{
"metadata": {
"name": "",
"signature": "sha256:ced402d1abd8ee6656b1d5779752e65300ae4ab42f06bdc7c60dba927fb54a5a"
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"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 12:Deflection of Beams"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Problem 12.1,page no.518"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Given\n",
"#Variable declaration\n",
"L=6*1000 #Length in mm\n",
"W=50*1000 #Point load in N\n",
"I=78e6 #Moment of Inertia in mm^4\n",
"E=2.1e5 #Young's modulus in N/sq.mm\n",
"\n",
"#Calculation\n",
"yc=round((W*L**3)/(48*E*I),3) #The deflection at the centre in mm\n",
"thetaB=round(math.degrees((W*L**2)/(16*E*I)),4) #The slope at the supports\n",
"\n",
"#Result\n",
"print \"Deflection at the centre =\",yc,\"mm\"\n",
"print \"NOTE:The answer given for slope at the support is wrong.The correct answer is,\"\n",
"print \"Slope at the support =\",thetaB,\"degree\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Deflection at the centre = 13.736 mm\n",
"NOTE:The answer given for slope at the support is wrong.The correct answer is,\n",
"Slope at the support = 0.3935 degree\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Problem 12.2,page no.518"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Given\n",
"#Variable declaration\n",
"L=4*1000 #Length in mm\n",
"\n",
"#Calculation\n",
"thetaA=round(math.radians(1),5) #Slope at the ends in radians\n",
"yc=float(str(thetaA*(L/3))[:5]) #Deflection at the centre in mm\n",
"\n",
"#Result\n",
"print \"Deflection at the centre =\",yc,\"mm\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Deflection at the centre = 23.26 mm\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Problem 12.3,page no.519"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Given\n",
"#Variable declaration\n",
"L=3*1000 #Length in mm\n",
"\n",
"#Calculation\n",
"thetaA=round(math.radians(1),5) #Slope at the ends in radians\n",
"yc=float(str(thetaA*(L/3))[:5]) #Deflection at the centre in mm\n",
"\n",
"#Result\n",
"print \"Deflection at the centre =\",yc,\"mm\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Deflection at the centre = 17.45 mm\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Problem 12.4,page no.526"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Given\n",
"#Variable declaration\n",
"L=5*1000 #Length in mm\n",
"W=5*1000 #Point load in N\n",
"a=3*1000 #Distance between point load and left end in mm\n",
"E=2e5 #Young's modulus in N/sq.mm\n",
"I=1e8 #Moment of Inertia in mm^4\n",
"\n",
"#Calculation\n",
"b=L-a #Width in mm\n",
"#case(i):The slope at the left support\n",
"thetaA=-(W*a*b)/(6*E*I*L)*(a+2*b)\n",
"#case(iii): The deflection under the load\n",
"yc=(W*a**2*b**2)/(3*E*I*L)\n",
"#case(iii):The maximum deflection\n",
"y_max=round((W*b)/(9*math.sqrt(3)*E*I*L)*(((a**2)+(2*a*b))**(3/2)),4)\n",
"\n",
"#Result\n",
"print\"slope at the left support =\",thetaA,\"radians\"\n",
"print\"Deflection under the load =\",yc,\"mm\"\n",
"print\"Maximum deflection =\",y_max,\"mm\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"slope at the left support = -0.00035 radians\n",
"Deflection under the load = 0.6 mm\n",
"Maximum deflection = 0.6173 mm\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Problem 12.5,page no,529"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"import math\n",
"\n",
"#Given\n",
"#Variable declaration\n",
"b=200 #Width in mm\n",
"d=300 #Depth in mm\n",
"L=5*1000 #Span in mm\n",
"L_star=5 #Span in m\n",
"w=9*1000 #Uniformly distributed load in N/m \n",
"E=1e4 #Young's modulus in N/sq.mm\n",
"\n",
"#Calculation\n",
"W=w*L_star #Total load in N\n",
"I=b*d**3/12 #Moment of Inertia in mm^4\n",
"\n",
"#case(i):the slope at the support\n",
"thetaA=round(-(W*(L**2))/(24*E*I),4)\n",
"\n",
"#case(ii):maximum deflection\n",
"yc=str((W*L**3)/(E*I)*(5/384))[:5]\n",
"\n",
"#Result\n",
"print\"Slope at the support =\",-thetaA,\"radians\"\n",
"print\"Maximum deflection =\",yc,\"mm\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Slope at the support = 0.0104 radians\n",
"Maximum deflection = 16.27 mm\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Problem 12.6,page no.529"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"#Variable declaration\n",
"L=5*1000 #Length in mm\n",
"L_star=5 #Length in m\n",
"w=9 #Uniformly distributed load in kN/m\n",
"f=7 #Bending stress in N/sq.mm\n",
"E=1e4 #Young's modulus in N/sq.mm\n",
"yc=10 #Central deflection in mm\n",
"\n",
"#Calculation\n",
"W=w*L_star*1e3 #Total load in N \n",
"bd3=((W*(L**3)*12*5)/(E*yc*384)) #width X depth^3 in mm^4\n",
"M=(W*L/8) #Maximum bending moment in Nmm \n",
"bd2=round(M*12/(f*2),2) #width X depth^2 in mm^3\n",
"d=round(bd3/bd2,2) #Depth of beam in mm\n",
"b=str(M*12/(f*2)/d**2)[:6] #Width of beam in mm\n",
"\n",
"#Result\n",
"print \"Depth of beam =\",d,\"mm\"\n",
"print \"Width of beam =\",b,\"mm\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Depth of beam = 364.58 mm\n",
"Width of beam = 181.36 mm\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Problem 12.7,page no.531"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given \n",
"#Variable declaration\n",
"L=5*1000 #Length in mm\n",
"f=8 #Bending stress in N/sq.mm\n",
"yc=10 #Central deflection in mm\n",
"E=1.2e4 #Young's modulus in N/sq.mm\n",
"\n",
"#Calculation\n",
"d=round((5*L**2*(f*2*8))/(E*384*yc)*1e-1,2) #Depth of beam in cm\n",
"\n",
"#Result\n",
"print \"Depth of beam =\",d,\"cm\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Depth of beam = 34.72 cm\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Problem 12.8,page no.534"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"#Variable declaration\n",
"L=6*1000 #Length in mm\n",
"W=40*1000 #Point load in N\n",
"a=4*1000 #Distance of point load from left support in mm\n",
"I=7.33e7 #Moment of Inertia in mm^4\n",
"E=2e5 #Young's modulus in sq.mm\n",
"\n",
"#Calculation\n",
"b=L-a #Width of beam in mm\n",
"yc=round(-(W*a**2*b**2)/(3*E*I*L),1) #Deflection under the load in mm\n",
"\n",
"#Result\n",
"print \"Deflection under the load =\",yc,\"mm\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Deflection under the load = -9.7 mm\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}