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+{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:645699e2826749157978cc3139b5b4362e98aa81aba9d727772115e7ecd189e3"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 13:Deflection of Cantilevers"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Problem 13.1,page no.557"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Given\n",
+ "#Variable declaration\n",
+ "L=3*1000 #Length in mm\n",
+ "W=25*1000 #Point load in N\n",
+ "I=1e8 #Moment of Inertia in mm^4\n",
+ "E=2.1e5 #Young's modulus in N/sq.mm\n",
+ "\n",
+ "#Calculation\n",
+ "#case(i):Slope of the cantilever at the free end\n",
+ "thetaB=round((W*(L**2))/(2*E*I),6)\n",
+ "#case(ii):Deflection at the free end\n",
+ "yB=round((W*L**3)/(E*I*3),2)\n",
+ "\n",
+ "#Result\n",
+ "print \"Slope at the free end =\",thetaB,\"rad\"\n",
+ "print \"Deflection at the free end =\",yB,\"mm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Slope at the free end = 0.005357 rad\n",
+ "Deflection at the free end = 10.71 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Problem 13.2,page no.557"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Given\n",
+ "#Variable declaration\n",
+ "L=3*1000 #Length in mm\n",
+ "W=50*1000 #Point load in N\n",
+ "a=2*1000 #Distance between the load and fixed end in mm\n",
+ "I=1e8 #Moment of Inertia in mm^4\n",
+ "E=2e5 #Young's modulus in N/sq.mm\n",
+ "\n",
+ "#Calculation\n",
+ "#case(i):Slope at the free end\n",
+ "thetaB=(W*(a**2))/(2*E*I)\n",
+ "#case(ii):Deflection at the free end\n",
+ "yB=round(((W*a**3)/(E*I*3))+((W*(a**2))/(2*E*I)*(L-a)),2)\n",
+ "\n",
+ "#Result\n",
+ "print \"Slope at the free end =\",thetaB,\"rad\"\n",
+ "print \"Deflection at the free end =\",yB,\"mm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Slope at the free end = 0.005 rad\n",
+ "Deflection at the free end = 11.67 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Problem 13.3,page no.559"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Given\n",
+ "#Variable declaration\n",
+ "L=2.5*1000 #Length in mm\n",
+ "w=16.4 #Uniformly distributed load in kN/m \n",
+ "I=7.95e7 #Moment of Inertia in mm^4\n",
+ "E=2e5 #Young's modulus in N/sq.mm\n",
+ "\n",
+ "#Calculation\n",
+ "W=w*L #Total load in N\n",
+ "yB=round((W*L**3)/(E*I*8),3) #Deflection at the free end in mm\n",
+ "\n",
+ "#Result\n",
+ "print \"Deflection at the free end =\",yB,\"mm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Deflection at the free end = 5.036 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Problem 13.4(A),page no.560"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Given\n",
+ "#Variable declaration\n",
+ "b=120 #Width in mm\n",
+ "d=200 #Depth in mm\n",
+ "L_star=2.5 #Length in m\n",
+ "L=2.5*1000 #Length in mm\n",
+ "yB=5 #Deflection at free end in mm\n",
+ "E=2e5 #Young's modulus in N/sq.mm\n",
+ "\n",
+ "#Calculation\n",
+ "I=(b*d**3)/12 #Moment of Inertia in mm^4\n",
+ "w=(yB*8*E*I)/(L**3*L_star)/1e3 #Uniformly distributed load in N/m\n",
+ "\n",
+ "#Result\n",
+ "print \"Uniformly distributed load =\",w,\"kN/m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Uniformly distributed load = 16.384 kN/m\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Problem 13.5,page no.563"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Given\n",
+ "#Variable declaration\n",
+ "L=3*1000 #Length in mm\n",
+ "w=10 #Uniformly distributed load in N/mm\n",
+ "a=2*1000 #Length of Uniformly distributed load from fixed end in mm\n",
+ "I=1e8 #Moment of Inertia in mm^4\n",
+ "E=2e5 #Young's modulus in N/sq.mm\n",
+ "\n",
+ "#Calculation\n",
+ "#case(i):Slope at the free end\n",
+ "thetaB=str((w*(a**3))/(6*E*I))[:7]\n",
+ "#case(ii):Deflection at the free end\n",
+ "yB=round(((w*a**4)/(E*I*8))+((w*(a**3))/(6*E*I)*(L-a)),2)\n",
+ "\n",
+ "#Result\n",
+ "print \"Slope at the free end =\",thetaB,\"rad\"\n",
+ "print \"Deflection at the free end =\",yB,\"mm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Slope at the free end = 0.00066 rad\n",
+ "Deflection at the free end = 1.67 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Problem 13.6,page no.563"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Given\n",
+ "#Variable declaration\n",
+ "L=3*1000 #Length in mm\n",
+ "w=10 #Uniformly distributed load in N/mm\n",
+ "a=2*1000 #Length of Uniformly distributed load from fixed end in mm\n",
+ "I=1e8 #Moment of Inertia in mm^4\n",
+ "E=2e5 #Young's modulus in N/sq.mm\n",
+ "\n",
+ "#Calculation\n",
+ "#case(i):Slope at the free end\n",
+ "thetaB=round(((w*(L**3))/(6*E*I))-((w*((L-a)**3))/(6*E*I)),6)\n",
+ "#case(ii):Deflection at the free end\n",
+ "yB=round(((w*L**4)/(E*I*8))-(((w*(L-a)**4)/(8*E*I))+((w*(L-a)**3)/(6*E*I)*a)),4)\n",
+ "\n",
+ "#Result\n",
+ "print \"Slope at the free end =\",thetaB,\"rad\"\n",
+ "print \"Deflection at the free end =\",yB,\"mm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Slope at the free end = 0.002167 rad\n",
+ "Deflection at the free end = 4.8333 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Problem 13.10,page no.569"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Given\n",
+ "#Variable declaration\n",
+ "L=4*1000 #Length in mm\n",
+ "w=50 #load at fixed end in N/mm\n",
+ "I=1e8 #Moment of Inertia in mm^4\n",
+ "E=2e5 #Young's modulus in N/sq.mm\n",
+ "\n",
+ "#Calculation\n",
+ "#case(i):Slope at the free end\n",
+ "thetaB=round(-(w*(L**3))/(24*E*I),5)\n",
+ "#case(ii):Deflection at the free end\n",
+ "yB=round((w*L**4)/(E*I*30),2)\n",
+ "\n",
+ "#Result\n",
+ "print \"Slope at the free end =\",-thetaB,\"rad\"\n",
+ "print \"Deflection at the free end =\",yB,\"mm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Slope at the free end = 0.00667 rad\n",
+ "Deflection at the free end = 21.33 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [],
+ "language": "python",
+ "metadata": {},
+ "outputs": []
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+} \ No newline at end of file
generated by cgit (git 2.34.1) at 2025-03-11 06:55:39 +0000