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+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 7 Internal Forces"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Ex 7.1 Page no 261"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "A_y = 8 kN\n",
+ "NC = 4 kN\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Example 7.1\n",
+ "\n",
+ "# Calculation\n",
+ "# Applying +ΣF_y(upward) = 0 Refer fig 7-4b\n",
+ "A_y = 16+4-12 #[kilo Newton]\n",
+ "\n",
+ "# Applying +ΣF_y(upward) = 0 to segment AB\n",
+ "NB = 8 #[kilo Newton]\n",
+ "\n",
+ "# Applying +ΣF_y(upward) = 0 to segment DC\n",
+ "NC = 4 #[kilo Newton]\n",
+ "\n",
+ "# Result\n",
+ "print\"A_y = \",(A_y),\"kN\"\n",
+ "print\"NC = \",(NC),\"kN\"\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Ex 7.2 Page no 262"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "TB = 5 N.m\n",
+ "TC = 25 N.m\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Example 7.2\n",
+ "\n",
+ "# Calculation\n",
+ "# Applying +ΣM_x = 0 Refer fig 7-5b\n",
+ "TD = -10+15+20 #[Newton meter]\n",
+ "\n",
+ "# Applying +ΣM_x = 0 to segment AB\n",
+ "TB = -10+15 #[Newton meter]\n",
+ "\n",
+ "# Applying +ΣM_x = 0 to segment CD\n",
+ "TC = 25 #[Newton meter]\n",
+ "\n",
+ "# Result\n",
+ "print\"TB = \",(TB),\"N.m\"\n",
+ "print\"TC = \",(TC),\"N.m\"\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Ex 7.3 Page no 263"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "NB = 0 kN\n",
+ "VB = 5 kN\n",
+ "MB = 15 kN.m\n",
+ "NC = 0 kN\n",
+ "VC = 1 kN\n",
+ "MC = 15 kN.m\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Example 7.3\n",
+ "from __future__ import division\n",
+ "\n",
+ "# Calculation\n",
+ "# Applying +ΣMD(counterclockwise) = 0 Refer fig 7-6b\n",
+ "A_y = (9+6*6)/9\n",
+ "\n",
+ "# Consider segment AB\n",
+ "# Applying +ΣF_x(right) = 0\n",
+ "NB = 0 #[kilo Newton]\n",
+ "# Applying +ΣF_y(upward) = 0\n",
+ "VB = 5 #[kilo Newton]\n",
+ "# Applying +ΣMB(counterclockwise) = 0 \n",
+ "MB = 5*3 #[kilo Newton meter]\n",
+ "\n",
+ "# Consider segment AC\n",
+ "# Applying +ΣF_x(right) = 0\n",
+ "NC = 0 #[kilo Newton]\n",
+ "# Applying +ΣF_y(upward) = 0\n",
+ "VC = 6-5 #[kilo Newton]\n",
+ "# Applying +ΣMC(counterclockwise) = 0\n",
+ "MC = 5*3 #[kilo Newton meter]\n",
+ "\n",
+ "# Result\n",
+ "print\"NB = \",(NB),\"kN\"\n",
+ "print\"VB = \",(VB),\"kN\"\n",
+ "print\"MB = \",(MB),\"kN.m\"\n",
+ "print\"NC = \",(NB),\"kN\"\n",
+ "print\"VC = \",(VC),\"kN\"\n",
+ "print\"MC = \",(MC),\"kN.m\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Ex 7.4 Page no 264"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "NB = 266.7 N\n",
+ "VB = 0 N\n",
+ "MB = 400 N.m\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Example 7.4\n",
+ "from __future__ import division\n",
+ "\n",
+ "# Calculation\n",
+ "# Refer fig 7-7b\n",
+ "# Applying +ΣMA(counterclockwise) = 0\n",
+ "FDC = (400*4)/((3/5)*8) #[Newton]\n",
+ "# Applying +ΣF_x(right) = 0\n",
+ "A_x = (4/5)*333.3 #[Newton]\n",
+ "# Applying +ΣF_y(upward) = 0\n",
+ "A_y = 400-((3/5)*333.3) #[Newton]\n",
+ "\n",
+ "# Applying equations of equilibrium to segment AB\n",
+ "# Applying +ΣF_x(right) = 0\n",
+ "NB = 266.7 #[Newton]\n",
+ "# Applying +ΣF_y(upward) = 0\n",
+ "VB = 200-200 #[Newton]\n",
+ "# Applying +ΣMB(counterclockwise) = 0\n",
+ "MB = 200*4-200*2 #[Newton meter]\n",
+ "\n",
+ "# Result\n",
+ "print\"NB = \",(NB),\"N\"\n",
+ "print\"VB = \",(VB),\"N\"\n",
+ "print\"MB = \",(MB),\"N.m\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Ex 7.5 Page no 265"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "VE = 600.0 N\n",
