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+{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:e4245d57622666881114047950aef2cecdad4d23a29878d669ecae5aa1b95679"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Ch:8 Springs"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "exa 8-1 - Page 224"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "d=5#\n",
+ "D=30#\n",
+ "G=84*(10**3)#\n",
+ "Na=15#\n",
+ "#Axial Load W\n",
+ "W=300#\n",
+ "#Spring index C\n",
+ "C=30/5#\n",
+ "#Shear stress Augmentation factor Ks\n",
+ "Ks=((2*C)+1)/(2*C)#\n",
+ "#Wahl's factor Kw\n",
+ "Kw=(((4*C)-1)/((4*C)-4))+(0.615/C)#\n",
+ "#Curvature correction factor Kc\n",
+ "Kc=Kw/Ks#\n",
+ "#Spring stiffness k\n",
+ "k=(G*(d**4))/(8*(D**3)*Na)#\n",
+ "#Axial deflection delta\n",
+ "delta=W/k#\n",
+ "print \" Ks is %0.4f \"%(Ks)#\n",
+ "print \"\\n Kw is %0.4f \"%(Kw)#\n",
+ "print \"\\n Kc is %0.3f \"%(Kc)#\n",
+ "print \"\\n The Spring Stiffness is %0.1f N/mm\"%(k)#\n",
+ "print \"\\n The Axial deflection is %0.3f mm\"%(delta)#"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ " Ks is 1.0000 \n",
+ "\n",
+ " Kw is 1.1025 \n",
+ "\n",
+ " Kc is 1.103 \n",
+ "\n",
+ " The Spring Stiffness is 16.0 N/mm\n",
+ "\n",
+ " The Axial deflection is 18.000 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "exa 8-2 - Page 224"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from math import pi\n",
+ "W=196.2#\n",
+ "lenthofscale=50#\n",
+ "k=196.2/50#\n",
+ "C=8#\n",
+ "Ks=(1+(0.5/C))#\n",
+ "\n",
+ "# Let us choose oil tempered wire 0.6-0.7 %C. Refer to Table 8-4 for constants A and m, relating strength wire \n",
+ "#diameter.\n",
+ "G=77.2*(10**3)#\n",
+ "A=1855#\n",
+ "m=0.187#\n",
+ "# equating Tmax=0.5*sig(ut).\n",
+ "# Ks*(8*W*D/(pi*(d**3)))=0.5*A/(d**2)\n",
+ "d1=(Ks*(8*W*C/(pi*A*0.5)))#\n",
+ "d=d1**(1/1.813)#\n",
+ "D=C*d#\n",
+ "Na=G*(d**4)/(8*(D**3)*k)#\n",
+ "#Solid length = SL\n",
+ "SL=(Na-1)*d\n",
+ "\n",
+ "print \" wire diameter is %0.3f mm \"%(d)#\n",
+ "print \"\\n mean diameter is %0.3f mm \"%(D)#\n",
+ "print \"\\n Number of acting coils are %0.3f \"%(Na)#\n",
+ "\n",
+ "#The difference in the values of d,D and Na is due to rounding-off the digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ " wire diameter is 2.314 mm \n",
+ "\n",
+ " mean diameter is 18.516 mm \n",
+ "\n",
+ " Number of acting coils are 11.117 \n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "exa 8-3 - Page 225"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "d=1.626#\n",
+ "A=2211#\n",
