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diff --git a/Solid_Mechanics_by_S_M_A_Kazimi/10-INTRODUCTION_TO_ENERGY_METHODS.ipynb b/Solid_Mechanics_by_S_M_A_Kazimi/10-INTRODUCTION_TO_ENERGY_METHODS.ipynb new file mode 100644 index 0000000..54e9dc6 --- /dev/null +++ b/Solid_Mechanics_by_S_M_A_Kazimi/10-INTRODUCTION_TO_ENERGY_METHODS.ipynb @@ -0,0 +1,254 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 10: INTRODUCTION TO ENERGY METHODS" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 10.11: Chapter10_Example_11.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"//initialization of variables\n", +"clear\n", +"A=100 //cm^2\n", +"E=2*10^6 //kg/cm^2\n", +"// calculations\n", +"del=1093.5*10^6/(E*A)\n", +"// 1093.5 from the table\n", +"// results\n", +"printf('Central deflection = %.2f mm',del)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 10.12: Chapter10_Example_12.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"//initialization of variables\n", +"clear\n", +"T=30 //degree celcius\n", +"alpha=0.0000117 // per degree celcius\n", +"//AB\n", +"L=6 //m\n", +"dl=T*alpha*L\n", +"df=0.375 //kg\n", +"tot=dl*df\n", +"//BC\n", +"dl=T*alpha*L\n", +"df=0.375 //kg\n", +"tot=tot+dl*df\n", +"//CD\n", +"dl=T*alpha*L\n", +"df=0.75 //kg\n", +"tot=tot+dl*df\n", +"tot=tot*100*2\n", +"// results\n", +"printf('The deflection is %.4f cm',tot)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 10.3: Chapter10_Example_3.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"//initialization of variables\n", +"clear\n", +"L=6000 //cm\n", +"L1=150 //cm\n", +"T=90 //W\n", +"Ip=%pi*10^4/32\n", +"E=2*10^6 //kg/cm^2\n", +"G=E/2.5\n", +"A=3 //cm^2\n", +"delta=0.5\n", +"//calculations\n", +"U=L/(2*E*A)+(T*T*L1/(2*G*Ip))\n", +"// U=0.5*W*delta\n", +"W=0.25/U\n", +"//results\n", +"printf('W = %.1f kg',W)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 10.4: Chapter10_Example_4.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"//initialization of variabes\n", +"clear\n", +"cA=10 //cm^2\n", +"wA=5 //cm^2\n", +"P=1 //tonne\n", +"E=2*10^6 //kg/cm^2\n", +"P=P*1000 //kg\n", +"// calculations\n", +"U_up=P^2*200/(2*E*cA)*1/sqrt(3)*(2+4+6+8+10+12)\n", +"U_do=P^2*200/(2*E*cA)*1/sqrt(3)*(1+3+5+7+9+11+13/2)\n", +"U_web=P^2*200/(2*E*wA)*1/sqrt(3)*(2*13)\n", +"U=U_up+U_do+U_web\n", +"delta=U*2/(P)\n", +"// results\n", +"printf('deflection = %.3f cm',delta)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 10.7: Chapter10_Example_7.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"//initialization of variables\n", +"clear\n", +"L=1 //m\n", +"w=10 //kg\n", +"h=50 //cm\n", +"A=1 //cm^2\n", +"E=2*10^6 //kg/cm^2\n", +"Ar=1 //cm^2\n", +"Ec=3*10^4 //kg/cm^2\n", +"// For steel\n", +"del=w*L*100/(A*E)\n", +"P=w*(1+sqrt(1+(2*h/del)))\n", +"printf('Stress in steeel = %d kg/cm^2 ',P)\n", +"\n", +"// for cloth laminate\n", +"del=w*L*100/(A*Ec)\n", +"P=w*(1+sqrt(1+(2*h/del)))\n", +"printf('\n Stress in cloth laminate = %.1f kg/cm^2 ',P)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 10.8: Chapter10_Example_8.