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authorPrashant S2020-04-14 10:25:32 +0530
committerGitHub2020-04-14 10:25:32 +0530
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tree2b1df110e24ff0174830d7f825f43ff1c134d1af /Machine_Design_by_U_C_Jindal/3-MECHANICS_OF_SOLIDS.ipynb
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+{
+"cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 3: MECHANICS OF SOLIDS"
+ ]
+ },
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3.10: MS10.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// sum 3-10\n",
+"clc;\n",
+"clear;\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",
+"\n",
+" // printing data in scilab o/p window\n",
+" printf('v is %0.4f ',v);\n",
+" printf('\n E is %0.3f kN/mm^2 ',E);"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3.11: MS11.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// sum 3-11\n",
+"clc;\n",
+"clear;\n",
+"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",
+"\n",
+" // printing data in scilab o/p window\n",
+" printf('t is %0.1f mm ',t);"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3.12: MS12.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// sum 3-12\n",
+"clc;\n",
+"clear;\n",
+"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",
+"\n",
+" // printing data in scilab o/p window\n",
+" printf('sigw is %0.2f N/mm^2 ',sigw);"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3.13: MS13.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// sum 3-13\n",
+"clc;\n",
+"clear;\n",
+"R1=50;\n",
+"p=75;\n",
+"pmax=125;\n",
+"R2=sqrt((pmax+p)*R1^2/(pmax-p));\n",
+"t=R2-R1;\n",
+"\n",
+" // printing data in scilab o/p window\n",
+" printf('t is %0.1f mm ',t);"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3.14: MS14.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// sum 3-14\n",
+"clc;\n",
+"clear;\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",
+"\n",
+" // printing data in scilab o/p window\n",
+" printf('Fa is %0.2f kN ',Fa);"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3.15: MS15.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// sum 3-15\n",
+"clc;\n",
+"clear;\n",
+"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",
+"\n",
+" // printing data in scilab o/p window\n",
+" printf('W is %0.3f kN ',W);"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3.16: MS16.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// sum 3-16\n",
+"clc;\n",
+"clear;\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",
+"\n",
+" // printing data in scilab o/p window\n",
+" printf('M is %0.3f Nm ',M);"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3.17: MS17.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// sum 3-17\n",
+"clc;\n",
+"clear;\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",
+"\n",
+" // printing data in scilab o/p window\n",
+" printf('Z1/Zr is %0.2f ',x);\n",
+" printf('\n sigmax is %0.2f N/mm^2 ',sigmax);"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3.18: MS18.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// sum 3-18\n",
+"clc;\n",
+"clear;\n",
+"//Tmax=F/(I*b)*[B*t(d/2+t/2)+(b*d*d/8)];\n",
+"//T1=F/(I*b)*[B*t*(d+t)/2];\n",
+"//Tmean=T1+2/3*(Tmax-T1);\n",
+"//T=Tmax-Tmean;\n",
+"//T=F*d^2/(24*I);\n",
+"disp('Difference between maximum and mean shear stresses in the web is ,T=F*d^2/(24*I)');"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3.19: MS19.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// sum 3-19\n",
+"clc;\n",
+"clear;\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",
+"\n",
+" // printing data in scilab o/p window\n",
+" printf('P is %0.2f kN ',P);"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3.1: MS1.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// sum 3-1\n",
+"clc;\n",
+"clear;\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",
+"\n",
+" // printing data in scilab o/p window\n",
+" printf('sigi is %f N/mm^2 ',sigi);\n",
+" printf('\n deli is %f mm ',deli);\n",
+" printf('\n siggradual is %f 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": [
+ "## Example 3.20: MS20.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// sum 3-20\n",
+"clc;\n",
+"clear;\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",
+"\n",
+" // printing data in scilab o/p window\n",
+" printf('sigmax is %0.2f kN/m^2 ',sigmax);\n",
+" printf('\n sigmin is %0.2f kN/m^2 ',sigmin);"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3.21: MS21.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// sum 3-21\n",
+"clc;\n",