+ "m=0.145#\n",
+ "rm=3#\n",
+ "ri=(rm-(d/2))#\n",
+ "sigma=A/(d**m)#\n",
+ "W=(sigma*pi*(d**3)*ri)/(32*(rm**2))#\n",
+ "print \" Ultimate tensile Strength is %0.1f MPa \"%(sigma)#\n",
+ "print \"\\n Force at which the spring hook fails is %0.1f N \"%(W)#\n",
+ "\n",
+ "#The difference in the values of sigma and W is due to rounding-off the digits."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ " Ultimate tensile Strength is 2060.5 MPa \n",
+ "\n",
+ " Force at which the spring hook fails is 211.3 N \n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "exa 8-4 - Page 226"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "Do=25#\n",
+ "# mean coil diameter D=25-d\n",
+ "W=150#\n",
+ "T=800#\n",
+ "G=81000#\n",
+ "# Substituting values in equation T=8*W*D/(pi*(d**3))\n",
+ "# therefore, the equation becomes d**3 + 0.477*d = 11.936\n",
+ "#consider d=2.2mm, (d can be taken between 2.2-2.3mm)\n",
+ "d=2.337# #(nearest available wire gauge)\n",
+ "C=9.5#\n",
+ "D=22.2# \n",
+ "Do=D+d#\n",
+ "Ks=1+(0.5/C)#\n",
+ "Tmax=Ks*8*W*D/(pi*(d**3))#\n",
+ "# check for safety- Tmax<T#\n",
+ "Lo=100#\n",
+ "Ls=40#\n",
+ "#Lo=Ls+delta+0.15*delta\n",
+ "delta=(Lo-Ls)/1.15#\n",
+ "delta=50#\n",
+ "k=150/50#\n",
+ "Na=(G*d**4)/(8*(D**3)*k)#\n",
+ "\n",
+ "N=Na+2#\n",
+ "Ls=N*d#\n",
+ "Lo=Ls+(1.15*delta)#\n",
+ "print \" d is %0.3fmm \"%(d)#\n",
+ "print \"\\n D is %0.2f mm\"%(D)#\n",
+ "print \"\\n Ls is %0.2f mm\"%(Ls)#\n",
+ "print \"\\n Lo is %0.2f mm\"%(Lo)#\n",
+ "if (Do<=25):\n",
+ " print '\\nThe diameter is within space constraints'"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ " d is 2.337mm \n",
+ "\n",
+ " D is 22.20 mm\n",
+ "\n",
+ " Ls is 26.18 mm\n",
+ "\n",
+ " Lo is 83.68 mm\n",
+ "\n",
+ "The diameter is within space constraints\n"
+ ]
+ }
+ ],
+ "prompt_number": 18
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "exa 8-5A - Page 227"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "Di=15#\n",
+ "Do=20#\n",
+ "d=2.3#\n",
+ "D=17.5#\n",
+ "C=D/d#\n",
+ "Ks=1+(0.5/C)#\n",
+ "Wmax=100#\n",
+ "Tmax=Ks*8*Wmax*D/(pi*(d**3))#\n",
+ "G=81000#\n",
+ "delmax=67.7/2.366#\n",
+ "k=100/28#\n",
+ "Na=G*(d**4)/(8*k*(D**3))#\n",
+ "Ls=Na+1# #(for plain ends)\n",
+ "delmax=28#\n",
+ "#TL= total working length\n",
+ "TL=Ls+delmax+(0.15*delmax)#\n",
+ "print \" d is %0.1fmm \"%(d)#\n",
+ "print \"\\n C is %0.1f \"%(C)#\n",
+ "print \"\\n Na is %0.1f \"%(Na)#"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ " d is 2.3mm \n",
+ "\n",
+ " C is 7.6 \n",
+ "\n",
+ " Na is 17.6 \n"
