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+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 25 Shear Force and Bending Moment"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Example 25.5 Shear Force and Bending Moment"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The graphs are the solutions\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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TwVbDNzuAdAP3AlOAV0nbjCyS04mEI4CHgd2Bp4E7gYN9oFTxvfZammXy+uvN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\nAAAAAElFTkSuQmCC\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x703ea20>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "%matplotlib inline\n",
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "# Initilization of variables\n",
+ "L_AB=3 # m , length of the beam\n",
+ "L_AC=1 # m\n",
+ "L_BC=2 # m\n",
+ "M_C=12 # kNm , clockwise moment at C\n",
+ "\n",
+ "# Calculations\n",
+ "R_B=M_C/L_AB # kN , moment at A\n",
+ "R_A=-M_C/L_AB # kN , moment at B\n",
+ "\n",
+ "#S.F\n",
+ "F_A=R_A # kN \n",
+ "F_B=R_A # kN\n",
+ "# B.M\n",
+ "M_A=0 # kNm\n",
+ "M_C1=R_A*L_AC #kNm , M_C1 is the BM just before C\n",
+ "M_C2=(R_A*L_AC)+M_C #kNm , M_C2 is the BM just after C\n",
+ "M_B=0 #kNm\n",
+ "\n",
+ "# Plotting SFD & BMD\n",
+ "x=([0],[0.99],[1],[3])\n",
+ "y=([-4],[-4],[-4],[-4])\n",
+ "a=([0],[0.99],[1],[3])\n",
+ "b=([0],[-4],[8],[0])\n",
+ "plt.subplot(2,1,1)\n",
+ "plt.xlabel(\"Span (m)\")\n",
+ "plt.ylabel(\"Shear Force (kN)\")\n",
+ "plt.plot(x,y)\n",
+ "plt.subplot(2,1,2)\n",
+ "plt.plot(a,b)\n",
+ "plt.xlabel(\"Span (m)\")\n",
+ "plt.ylabel(\"Bending Moment (kNm)\")\n",
+ "\n",
+ "#Results\n",
+ "print('The graphs are the solutions')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Example 25.7 Shear Force and Bending Moment"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The graphs are the solutions\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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9dNQZr6O63qWThvFFapddja9fv++r8S1aFM/z67NXORpM9maWOa+/G5BdSKeh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\nPtuKFeHovlOncJ5KpNxUV8MVV4Sucbf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+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x71794a8>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "%matplotlib inline\n",
+ "import matplotlib.pyplot as plt\n",
+ "import numpy as np\n",
+ "\n",
+ "# Initilization of variables\n",
+ "L_AD=8 # m , length of the beam\n",
+ "L_AB=2 # m \n",
+ "L_BC=4 # m\n",
+ "L_CD=2 # m\n",
+ "UDL=1 # kN/m\n",
+ "P=2 # kN , point load at A\n",
+ "# Calculations\n",
+ "\n",
+ "# Solving eqn's 1&2 using matrix to get R_B & R_C as,\n",
+ "A=np.matrix([[1,1],[1,3]])\n",
+ "B=np.matrix([[8],[30]])\n",
+ "C=np.linalg.inv(A)*B\n",
+ "\n",
+ "# SHEAR FORCE\n",
+ "# the term F with suffixes 1 & 2 indicates SF just to left and right \n",
+ "F_A=-P # kN\n",
+ "F_B1=-P # kN\n",
+ "F_B2=-P+C[0] # kN\n",
+ "F_C1=-P+C[0]-(UDL*L_BC) #kN\n",
+ "F_C2=-P+C[0]-(UDL*L_BC)+C[1] # kN\n",
+ "F_D=0\n",
+ "\n",
+ "# BENDING MOMENT\n",
+ "# the term F with suffixes 1 & 2 indicates BM just to left and right\n",
+ "M_A=0 #kNm\n",
+ "M_B=(-P*L_CD) #kNm\n",
+ "M_C=(-P*(L_AB+L_BC))+(C[0]*L_BC)-(UDL*L_BC*(L_BC/2)) #kNm\n",
+ "M_D=0 #kNm\n",
+ "\n",
+ "# LOCATION OF MAXIMUM BM\n",
+ "#Max BM occurs at E at a distance of 2.5 m from B i.e x=L_AE=4.5 m from free end A. Thus max BM is given by taking moment at B\n",
+ "L_AE=4.5 # m , given\n",
+ "M_E=(-2*L_AE)+(4.5*(L_AE-2))-((1/2)*(L_AE-2)**2) #kNm\n",
+ "\n",
+ "# PLOTTING SFD & BMD\n",
+ "x=([0],[1.99],[2],[4.5],[5.99],[6],[8])\n",
+ "y=([-2],[-2],[2.5],[0],[-1.5],[2],[0])\n",
+ "a=([0],[2],[4.5],[6],[8])\n",
+ "b=([0],[-4],[-0.875],[-2],[0])\n",
+ "fig = plt.figure(figsize=(8,8))\n",
+ "ax = fig.add_subplot(311)\n",
+ "plt.subplot(311)\n",
+ "plt.xlabel(\"Span (m)\")\n",
+ "plt.ylabel(\"Shear Force (kN)\")\n",
+ "ax.plot(x,y)\n",
+ "plt.subplot(313)\n",
+ "plt.plot(a,b)\n",
+ "plt.xlabel(\"Span (m)\")\n",
+ "plt.ylabel(\"Bending Moment (kNm)\")\n",
+ "\n",
+ "#Results\n",
+ "print('The graphs are the solutions')"
+ ]
+ }
+ ],
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+ "anaconda-cloud": {},
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+ "display_name": "Python [Root]",
+ "language": "python",
+ "name": "Python [Root]"
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+}