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diff --git a/Advanced_Strength_and_Applied_Elasticity/Chapter6.ipynb b/Advanced_Strength_and_Applied_Elasticity/Chapter6.ipynb new file mode 100755 index 00000000..aad26d04 --- /dev/null +++ b/Advanced_Strength_and_Applied_Elasticity/Chapter6.ipynb @@ -0,0 +1,151 @@ +{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:3332a69be3bda89d0bbf53dbcf52a61ce9890c1e2f91bf32984da88ae13bb216"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "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": {}
+ }
+ ]
+}
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