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+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Ch:6 Levers"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 6-1 - Page 171"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " d1 is 20.0 mm \n",
+ "\n",
+ " D is 40.0 mm \n"
+ ]
+ }
+ ],
+ "source": [
+ "from math import sqrt, pi\n",
+ "Del=10#\n",
+ "k=500#\n",
+ "W=k*Del#\n",
+ "#Let load arm be l1\n",
+ "l1=200#\n",
+ "#Let effort arm be l2\n",
+ "l2=500#\n",
+ "P=W*l1/l2#\n",
+ "Ro=sqrt(W**2+P**2)#\n",
+ "Ta=40#\n",
+ "d=sqrt(Ro*4/(2*pi*Ta))#\n",
+ "d=10#\n",
+ "pb=10#\n",
+ "d1=sqrt(Ro/(pb*1.5))#\n",
+ "d1=20#\n",
+ "l=1.5*d#\n",
+ "t=10#\n",
+ "T=Ro*4/(2*pi*d1**2)#\n",
+ "M=(Ro/2*(l/2+t/3))-(Ro/2*l/4)#\n",
+ "sigb=32*M/(pi*d1**3)#\n",
+ "sigmax=(sigb/2)+sqrt((sigb/2)**2+T**2)#\n",
+ "P=Ro/(l*d1)#\n",
+ "D=2*d1#\n",
+ "print \" d1 is %0.1f mm \"%(d1)#\n",
+ "print \"\\n D is %0.1f mm \"%(D)#"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 6-2 - Page 172"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " h is 50.00 mm \n",
+ "\n",
+ " pmax is 74.43 MPa \n"
+ ]
+ }
+ ],
+ "source": [
+ "from math import sqrt, pi\n",
+ "d1=80#\n",
+ "p=0.981#\n",
+ "Ta=40#\n",
+ "siga=80#\n",
+ "pa=15#\n",
+ "W=pi*(d1**2)*p/4#\n",
+ "P=W/8#\n",
+ "Ws=W-P#\n",
+ "d=sqrt(W*4/(pi*2*Ta))#\n",
+ "l=1.5*d#\n",
+ "D=2*d#\n",
+ "T=W/(2*pi*pa**2/4)#\n",
+ "M1=P*(700-87.5-(D/2))#\n",
+ "h=50#\n",
+ "b=h/4#\n",
+ "Z=b*h**2/6#\n",
+ "sigb=M1/Z#\n",
+ "pmax=80#\n",
+ "T=2465.6/h**2#\n",
+ "pmax=(sigb/2)+sqrt((sigb/2)**2+T**2)#\n",
+ "print \" h is %0.2f mm \"%(h)#\n",
+ "print \"\\n pmax is %0.2f MPa \"%(pmax)#\n",
+ " \n",
+ "#The difference in the value of pmax is due to rounding-off the digits."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 6-3 - Page 173"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "P is 2.0 KN \n",
+ "\n",
+ "pmax is 69.53 MPa \n"
+ ]
+ }
+ ],
+ "source": [
+ "from math import sqrt, pi\n",
+ "P=((4*360)+(2*360))/900#\n",
+ "Fv=4-2#\n",
+ "Fh=P#\n",
+ "Fr=sqrt(Fv**2+Fh**2)#\n",
+ "P1=4*0.36/0.9#\n",
+ "Rf=sqrt(4**2+1.6**2)#\n",
+ "d=sqrt(Rf*10**3/(15*1.25))#\n",
+ "d=16#\n",
+ "l=1.25*d#\n",
+ "T=Rf*10**3*4/(2*pi*d**2)#\n",
+ "D=2*d#\n",
+ "M1=Rf*10**3*(360-(D/2))#\n",
+ "pa=15#\n",
+ "h=80#\n",
+ "b=h/4#\n",
+ "Z=b*h**2/6#\n",
+ "sigb=M1/Z#\n",
+ "T=4310/(b*h)#\n",
+ "pmax=(sigb/2)+sqrt((sigb/2)**2+T**2)#\n",
+ "print \"P is %0.1f KN \"%(P)#\n",
+ "print \"\\npmax is %0.2f MPa \"%(pmax)#"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 6-4 - Page 174"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "d is 30.0 mm \n",
+ "\n",
+ "D is 30.0 mm \n"
+ ]
+ }
+ ],
+ "source": [
+ "from math import sqrt, pi\n",
+ "l=360#\n",
+ "P=400#\n",
+ "Mh=2*P*l/3#\n",
+ "sigb=50#\n",
+ "l1=60#\n",
+ "d=(Mh*32/(pi*l1))**(1/3)#\n",
+ "d=30#\n",
+ "L=420#\n",
+ "siga=60#\n",
+ "H=20#\n",
+ "B=H/3#\n",
+ "Mx=P*(L-H/2)#\n",
+ "Tx=2*P*l/3#\n",
+ "sigb1=Mx*18/H**3#\n",
+ "Td=P/(B*H)#\n",
