n",
- "d=D-2*t #m #Internal Diameter\n",
- "A=pi*4**-1*(D**2-d**2)*10**-4 #m**2 #Areaof Tube\n",
- "I=pi*64**-1*(D**4-d**4)*10**-4 #m**4 #M.I of tube\n",
- "k=(I*A**-1)**0.5 #m #Radius of Gyration\n",
- "\n",
- "P_e=pi**2*E*I*(L**2)**-1 #Euler's Load\n",
- "P_R=sigma_c*A*(1+alpha*(L*k**-1)**2)**-1 #According to Rankine's Formula\n",
- "\n",
- "#The Answer in Textbook is incorrect for P_R \n",
- "\n",
- "#Now again from Rankine's Formula\n",
- "#As K=I*A**-1,so substituting in below equation\n",
- "#Thus Stress calculated from Euler's Formula cannot exceed the yield stress of 550 MPa\n",
- "L=(pi**2*E*k**2*(550*10**6)**-1)**0.5*10**-2 #m #Length of cyclinder\n",
- "\n",
- "#Result\n",
- "print\"The Length of strut is\",round(L,2),\"cm\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Length of strut is 1.76 cm\n"
- ]
- }
- ],
- "prompt_number": 11
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 9.2,Page no.233"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "\n",
- "L=1.5 #m #Length of steelbar\n",
- "b=2 #cm #bredth of steelbar\n",
- "d=0.5 #cm #depth of steelbar\n",
- "sigma=320 #MPa #Yield point\n",
- "E=210 #GPa #modulus of Elasticity of steelbar\n",
- "\n",
- "#Calculations\n",
- "\n",
- "I_min=b*d**3*12**-1*10**-8 #m**4 #Moment of Inertia \n",
- "P=pi**2*E*10**9*I_min*(L**2)**-1 #N #N #Crippling Load\n",
- "\n",
- "#Let dell=Central Deflection\n",
- "\n",
- "#M=P*dell #Max Bending moment\n",
- "#After substituting value in above equation we get\n",
- "#M=191.9*dell\n",
- "\n",
- "A=b*d*10**-4 #m**2 #Area of steel bar\n",
- "sigma_1=P*A**-1*10**-6 #Mpa #Direct stress\n",
- "\n",
- "Z=b*d**3*10**-6 #Section modulus \n",
- "#sigma_2=M*Z**-1 #N/m**2 #Bending stress\n",
- "#After substituting value in above equation we get\n",
- "#sigma_2=dell*2302.8*10**6 #N/m**2 \n",
- "\n",
- "#sigma=sigma_1+sigma_2\n",
- "#Now substituting value of Bending stress and direct stress in above equation we get\n",
- "\n",
- "#320*10**6=1.919*10**6+2302.8*10**6*dell\n",
- "dell=((320*10**6-1.919*10**6)*(2302.8*10**6)**-1)*10**2 #cm #Central Deflection\n",
- "\n",
- "#Result\n",
- "print\"Maximum Central Deflection is\",round(dell,2),\"cm\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Maximum Central Deflection is 13.81 cm\n"
- ]
- }
- ],
- "prompt_number": 9
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 9.3,Page no.233"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "dell=1 #cm #Deflection\n",
- "FOS=4 #Factor of safety\n",
- "E=210 #GPa #Modulus of Elasticity of steel bar\n",
- "W=40 #KN #Load \n",
- "\n",
- "#Flange Dimensions\n",
- "b=30 #cm #width of flange\n",
- "d=5 #cm #depth of flange\n",
- "\n",
- "#Web Dimensions\n",
- "d_1=100 #cm #Depth of web\n",
- "t_1=2 #cm #Thcikness of web\n",
- "\n",
- "#Calculations\n",
- "\n",
- "I_xx=(0.3*1.1**3-0.28*1**3)*12**-1 #m**4 #M.I about x-x axis\n",
- "I_yy=2*0.05*0.3**3*12**-1+1*0.02**3*12**-1 #m**4 #M.I about y-y axis\n",
- "\n",
- "#From the equation of deflection we get\n",
- "L=(dell*10**-2*384*E*10**9*I_xx*(5*40*10**3)**-1)**0.25 #m #Length of beam\n",
- "P=pi**2*210*I_yy*10**9*4*(L**2)**-1 #N #crippling Load\n",
- "S=P*4**-1 #N #Safe Load\n",
- "\n",
- "#Result\n",
