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Diffstat (limited to 'Engineering_Mechanics,_Schaum_Series_by_McLean/chapter8.ipynb')
-rwxr-xr-x | Engineering_Mechanics,_Schaum_Series_by_McLean/chapter8.ipynb | 311 |
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diff --git a/Engineering_Mechanics,_Schaum_Series_by_McLean/chapter8.ipynb b/Engineering_Mechanics,_Schaum_Series_by_McLean/chapter8.ipynb new file mode 100755 index 00000000..06319089 --- /dev/null +++ b/Engineering_Mechanics,_Schaum_Series_by_McLean/chapter8.ipynb @@ -0,0 +1,311 @@ +{
+ "metadata": {
+ "name": "chapter8.ipynb"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 8: Forces in Beams"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.8-1, Page no 118"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of variables\n",
+ "R_A=100 #N\n",
+ "R_B=200 #N\n",
+ "\n",
+ "#Calculations\n",
+ "#Shear force at 2m\n",
+ "V=100 #N\n",
+ "#Moment at 2m\n",
+ "M=R_A*2 #N.m\n",
+ "\n",
+ "#Result\n",
+ "print'The shear force at 2m is +',round(V),\"N\"\n",
+ "print'The moment at 2m is +',round(M),\"N-m\" \n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The shear force at 2m is + 100.0 N\n",
+ "The moment at 2m is + 200.0 N-m\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.8-2, Page no 118"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import matplotlib.pyplot as plt\n",
+ "%matplotlib inline\n",
+ "\n",
+ "#Initilization of variables\n",
+ "#length matrix\n",
+ "L1=[0,3.99,4,5.99,6] #m\n",
+ "#Bending moment matrix\n",
+ "B=[0,400,400,0.00001,0] #N.m\n",
+ "#Shear force plotting\n",
+ "#Here the left side and right side lengths are considered as close as 4 to keep up with right and left distinctions\n",
+ "L=[0,3.99,4,5.99,6]\n",
+ "S=[100,100,-200,-200,0]\n",
+ "g=[0,0,0,0,0]\n",
+ "\n",
+ "#Calculations cum Result\n",
+ "d=transpose(L1)\n",
+ "e=transpose(S)\n",
+ "plt.plot(d,B)\n",
+ "xlabel('distance (m)')\n",
+ "ylabel('B.M (N.m)')\n",
+ "plt.show()\n",
+ "plt.plot(L,e,L,g)\n",
+ "xlabel('distance (m)')\n",
+ "ylabel('S.F (N)')\n",
+ "plt.show()\n",
+ "\n",
+ "print'The graphs are the solutions'\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x514d530>"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x5a12d10>"
+ ]
+ },
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The graphs are the solutions\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.8-3, Page no 119"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import matplotlib.pyplot as plt\n",
+ "%matplotlib inline\n",
+ "\n",
+ "#Initilization of variables\n",
+ "w=196 #N/m\n",
+ "M_app=4000 #N.m\n",
+ "L=6 #m\n",
+ "\n",
+ "#Calculations\n",
+ "#Taking Moment about Point L and equating it to 0\n",
+ "R_r=(M_app+w*L*L*0.5)/(3*L) #N\n",
+ "#Taking Moment about Point R and equating it to 0\n",
+ "R_l= ((((2*L)+(L/2))*(w*L))-(M_app))/(3*L) #N\n",
+ "#finding point of zero shear\n",
+ "a=R_l*w**-1\n",
+ "#defining x\n",
+ "x0=[0,18]\n",
+ "x=[0,0.5,1,1.5,2,2.5,3,3.5,a,4,4.5,5,5.5,6] #for 0<x<6\n",
+ "x1=[6,12] #for6<x<12\n",
+ "x2=[12,18] #for 12<x<18\n",
+ "xv=[6,12,18] #specially for shear force\n",
+ "xo=[12.001,12.002] #Straight line plot\n",
+ "#Shear Force Calculations\n",
+ "#Summing forces in vertical direction and equating to 0\n",
+ "V1=(R_l-w*x[0],R_l-w*x[1],R_l-w*x[2],R_l-w*x[3],R_l-w*x[4],R_l-w*x[5],R_l-w*x[6],R_l-w*x[7],R_l-w*x[8],R_l-w*x[9],R_l-w*x[10],R_l-w*x[11],R_l-w*x[12],R_l-w*x[13]) #N for 0<x<6\n",
+ "V2=(R_l)-(w*L) #N for 6<x<18\n",
+ "#Bending Moment Calculations\n",
+ "M1=(R_l*x[0]-w*x[0]**2*0.5,R_l*x[1]-w*x[1]**2*0.5,R_l*x[2]-w*x[2]**2*0.5,R_l*x[3]-w*x[3]**2*0.5,R_l*x[4]-w*x[4]**2*0.5,R_l*x[5]-w*x[5]**2*0.5,R_l*x[6]-w*x[6]**2*0.5,R_l*x[7]-w*x[7]**2*0.5,R_l*x[8]-w*x[8]**2*0.5,R_l*x[9]-w*x[9]**2*0.5,R_l*x[10]-w*x[10]**2*0.5,R_l*x[11]-w*x[11]**2*0.5,R_l*x[12]-w*x[12]**2*0.5,R_l*x[13]-w*x[13]**2*0.5) #N.m for 0<x<6\n",