+ ]
+ }
+ ],
+ "prompt_number": 19
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "exa 8-6 - Page- 228"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# 18 SWG=1.219MM in dia\n",
+ "d=1.219#\n",
+ "E=198.6*10**3#\n",
+ "G=80.7*10**3#\n",
+ "m=0.19#\n",
+ "A=1783#\n",
+ "sig=A/(d**m)#\n",
+ "Tys=(0.4*sig)#\n",
+ "Do=12.5#\n",
+ "D=Do-d#\n",
+ "C=D/d#\n",
+ "Ks=((2*C)+1)/(2*C)#\n",
+ "W=(Tys*pi*(d**3))/(8*D*Ks)#\n",
+ "Nt=13.5#\n",
+ "Na=Nt-2#\n",
+ "Del=(8*W*(D**3)*Na)/(G*(d**4))#\n",
+ "Ls=(Nt-1)*d#\n",
+ "Lo=Ls+Del+(0.15*Del)#\n",
+ "print \" Tys is %0.1f MPa \"%(Tys)#\n",
+ "print \"\\n W is %0.1f N \"%(W)#\n",
+ "print \"\\n del is %0.3f mm \"%(Del)#\n",
+ "print \"\\n Ls is %0.4f mm \"%(Ls)#\n",
+ "print \"\\n Lo is %0.2f mm \"%(Lo)#\n",
+ " \n",
+ "#Answers in the book for Torsional yeild strength have been rounded-off to the nearest whole number."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ " Tys is 686.9 MPa \n",
+ "\n",
+ " W is 41.1 N \n",
+ "\n",
+ " del is 30.457 mm \n",
+ "\n",
+ " Ls is 15.2375 mm \n",
+ "\n",
+ " Lo is 50.26 mm \n"
+ ]
+ }
+ ],
+ "prompt_number": 20
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "exa 8-7 - Page 228"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "d=1.016#\n",
+ "A=2211#\n",
+ "m=0.145#\n",
+ "G=81000#\n",
+ "Nt=16#\n",
+ "Na=16-2#\n",
+ "sig=A/(d**m)#\n",
+ "Tys=0.45*sig#\n",
+ "Do=12.6#\n",
+ "D=Do-d#\n",
+ "C=D/d#\n",
+ "Ks=1+(0.5/C)#\n",
+ "W=(Tys*pi*(d**3))/(8*D*Ks)#\n",
+ "k=(G*(d**4))/(8*(D**3)*Na)#\n",
+ "Del=W/k#\n",
+ "Ls=(Nt-1)*d#\n",
+ "Lo=Ls+(1.15*Del)#\n",
+ "\n",
+ "print \"Tys is %0.1f MPa \"%(Tys)#\n",
+ "print \"\\n Do is %0.1f N \"%(Do)#\n",
+ "print \"\\n W is %0.1f N \"%(W)#\n",
+ "print \"\\n k is %0.3f N \"%(k)#\n",
+ "print \"\\n del is %0.2f mm \"%(Del)#\n",
+ "print \"\\n Ls is %0.2f mm \"%(Ls)#\n",
+ "print \"\\n Lo is %0.3f mm \"%(Lo)#\n",
+ " \n",
+ "if ((Lo/D)>=5.26):\n",
+ " print 'The spring will fail under buckling'\n",
+ "\n",
+ "\n",
+ "#Values after the decimal point has not been considered for answer of Torsional yeild strength in the book, whereas answers for deflection and free-length is different as entire value of variables is taken for calculation in the code."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Tys is 992.7 MPa \n",
+ "\n",
+ " Do is 12.6 N \n",
+ "\n",
+ " W is 33.8 N \n",
+ "\n",
+ " k is 0.496 N \n",
+ "\n",
+ " del is 68.20 mm \n",
+ "\n",
+ " Ls is 15.24 mm \n",
+ "\n",
+ " Lo is 93.669 mm \n",
+ "The spring will fail under buckling\n"
+ ]
+ }
