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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 8:Shear Stresses in Beams"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Problem 8.6,page no.355"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"import math\n",
"#Given\n",
"#Variable declaration\n",
"D=100 #Diameter in mm\n",
"R=D/2 #Radius in mm\n",
"F=5*10**3 #Shear force in N\n",
"y=40 #given distance from N.A. in mm\n",
"\n",
"#Calculation\n",
"#case(i):Average shear stress \n",
"A=math.pi*R**2\n",
"tau_avg=round(F/A,4)\n",
"#case(ii):Maximum shear stress for a circular section\n",
"tau_max=round(4/3*tau_avg,4)\n",
"#case(iii):Shear stress at a distance 40mm from N.A.\n",
"I=math.pi/64*D**4\n",
"tau=float(str(F/(3*I)*(R**2-y**2))[:6])\n",
"\n",
"#Result\n",
"print \"Average shear stress =\",tau_avg,\"N/mm^2\"\n",
"print \"Maximum shear stress =\",tau_max,\"N/mm^2\"\n",
"print \"Shear stress at a distance 40mm from N.A. =\",tau,\"N/mm^2\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Average shear stress = 0.6366 N/mm^2\n",
"Maximum shear stress = 0.8488 N/mm^2\n",
"Shear stress at a distance 40mm from N.A. = 0.3055 N/mm^2\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Problem 8.12,page no.369"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"import math\n",
"\n",
"#Given\n",
"#Variable declaration\n",
"F=50*10**3 #Shear force in N\n",
"b=250 #Base width in mm\n",
"h=200 #height in mm\n",
"\n",
"#Calculation\n",
"tau_max=int((3*F)/(b*h)) #Maximum shear stress in N/sq.mm\n",
"tau=round((8*F)/(3*b*h),2) #Shear stress at N.A. in N/sq.mm\n",
"\n",
"#Result\n",
"print \"Maximum shear stress =\",tau_max,\"N/mm^2\"\n",
"print \"Shear stress at N.A. =\",tau,\"N/mm^2\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Maximum shear stress = 3 N/mm^2\n",
"Shear stress at N.A. = 2.67 N/mm^2\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}
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