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+{
+"cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 5: UNIAXIAL DEFORMATIONS"
+ ]
+ },
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 5.10: Chapter5_Example_10.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clc\n",
+"// initialization\n",
+"clear\n",
+"d=10 //cm\n",
+"id=9.99 //cm\n",
+"t=3 //mm\n",
+"E=1.0*10^6 //kg/cm^2\n",
+"a=2.02*10^-5 // degree/celcius\n",
+"// part(a)\n",
+"Tr=10 //degree C\n",
+"T=(d-id)/id*1/a\n",
+"printf('part(a) \n The sleeve must be heated to %.1f degree C or more for this purpose',T+Tr)\n",
+"\n",
+"//part(b)\n",
+"s_th=a*T*E\n",
+"p=s_th*t*2/(d*10)\n",
+"printf('\n part(b) \n The pressure developed between the rod and sleeve is %d kg/cm^2',p)\n",
+"\n",
+"// part(c)\n",
+"f=0.2\n",
+"o=10 // overlap: cm\n",
+"A=%pi*d*o\n",
+"F=f*p*A\n",
+"printf('\n part (c) \n The axial force required is %d kg',F)\n",
+"\n",
+"//part (d)\n",
+"// linked to part c\n",
+"T2=20 //degree C\n",
+"a2=1.17*10^-5 // /degree C\n",
+"Ts=(a-a2)*(T2-Tr)*E\n",
+"Ts=s_th-Ts\n",
+"p2=p*Ts/s_th\n",
+"F2=F*Ts/s_th\n",
+"printf('\n part(d)\n The pressure developed between the rod and sleeve is %.1f kg/cm^2',p2)\n",
+"printf('\n The axial force required is %d kg',F2)\n",
+"//part(e)\n",
+"T3=Tr+(s_th/((a-a2)*10^6))\n",
+"printf('\n part(e) \n The temperature at which the sleeve comes off easily is %.1f C',T3)\n",
+"\n",
+"// calculations in the text: rounding off errors\n",
+""
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 5.11: Chapter5_Example_11.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clc\n",
+"//initialization of variables\n",
+"clear\n",
+"T1=37.8 // degre C\n",
+"t=0.355 //mm\n",
+"T2=93.3 // degree C\n",
+"L=2 //cm\n",
+"m=1\n",
+"n=1.53\n",
+"a=1.86*10^-5\n",
+"//calculations\n",
+"R=2*t*(3*(1+m)^2+(1+m*n)*(m^2+(m*n)^-1))\n",
+"R=R/(6*a*(T2-T1)*(1+m^2)) // mm\n",
+"R=R/10\n",
+"def=L^2/(8*R)\n",
+"// results\n",
+"printf('The radius of curvature is %.1f cm',R)\n",
+"printf('\n The deflection is %.6f cm',def)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 5.12: Chapter5_Example_12.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clc\n",
+"// initialization of variables\n",
+"clear\n",
+"L=5 //cm\n",
+"D=1.8 //cm\n",
+"l=2.5 //cm\n",
+"d=1.5 //cm\n",
+"F=1 //tonne\n",
+"E=2.1*10^6 //kg/cm^2\n",
+"// calculations\n",
+"s1=F*1000*4/(D^2*%pi)\n",
+"s2=F*1000*4/(d^2*%pi)\n",
+"U1=1/2*s1^2/E\n",
+"U1=U1*L*D^2*%pi/4\n",
+"U2=1/2*s2^2/E\n",
+"U2=U2*l*d^2*%pi/4\n",
+"U=U1+U2\n",
+"// results\n",
+"printf('The energy stored in the bolt is %.3f kg-cm',U)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 5.13: Chapter5_Example_13.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clc\n",
+"// initialization of variables\n",
+"clear\n",
+"t=16 //mm\n",
+"Pt=1500 //kg/cm^2\n",
+"Ps=1025 //kg/cm^2\n",
+"Pb=2360 //kg/cm^2\n",
+"\n",
+"//part (a)\n",
+"p=6 //cm\n",
+"r=24 //mm\n",
+"d=r/10+0.15\n",
+"Ft=t*(p-d)*Pt/10\n",
+"Fs=%pi*d^2*Ps/4\n",
+"Fb=d*t*Pb\n",
+"x=min(Ft,Fs,Fb)\n",
+"effA=x*100/(p*t/10*Pt)\n",
+"\n",
+"//part (b)\n",
+"p=9 //cm\n",
+"r=30 //mm\n",
+"d=r/10+0.2\n",
+"Ft=t*(p-d)*Pt/10\n",
+"Fs=%pi*d^2*Ps/4\n",
+"Fb=d*t*Pb\n",
+"x=min(Ft,Fs,Fb)\n",
+"effB=x*100/(p*t/10*Pt)\n",
+"\n",
+"// results\n",
+"printf('The efficiencies corresponding to cases a and b are %.1f, %.1f',effA,effB)\n",
+"printf('\n Hence part b is better than part a')"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 5.1: Chapter5_Example_1.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clc\n",
+"//initialization of variables\n",