+ "M2=(R_l*x1[0]-((w*L)*(x1[0]-3)),R_l*x1[1]-((w*L)*(x1[1]-3))) #N.m for 6<x<12\n",
+ "M3=(R_l*x2[0]-((w*L)*(x2[0]-3))+M_app,R_l*x2[1]-((w*L)*(x2[1]-3))+M_app) #N.m for 12<x<18\n",
+ "Mo=[-1464.8652,2509.3333]\n",
+ "#Maximum bending moment\n",
+ "M_max=R_l*a*0.5 #N.m\n",
+ "\n",
+ "#Plotting SFD & BMD\n",
+ "p=[0,a,5.99,6,11.99,12,17.99,18]\n",
+ "y=[0,1467,1020,1020,-1486,2514,0,0]\n",
+ "z=[0,a,5.99,6,11.99,12,17.99,18]\n",
+ "b=[758,0,-418,-418,-418,-418,-418,0]\n",
+ "g=[0,0,0,0,0,0,0,0]\n",
+ "d=transpose(p)\n",
+ "e=transpose(b)\n",
+ "plt.plot(d,y)\n",
+ "xlabel('distance (m)')\n",
+ "ylabel('B.M (N.m)')\n",
+ "plt.show()\n",
+ "xlabel('distance (m)')\n",
+ "ylabel('S.F (N)')\n",
+ "plt.plot(z,e,z,g)\n",
+ "plt.show()\n",
+ "\n",
+ "#Result\n",
+ "print'The value of reactions are: R_l=',round(R_l),\"N\",'and R_r=',round(R_r),\"N\"\n",
+ "print'The point of maximum bending moment is',round(a,2),\"meters from left support\",'and maximum bending moment is',round(M_max),\"N.m\"\n",
+ "print'The bending moment and shear force diagrams have been plotted'\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x5d1cd10>"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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vfWbxEN/3zDPuvc7vugvatzedRqRxOP3B+scfYfFiqKiY69X5tVY8qhIVFUVx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\nhT7EAAAAAElFTkSuQmCC\n",
+ "text": [
+ "<matplotlib.figure.Figure at 0x60b29d0>"
+ ]
+ },
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The value of reactions are: R_l= 757.0 N and R_r= 418.0 N\n",
+ "The point of maximum bending moment is 3.86 meters from left support and maximum bending moment is 1462.0 N.m\n",
+ "The bending moment and shear force diagrams have been plotted\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.8-4, Page no 121"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initlization of variables\n",
+ "F1=2000 #lb\n",
+ "w=100 #lb/ft\n",
+ "\n",
+ "#Calculations\n",
+ "R_r=(-F1*5+w*14*13)/20 #lb\n",
+ "R_l=(F1*25+w*14*7)/20 #lb\n",
+ "#Shear Force matrix\n",
+ "V=[-2000,-2000,990,990,-410,0] #lb\n",
+ "#Bending Moment matrix\n",
+ "B=[0,-10000,-10000,-4060,840,0]\n",
+ "#Length matrix for shear force\n",
+ "X_v=[0,5,5.0001,11,20.89999,20.9]\n",
+ "#Length matrix for bendimg moment\n",
+ "X_b=[0,4.99,5,11,19.9,20.9]\n",
+ "g=[0,0,0,0,0,0]\n",
+ "\n",
+ "#Plotting of SFD & BMD.\n",
+ "d=transpose(X_v)\n",
+ "e=transpose(V)\n",
+ "plt.plot(d,B)\n",
+ "xlabel('distance (ft)')\n",
+ "ylabel('B.M (lb.ft)')\n",
+ "plt.show()\n",
+ "plt.plot(X_b,e,X_b,g)\n",
+ "xlabel('distance (ft)')\n",
+ "ylabel('S.F (lb)')\n",
+ "plt.show()\n",
+ "\n",
+ "#Result\n",
+ "print'The bending Moment and Shear Force diagrams have been plotted'\n",
+ "#Note\n",
+ "#The textbook does not specify the span and hence there seems to be a disagreement between the textbook and python solution.here the values have just been plotted\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ "<matplotlib.figure.Figure at 0x5c00290>"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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Z2YwaNYrQ0FDCw8OJiIhg27ZtlJaWUlFRQUJCAgBjx45l9erVAKxZs4a0tDQA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\nRMRjFCoiIuIxChUREfEYhYqIiHjM/wMjUibUs6KdhgAAAABJRU5ErkJggg==\n",
+ "text": [
+ "<matplotlib.figure.Figure at 0x5a4e330>"
+ ]
+ },
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The bending Moment and Shear Force diagrams have been plotted\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file |