{ "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": {} } ] }