+"clear\n",
+"l=20 //cm\n",
+"dL=1 //m\n",
+"dl=0.004 //cm\n",
+"//calculations\n",
+"L=l*dL/dl //m\n",
+"//results\n",
+"printf('The depth of the clay bed is %d m',L)\n",
+""
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 5.2: Chapter5_Example_2.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clc\n",
+"//initialization of variables\n",
+"clear\n",
+"A=1 //unit area\n",
+"E=2*10^6 //kg/cm^2\n",
+"// calculations\n",
+"db=3000*90/(A*E)\n",
+"dc=db+5000*60/(A*E)\n",
+"dd=dc+4000*30/(A*E)\n",
+"//results\n",
+"printf('The extension of the rod in part AB is %.2e cm in part BC is %.2e cm \n and in part CD is %.2e cm',db,dc,dd)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 5.3: Chapter5_Example_3.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clc\n",
+"//initialization of variables\n",
+"clear\n",
+"A=3 //cm^2\n",
+"L=18 //m\n",
+"E= 2*10^6 //kg/cm^2\n",
+"r=7833 //kg/m^3\n",
+"//calculations\n",
+"e=r*(L*100)^2/(2*E*10^6)\n",
+"// results\n",
+"printf('The elongation is %.5f cm',e)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 5.4: Chapter5_Example_4.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clc\n",
+"//initialization of variables\n",
+"clear\n",
+"// linked to 5_3\n",
+"P=3 //tonne\n",
+"E=2*10^6 //kg/cm^2\n",
+"d_0= 1 //cm\n",
+"d_l=2.8 //cm\n",
+"// calculations\n",
+"e=4*P*1000*d_l*10^3/(d_l^2*%pi*E*(1-((d_l-d_0)/d_l)))\n",
+"//results\n",
+"printf('The total elongation is %.2f cm',e)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 5.6: Chapter5_Example_6.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clc\n",
+"//initialization of variables\n",
+"clear\n",
+"P=10 //tonne\n",
+"E=2*10^6 //kg/cm^2\n",
+"// calculations\n",
+"// We have to solve linear system Ax=B\n",
+"A=[1 1 1 0\n",
+" 3 1 -3 0\n",
+" -2 2 0 -E\n",
+" 0 -1 2 -E]\n",
+"B=[P*10^3;0;0;0]\n",
+"x=inv(A)*B\n",
+"W1=x(1,1)/1000\n",
+"W2=x(2,1)/1000\n",
+"W3=x(3,1)/1000\n",
+"th=x(4,1)\n",
+"//results\n",
+"printf('The load taken by each rod is %.2f tonne, %.1f tonne, %.3f tonne',W1,W2,W3)\n",
+"printf('\n and the slope is theta = %.2e. radians',th) "
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 5.8: Chapter5_Example_8.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clc\n",
+"// initialization of variables\n",
+"clear\n",
+"b=30 // cm\n",
+"h=30 //cm\n",
+"n=6\n",
+"A=36 //cm^2\n",
+"ss_s=1500 //kg/cm^2\n",
+"ss_c=60 //kg/cm^2\n",
+"Er=15 // Elasticity ratio\n",
+"// calculations\n",
+"L=A*Er*ss_c+(b*h-A)*ss_c\n",
+"// results\n",
+"printf('The safe load is %d.kg',L)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 5.9: Chapter5_Example_9.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clc\n",
+"// initiaization of variables\n",
+"clear\n",
+"gs_b=10 //cm\n",
+"gs_h=10 //cm\n",
+"d_b=2 //cm\n",
+"d_h=2 //cm\n",
+"As= 1 //cm^2\n",
+"s=10000 //kg/cm^2\n",
+"// part (a)\n",
+"Es=2*10^6 //kg/cm^2\n",
+"Ec=2*10^5 //kg/cm^2\n",
+"// calculations\n",
+"e=s/Es\n",
+"Ac=gs_b*gs_h-(d_b*d_h)\n",
+"e_c=e*Es*As/(Ec*Ac+Es*As)\n",
+"s_c=Ec*e_c\n",
+"e_s=e-e_c\n",
+"s_s=Es*e_s\n",
+"// results\n",
+"printf('part (a) \n The stress in steel and concrete are respectively %d , %.2e kg/cm^2',s_s,s_c)\n",
+"// part(b)\n",
+"P=8000 //kg\n",
+"// calculations\n",
+"e_c=(e*Es*As-P)/(Ec*Ac+Es*As)\n",
+"e_s=e-e_c\n",
+"s_c=Ec*e_c\n",
+"s_s=Es*e_s\n",
+"// results\n",
+"printf('\n part (b) \n The stress in steel and concrete are respectively %.1f , %.2f kg/cm^2',s_s,s_c)\n",
+"\n",
+""
+ ]
+ }
+],
+"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
+}
generated by cgit (git 2.34.1) at 2024-12-19 17:03:20 +0000