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diff --git a/Machine_Design_by_U.C._Jindal/Ch3_1.ipynb b/Machine_Design_by_U.C._Jindal/Ch3_1.ipynb new file mode 100644 index 00000000..eab09e70 --- /dev/null +++ b/Machine_Design_by_U.C._Jindal/Ch3_1.ipynb @@ -0,0 +1,1391 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Ch : 3 Mechanics of solids" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## exa 3-1 - Page 72" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " sigi is 146.37 N/mm**2 \n", + "\n", + " deli is 1.05 mm \n", + "\n", + " siggradual is 1.50 N/mm**2 \n" + ] + } + ], + "source": [ + "from math import pi, sqrt\n", + "d=10 \n", + "l=1500 \n", + "m=12 \n", + "h=50 \n", + "E=210*10**3 \n", + "sigut=450 \n", + "A=pi*d**2/4 \n", + "W=m*9.81 \n", + "sigi=W/A*(1+sqrt(1+(2*E*A*h)/(W*l))) \n", + "deli=sigi*l/E \n", + "siggradual=W/A \n", + "sigsudden=2*siggradual \n", + "print \" sigi is %0.2f N/mm**2 \"%(sigi) \n", + "print \"\\n deli is %0.2f mm \"%(deli) \n", + "print \"\\n siggradual is %0.2f N/mm**2 \"%(siggradual) \n", + "\n", + "# The difference in the answer of sigi and siggradual is due to round-off errors." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## exa 3-2 - Page 73" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "del is 16.42 mm \n" + ] + } + ], + "source": [ + "from math import pi, sqrt\n", + "d=5 \n", + "A=pi*d**2/4 \n", + "l=100*10**3 \n", + "W=600 \n", + "E=210*10**3 \n", + "w=0.0784*10**-3 \n", + "del1=W*l/(A*E) \n", + "del2=w*l**2/(2*E) \n", + "Del=del1+del2 \n", + "print \"del is %0.2f mm \"%(Del) " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## exa 3-3 - Page 73" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "del is 69.41 N/mm**2 \n" + ] + } + ], + "source": [ + "from math import pi, sqrt\n", + "m=25 \n", + "v=3 \n", + "E=210*10**3 \n", + "KE=0.5*m*v**2 \n", + "d=30 \n", + "L=2000 \n", + "A=pi*d**2/4 \n", + "U=A*L/(2*E) \n", + "Del=4*10**-5*A \n", + "W=A*Del \n", + "sigi=sqrt(KE*10**3/(W+U)) \n", + "print \"del is %0.2f N/mm**2 \"%(sigi) " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## exa 3-4 - Page 74" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "sigmax1 is 62.96 N/mm**2 \n", + "\n", + "sigmax2 is 55.56 N/mm**2 \n" + ] + } + ], + "source": [ + "P=40*10**3 \n", + "A=60*18 \n", + "sig=P/A \n", + "r1=12 \n", + "b1=60 \n", + "SCF1=1.7 \n", + "sigmax1=sig*SCF1 \n", + "r2=24 \n", + "b2=60 \n", + "SCF2=1.5 \n", + "sigmax2=sig*SCF2 \n", + "print \"sigmax1 is %0.2f N/mm**2 \"%(sigmax1) \n", + "print \"\\nsigmax2 is %0.2f N/mm**2 \"%(sigmax2) " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## exa 3-5 - Page 75" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "sigt is 33.87 N/mm**2 \n", + "\n", + "sigb is 52.26 N/mm**2 \n" + ] + } + ], + "source": [ + "from math import pi, sqrt\n", + "p=2.4 \n", + "#Let axial movement of nut be La\n", + "La=p*45/360 \n", + "d=20 \n", + "D=30 \n", + "L=500 \n", + "d1=18 \n", + "As=pi*d1**2/4 \n", + "Ac=pi*(D**2-d**2)/4 \n", + "sigt=120/(3.543) \n", + "sigb=1.543*sigt \n", + "print \"sigt is %0.2f N/mm**2 \"%(sigt) \n", + "print \"\\nsigb is %0.2f N/mm**2 \"%(sigb) " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## exa 3-6 - Page 76" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " P is 162.73 kN \n", + "\n", + " delL is 0.38 mm \n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "delT=100 \n", + "ab=18*10**-6 \n", + "aa=23*10**-6 \n", + "delta=(360*ab*delT)+(450*aa*delT) \n", + "lc=delta-0.6 \n", + "Ea=70*10**3 \n", + "Eb=105*10**3 \n", + "Aa=1600 \n", + "Ab=1300 \n", + "P=lc/((360/(Ab*Eb))+(450/(Aa*Ea))) \n", + "P=P*10**-3 \n", + "#Let the change in length be delL\n", + "delL=(aa*450*delT)-(P*10**3*450/(Aa*Ea)) \n", + "print \" P is %0.2f kN \"%(P) \n", + "print \"\\n delL is %0.2f mm \"%(delL) \n", + " \n", + "# The difference in the answer of delL is due to round-off errors." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## exa 3-7 - Page 77" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "delT is 68.12 degC \n" + ] + } + ], + "source": [ + "a=23*10**-6 \n", + "E=70*10**3 \n", + "l=750 \n", + "sig=35 \n", + "delT=((sig*l/E)+0.8)/(l*a) \n", + "print \"delT is %0.2f degC \"%(delT) " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## exa 3-8 - Page 78" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " Stress on plane AB is 14.00 MPa \n", + "\n", + " Stress on plane AB is 49.50 MPa \n", + "\n", + " Principal stress p1 is 70.00 MPa \n", + "\n", + " Principal stress p2 is -30.00 MPa \n", + "\n", + " Principal angle theta1 is -18.50 deg \n", + "\n", + " Principal angle theta2 is 71.50 deg \n", + "\n", + " Maximum shear stress is 50.00 MPa \n", + "\n", + " Direction of plane theta3 is 26.50 deg \n", + "\n", + " Direction of plane theta4 is 116.50 deg \n" + ] + } + ], + "source": [ + "OA=60 \n", + "AB=30 \n", + "OC=-20 \n", + "CD=-30 \n", + "theta=30 \n", + "angBEK=2*theta \n", + "OM=14 \n", + "KM=49.5 \n", + "p1=70 \n", + "p2=-30 \n", + "angBEH=-37 \n", + "angBEI=143 \n", + "theta1=angBEH/2 \n", + "theta2=angBEI/2 \n", + "Tmax=50 \n", + "angBEL=53 \n", + "angBEN=233 \n", + "theta3=angBEL/2 \n", + "theta4=angBEN/2 \n", + "print \" Stress on plane AB is %0.2f MPa \"%(OM) \n", + "print \"\\n Stress on plane AB is %0.2f MPa \"%(KM) \n", + "print \"\\n Principal stress p1 is %0.2f MPa \"%(p1) \n", + "print \"\\n Principal stress p2 is %0.2f MPa \"%(p2) \n", + "print \"\\n Principal angle theta1 is %0.2f deg \"%(theta1) \n", + "print \"\\n Principal angle theta2 is %0.2f deg \"%(theta2) \n", + "print \"\\n Maximum shear stress is %0.2f MPa \"%(Tmax) \n", + "print \"\\n Direction of plane theta3 is %0.2f deg \"%(theta3) \n", + "print \"\\n Direction of plane theta4 is %0.2f deg \"%(theta4) \n", + "\n", + "#The answers in the book are written in form of degrees and minutes." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## exa 3-9 - Page 78" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "p1 is 121.76 MN/mm**2 \n", + "\n", + " p2 is -76.69 MN/mm**2 \n" + ] + } + ], + "source": [ + "E=200*10**3 \n", + "v=0.29 \n", + "E1=720*10**-6 \n", + "E2=560*10**-6 \n", + "p1=121.76 \n", + "p2=-76.69 \n", + "print \"p1 is %0.2f MN/mm**2 \"%(p1) \n", + "print \"\\n p2 is %0.2f MN/mm**2 \"%(p2) " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## exa 3-10 - Page 79" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "v is 0.3136 \n", + "\n", + "E is 99.837 kN/mm**2 \n" + ] + } + ], + "source": [ + "from math import pi, sqrt\n", + "G=38*10**3 \n", + "d=10 \n", + "P=5*10**3 \n", + "A=pi*d**2/4 \n", + "sig=P/A \n", + "deld=0.0002 \n", + "#Let the lateral strain be E1\n", + "E1=deld/d \n", + "v=2*deld*G/(sig-(2*deld*G)) \n", + "E=2*G*(1+v)*10**-3 \n", + "print \"v is %0.4f \"%(v) \n", + "print \"\\nE is %0.3f kN/mm**2 \"%(E) " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## exa 3-11 - Page 79" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "t is 12.0 mm \n" + ] + } + ], + "source": [ + "D=1500 \n", + "p=1.2 \n", + "sigt=100 \n", + "sigc=p*D/2 \n", + "siga=p*D/4 \n", + "P=sigc*2*10**3 \n", + "n=0.75 \n", + "t=sigc/(n*sigt) \n", + "print \"t is %0.1f mm \"%(t) " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## exa 3-12 - Page 80" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "sigw is 64.52 N/mm**2 \n" + ] + } + ], + "source": [ + "D=50 \n", + "t=1.25 \n", + "d=0.5 \n", + "n=1/d \n", + "p=1.5 \n", + "siga=p*D/(4*t) \n", + "sigc=20.27 \n", + "sigw=sigc/0.31416 \n", + "print \"sigw is %0.2f N/mm**2 \"%(sigw) " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## exa 3-13 - Page 81" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "t is 50.0 mm \n" + ] + } + ], + "source": [ + "from math import pi, sqrt\n", + "R1=50 \n", + "p=75 \n", + "pmax=125 \n", + "R2=sqrt((pmax+p)*R1**2/(pmax-p)) \n", + "t=R2-R1 \n", + "print \"t is %0.1f mm \"%(t) " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## exa 3-14 - Page 82" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Fa is 13.52 kN \n" + ] + } + ], + "source": [ + "from math import pi, sqrt\n", + "R1=40 \n", + "R2=60 \n", + "B=50 \n", + "E=210*10**3 \n", + "e=41*10**-6 \n", + "sig=2*R1**2/(R2**2-R1**2) \n", + "p=E*e/sig \n", + "Fr=p*2*pi*R1*B \n", + "u=0.2 \n", + "Fa=u*Fr*10**-3 \n", + "print \"Fa is %0.2f kN \"%(Fa) " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## exa 3-15 - Page 83" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "W is 1.333 kN \n" + ] + } + ], + "source": [ + "a1=10*1.5 \n", + "x1=15-0.75 \n", + "a2=1.5*(15-1.5) \n", + "x2=(15-1.5)/2 \n", + "y1=((a1*x1)+(a2*x2))/(a1+a2) \n", + "y2=a1-y1 \n", + "Ixx=(10*1.5**3)/12+(10*1.5*(5.06-1.5/2)**2)+(1.5*13.5**3/12)+(1.5*13.5*(9.94-6.75)**2) \n", + "Z1=Ixx/y1 \n", + "Z2=Ixx/y2 \n", + "L=3 \n", + "sigc=50 \n", + "W=sigc*Z1/L*10**-3 \n", + "print \"W is %0.3f