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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 01:Stress"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.1.1, Page No:9"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#NOTE:The notation has been changed to simplify the coding process\n",
"\n",
"#Variable Decleration\n",
"P_AB=4000 #Axial Force at section 1 in lb\n",
"P_BC=5000 #Axial Force at section 2 in lb\n",
"P_CD=7000 #Axial Force at section 3 in lb\n",
"A_1=1.2 #Area at section 1 in in^2\n",
"A_2=1.8 #Area at section 2 in in^2\n",
"A_3=1.6 #Area at section 3 in in^2\n",
"\n",
"#Calculation\n",
"#S indicates sigma here\n",
"S_AB=P_AB/A_1 #Stress at section 1 in psi (T)\n",
"S_BC=P_BC/A_2 #Stress at section 2 in psi (C)\n",
"S_CD=P_CD/A_3 #Stress at section 3 in psi (C)\n",
"\n",
"#Result\n",
"print \"The stress at the three sections is given as\"\n",
"print \"Stress at section 1=\",round(S_AB),\"section 2=\",round(S_BC),\"section 3=\",S_CD\n",
"\n",
"#NOTE:The answer for the following example for section 1 and section 2\n",
"#are incorrect due to rounding in the textbook\n",
"#Computed values are correct"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The stress at the three sections is given as\n",
"Stress at section 1= 3333.0 section 2= 2778.0 section 3= 4375.0\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.1.2, Page No:10"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable Decleration\n",
"Ay=40 #Vertical Reaction at A in kN\n",
"Hy=60 #Vertical Reaction at H in kN\n",
"Hx=0 #Horizontal Reaction at H in kN\n",
"y=3 #Height in m\n",
"x=5 #Distance in m\n",
"p=4 #Panel distance in m\n",
"A=900 #Area of the member in mm^2\n",
"P_C=30 #Force at point C in kN\n",
"\n",
"#Calculation\n",
"#Part 1\n",
"#Applying summation of forces in the x and y direction and equating to zero\n",
"P_AB=(-Ay)*(x*y**-1) #Force in member AB in kN\n",
"P_AC=-(p*x**-1*P_AB) #Force in member AC in kN\n",
"#Using stress=force/area\n",
"S_AC=(P_AC/A)*10**3 #Stress in member AC in MPa (T)\n",
"\n",
"#Part 2\n",
"#Sum of moments about point E to zero\n",
"P_BD=(Ay*p*2-(P_C*p))*y**-1 #Force in memeber AB in kN (C)\n",
"S_BD=(P_BD/A)*10**3 #Stress in member in MPa (C)\n",
"\n",
"#Result\n",
"print \"The Stress in member AC is\",round(S_AC,1),\"MPa (T)\"\n",
"print \"The Stress in member BD is\",round(S_BD,1),\"MPa (C)\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The Stress in member AC is 59.3 MPa (T)\n",
"The Stress in member BD is 74.1 MPa (C)\n"
]
}
],
"prompt_number": 12
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.1.3, Page No:11"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"import numpy as num\n",
"\n",
"#Variable Decleration\n",
"A_AB=800 #Area of member AB in m^2\n",
"A_AC=400 #Area of member AC in m^2\n",
"W_AB=110 #Safe value of stress in Pa for AB\n",
"W_AC=120 #Safe value of stress in Pa for AC\n",
"theta1=60*3.14*180**-1 #Angle in radians\n",
"theta2=40*3.14*180**-1 #Angle in radians \n",
"\n",
"#Calculations\n",
"#Applying sum of forces \n",
"#Solving by matrix method putting W as 1\n",
"A=num.array([[-cos(theta1),cos(theta2)],[sin(theta1),sin(theta2)]])\n",
"B=num.array([[1],[1]])\n",
"C=inv(A)\n",
"D=C*B\n",
"\n",
"#Using newtons third law\n",
"#Two values of W hence the change in the notation\n",
"W1=(W_AB*A_AB)*(D[1,1])**-1 #Weight W in N\n",
"W2=(W_AC*A_AC)*(D[0,1])**-1 #Weight W in N\n",
"\n",
"#Result\n",
"print \"The maximum value of W allowable is\",round(W2*1000**-1,1),\"kN\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The maximum value of W allowable is 61.7 kN\n"
]
}
],
"prompt_number": 48
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.1.4, Page No:19"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable Decleration\n",
"d=3*4**-1 #Rivet diameter in inches\n",
"t=7*8**-1 #Thickness of the plate in inches\n",
"tau=14000 #Shear stress limit in psi\n",
"sigma_b=18000 #Normal stress limit in psi\n",
"\n",
"#Calculations\n",
"#Design Shear Stress in Rivets\n",
"V=tau*(d**2*(pi/4))*4 #Shear force maximum allowable in lb\n",
"#Design for bearing stress in plate\n",
"Pb=sigma_b*t*d*4 #lb\n",
"\n",
"#Result\n",
"print \"The maximum load that the joint can carry is\",round(V),\"lb\"\n",
"\n",
"#NOTE:The answer in the textbook is off by 40lb"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The maximum load that the joint can carry is 24740.0 lb\n"
]
}
],
"prompt_number": 55
}
],
"metadata": {}
}
]
}