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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": {}
}
]
}
|