+ "Tr=17.17*Tx/H**4#\n",
+ "T=Tr+Td#\n",
+ "sigmax=(sigb1/2)+sqrt((sigb1/2)**2+T**2)#\n",
+ "Tmax=sqrt((sigb1/2)**2+T**2)#\n",
+ "T=P*L#\n",
+ "M=P*(l1+(2/3*l))#\n",
+ "Te=sqrt(T**2+M**2)#\n",
+ "Ta=40#\n",
+ "D=(Te*16/(pi*Ta))**(1/3)#\n",
+ "D=30# #Rounding off to nearest whole number\n",
+ "print \"d is %0.1f mm \"%(d)#\n",
+ "print \"\\nD is %0.1f mm \"%(D)#"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 6-5 - Page 175"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " d is 35.0 mm \n",
+ "\n",
+ " dh is 22.0 mm \n",
+ "\n",
+ " d1 is 56.0 mm \n",
+ "\n",
+ " l1 is 52.5 mm \n",
+ "\n",
+ " d2 is 32.0 mm \n",
+ "\n",
+ " b is 9.0 mm \n",
+ "\n",
+ " t is 6.0 mm \n"
+ ]
+ }
+ ],
+ "source": [
+ "from math import sqrt, pi\n",
+ "l2=300#\n",
+ "l=450#\n",
+ "P=400#\n",
+ "Mx=2*P*l2/3#\n",
+ "siga=80#\n",
+ "dh=(Mx*32/(pi*siga))**(1/3)#\n",
+ "dh=22#\n",
+ "L=(2*l2/3)+l#\n",
+ "T=P*L#\n",
+ "Ta=40#\n",
+ "d=(T*16/(pi*Ta))**(1/3)#\n",
+ "d=35#\n",
+ "d1=1.6*d#\n",
+ "Th=T*16*d1/(pi*(d1**4-d**4))#\n",
+ "l1=1.5*d#\n",
+ "My=P*(L-(d1/2))#\n",
+ "B=dh#\n",
+ "H=sqrt(3.66*75)#\n",
+ "H=30#\n",
+ "Mz=P*l1/2#\n",
+ "Te=sqrt(T**2+Mz**2)#\n",
+ "d2=(Te*16/(pi*Ta))**(1/3)#\n",
+ "d2=32#\n",
+ "b=d/4#\n",
+ "b=9# #Rounding off to nearest whole number\n",
+ "t=d/6#\n",
+ "t=6# #Rounding off to nearest whole number\n",
+ "print \" d is %0.1f mm \"%(d)#\n",
+ "print \"\\n dh is %0.1f mm \"%(dh)#\n",
+ "print \"\\n d1 is %0.1f mm \"%(d1)#\n",
+ "print \"\\n l1 is %0.1f mm \"%(l1)#\n",
+ "print \"\\n d2 is %0.1f mm \"%(d2)#\n",
+ "print \"\\n b is %0.1f mm \"%(b)#\n",
+ "print \"\\n t is %0.1f mm \"%(t)#\n",
+ " "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## exa 6-6 - Page 175"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " d is 32.0 mm \n",
+ "\n",
+ " d1 is 52.0 mm \n",
+ "\n",
+ " l1 is 40.0 mm \n",
+ "\n",
+ " B is 15.0 mm \n",
+ "\n",
+ " H is 45.0 mm \n",
+ "\n",
+ " d2 is 38.0 mm \n"
+ ]
+ }
+ ],
+ "source": [
+ "from math import sqrt, pi\n",
+ "L=450#\n",
+ "P=700#\n",
+ "T=P*L#\n",
+ "Ta=50#\n",
+ "d=(T*16/(pi*Ta))**(1/3)#\n",
+ "d=32#\n",
+ "d1=1.6*d#\n",
+ "d1=52# #Rounding off to nearest whole number\n",
+ "l1=1.25*d#\n",
+ "My=P*(L-d1/2)#\n",
+ "sigb=65#\n",
+ "H=(My*18/sigb)**(1/3)#\n",
+ "H=45#\n",
+ "B=H/3#\n",
+ "T1=P/(B*H)#\n",
+ "sigmax=(sigb/2)+sqrt((sigb/2)**2+T**2)#\n",
+ "Mx=P*l1/2#\n",
+ "Te=sqrt((T)**2+(Mx**2))#\n",
+ "d2=(Te*16/(pi*Ta))**(1/3)#\n",
+ "d2=d2+6#\n",
+ "d2=38# #Rounding off to nearest whole number\n",
+ "print \" d is %0.1f mm \"%(d)#\n",
+ "print \"\\n d1 is %0.1f mm \"%(d1)#\n",
+ "print \"\\n l1 is %0.1f mm \"%(l1)#\n",
+ "print \"\\n B is %0.1f mm \"%(B)#\n",
+ "print \"\\n H is %0.1f mm \"%(H)#\n",
+ "print \"\\n d2 is %0.1f mm \"%(d2)#\n",
+ " "
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "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": "2.7.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
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