+ "NE = 600.0 N\n",
+ "ME = 300.0 N.m\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Example 7.5\n",
+ "import math\n",
+ "\n",
+ "# Calculation\n",
+ "# Using +ΣF_y(upward) = 0 Refer fig 7-8b\n",
+ "R = round(600/math.sin(math.pi*45/180),1) #[Newton]\n",
+ "# Applying equations of equilibrium \n",
+ "# Applying +ΣF_x(right) = 0\n",
+ "VE = round(R*math.cos(math.pi*45/180),1) #[Newton]\n",
+ "# Applying +ΣF_y(upward) = 0\n",
+ "NE = round(R*math.sin(math.pi*45/180),1) #[Newton]\n",
+ "# Applying +ΣME(counterclockwise) = 0\n",
+ "ME = round(R*math.cos(math.pi*45/180)*0.5,1) #[Newton meter]\n",
+ "\n",
+ "# Result\n",
+ "print\"VE = \",(VE),\"N\"\n",
+ "print\"NE = \",(NE),\"N\"\n",
+ "print\"ME = \",(ME),\"N.m\"\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Ex 7.6 Page no 266"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "MA_x = -19.1 kN.m\n",
+ "MA_y = 70.9 kN.m\n",
+ "MA_z = -40.5 kN.m\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Example 7.6\n",
+ "from __future__ import division\n",
+ "import numpy as np\n",
+ "\n",
+ "# Calculation\n",
+ "W = 650*9.81 #[kilo Newton]\n",
+ "Fw = 900/(6*2.5) #[kilo Newton]\n",
+ "# Using +ΣF_x(right) = 0\n",
+ "FA_x = 13.5 #[kilo Newton]\n",
+ "FA_y = 0 #[kilo Newton]\n",
+ "FA_z = 6.376 #[kilo Newton]\n",
+ "# Using ΣMA = 0, MA + r X (Fw + W)\n",
+ "a = np.cross([0,3,5.25],[-13.5,0,6.376])\n",
+ "MA_x = round(-a[0],1) #[kilo Newton meter]\n",
+ "MA_y = round(-a[1],1) #[kilo Newton meter]\n",
+ "MA_z = round(-a[2],1) #[kilo Newton meter]\n",
+ "\n",
+ "# Result\n",
+ "print\"MA_x = \",(MA_x),\"kN.m\"\n",
+ "print\"MA_y = \",(MA_y),\"kN.m\"\n",
+ "print\"MA_z = \",(MA_z),\"kN.m\" # Correction in MA_z\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Ex 7.13 Page no 286"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 30,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "TBC = 10.2 kN\n",
+ "TAB = 13.6 kN\n",
+ "TCD = 9.5 kN\n",
+ "TED = 11.8 kN\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Example 7.13\n",
+ "from __future__ import division\n",
+ "import math \n",
+ "\n",
+ "# Calculation\n",
+ "# Consider free body diagram Refer fig 7-21b\n",
+ "# Using +ΣME(counterclockwise) = 0\n",
+ "A_y = (4*15+15*10+3*2)/18 #[kilo Newton]\n",
+ "# Using +ΣF_y(upward) = 0\n",
+ "E_y = -12+4+15+3 #[kilo Newton]\n",
+ "\n",
+ "# Consider leftmost section which cuts cable BC Refer fig 7-21b\n",
+ "# Using +ΣMC(counterclockwise) = 0\n",
+ "A_x = (12*8-4*5)/12 #[kilo Newton]\n",
+ "thetaBC = round(math.degrees(math.atan((12-4)/6.33)),1) #[Degrees]\n",
+ "# Using +ΣF_x(right) = 0\n",
+ "TBC = round(6.33/math.cos(math.pi*thetaBC/180),1) #[kilo Newton]\n",
+ "thetaAB = round(math.degrees(math.atan(12/6.33)),1) #[Degrees]\n",
+ "\n",
+ "# Applying +ΣF_x(right) = 0 at point A\n",
+ "TAB = round(12/math.sin(math.pi*thetaAB/180),1) #[kilo Newton]\n",
+ "thetaCD = round(math.degrees(math.atan((-10.2*math.sin(math.pi*51.6/180)+15)/(10.2*math.cos(math.pi*51.6/180)))),1) #[Degrees]\n",
+ "\n",
+ "# Applying +ΣF_x(right) = 0 at point C\n",
+ "TCD = round((10.2*math.cos(math.pi*51.6/180))/math.cos(math.pi*thetaCD/180),1) #[kilo Newton]\n",
+ "thetaED = round(math.degrees(math.atan(10/6.33)),1) #[Degrees]\n",
+ "\n",
+ "# Applying +ΣF_x(right) = 0 at point E\n",
+ "TED = round(10/math.sin(math.pi*thetaED/180),1) #[kilo Newton]\n",
+ "\n",
+ "print\"TBC = \",(TBC),\"kN\"\n",
+ "print\"TAB = \",(TAB),\"kN\"\n",
+ "print\"TCD = \",(TCD),\"kN\"\n",
+ "print\"TED = \",(TED),\"kN\" "
+ ]
+ },
+ {
+ "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
+}
generated by cgit (git 2.34.1) at 2024-12-19 11:51:50 +0000