+ ],
+ "prompt_number": 21
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "exa 8-8 - Page 229"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "d=2#\n",
+ "Do=20#\n",
+ "D=Do-d#\n",
+ "C=D/d#\n",
+ "Na=9#\n",
+ "#Material hard drawn spring steel\n",
+ "A=1783#\n",
+ "m=0.19#\n",
+ "G=81000#\n",
+ "sig=A/(d**m)#\n",
+ "Tys=0.45*sig\n",
+ "Kf=1.5#\n",
+ "Ta=Tys/Kf#\n",
+ "Ks=1+(0.5/C)#\n",
+ "W=(Ta*pi*(d**3))/(8*D*Ks)#\n",
+ "k=(G*(d**4))/(8*(D**3)*Na)#\n",
+ "Del=W/k#\n",
+ "Lo=((Na+1)*d)+(1.15*Del)#\n",
+ "p=(Lo-d)/Na#\n",
+ "print \"k is %0.3f N/mm \"%(k)#\n",
+ "print \"\\n W is %0.1f N \"%(W)#\n",
+ "print \"\\n Lo is %0.3f mm \"%(Lo)#\n",
+ "print \"\\n p is %0.3f mm \"%(p)#\n",
+ " \n",
+ " \n",
+ "if ((Lo)>=47.34):\n",
+ " print 'The spring will fail under buckling'\n",
+ "\n",
+ "#The answer for value of spring rate 'k' is misprinted in the book. Due to this all subsequent values of del,Lo,p is calucated incorrectly in the book."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "k is 3.000 N/mm \n",
+ "\n",
+ " W is 77.5 N \n",
+ "\n",
+ " Lo is 49.720 mm \n",
+ "\n",
+ " p is 5.302 mm \n",
+ "The spring will fail under buckling\n"
+ ]
+ }
+ ],
+ "prompt_number": 22
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "exa 8-9 - Page 230"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# for music wire\n",
+ "d1=11.5#\n",
+ "A=2211#\n",
+ "d=1.5#\n",
+ "m=0.145#\n",
+ "sigut=A/(d**m)#\n",
+ "sigy=0.78*sigut#\n",
+ "Do=16#\n",
+ "E=2*(10**5)#\n",
+ "Nb=4.25#\n",
+ "D=Do-d#\n",
+ "C=D/d#\n",
+ "Ki=((4*(C**2))-C-1)/(4*C*(C-1))#\n",
+ "Mmax=(sigy*pi*(d**3))/(32*Ki)#\n",
+ "kc=((d**4)*E)/(10.8*D*Nb)#\n",
+ "theta3=Mmax/kc#\n",
+ "l1=20#\n",
+ "l2=20#\n",
+ "Ne=(l1+l2)/(3*pi*D)#\n",
+ "Na=Nb+Ne#\n",
+ "k=((d**4)*E)/(10.8*Na*D)#\n",
+ "thetat=Mmax/k#\n",
+ "ke=(3*pi*(d**4)*E)/(10.8*(l1+l2))#\n",
+ "# angdisp=theta1+theta2=Mmax/ke#\n",
+ "angdisp=Mmax/ke#\n",
+ "#D1 is final coil diameter\n",
+ "D1=(Nb*D)/(Nb+theta3)#\n",
+ "#IRC=Initial radial clearance\n",
+ "IRC=((D-d)-d1)/2#\n",
+ "#FRC=Final radial clearance\n",
+ "FRC=((D1-d)-d1)/2#\n",
+ "\n",
+ "\n",
+ "\n",
+ "print \" Maximum Torque is %0.2f Nmm \"%(Mmax)#\n",
+ "print \"\\n theta3 is %0.3f turns \"%(theta3)#\n",
+ "print \"\\n Ne is %0.3f turns \"%(Ne)#\n",
+ "print \"\\n ke is %0.1f N/mm \"%(ke)#\n",
+ "print \"\\n theta1+theta2 is %0.4f turns \"%(angdisp)#\n",
+ "print \"\\n D1 is %0.2f mm \"%(D1)#\n",
+ "print \"\\n IRC is %0.2f mm \"%(IRC)#\n",