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"//initialization of variables\n", +"clear\n", +"w=64 //kg\n", +"H=60 //cm\n", +"b=40 //cm\n", +"h=5 //cm\n", +"E=0.12*10^6 //kg/cm^2\n", +"Es=2*10^6 //kg/cm^2\n", +"// for part (a) and (b)\n", +"I=b*h^3/12\n", +"del=4*w*120^3/(E*I)\n", +"P=w*(1+sqrt(1+(2*H/del)))\n", +"str=P*240*6/(b*h^2)\n", +"printf('part (a) and (b)')\n", +"printf('\n Maximum stress in wood = %d kg/cm^2',str)\n", +"printf('\n Max. force on divers feet = %d kg',P)\n", +"\n", +"//for part (c)\n", +"Ixx=I*E/Es\n", +"Zxx=19.4 //cm^2\n", +"Ixx=72.7 //cm^4\n", +"del=4*w*120^3/(Es*Ixx)\n", +"P=w*(1+sqrt(1+(2*H/del)))\n", +"str=P*240/Zxx\n", +"// results\n", +"printf('\n part (c)')\n", +"printf('\n Maximum stress in steel = %d kg/cm^2',str)\n", +"printf('\n Max. force on divers feet = %d kg',P)\n", +"printf('\n Hence wood is better than steel')\n", +"\n", +"// wrong calculations in some parts" + ] + } +], +"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 +} diff --git a/Solid_Mechanics_by_S_M_A_Kazimi/2-ANALYSIS_OF_STRESS_.ipynb b/Solid_Mechanics_by_S_M_A_Kazimi/2-ANALYSIS_OF_STRESS_.ipynb new file mode 100644 index 0000000..2816af0 --- /dev/null +++ b/Solid_Mechanics_by_S_M_A_Kazimi/2-ANALYSIS_OF_STRESS_.ipynb @@ -0,0 +1,304 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 2: ANALYSIS OF STRESS " + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.10: Chapter2_Example_10.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"// initialization of variables\n", +"clear\n", +"tau_xx= -1 // kgf/cm^2\n", +"tau_yy= 0 // kgf/cm^2\n", +"tau_xy= 7 // kgf/cm^2\n", +"// calculations \n", +"sigma_1=(tau_xx+tau_yy)/2+sqrt((1/2*(tau_xx-tau_yy))^2+tau_xy^2)\n", +"sigma_2=(tau_xx+tau_yy)/2-sqrt((1/2*(tau_xx-tau_yy))^2+tau_xy^2)\n", +"x=sigma_1 // positive one is tension\n", +"if(sigma_2>sigma_1)\n", +" x=sigma_2\n", +"end\n", +"// Results\n", +"printf('The diagonal tension is %.3f kgf/cm^2',x)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.11: Chapter2_Example_11.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"// initialization of variables\n", +"clear\n", +"d=2 // m\n", +"l=10 // m\n", +"t=1 // cm\n", +"p=15 // kgf/cm^2\n", +"pitch= 2*%pi //m\n", +"//calculations\n", +"w=2*%pi*d/2 // m\n", +"theta=atan(w/(2*%pi))\n", +"sigma_z=p*d*100/(4*t)\n", +"sigma_th=p*d*100/(2*t)\n", +"sigma_th_new=(sigma_th+sigma_z)/2+(sigma_th-sigma_z)/2*cos(2*theta)\n", +"tau_thz=(sigma_z-sigma_th)*sin(2*theta)/2\n", +"// results\n", +"printf('At the junction, the normal and shear stresses are %d and %d kgf/cm^2 \n respectively, and the rivets must be designed for this',sigma_th_new,-tau_thz)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.4: Chapter2_Example_4.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"// initialization of variables\n", +"clear\n", +"tau=[200 100 0\n", +" 100 0 0\n", +" 0 0 500] // some units\n", +"theta=60 // degrees\n", +"//calculations\n", +"theta=theta*%pi/180\n", +"a=[cos(theta) sin(theta) 0\n", +" -sin(theta) cos(theta) 0\n", +" 0 0 1]\n", +"b=a.'\n", +"tau_new=a*tau*b\n", +"// Results\n", +"printf('The new stress tensor is')\n", +"disp(tau_new)\n", +"\n", +" \n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.5: Chapter2_Example_5.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"// initialization of variables\n", +"clear\n", +"sigma_1=100 //kg*f/cm^2\n", +"sigma_2=100 //kg*f/cm^2\n", +"sigma_3=-200 //kg*f/cm^2\n", +"// calculations\n", +"tau_oct=1/3*sqrt((sigma_1-sigma_2)^2+(sigma_2-sigma_3)^2+(sigma_3-sigma_1)^2)\n", +"// Results\n", +"printf('Octahedra shear stress at the point is=%.1f kgf/cm^2',tau_oct)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.7: Chapter2_Example_7.