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{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter6-Torsion of Prismatic Bars"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex2-177"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#calculate applied torque and shearing stress and angle of twist per unit length \n",
"G=28. ##GPa\n",
"t1=0.012\n",
"t2=0.006\n",
"t3=0.01\n",
"t4=0.006\n",
"A=0.125\n",
"h=226000. ##N/m\n",
"Mt=2.*A*h\n",
"print'%s %.2f %s'%(\"applied torque in Nm is=\",Mt,\"\")\n",
"\n",
"tau1=(h/t1)\n",
"print'%s %.2f %s'%(\"shearing stress in Pa is= \",tau1,\"\")\n",
"tau2=(h/t2)\n",
"print'%s %.2f %s'%(\"shearing stress in Pa is= \",tau2,\"\")\n",
"tau3=(h/t3)\n",
"print'%s %.2f %s'%(\"shearing stress in Pa is= \",tau3,\"\")\n",
"tau4=(h/t4)\n",
"print'%s %.2f %s'%(\"shearing stress in Pa is= \",tau4,\"\")\n",
"\n",
"##theta=(h/2*G*A)intc((1/t)ds)\n",
"theta=(h/(2*G*10**9*A))*((0.25/t1)+2*(0.5/t2)+(0.25/t3))\n",
"print'%s %.4f %s'%(\"angle of twist per unit length in rad/m is= \",theta,\"\")\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"applied torque in Nm is= 56500.00 \n",
"shearing stress in Pa is= 18833333.33 \n",
"shearing stress in Pa is= 37666666.67 \n",
"shearing stress in Pa is= 22600000.00 \n",
"shearing stress in Pa is= 37666666.67 \n",
"angle of twist per unit length in rad/m is= 0.0069 \n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex4-pg185"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#calculate torsional rigidity of the beam and maxi longitudinal bending stress in the flange and total angle of twist\n",
"G=80. ##GPa\n",
"E=200. ##GPa\n",
"tf=10. ##mm\n",
"tw=0.007 ##m\n",
"t1=tw\n",
"t2=0.01\n",
"h=0.2 ##m\n",
"b=0.1 ##m\n",
"b2=b\n",
"b1=0.19\n",
"L=2.4 ##m\n",
"If=0.01*0.1**3\n",
"Mt=1200.\n",
"L=2.4\n",
"\n",
"##solution a:\n",
"##C=Mt/theta\n",
"##C=(b1*t1**3+2*b2*t2**3)*(G/3)\n",
"C=((b1*t1**3.+2.*b2*t2**3)/3.)## without substituting the value of G we get C\n",
"print'%s %.8f %s'%(\"torsional rigidity of the beam is= \",C,\"\")\n",
"\n",
"##a=(If*E)/12\n",
"a=If/12.## without substituting the value of E we get a\n",
"print(a)\n",
"##alpha=1/(h*sqrt((E*If)/(2*C)))\n",
"y=math.sqrt((2.5*a)/(2.*C))## without substituting the value of h\n",
"print(y)\n",
"##(1/alpha)==y\n",
"##sigmafmax=(Mfmax*x)/If\n",
"sigmafmax=(3.43*Mt*0.05)/a\n",
"print'%s %.2f %s'%(\"maxi longitudinal bending stress in the flange in MPa is= \",sigmafmax,\"\")\n",
"\n",
"##soluton b:\n",
"si=(Mt/(C*G*10**9))*(L-y*h)\n",
"print'%s %.2f %s'%(\"the angle of twist at the free end in radian is =\",si,\"\")\n",
"si1=(Mt*L)/(C*G*10**9.)\n",
"print'%s %.2f %s'%(\"total angle of twist in radians is= \",si1,\"\")\n",
"\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"torsional rigidity of the beam is= 0.00000009 \n",
"8.33333333333e-07\n",
"3.43291315217\n",
"maxi longitudinal bending stress in the flange in MPa is= 246960000.00 \n",
"the angle of twist at the free end in radian is = 0.29 \n",
"total angle of twist in radians is= 0.41 \n"
]
}
],
"prompt_number": 3
}
],
"metadata": {}
}
]
}
|
