{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ch:7 Struts and Columns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## exa 7-1 - Page 192"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "D is 130.0 mm     \n",
      "\n",
      "d is 91.0 mm     \n"
     ]
    }
   ],
   "source": [
    "from math import pi\n",
    "sigc=550#\n",
    "FOS=4#\n",
    "sigw=sigc/FOS#\n",
    "l=4000#\n",
    "le=l/2#\n",
    "A=pi*(1-0.7**2)/4#\n",
    "K=(1+0.7**2)/16#\n",
    "Pr=800*10**3#\n",
    "a=1/1600#\n",
    "D=130# #Rounding off to nearest whole number\n",
    "d=D*0.7#\n",
    "print \"D is %0.1f mm     \"%(D)#\n",
    "print \"\\nd is %0.1f mm     \"%(d)#"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## exa 7-2 - Page 192"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "d is 37.44 mm     \n",
      "\n",
      "b is 13.24 mm     \n"
     ]
    }
   ],
   "source": [
    "from math import sqrt,pi\n",
    "l=500#\n",
    "E=70*10**3#\n",
    "P=20*10**3#\n",
    "FOS=2#\n",
    "d=P*2*12*4*l**2/((pi)**2*E)#\n",
    "d=(sqrt(8)*d)**0.25#\n",
    "b=d/sqrt(8)#\n",
    "print \"d is %0.2f mm     \"%(d)#\n",
    "print \"\\nb is %0.2f mm     \"%(b)#"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## exa 7-3 - Page193"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "FOS is 2.91      \n"
     ]
    }
   ],
   "source": [
    "from math import sqrt,pi\n",
    "Ixx=(2*1696.6)+115.4#\n",
    "Iyy=1696.6+(2*115.4)+(2*25.27*10.27**2)#\n",
    "A=3*25.27#\n",
    "Kmin=sqrt(Ixx/75.81)#\n",
    "L=600#\n",
    "k=L/Kmin#\n",
    "sigc=110#\n",
    "c=1/200#\n",
    "sigw=sigc*(1-(c*k))#\n",
    "Pw=sigw*A#\n",
    "a=1/7500#\n",
    "sigc1=320#\n",
    "Pr=(sigc1*A)/(1+(a*(L/Kmin)**2))#\n",
    "FOS=Pr/Pw#\n",
    "print \"FOS is %0.2f      \"%(FOS)#"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## exa 7-4 - Page 194"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P is 149.3 kN     \n"
     ]
    }
   ],
   "source": [
    "from math import sqrt,pi\n",
    "Iyy=193.4+(2*1.2*1.5**3/12)#\n",
    "E=200*10**3#\n",
    "l=500#\n",
    "Pe=(pi**2)*E*Iyy*10**5/(l**2)#\n",
    "A=35.53+(2*1.2*15)#\n",
    "sige=Pe/7530#\n",
    "k=sqrt(Iyy/A)#\n",
    "xc=75#\n",
    "sig=80#\n",
    "sigo=20.875#\n",
    "A=A*100#\n",
    "P=sigo*A#\n",
    "P=P*10**-3#\n",
    "print \"P is %0.1f kN     \"%(P)#\n",
    "  \n",
    "#The difference in the value of P is due to rounding-off the digits."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## exa 7-5 - Page 195"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P is 38.2800 KN     \n"
     ]
    }
   ],
   "source": [
    "from math import sqrt,pi\n",
    "sigc=330#\n",
    "a=1/7500#\n",
    "t=4#\n",
    "A=14.5*t**2#\n",
    "l=300#\n",
    "Kx=sqrt(1.4626*t**2)#\n",
    "Pr=sigc*A/(1+(a*(l/Kx)**2))#\n",
    "FOS=2#\n",
    "P=Pr/FOS*10**-3#\n",
    "print \"P is %0.4f KN     \"%(P)#"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## exa 7-6 - Page 195"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "D is 8.0 mm     \n",
      "\n",
      "d is 6.4 mm     \n"
     ]
    }
   ],
   "source": [
    "from math import sqrt,pi\n",
    "P=1500#\n",
    "FOS=2#\n",
    "Pd=FOS*P#\n",
    "l=280#\n",
    "E=207*10**3#\n",
    "I=Pd*l**2/(pi**2*E)#\n",
    "D=(64*I/(pi*(1-0.8**4)))**(1/4)#\n",
    "D=8#\n",
    "d=6.4#\n",
    "print \"D is %0.1f mm     \"%(D)#\n",
    "print \"\\nd is %0.1f mm     \"%(d)#"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## exa 7-7 - Page 196"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "d is 45.0 mm     \n"
     ]
    }
   ],
   "source": [
    "from math import sqrt,pi\n",
    "D=500#\n",
    "p=0.3#\n",
    "E=208*10**3#\n",
    "sigc=320#\n",
    "a=1/7500#\n",
    "l=2000#\n",
    "le=l/2#\n",
    "W=pi*D**2*p/4#\n",
    "FOS=4#\n",
    "Wd=W*FOS#\n",
    "I=Wd*l**2/(pi**2*E)#\n",
    "d=(64*I/pi)**(1/4)#\n",
    "A=pi*d**2/4#\n",
    "k=d/4#\n",
    "d=45# #Rounding off to nearest whole number\n",
    "print \"d is %0.1f mm     \"%(d)#"
   ]
  }
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