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"// initialization of variables\n", +"clear\n", +"tau=[200 100 0\n", +" 100 0 0\n", +" 0 0 500] // some units\n", +"theta=60 // degrees\n", +"//calculations\n", +"theta=theta*%pi/180\n", +"a=[cos(theta) sin(theta) 0\n", +" -sin(theta) cos(theta) 0\n", +" 0 0 1]\n", +"b=a.'\n", +"tau_new=a*tau*b\n", +"\n", +"// stress invariants :old \n", +"I1=tau(1,1)+tau(2,2)+tau(3,3)\n", +"I2=tau(1,1)*tau(2,2)+tau(2,2)*tau(3,3)+tau(3,3)*tau(1,1)-(tau(1,2)^2+tau(2,3)^2+tau(3,1)^2)\n", +"I3=tau(1,1)*tau(2,2)*tau(3,3)+2*tau(1,2)*tau(2,3)*tau(3,1)-(tau(1,1)*tau(2,3)^2+tau(2,2)*tau(3,1)^2+tau(3,3)*tau(1,2)^2)\n", +"\n", +"// stress invariants :new\n", +"I11=tau_new(1,1)+tau_new(2,2)+tau_new(3,3)\n", +"I22=tau_new(1,1)*tau_new(2,2)+tau_new(2,2)*tau_new(3,3)+tau_new(3,3)*tau_new(1,1)-(tau_new(1,2)^2+tau_new(2,3)^2+tau_new(3,1)^2)\n", +"I33=tau_new(1,1)*tau_new(2,2)*tau_new(3,3)+2*tau_new(1,2)*tau_new(2,3)*tau_new(3,1)-(tau_new(1,1)*tau_new(2,3)^2+tau_new(2,2)*tau_new(3,1)^2+tau_new(3,3)*tau_new(1,2)^2)\n", +"\n", +"// Results\n", +"printf('The invariants of old stress tensor are I1=%0.2f I2=%.e I3=%.e \n and that of the new stress tensor are I1=%0.2f I2=%.e I3=%.e',I1,I2,I3,I11,I22,I33)\n", +"printf('\n Hence the same stress tensor invariants')\n", +"\n", +"\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.8: Chapter2_Example_8.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"// initialization of variables\n", +"clear\n", +"sigma_3=0 // kgf/cm^2\n", +"tau_oct=1500 // kgf/cm^2\n", +"n=2 // given that sigma_1=n*sigma_2\n", +"// calculations\n", +"sigma_2=1500*3/(sqrt(2*n^2-2*n+2)) // // kgf/cm^2\n", +"sigma_1=n*sigma_2 // kgf/cm^2 \n", +"sigma_0=4500/sqrt(2) // kgf/cm^2\n", +"// Results\n", +"printf('The necessary stresses sigma_1, sigma_2 for biaxial yielding are \n %d kgf/cm^2, %d kgf/cm^2 and for uniaxial yielding sigma_0 %0.2f kgf/cm^2.',sigma_1,sigma_2,sigma_0);\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.9: Chapter2_Example_9.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"// initialization of variables\n", +"clear\n", +"// part (a)\n", +"tau_xx=300 // kgf/cm^2\n", +"tau_yy=0 // kgf/cm^2\n", +"tau_xy=600 // kgf/cm^2\n", +"// calculations\n", +"sigma_1=(tau_xx+tau_yy)/2+sqrt((1/2*(tau_xx-tau_yy))^2+tau_xy^2)\n", +"sigma_2=(tau_xx+tau_yy)/2-sqrt((1/2*(tau_xx-tau_yy))^2+tau_xy^2)\n", +"Beta=atan(2*tau_xy/(tau_xx-tau_yy))\n", +"Beta=Beta*180/%pi\n", +"// Results\n", +"printf('Part (a) \n The magnitude of principal stresses are %d,%d kgf/cm^2 and \n the direction is given by 2*beta=%.2f degrees',sigma_1,sigma_2,Beta)\n", +"\n", +"//part (b)\n", +"tau_xx=1000 // kgf/cm^2\n", +"tau_yy=150 // kgf/cm^2\n", +"tau_xy=450 // kgf/cm^2\n", +"// calculations\n", +"sigma_1=(tau_xx+tau_yy)/2+sqrt((1/2*(tau_xx-tau_yy))^2+tau_xy^2)\n", +"sigma_2=(tau_xx+tau_yy)/2-sqrt((1/2*(tau_xx-tau_yy))^2+tau_xy^2)\n", +"Beta=atan(2*tau_xy/(tau_xx-tau_yy))\n", +"Beta=Beta*180/%pi\n", +"// Results\n", +"printf('\n Part (b) \n The magnitude of principal stresses are %d,%d kgf/cm^2 and \n the direction is given by 2*beta=%.2f degrees',sigma_1,sigma_2,Beta)\n", +"\n", +"// part (c)\n", +"tau_xx=-850 // kgf/cm^2\n", +"tau_yy=350 // kgf/cm^2\n", +"tau_xy=700 // kgf/cm^2\n", +"// calculations\n", +"sigma_1=(tau_xx+tau_yy)/2+sqrt((1/2*(tau_xx-tau_yy))^2+tau_xy^2)\n", +"sigma_2=(tau_xx+tau_yy)/2-sqrt((1/2*(tau_xx-tau_yy))^2+tau_xy^2)\n", +"Beta=atan(2*tau_xy/(tau_xx-tau_yy))\n", +"Beta=Beta*180/%pi\n", +"// Results\n", +"printf('\n