kN \"%(W) " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## exa 3-16 - Page 83" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "M is 46.410 Nm \n" + ] + } + ], + "source": [ + "from math import pi, sqrt\n", + "D=22 \n", + "d=20 \n", + "r=1 \n", + "K=2.2 \n", + "sigmax=130 \n", + "sigmax=sigmax/K \n", + "Z=pi*d**3/32 \n", + "M=sigmax*Z*10**-3 \n", + "print \"M is %0.3f Nm \"%(M) " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## exa 3-17 - Page 84" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Z1/Zr is 4.84 \n", + "\n", + "sigmax is 41.33 N/mm**2 \n" + ] + } + ], + "source": [ + "from math import pi, sqrt\n", + "A=(12*2)+(12*2)+(30-4) \n", + "B=sqrt(A/2) \n", + "D=2*B \n", + "B1=12 \n", + "D1=30 \n", + "d=26 \n", + "b=1 \n", + "Z1=((B1*D1**3)-((B1-b)*d**3))/(B1*D1/2) \n", + "Zr=B*D**2/6 \n", + "#Let the ratio of both the sections be x\n", + "x=Z1/Zr \n", + "M=30*10**6 \n", + "sigmax=M/(Z1*10**3) \n", + "print \"Z1/Zr is %0.2f \"%(x) \n", + "print \"\\nsigmax is %0.2f N/mm**2 \"%(sigmax) " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## exa 3-19 - Page 85" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "P is 49.38 kN \n" + ] + } + ], + "source": [ + "from math import pi, sqrt\n", + "x1=((13*3*1.5)+(2*15*8))/(39+30) \n", + "x2=13-x1 \n", + "A=30+39 \n", + "E=2*10**7 \n", + "Iyy=995.66 \n", + "e=54.32 \n", + "x=x2-3 \n", + "sigb=e*x/Iyy \n", + "sigd=1/69 \n", + "sigr=sigd+sigb \n", + "#Let the strain be E1\n", + "E1=800*10**-6 \n", + "P=E1*E/sigr \n", + "P=P*10**-3 \n", + "print \"P is %0.2f kN \"%(P) " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## exa 3-20 - Page 86" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "sigmax is 607.24 kN/m**2 \n", + "\n", + "sigmin is 232.76 kN/m**2 \n" + ] + } + ], + "source": [ + "from math import pi, sqrt\n", + "H=20 \n", + "D=5 \n", + "d=3 \n", + "rho=21 \n", + "sigd=rho*H \n", + "p=2 \n", + "A=D*H \n", + "P=p*A \n", + "M=P*H/2 \n", + "Z=pi*(D**4-d**4)/(32*D) \n", + "sigb=M/Z \n", + "sigmax=420+sigb \n", + "sigmin=420-sigb \n", + "print \"sigmax is %0.2f kN/m**2 \"%(sigmax) \n", + "print \"\\nsigmin is %0.2f kN/m**2 \"%(sigmin) " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## exa 3-21 - Page 87" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " T1 is 105.63 N/mm**2 \n", + "\n", + " theta is 4.92 deg \n", + "\n", + " Tr is 70.42 N/mm**2 \n" + ] + } + ], + "source": [ + "from math import pi, sqrt\n", + "D=30 \n", + "R=15 \n", + "T=0.56*10**6 \n", + "G=82*10**3 \n", + "J=pi*R**4/2 \n", + "T1=T*R/J \n", + "l=1000 \n", + "theta=T*l/(G*J)*180/pi \n", + "r=10 \n", + "Tr=T1*r/R \n", + "print \" T1 is %0.2f N/mm**2 \"%(T1) \n", + "print \"\\n theta is %0.2f deg \"%(theta) \n", + "print \"\\n Tr is %0.2f N/mm**2 \"%(Tr) " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## exa 3-22 - Page 87" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " Ts1 is 34.796 N/mm**2 \n", + "\n", + " Tc1 is 