+"clear;\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",
+"\n",
+" // printing data in scilab o/p window\n",
+" printf('T1 is %0.2f N/mm^2 ',T1);\n",
+" printf('\n theta is %0.2f deg ',theta);\n",
+" printf('\n Tr is %0.2f N/mm^2 ',Tr);"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3.22: MS22.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// sum 3-22\n",
+"clc;\n",
+"clear;\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",
+"\n",
+" // printing data in scilab o/p window\n",
+" printf('Ts1 is %0.3f N/mm^2 ',Ts1);\n",
+" printf('\n Tc1 is %0.1f N/mm^2 ',Tc1);\n",
+" printf('\n theta/length is %0.3f deg/m ',tl);\n",
+" printf('\n Ts2 is %0.3f N/mm^2 ',Ts2);\n",
+" printf('\n Tc2 is %0.2f N/mm^2 ',Tc2);"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3.23: MS23.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// sum 3-23\n",
+"clc;\n",
+"clear;\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",
+"\n",
+" // printing data in scilab o/p window\n",
+" printf('Tmax is %0.3f MPa ',Tmax);"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3.24: MS24.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// sum 3-24\n",
+"clc;\n",
+"clear;\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",
+"\n",
+" // printing data in scilab o/p window\n",
+" printf('d is %0.1f mm ',d);"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3.25: MS25.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// sum 3-25\n",
+"clc;\n",
+"clear;\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",
+"\n",
+" // printing data in scilab o/p window\n",
+" printf('d is %0.1f mm ',d2);"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3.26: MS26.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// sum 3-26\n",
+"clc;\n",
+"clear;\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",
+"\n",
+" // printing data in scilab o/p window\n",
+" printf('d1 is %0.2f mm ',d1);\n",
+" printf('\n d2 is %0.1f mm ',d2);\n",
+" printf('\n d3 is %0.2f mm ',d3);"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3.27: MS27.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// sum 3-27\n",
+"clc;\n",
+"clear;\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) then\n",
+" printf('The component is safe')\n",
+"end\n",
+"\n",
+" // printing data in scilab o/p window\n",
+" printf('\n Tmax is %0.1f MPa ',Tmax);"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3.28: MS28.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// sum 3-28\n",
+"clc;\n",
+"clear;\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",
+"\n",
+" // printing data in scilab o/p window\n",
+" printf('N is %0.3f rpm ',N);"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3.29: MS29.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// sum 3-29\n",
+"clc;\n",
+"clear;\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=50:200\n",
+"n=length(r);\n",
+"for i=1:n\n",
+" sigr(i)=x-(y/r(i)^2)-(r(i)^2*y1)\n",
+"end\n",
+"\n",
+"for j=1:n\n",
+" sigc(j)=x+(y/r(j)^2)-(r(j)^2*z)\n",
+"end\n",
+"\n",
+"plot (r,sigr);\n",
+"plot (r,sigc);\n",
+"xtitle('','r mm');\n",
+"ylabel('stress N/mm^2');\n",
+"xgrid(2);\n",
+"\n",
+" // printing data in scilab o/p window\n",
+" printf('sigrmax is %0.1f MPa ',sigrmax);"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3.2: MS2.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// sum 3-2\n",
+"clc;\n",
+"clear;\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",
+"\n",
+" // printing data in scilab o/p window\n",
+" printf('del is %f mm ',del);"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3.30: MS30.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// sum 3-30\n",
+"clc;\n",
+"clear;\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",
+"\n",
+" // printing data in scilab o/p window\n",
+" printf('t is %0.3f mm ',t);"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3.31: MS31.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// sum 3-31\n",
+"clc;\n",
+"clear;\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",
+"// printing data in scilab o/p window\n",
+" printf('sigB is %0.1f MPa ',sigB);\n",
+" printf('\n sigA 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": [
+ "## Example 3.32: MS32.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// sum 3-32\n",
+"clc;\n",
+"clear;\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",
+"// printing data in scilab o/p window\n",
+" printf('Ra is %0.2f N/mm^2 ',Ra);\n",
+" printf('\n Rb is %0.2f N/mm^2 ',Rb);\n",
+"\n",
+"//The difference in the answers are due to rounding-off of values."