+ "print \"\\n FRC is %0.2f mm \"%(FRC)#"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ " Maximum Torque is 497.25 Nmm \n",
+ "\n",
+ " theta3 is 0.327 turns \n",
+ "\n",
+ " Ne is 0.293 turns \n",
+ "\n",
+ " ke is 22089.3 N/mm \n",
+ "\n",
+ " theta1+theta2 is 0.0225 turns \n",
+ "\n",
+ " D1 is 13.46 mm \n",
+ "\n",
+ " IRC is 0.75 mm \n",
+ "\n",
+ " FRC is 0.23 mm \n"
+ ]
+ }
+ ],
+ "prompt_number": 23
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "exa 8-10 - Page 231"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "A=1783#\n",
+ "m=0.190#\n",
+ "d=1.5#\n",
+ "D=15#\n",
+ "M=300#\n",
+ "E=20800#\n",
+ "k=30#\n",
+ "#sigult= ultimate strength of the material\n",
+ "# sigy= yield strength of the material\n",
+ "sigult=A/(d**m)#\n",
+ "sigy=0.7*sigult#\n",
+ "#siga= allowable yield strength of the material\n",
+ "siga=sigy/2#\n",
+ "C=D/d#\n",
+ "Ki=(4*(C**2)-C-1)/(4*C*(C-1))#\n",
+ "Z=pi*(d**3)/32#\n",
+ "#sigb=bending strength of the material#\n",
+ "sigb=Ki*M/Z#\n",
+ "while (sigb>=siga) :\n",
+ " d=d+0.15#\n",
+ " D=15#\n",
+ " C=D/d#\n",
+ " sigult=A/(d**m)#\n",
+ " sigy=0.7*sigult#\n",
+ " siga=sigy/2#\n",
+ " Ki=(4*(C**2)-C-1)/(4*C*(C-1))#\n",
+ " Z=pi*(d**3)/32#\n",
+ " sigb=Ki*M/Z#\n",
+ "\n",
+ "d=2## rounding off the value of the diameter.\n",
+ "Na=(d**4)*E/(64*D*k)#\n",
+ "print \" d is %0.1f mm \"%(d)#\n",
+ "print \"\\n D is %0.1f mm \"%(D)#\n",
+ "print \"\\n Na is %0.2f mm \"%(Na)#"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ " d is 2.0 mm \n",
+ "\n",
+ " D is 15.0 mm \n",
+ "\n",
+ " Na is 11.00 mm \n"
+ ]
+ }
+ ],
+ "prompt_number": 24
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "exa 8-11 - Page 231"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "L=1180#\n",
+ "W=40*(10**3)#\n",
+ "Nf=2#\n",
+ "Ng=8#\n",
+ "E=207*(10**3)#\n",
+ "#sigut is ultimate strength\n",
+ "sigut=1400#\n",
+ "FOS=2#\n",
+ "#siga= allowable yield strength of the material\n",
+ "siga=1400/2#\n",
+ "#sigbf=bending strength in full length\n",
+ "sigbf=700#\n",
+ "b=75#\n",
+ "t=((4.5*W*L)/(((3*Nf)+(2*Ng))*sigbf))**(0.5)#\n",
+ "t=14#\n",
+ "I=(Nf*b*(t**3))/12#\n",
+ "Wf=(3*Nf*W)/((3*Nf)+(2*Ng))#\n",
+ "Del=(Wf*(L**3))/(48*E*I)#\n",
+ "print \" t is %0.0f mm \"%(t)#\n",
+ "print \"\\n Wf is %0.0f N \"%(Wf)#\n",
+ "print \"\\n I is %0.0f mm**4 \"%(I)#\n",
+ "print \"\\n del is %0.1f mm \"%(Del)#"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ " t is 14 mm \n",
+ "\n",
+ " Wf is 10909 N \n",
+ "\n",
+ " I is 34300 mm**4 \n",
+ "\n",
+ " del is 52.0 mm \n"
+ ]
+ }
+ ],
+ "prompt_number": 25