- "print\"The Safe Load is\",round(S,2),\"N\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Safe Load is 2336127.78 N\n"
- ]
- }
- ],
- "prompt_number": 32
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 9.5,Page no.235"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "L=4 #m #Length of column\n",
- "W=250 #KN #Safe Load\n",
- "FOS=5 #Factor of safety\n",
- "#d=0.8*D #Internal diameter is 0.8 times Extarnal Diameter\n",
- "sigma_c=550 #MPa #Compressive stress\n",
- "alpha=1*1600**-1 #constant\n",
- "\n",
- "#Calculations\n",
- "\n",
- "P=W*FOS #N #Crippling Load\n",
- "\n",
- "#A=pi*4**-1(D**2-d**2) #m**2 #Area of hollow cyclinder\n",
- "#After substituting value of d we get\n",
- "\n",
- "#A=pi*0.09*D**2\n",
- "\n",
- "#I=pi*64**-1*(D**4-d**4) #m**4 #Mo,ent Of Inertia\n",
- "#After substituting value of d we get d we get\n",
- "\n",
- "#I=0.009225*pi*D**4\n",
- "\n",
- "#K=(I*A**-1)**0.5 #Radius of Gyration\n",
- "#After substituting value of I and A and further simplifying we get\n",
- "#K=0.32*D\n",
- "\n",
- "#Now using the Relation we get\n",
- "#P=sigma_c*A*(1+alpha*(l_e*k)**2)**-1 #Rankines Formula\n",
- "#Now Substituting values in above equation we get\n",
- "#125*10**4=550*10**6*pi*0.09*D**2*(1+1*1600**-1*((2*0.32)**2)**-1)**-1\n",
- "\n",
- "#Further simplifying and rearranging we get\n",
- "#D**4-0.008038*D**2-0.0001962397=0\n",
- "\n",
- "a=1\n",
- "b=-0.008038\n",
- "c=-0.0001962397\n",
- "\n",
- "X=b**2-4*a*c\n",
- "\n",
- "D_1=((-b+X**0.5)*(2*a)**-1)**0.5*10**2\n",
- "D_2=((-b-X**0.5)*(2*a)**-1)**0.5\n",
- "\n",
- "#Thus Diameter cannot be negative, discard value of D_2\n",
- "d=0.8*D_1\n",
- "\n",
- "#Result\n",
- "print\"The Minimum Diameter is\",round(d,2),\"cm\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Minimum Diameter is 10.91 cm\n"
- ]
- }
- ],
- "prompt_number": 33
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 9.6,Page no.236"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "d=0.04 #m #Internal Diameter of tube\n",
- "D=0.05 #m #External Diameter of tube\n",
- "P_1=240*10**3 #N #Compressive Load\n",
- "P_2=158*10**3#N #Failure Load\n",
- "L=2 #m #Length of tube\n",
- "l=3 #m #Length of strut\n",
- "\n",
- "#Calculations\n",
- "\n",
- "A=pi*4**-1*(D**2-d**2) #m**2 #Areaof Tube\n",
- "I=pi*64**-1*(D**4-d**4) #m**4 #M.I of tube\n",
- "k=(I*A**-1)**0.5 #m #Radius of Gyration\n",
- "sigma_c=P*A**-1 #Pa #Compressive stress\n",
- "\n",
- "l_e=L*2**-1 #m #According to given condition i.e Both ends fixed\n",
- "\n",
- "#Now from crippling Load Equation we get\n",
- "alpha=((sigma_c*A*P_2**-1-1)*((l_e*k**-1)**2)**-1)*10**4\n",
- "\n",
- "#Now Crippling Load when L=3 m Is used as strut\n",
- "l_e_2=l*(2**0.5)**-1\n",
- "P_3=sigma_c*A*(1+alpha*10**-4*(l_e_2*k**-1)**2)**-1 \n",
- "\n",
- "\n",
- "print\"The Value of constant value alpha is\",round(alpha,2)\n",
- "print\"The Crippling Load of Tube is\",round(P_3,2),\"N\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Value of constant value alpha is 1.33\n",
- "The Crippling Load of Tube is 71954.46 N\n"
- ]
- }
- ],
- "prompt_number": 54
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 9.8,Page no.239"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "D=0.038 #m #External diameter\n",
- "d=0.035 #m #Internal diameter\n",