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3.33: MS33.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// sum 3-33\n",
+"clc;\n",
+"clear;\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",
+"// printing data in scilab o/p window\n",
+" printf('sigA is %0.2f MPa ',sigA);\n",
+" printf('\n sigB is %0.2f MPa ',sigB);\n",
+" \n",
+" //The difference in the answers are due to rounding-off of values.\n",
+""
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3.3: MS3.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// sum 3-3\n",
+"clc;\n",
+"clear;\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",
+"\n",
+" // printing data in scilab o/p window\n",
+" printf('del is %f N/mm^2 ',sigi);"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3.4: MS4.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// sum 3-4\n",
+"clc;\n",
+"clear;\n",
+"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",
+"\n",
+" // printing data in scilab o/p window\n",
+" printf('sigmax1 is %f N/mm^2 ',sigmax1);\n",
+" printf('\n sigmax2 is %f N/mm^2 ',sigmax2);"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3.5: MS5.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// sum 3-5\n",
+"clc;\n",
+"clear;\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",
+"\n",
+" // printing data in scilab o/p window\n",
+" printf('sigt is %f N/mm^2 ',sigt);\n",
+" printf('\n sigb is %f N/mm^2 ',sigb);"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3.6: MS6.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// sum 3-6\n",
+"clc;\n",
+"clear;\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",
+"\n",
+" // printing data in scilab o/p window\n",
+" printf('P is %f kN ',P);\n",
+" printf('\n delL is %f mm ',delL);\n",
+" \n",
+" // The difference in the answer of delL is due to round-off errors."
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3.7: MS7.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// sum 3-7\n",
+"clc;\n",
+"clear;\n",
+"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",
+"\n",
+" // printing data in scilab o/p window\n",
+" printf('delT is %f degC ',delT);"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3.8: MS8.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// sum 3-8\n",
+"clc;\n",
+"clear;\n",
+"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",
+"// printing data in scilab o/p window\n",
+" printf('Stress on plane AB is %f MPa ',OM);\n",
+" printf('\n Stress on plane AB is %f MPa ',KM);\n",
+" printf('\n Principal stress p1 is %f MPa ',p1);\n",
+" printf('\n Principal stress p2 is %f MPa ',p2);\n",
+" printf('\n Principal angle theta1 is %f deg ',theta1);\n",
+" printf('\n Principal angle theta2 is %f deg ',theta2);\n",
+" printf('\n Maximum shear stress is %f MPa ',Tmax);\n",
+" printf('\n Direction of plane theta3 is %f deg ',theta3);\n",
+" printf('\n Direction of plane theta4 is %f deg ',theta4);\n",
+"\n",
+"//The answers in the book are written in form of degrees and minutes.\n",
+"\n",
+"\n",
+"\n",
+"\n",
+""
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 3.9: MS9.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// sum 3-9\n",
+"clc;\n",
+"clear;\n",
+"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",
+"\n",
+" // printing data in scilab o/p window\n",
+" printf('p1 is %f MN/mm^2 ',p1);\n",
+" printf('\n p2 is %f MN/mm^2 ',p2);"
+ ]
+ }
+],
+"metadata": {
+ "kernelspec": {
+ "display_name": "Scilab",
+ "language": "scilab",
+ "name": "scilab"
+ },
+ "language_info": {
+ "file_extension": ".sce",
+ "help_links": [
+ {
+ "text": "MetaKernel Magics",
+ "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
+ }
+ ],
+ "mimetype": "text/x-octave",
+ "name": "scilab",
+ "version": "0.7.1"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}