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "exa 8-12A - Page 232"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "W=80000#\n",
+ "sigbfr=500#\n",
+ "L=1100#\n",
+ "Nf=3#\n",
+ "Ng=10#\n",
+ "N=Nf+Ng#\n",
+ "t=((1.5*W*L)/(N*6*sigbfr))**(1/3)#\n",
+ "t=15#\n",
+ "b=6*t#\n",
+ "E=207*10**3#\n",
+ "deli=(W*(L**3))/(8*E*N*b*(t**3))#\n",
+ "Wi=(W*Nf*Ng)/(N*((3*Nf)+(2*Ng)))#\n",
+ "print \" t is %0.1f mm \"%(t)#\n",
+ "print \"\\n deli is %0.1f mm \"%(deli)#\n",
+ "print \"\\n Wi is %0.0f N \"%(Wi)#"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ " t is 15.0 mm \n",
+ "\n",
+ " deli is 16.0 mm \n",
+ "\n",
+ " Wi is 6366 N \n"
+ ]
+ }
+ ],
+ "prompt_number": 26
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "exa 8-13 - Page 233"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#ultimate strength=sigut\n",
+ "sigut=1500#\n",
+ "C=7#\n",
+ "d=3#\n",
+ "D=C*d#\n",
+ "Ks=1+(0.5/C)#\n",
+ "Kw=(((4*C)-1)/((4*C)-4))+(0.615/C)#\n",
+ "Pmax=120#\n",
+ "Pmin=40#\n",
+ "Pm=80#\n",
+ "Tm=(Ks*8*Pm*D)/(pi*(d**3))#\n",
+ "Ta=(Kw*8*Pmin*D)/(pi*(d**3))#\n",
+ "Tse=0.22*sigut#\n",
+ "Tys=0.45*sigut#\n",
+ "x=(Tys-(0.5*Tse))/(0.5*Tse)#\n",
+ "y=((x)*Ta)+Tm#\n",
+ "FOS=(Tys/y)#\n",
+ "print \" Tm is %0.2f MPa \"%(Tm)#\n",
+ "print \"\\n Ta is %0.1f MPa \"%(Ta)#\n",
+ "print \"\\n FOS is %0.3f \"%(FOS)#"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ " Tm is 169.77 MPa \n",
+ "\n",
+ " Ta is 86.2 MPa \n",
+ "\n",
+ " FOS is 1.548 \n"
+ ]
+ }
+ ],
+ "prompt_number": 27
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "exa 8-14 - Page 234"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "Tse=360#\n",
+ "Tys=660#\n",
+ "d=25#\n",
+ "P=0.03#\n",
+ "m=40#\n",
+ "Pmin=((pi*(d**2)*P)/4)+(m*9.81/1000)#\n",
+ "k=6#\n",
+ "#Additional load= Padd=k*further compression in spring\n",
+ "Padd=k*10#\n",
+ "Pmax=Padd+Pmin#\n",
+ "Pm=(Pmax+Pmin)/2#\n",
+ "Pa=(Pmax-Pmin)/2#\n",
+ "d=2#\n",
+ "D=12#\n",
+ "C=6#\n",
+ "Ks=1+(0.5/C)#\n",
+ "Ks=1.083#\n",
+ "Kw=(((4*C)-1)/((4*C)-4))+(0.615/C)#\n",
+ "Ta=(Kw*8*Pa*D)/(pi*(d**3))#\n",
+ "Tm=(Ks*8*Pm*D)/(pi*(d**3))#\n",
+ "x=(Tys-(0.5*Tse))/(0.5*Tse)#\n",
+ "y=((x)*Ta)+Tm#\n",
+ "FOS=(Tys/y)#\n",
+ "print \" Tm is %0.2f MPa \"%(Tm)#\n",
+ "print \"\\n Ta is %0.3f MPa \"%(Ta)#\n",
+ "print \"\\n FOS is %0.2f \"%(FOS)#"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ " Tm is 186.64 MPa \n",
+ "\n",
+ " Ta is 126.337 MPa \n",
+ "\n",
+ " FOS is 1.26 \n"
+ ]
+ }
+ ],
+ "prompt_number": 28
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+} \ No newline at end of file