- "P=20*10**3 #N #Load\n",
- "E=210*10**9 #Pa \n",
- "e=0.002 #m #Eccentricity\n",
- "L=1.5 #m #Lenght of tube\n",
- "\n",
- "#Calculations\n",
- "\n",
- "A=pi*4**-1*(D**2-d**2) #m**2 column\n",
- "I=pi*64**-1*(D**4-d**4) #m**4 #M.I of column\n",
- "m=(P*(E*I)**-1)**0.5 \n",
- "\n",
- "#Let X=secmL*2**-1\n",
- "X=(1*(cos(m*L*2**-1))**-1)\n",
- "M=P*e*X #N-m #MAx Bending Moment\n",
- "sigma_1=P*A**-1*10**-6 #Pa #Direct stress\n",
- "sigma_2=M*0.019*I**-1*10**-6 #Pa #Bending stress\n",
- "\n",
- "sigma_c_max=(sigma_1+sigma_2) #MPa #Max compressive stress\n",
- "\n",
- "#Result\n",
- "print\"The Max stress developed is\",round(sigma_c_max,2),\"MPa\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Max stress developed is 246.79 MPa\n"
- ]
- }
- ],
- "prompt_number": 130
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 9.9,Page no.239"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "L=5 #m #Length of column\n",
- "D=0.2 #m #External Diameter\n",
- "d=0.14 #m #Internal diameter\n",
- "P=200*10**3 #N #Load\n",
- "e=0.015 #m #Eccentricity\n",
- "E=95 *10**9 #Pa \n",
- "\n",
- "#Calculations\n",
- "\n",
- "L_2=L*2**-1 #m #half length of column\n",
- "A=pi*4**-1*(D**2-d**2) #m**2 column\n",
- "I=pi*64**-1*(D**4-d**4) #m**4 #M.I of column\n",
- "m=(P*(E*I)**-1)**0.5 \n",
- "\n",
- "#Let X=secmL*2**-1\n",
- "X=(1*(cos(m*L_2*2**-1))**-1)\n",
- "M=P*e*X #N-m #MAx Bending Moment\n",
- "sigma_1=P*A**-1*10**-6 #Pa #Direct stress\n",
- "sigma_2=M*0.1*I**-1*10**-6 #Pa #Bending stress\n",
- "\n",
- "sigma_c_max=(sigma_1+sigma_2) #MPa #Max compressive stress\n",
- "\n",
- "print\"The Max stress developed is\",round(sigma_c_max,2),\"MPa\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The Max stress developed is 17.65 MPa\n"
- ]
- }
- ],
- "prompt_number": 125
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Problem no 9.10,Page no.240"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "\n",
- "L=3 #m #Length of strut\n",
- "b=0.04 #m #Width of rectangle\n",
- "d=0.10 #m #Depth if rectangle\n",
- "P=100*10**3 #N #Axial thrust\n",
- "w=10*10**3 #N #Uniformly Distributed Load\n",
- "E=210*10**9 #Pa \n",
- "\n",
- "#Calculations\n",
- "\n",
- "A=b*d #m**2 #Area of strut\n",
- "I=b*d**3*12**-1 #m**4 #M.I \n",
- "m=(P*(E*I)**-1)**0.5 \n",
- "\n",
- "#Let X=secmL*2**-1\n",
- "X=(1*(cos(m*L*2**-1))**-1)\n",
- "\n",
- "M=w*E*I*P**-1*(X-1)*3**-1 #N*m #Max Bending Moment\n",
- "sigma_1=P*A**-1 #Pa #Direct stress\n",
- "sigma_2=M*0.05*I**-1 #Pa #Bending stress\n",
- "\n",
- "sigma_c_max=sigma_1+sigma_2 #Max compressive stress\n",
- "\n",
- "#If the Eccentricity of thrust is neglected\n",
- "M_2=w*L**2*(3*8)**-1 #Max Bending moment\n",
- "sigma_2_2=M_2*0.05*I**-1 #Pa #Bending stress\n",
- "\n",
- "sigma_c_max_2=(sigma_1+sigma_2_2)*10**-6 #Pa\n",
- "\n",
- "#Let Y=Percentage error\n",
- "Y=((sigma_c_max-sigma_c_max_2*10**6)*sigma_c_max**-1)*100\n",
- "\n",
- "#Result\n",
- "print\"Max stress induced is\",round(sigma_c_max_2,2),\"MPa\"\n",
- "print\"The Percentage Error is\",round(Y,3),\"%\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Max stress induced is 81.25 MPa\n",
- "The Percentage Error is 9.638 %\n"
- ]
- }
- ],
- "prompt_number": 98
- }
- ],
- "metadata": {}
- }
- ]
-}
\ No newline at end of file |