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diff --git a/Engineering_Mechanics_Statics_and_Dynamics_by_Hibbeler_and_Gupta/Chapter_6.ipynb b/Engineering_Mechanics_Statics_and_Dynamics_by_Hibbeler_and_Gupta/Chapter_6.ipynb new file mode 100644 index 00000000..4fe7e652 --- /dev/null +++ b/Engineering_Mechanics_Statics_and_Dynamics_by_Hibbeler_and_Gupta/Chapter_6.ipynb @@ -0,0 +1,768 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 6 Structural Analysis" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 6.1 Page No 212" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "FBC = 707.1 N\n", + "FBA = 500.0 N\n", + "FCA = 500.0 N\n", + "C_y = 500.0 N\n", + "A_x = 500 N\n", + "A_y = 500 N\n" + ] + } + ], + "source": [ + "# Example 6.1\n", + "import math\n", + "\n", + "# Calculation\n", + "\n", + "# Joint B\n", + "# Using +ΣF_x(right) = 0\n", + "FBC = round(500/math.sin(math.pi*45/180),1) #[Newton]\n", + "\n", + "# Using +ΣF_y(upward) = 0\n", + "FBA = round(FBC*math.cos(math.pi*45/180),1) #[Newton]\n", + "\n", + "# Joint C\n", + "# Using +ΣF_x(right) = 0\n", + "FCA = round(FBC*math.cos(math.pi*45/180),1) #[Newton]\n", + "\n", + "# Using +ΣF_y(upward) = 0\n", + "C_y = round(FBC*math.sin(math.pi*45/180),1) #[Newton]\n", + "\n", + "# Joint A\n", + "# # Using +ΣF_x(right) = 0\n", + "A_x = 500 #[Newton]\n", + "A_y = 500 #[Newton]\n", + "\n", + "# Result\n", + "print\"FBC = \",(FBC),\"N\"\n", + "print\"FBA = \",(FBA),\"N\"\n", + "print\"FCA = \",(FCA),\"N\"\n", + "print\"C_y = \",(C_y),\"N\"\n", + "print\"A_x = \",(A_x),\"N\"\n", + "print\"A_y = \",(A_y),\"N\"\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 6.2 Page No 213" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "FCB = 5.02 kN\n", + "FCD = 4.1 kN\n", + "FDA = 4.1 kN\n", + "FDB = 4.1 kN\n" + ] + } + ], + "source": [ + "# Example 6.2\n", + "import math\n", + "import numpy as np\n", + "\n", + "# Calculation\n", + "# Joint C\n", + "# Using +ΣF_x(right) = 0 and +ΣF_y(upward) = 0\n", + "a = np.array([[-math.cos(math.pi*30/180),math.sin(math.pi*45/180)],[math.sin(math.pi*30/180),-math.cos(math.pi*45/180)]])\n", + "b = np.array([0,-1.5])\n", + "x = np.linalg.solve(a, b)\n", + "FCD = round(x[0],2) #[kilo Newton]\n", + "FCB = round(x[1],2) #[kilo Newton]\n", + "\n", + "# Calculation\n", + "# Joint D\n", + "# Using +ΣF_x(right) = 0\n", + "FDA = round(FCD*math.cos(math.pi*30/180)/math.cos(math.pi*30/180),2) #[kilo Newton]\n", + "# Using +ΣF_y(upward) = 0\n", + "FDB = round(2*FCD*math.sin(math.pi*30/180),2) #[kilo Newton]\n", + "\n", + "# Result\n", + "print\"FCB = \",(FCB),\"kN\"\n", + "print\"FCD = \",(FCD),\"kN\"\n", + "print\"FDA = \",(FDA),\"kN\"\n", + "print\"FDB = \",(FDB),\"kN\"\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 6.3 Page No 214" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "FAB = 750.0 N\n", + "FAD = 450.0 N\n", + "FDB = -250.0 N\n", + "FDC = 200.0 N\n", + "FCB = 600 N\n" + ] + } + ], + "source": [ + "# Example 6.3\n", + "from __future__ import division\n", + "\n", + "# Calculation\n", + "# Using +ΣF_x(right) = 0\n", + "C_x = 600 #[Newton]\n", + "# Using +ΣMC(counterclockwise) = 0\n", + "A_y = (400*3+600*4)/6 #[Newton]\n", + "# Using +ΣF_y(upward) = 0\n", + "C_y = A_y - 400 #[Newton]\n", + "\n", + "# Joint A\n", + "# Using +ΣF_y(upward) = 0\n", + "FAB = 600*(5/4) #[Newton]\n", + "# Using +ΣF_x(right) = 0\n", + "FAD = (3/5)*FAB #[Newton]\n", + "\n", + "# Joint D\n", + "# Using +ΣF_x(right) = 0\n", + "FDB = (450-600)*(5/3) #[Newton]\n", + "# Using +ΣF_y(upward) = 0\n", + "FDC = (-4/5)*(FDB) #[Newton]\n", + "\n", + "# Joint C\n", + "# Using +ΣF_x(right) = 0\n", + "FCB = 600 #[Newton]\n", + "\n", + "# Result\n", + "print\"FAB = \",(FAB),\"N\"\n", + "print\"FAD = \",(FAD),\"N\"\n", + "print\"FDB = \",(FDB),\"N\"\n", + "print\"FDC = \",(FDC),\"N\"\n", + "print\"FCB = \",(FCB),\"N\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "## Ex 6.4 Page No 218" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "FGC = 0 N\n", + "FDF= 0 N\n" + ] + } + ], + "source": [ + "# Example 6.4\n", + "\n", + "# Calculation\n", + "# Using +ΣF_y(upward) = 0 at joint G\n", + "FGC = 0 #[Newton]\n", + "\n", + "# GC is a zero force menber means that 5-kN load at C must be supported by members CB,CH,CF and CD\n", + "# Using +ΣF_y(upward) = 0 at joint F\n", + "FDF = 0 #[Newton]\n", + "\n", + "# Result\n", + "print\"FGC = \",(FGC),\"N\"\n", + "print\"FDF= \",(FDF),\"N\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 6.5 Page No 225" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "FBC = 800.0 N\n", + "FGE = 800.0 N\n", + "FGC = 500.0 N\n" + ] + } + ], + "source": [ + "# Example 6.5\n", + "from __future__ import division\n", + "\n", + "# Calculation\n", + "# Applying equations of equilibrium\n", + "# Using +ΣF_x(right) = 0\n", + "A_x = 400 #[Newton]\n", + "\n", + "# Using +ΣMA(counterclockwise) = 0\n", + "D_y = (400*3+1200*8)/12 #[Newton]\n", + "\n", + "# Using +ΣF_y(upward) = 0\n", + "A_y = 1200-900 #[Newton]\n", + "\n", + "# Using +ΣMG(counterclockwise) = 0\n", + "FBC = (400*3+300*4)/3 #[Newton]\n", + "\n", + "# Using +ΣMC(counterclockwise) = 0\n", + "FGE = (300*8)/3 #[Newton]\n", + "\n", + "# Using +ΣF_y(upward) = 0\n", + "FGC = (300*5)/3 #[Newton]\n", + "\n", + "# Result\n", + "print\"FBC = \",(FBC),\"N\"\n", + "print\"FGE = \",(FGE),\"N\"\n", + "print\"FGC = \",(FGC),\"N\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 6.6 Page No 226" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "FCF = 0.589 kN\n" + ] + } + ], + "source": [ + "# Example 6.6\n", + "import math\n", + "from __future__ import division\n", + "\n", + "# Calculation\n", + "# Using +ΣMO(counterclockwise) = 0\n", + "FCF = round((3*8-4.75*4)/(12*math.sin(math.pi*45/180)),3) #[kilo Newton]\n", + "\n", + "# Result\n", + "print\"FCF = \",(FCF),\"kN\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 6.7 Page No 227" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "FEB = 2000.0 N\n" + ] + } + ], + "source": [ + "# Example 6.7\n", + "import math\n", + "\n", + "# Calculation\n", + "# Using +ΣMB(counterclockwise) = 0\n", + "FED = (-1000*4-3000*2+4000*4)/(math.sin(math.pi*30/180)*4) #[Newton]\n", + "\n", + "# Using +ΣF_x(right) = 0 for section bb Fig 6-18c\n", + "FEF = 3000*math.cos(math.pi*30/180)/math.cos(math.pi*30/180) #[Newton]\n", + "\n", + "# Using +ΣF_y(upward) = 0\n", + "FEB = 2*3000*math.sin(math.pi*30/180)-1000 #[Newton]\n", + "\n", + "# Result\n", + "print\"FEB = \",(FEB),\"N\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 6.8 Page No 231" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "FAE = 0.0 kN\n", + "FAB = 4.0 kN\n", + "FAC = 0.0 kN\n", + "RB = 5.66 kN\n", + "FBE = 5.66 kN\n", + "FBD = 2.0 kN\n", + "FDE = 0 kN\n", + "FDC = 0 kN\n", + "FCE = 0 kN\n" + ] + } + ], + "source": [ + "# Example 6.8\n", + "import numpy as np\n", + "import math\n", + "\n", + "# Calculation\n", + "# At joint A, ΣF_x = 0, ΣF_y = 0, ΣF_z = 0\n", + "a = np.array([[0.577,0,0],[0.577,1,0],[-0.577,0,-1]])\n", + "b = np.array([0,4,0])\n", + "x = np.linalg.solve(a, b)\n", + "FAE = round(x[0],2) #[kilo Newton]\n", + "FAB = round(x[1],2) #[kilo Newton]\n", + "FAC = round(x[2],2) #[kilo Newton]\n", + "\n", + "# At joint B, ΣF_x = 0, ΣF_y = 0, ΣF_z = 0\n", + "a = np.array([[-math.cos(math.pi*45/180),0.707,0],[math.sin(math.pi*45/180),0,0],[0,-0.707,1]])\n", + "b = np.array([0,4,-2])\n", + "x = np.linalg.solve(a, b)\n", + "RB = round(x[0],2) #[kilo Newton]\n", + "FBE = round(x[1],2) #[kilo Newton]\n", + "FBD = round(x[2],2) #[kilo Newton]\n", + "\n", + "# The scalar equation of equilibrium can be applied at joints D and C\n", + "FDE = FDC = FCE = 0 #[kilo Newton]\n", + "\n", + "# Result\n", + "print\"FAE = \",(FAE),\"kN\"\n", + "print\"FAB = \",(FAB),\"kN\"\n", + "print\"FAC = \",(-FAC),\"kN\"\n", + "print\"RB = \",(RB),\"kN\"\n", + "print\"FBE = \",(FBE),\"kN\"\n", + "print\"FBD = \",(FBD),\"kN\"\n", + "print\"FDE = \",(FDE),\"kN\"\n", + "print\"FDC = \",(FDC),\"kN\"\n", + "print\"FCE = \",(FCE),\"kN\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 6.14 Page No 241" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "C_x = 577.4 N\n", + "C_y = 1000.0 N\n" + ] + } + ], + "source": [ + "# Example 6.14\n", + "import math\n", + "from __future__ import division\n", + "\n", + "# Calculation\n", + "\n", + "# Solution 1\n", + "# Applying equations of equilibrium to member CB\n", + "# Using +ΣMC(counterclockwise) = 0\n", + "FAB = round((2000*2)/(math.sin(math.pi*60/180)*4),1) #[Newton meter]\n", + "# Using +ΣF_x(right) = 0\n", + "C_x = round(FAB*math.cos(math.pi*60/180),1) #[Newton]\n", + "# Using +ΣF_y(upward) = 0\n", + "C_y = round(-FAB*math.sin(math.pi*60/180)+2000,1) #[Newton]\n", + "\n", + "# Solution 2 \n", + "# Using +ΣMC(counterclockwise) = 0 at Member BC\n", + "B_y = (2000*2)/4 #[Newton]\n", + "# Using +ΣMA(counterclockwise) = 0 at Member AB\n", + "B_x = round(B_y*3*math.cos(math.pi*60/180)/(3*math.sin(math.pi*60/180)),1) #[Newton]\n", + "# Using +ΣF_y(upward) = 0 at member BC\n", + "C_x = B_x #[Newton]\n", + "C_y = 2000-B_y #[Newton]\n", + "# Result\n", + "print\"C_x = \",(C_x),\"N\"\n", + "print\"C_y = \",(C_y),\"N\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 6.15 Page No 242" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "A_x = 6.0 kN\n", + "A_y = 12.0 kN\n", + "MA = 32.0 kN.m\n", + "B_x = 0 kN\n", + "B_y = 4.0 kN\n", + "C_y = 4.0 kN\n" + ] + } + ], + "source": [ + "# Example 6.15\n", + "from __future__ import division\n", + "\n", + "# Calculation\n", + "# Using +ΣF_x(right) = 0 at member BC\n", + "B_x = 0 #[kilo Newton]\n", + "# Using +ΣMB(counterclockwise) = 0 at member BC\n", + "C_y = (8*1)/2 #[kilo Newton]\n", + "# Using +ΣF_y(upward) = 0 at member BC\n", + "B_y = 8-C_y #[kilo Newton]\n", + "# Using +ΣF_x(right) = 0 at member AB\n", + "A_x = 10*(3/5)-B_x #[kilo Newton]\n", + "# Using +ΣMA(counterclockwise) = 0 at member AB\n", + "MA = 10*(4/5)*2+B_y*4 #[kilo Newton meter]\n", + "# Using +ΣF_y(upward) = 0 at member AB\n", + "A_y = 10*(4/5)+B_y #[kilo Newton]\n", + "\n", + "# Result\n", + "print\"A_x = \",(A_x),\"kN\"\n", + "print\"A_y = \",(A_y),\"kN\"\n", + "print\"MA = \",(MA),\"kN.m\"\n", + "print\"B_x = \",(B_x),\"kN\"\n", + "print\"B_y = \",(B_y),\"kN\"\n", + "print\"C_y = \",(C_y),\"kN\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 6.16 Page No 243" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "C_x = 1226.3 N\n", + "C_y = -245.3 N\n" + ] + } + ], + "source": [ + "# Example 6.16\n", + "import math\n", + "\n", + "# Calculation\n", + "# Using +ΣMA(counterclockwise) = 0\n", + "D_x = (981*2)/2.8 #[Newton]\n", + "# Using +ΣF_x(right) = 0\n", + "A_x = D_x #[Newton]\n", + "# Using +ΣF_y(upward) = 0\n", + "A_y = 981 #[Newton]\n", + "\n", + "# Consider member CEF\n", + "# Using +ΣMC(counterclockwise) = 0\n", + "FB = round((-981*2)/(math.sin(math.pi*45/180)*1.6),1) #[Newton]\n", + "# Using +ΣF_x(right) = 0\n", + "C_x = round(-FB*math.cos(math.pi*45/180),1) #[Newton]\n", + "# Using +ΣF_y(upward) = 0\n", + "C_y = round(FB*math.sin(math.pi*45/180)+981,1) #[Newton]\n", + "\n", + "# Result\n", + "print\"C_x = \",(C_x),\"N\"\n", + "print\"C_y = \",(C_y),\"N\"" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "## Ex 6.17 Page No 243" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "B_x = 18.2 N\n", + "B_y = 20 N\n", + "D_x = 0 N\n", + "D_y = 20 N\n" + ] + } + ], + "source": [ + "# Example 6.17\n", + "\n", + "# Calculation\n", + "# Consider entire frame\n", + "# Using +ΣMA(counterclockwise) = 0\n", + "C_x = (20*1)/1.1 #[Newton]\n", + "# Using +ΣF_x(right) = 0\n", + "A_x = 18.2 #[Newton]\n", + "A_y = 20 #[Newton]\n", + "\n", + "# Consider member AB\n", + "# Using +ΣF_x(right) = 0\n", + "B_x= 18.2 #[Newton]\n", + "# Using +ΣMB(counterclockwise) = 0\n", + "ND = (20*2)/1 #[Newton]\n", + "# Using +ΣF_y(upward) = 0\n", + "B_y = 40-20 #[Newton]\n", + "\n", + "# Consider Disk\n", + "# Using +ΣF_x(right) = 0\n", + "D_x = 0 #[Newton]\n", + "# Using +ΣF_y(upward) = 0\n", + "D_y = 40-20 #[Newton]\n", + "\n", + "# Result\n", + "print\"B_x = \",(B_x),\"N\"\n", + "print\"B_y = \",(B_y),\"N\"\n", + "print\"D_x = \",(D_x),\"N\"\n", + "print\"D_y = \",(D_y),\"N\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 6.18 Page No 245" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "P = 200 N\n", + "T = 400 N\n", + "R = 800 N\n" + ] + } + ], + "source": [ + "# Example 6.18\n", + "\n", + "# Calculation\n", + "# Using equations of equilibrium\n", + "\n", + "# Pulley A\n", + "# Using +ΣF_y(upward) = 0\n", + "P = 600/3 #[Newton]\n", + "\n", + "# Pulley B\n", + "# Using +ΣF_y(upward) = 0\n", + "T = 2*P #[Newton]\n", + "\n", + "# Pulley C\n", + "# Using +ΣF_y(upward) = 0\n", + "R = 2*P+T #[Newton]\n", + "\n", + "# Result\n", + "print\"P = \",(P),\"N\"\n", + "print\"T = \",(T),\"N\"\n", + "print\"R = \",(R),\"N\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex 6.19 Page No 246" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "B_x = 346.8 N\n", + "B_y = 837.3 N\n", + "FCB = 1659.8 N\n", + "FAB = 1342.7 N\n" + ] + } + ], + "source": [ + "# Example 6.19\n", + "import math\n", + "from __future__ import division\n", + "\n", + "# Calculation\n", + "# Applying equations of equilibrium to pulley B\n", + "# Using +ΣF_x(right) = 0\n", + "B_x = round(490.5*math.cos(math.pi*45/180),1) #[Newton]\n", + "# Using +ΣF_y(upward) = 0\n", + "B_y = round(490.5*math.sin(math.pi*45/180)+490.5,1) #[Newton]\n", + "\n", + "# Applying equations of equilibrium to pin\n", + "# Using +ΣF_y(upward) = 0\n", + "FCB = round((B_y+490.5)*(5/4),1) #[Newton]\n", + "# Using +ΣF_x(right) = 0\n", + "FAB = round((3/5)*FCB+B_x,1) #[Newton]\n", + "\n", + "# Result\n", + "print\"B_x = \",(B_x),\"N\"\n", + "print\"B_y = \",(B_y),\"N\"\n", + "print\"FCB = \",(FCB),\"N\"\n", + "print\"FAB = \",(FAB),\"N\"" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python [default]", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} |