23.9 N/mm**2 \n", + "\n", + " theta/length is 0.623 deg/m \n", + "\n", + " Ts2 is 17.398 N/mm**2 \n", + "\n", + " Tc2 is 11.96 N/mm**2 \n" + ] + } + ], + "source": [ + "from math import pi, sqrt\n", + "T=8*10**3 \n", + "d=80 \n", + "D=110 \n", + "l=2000 \n", + "Gst=80*10**3 \n", + "Gcop=Gst/2 \n", + "Js=pi*d**4/32 \n", + "Jc=pi*(D**4-d**4)/32 \n", + "#Ts=0.777*Tc\n", + "Tc=T/1.777*10**3 \n", + "Ts=0.777*Tc \n", + "Ts1=Ts/Js*d/2 \n", + "Tc1=Tc/Jc*D/2 \n", + "#Let tl be Angular twist per unit length\n", + "tl=Ts*10**3/(Js*Gst)*180/pi \n", + "# Let the maximum stress developed when the Torque is acting in the centre of the shaft be Ts2 & Tc2 resp. for steel and copper\n", + "Ts2=Ts1/2 \n", + "Tc2=Tc1/2 \n", + "print \" Ts1 is %0.3f N/mm**2 \"%(Ts1) \n", + "print \"\\n Tc1 is %0.1f N/mm**2 \"%(Tc1) \n", + "print \"\\n theta/length is %0.3f deg/m \"%(tl) \n", + "print \"\\n Ts2 is %0.3f N/mm**2 \"%(Ts2) \n", + "print \"\\n Tc2 is %0.2f N/mm**2 \"%(Tc2) " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## exa 3-23 - Page 88" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Tmax is 6.235 MPa \n" + ] + } + ], + "source": [ + "from math import pi, sqrt\n", + "D=100 \n", + "d=75 \n", + "r=6 \n", + "K=1.45 \n", + "P=20*746 \n", + "N=400 \n", + "w=2*pi*N/60 \n", + "T=P/w \n", + "Ts=16*T*10**3/(pi*d**3) \n", + "Tmax=K*Ts \n", + "print \"Tmax is %0.3f MPa \"%(Tmax) " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## exa 3-24 - Page 88" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "d is 21.0 mm \n" + ] + } + ], + "source": [ + "from math import pi, sqrt\n", + "G=84*10**3 \n", + "T=28*10**3 \n", + "l=1000 \n", + "theta=pi/180 \n", + "J=T*l/(G*theta) \n", + "d=(J*32/pi)**(1/4) \n", + "print \"d is %0.1f mm \"%(d) " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## exa 3-25 - Page 89" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "d is 280.5 mm \n" + ] + } + ], + "source": [ + "from math import pi, sqrt\n", + "P=2*10**6 \n", + "N=200 \n", + "w=2*pi*N/60 \n", + "Tm=P/w \n", + "W=5*10**3*9.81 \n", + "l=1800 \n", + "Mmax=W*l/4 \n", + "Tmax=1.8*Tm*10**3 \n", + "Me=(Mmax+sqrt(Mmax**2+Tmax**2))/2 \n", + "Te=sqrt(Mmax**2+Tmax**2) \n", + "sig=60 \n", + "Ts=40 \n", + "d1=(32*Me/(pi*sig))**(1/3) \n", + "d2=(16*Te/(pi*Ts))**(1/3) \n", + "print \"d is %0.1f mm \"%(d2) " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## exa 3-26 - Page 90" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " d1 is 11.38 mm \n", + "\n", + " d2 is 12.3 mm \n", + "\n", + " d3 is 11.74 mm \n" + ] + } + ], + "source": [ + "from math import pi, sqrt\n", + "Q=4*10**3 \n", + "P=8*10**3 \n", + "sig=P \n", + "T=Q \n", + "p1=(sig/2+sqrt((sig/2)**2+T**2)) \n", + "p2=(sig/2-sqrt((sig/2)**2+T**2)) \n", + "sigyp=285 \n", + "FOS=3 \n", + "siga=sigyp/3 \n", + "A1=p1/siga \n", + "d1=sqrt(4*A1/pi) \n", + "A2=(p1-p2)*2/(siga*2) \n", + "d2=sqrt(4*A2/pi) \n", + "v=0.3 \n", + "A3=sqrt(p1**2+p2**2-(2*v*p1*p2))/siga \n", + "d3=sqrt(4*A3/pi) \n", + "print \" d1 is %0.2f mm \"%(d1) \n", + "print \"\\n d2 is %0.1f mm \"%(d2) \n", + "print \"\\n d3 is %0.2f mm \"%(d3) " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## exa 3-27 - Page 91" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The component is safe\n", + "\n", + "Tmax is 117.4 MPa \n" + ] + } + ], + "source": [ + "from math import pi, sqrt\n", + "sigx=-105 \n", + "Txy=105 \n", + "sigy=270 \n", + "p1=(sigx/2+sqrt((sigx/2)**2+Txy**2)) \n", + "p2=(sigx/2-sqrt((sigx/2)**2+Txy**2)) \n", + "p3=0 \n", + "Tmax=(p1-p2)/2 \n", + "siga=sigy/2 \n", + "if (Tmax<=siga) :\n", + " print \"The component is safe\"\n", + "print \"\\nTmax is %0.1f MPa \"%(Tmax) " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## exa 3-28 - Page 91" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "N is 1324.249 rpm \n" + ] + } + ], + "source": [ + "from math import pi, sqrt\n", + "rho=0.0078*9.81*10**-6 \n", + "sigc=150 \n", + "g=9.81 \n", + "V=sqrt(sigc*g/rho)*10**-3 \n", + "R=1 \n", + "w=V/R \n", + "N=w*60/(2*pi) \n", + "print \"N is %0.3f rpm \"%(N) " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## exa 3-29 - Page 92" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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qDmecAf/5DzRs6Heq7IvE9TAibTLuGhyEvk7yMUuWdu50k37++1+/k0SnAjEF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\nMMYYky3/B0TYOSGQpC4+AAAAAElFTkSuQmCC\n", + "text/plain": [ + "<matplotlib.figure.Figure at 0x7feb0a76e790>" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "sigrmax is 28.4 MPa \n" + ] + } + ], + "source": [ + "from math import pi, sqrt\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot, xlabel, ylabel, show, grid\n", + "\n", + "R1=50 \n", + "R2=200 \n", + "N=6*10**3 \n", + "w=2*pi*N/60 \n", + "v=0.28 \n", + "rho=7800*10**-9 \n", + "g=9810 \n", + "k1=(3+v)/8 \n", + "k2=(1+(3*v))/8 \n", + "W=rho*9.81 \n", + "x=k1*w**2*W*(R1**2+R2**2)/g \n", + "y=k1*w**2*W*(R1*R2)**2/g \n", + "y1=k1*w**2*W/g \n", + "z=k2*w**2*W/g \n", + "r=sqrt(R1*R2) \n", + "sigrmax=x-(y/r**2)-(r**2*y1) \n", + "r=range(50,201)\n", + "n=len(r) \n", + "sigr = range(0,n)\n", + "for i in range(0,n):\n", + " sigr[i]=x-(y/r[i]**2)-(r[i]**2*y1)\n", + "\n", + "sigc = range(0,n)\n", + "for j in range(0,n):\n", + " sigc[j]=y/r[j]**2-(r[j]**2*z)\n", + "\n", + "plot(r,sigr) \n", + "plot (r,sigc) \n", + "xlabel('r in mm') \n", + "ylabel('stress in N/mm**2') \n", + "grid()\n", + "show()\n", + "print \"sigrmax is %0.1f MPa \"%(sigrmax) " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## exa 3-30 - Page 93" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "t is 2.923 mm \n" + ] + } + ], + "source": [ + "from numpy import exp\n", + "r=500 \n", + "to=15 \n", + "N=3500 \n", + "w=2*pi*N/60 \n", + "sig=80 \n", + "w1=0.07644*10**-3 \n", + "g=9810 \n", + "a=w1*w**2*r**2/(2*sig*g) \n", + "t=to*exp(-a) \n", + "print \"t is %0.3f mm \"%(t) " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## exa 3-31 - Page 93" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "sigB is 61.5 MPa \n", + "\n", + "sigA is 36 MPa \n" + ] + } + ], + "source": [ + "from numpy import log\n", + "M=60*10**3 \n", + "y1=((5*1*2.5)+(6*1*5.5))/(5+6) \n", + "y2=6-y1 \n", + "R=12 \n", + "R1=R-y2 \n", + "R1=10.136\n", + "R2=11.136 \n", + "R3=R1+6 \n", + "B=6 \n", + "b=1 \n", + "A=(B*b)+((B-1)*b) \n", + "#Let x= h**2/R**2\n", + "x=R/A*((B*log(R2/R1))+(b*log(R3/R2)))-1 \n", + "x=1/x \n", + "#Let Maximum compressive stress at B be sigB\n", + "sigB=M/(A*R)*(1+(x*y1/(R+y1)))*10**-2 \n", + "#Let Maximum tensile stress at A be sigA\n", + "sigA=M/(A*R)*((y2*x/(R-y2))-1)*10**-2 \n", + "print \"sigB is %0.1f MPa \"%(sigB) \n", + "print \"\\nsigA is %0.0f MPa \"%(sigA) \n", + " \n", + "#The answer to R**2/h**2 is calculated incorrectly in the book." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## exa 3-32 - Page 94" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Ra is 96.70 N/mm**2 \n", + "\n", + "Rb is 70.14 N/mm**2 \n" + ] + } + ], + "source": [ + "from numpy import log\n", + "R1=24 \n", + "R2=30 \n", + "R3=50 \n", + "R4=54 \n", + "F=200 \n", + "y1=((16*4*2)+(2*20*14*4)+(24*6*27))/((16*4)+(2*20*4)+(24*6)) \n", + "y2=30-y1 \n", + "R=24+y2 \n", + "A=(24*6)+(2*4*20)+(4*16) \n", + "#Let x= h**2/R**2\n", + "x=R/A*((24*log(R2/R1))+(2*4*log(R3/R2))+(16*log(R4/R3)))-1 \n", + "x=1/x \n", + "M=F*(60+R) \n", + "sigd=F/A \n", + "#Let bending stress at a be sigA\n", + "sigA=M/(A*R)*((y2*x/(R-y2))-1) \n", + "#Let bending stress at b be sigB\n", + "sigB=M/(A*R)*(1+(x*y1/(R+y1))) \n", + "#Let resultant at a be Ra\n", + "Ra=(sigA+sigd)*10 \n", + "#Let resultant at b be Rb\n", + "Rb=(sigB-sigd)*10 \n", + "print \"Ra is %0.2f N/mm**2 \"%(Ra) \n", + "print \"\\nRb is %0.2f N/mm**2 \"%(Rb) \n", + "#The difference in the answers are due to rounding-off of values." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## exa 3-33 - Page 95" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "sigA is 31.59 MPa \n", + "\n", + "sigB is 71.64 MPa \n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "from numpy import log\n", + "F=50 \n", + "B1=4 \n", + "B2=8 \n", + "D=12 \n", + "y1=D/3*(B1+(2*B2))/(B1+B2) \n", + "y2=12-y1 \n", + "R=6+y2 \n", + "A=(B1+B2)/2*D \n", + "#Let x= h**2/R**2\n", + "a=(B1+((B2-B1)*(y1+R)/D))*log((R+y1)/(R-y2))\n", + "x=R/(A)*(a -(B2-B1)) \n", + "x=x-1 \n", + "x=1/x \n", + "KG=y2+8 \n", + "M=F*KG \n", + "sigd=F/A \n", + "#Let bending stress at a be sigA\n", + "sigA=M/(A*R)*(1+(x*y1/(R+y1))) \n", + "#Let bending stress at b be sigB\n", + "sigB=M/(A*R)*((y2*x/(R-y2))-1) \n", + "sigA=(sigA-sigd)*10 \n", + "sigB=(sigB+sigd)*10 \n", + "print \"sigA is %0.2f MPa \"%(sigA) \n", + "print \"\\nsigB is %0.2f MPa \"%(sigB) \n", + "#The difference in the answers are due to rounding-off of values." + ] + } + ], + "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 +} |