Part (c) \n The magnitude of principal stresses are %d,%d kgf/cm^2 and \n the direction is given by 2*beta=%0.2f',sigma_1,sigma_2,-Beta)\n", +"\n", +"// wrong answers were given in textbook for part (b)\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 +} diff --git a/Solid_Mechanics_by_S_M_A_Kazimi/3-ANALYSIS_OF_STRAINS.ipynb b/Solid_Mechanics_by_S_M_A_Kazimi/3-ANALYSIS_OF_STRAINS.ipynb new file mode 100644 index 0000000..0aaefd2 --- /dev/null +++ b/Solid_Mechanics_by_S_M_A_Kazimi/3-ANALYSIS_OF_STRAINS.ipynb @@ -0,0 +1,217 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 3: ANALYSIS OF STRAINS" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.3: Chapter3_Example_3.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"// initialization of variables\n", +"clear\n", +"epsillon=[0.01 0 0\n", +" 0 0.02 0.02\n", +" 0 0.02 0.01] // dimensionless\n", +"theta=30 // degrees\n", +"//calculations\n", +"theta=theta*%pi/180\n", +"a=[cos(theta) sin(theta) 0\n", +" -sin(theta) cos(theta) 0\n", +" 0 0 1]\n", +"b=a.'\n", +"epsillon_new=a*epsillon*b\n", +"// calculation of strain invariants\n", +"// for epsillon\n", +"J1=epsillon(1,1)+epsillon(2,2)+epsillon(3,3)\n", +"J2=epsillon(1,1)*epsillon(2,2)+epsillon(2,2)*epsillon(3,3)+epsillon(3,3)*epsillon(1,1)-2*(epsillon(1,2)^2+epsillon(2,3)^2+epsillon(3,1)^2)\n", +"J3=epsillon(1,1)*epsillon(2,2)*epsillon(3,3)+2*epsillon(1,2)*epsillon(2,3)*epsillon(3,1)-(epsillon(1,1)*epsillon(2,3)^2+epsillon(2,2)*epsillon(3,1)^2+epsillon(3,3)*epsillon(1,2)^2)\n", +"\n", +"// for epsillon_new\n", +"J11=epsillon_new(1,1)+epsillon_new(2,2)+epsillon_new(3,3)\n", +"J22=epsillon_new(1,1)*epsillon_new(2,2)+epsillon_new(2,2)*epsillon_new(3,3)+epsillon_new(3,3)*epsillon_new(1,1)-2*(epsillon_new(1,2)^2+epsillon_new(2,3)^2+epsillon_new(3,1)^2)\n", +"J33=epsillon_new(1,1)*epsillon_new(2,2)*epsillon_new(3,3)+2*epsillon_new(1,2)*epsillon_new(2,3)*epsillon_new(3,1)-(epsillon_new(1,1)*epsillon_new(2,3)^2+epsillon_new(2,2)*epsillon_new(3,1)^2+epsillon_new(3,3)*epsillon_new(1,2)^2)\n", +"\n", +"// results\n", +"printf('The new strain tensor is');\n", +"disp(epsillon_new);\n", +"printf('The strain invariants of old strain tensor are J1=%0.2f J2=%.e J3=%.e \n and that of the new strain tensor are J1=%0.2f J2=%.e J3=%.e',J1,J2,J3,J11,J22,J33)\n", +"printf('\n Hence the same strain invariants')\n", +"\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.4: Chapter3_Example_4.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"// initialization of variables\n", +"clear\n", +"epsillon=[0.01 -0.02 0\n", +" -0.02 0.03 -0.01\n", +" 0 -0.01 0] // dimensionless\n", +"a_xx=0.6 \n", +"theta=acos(a_xx) // radians\n", +"//calculations\n", +"// theta=theta*%pi/180\n", +"a=[cos(theta) 0 -sin(theta)\n", +" 0 1 0\n", +" sin(theta) 0 cos(theta)]\n", +"b=a.'\n", +"epsillon_new=a*epsillon*b\n", +"\n", +"// calculation of strain invariants\n", +"// for epsillon\n", +"J1=epsillon(1,1)+epsillon(2,2)+epsillon(3,3)\n", +"\n", +"J2=epsillon(1,1)*epsillon(2,2)+epsillon(2,2)*epsillon(3,3)+epsillon(3,3)*epsillon(1,1)-2*(epsillon(1,2)^2+epsillon(2,3)^2+epsillon(3,1)^2)\n", +"\n", +"J3=epsillon(1,1)*epsillon(2,2)*epsillon(3,3)+2*epsillon(1,2)*epsillon(2,3)*epsillon(3,1)-(epsillon(1,1)*epsillon(2,3)^2+epsillon(2,2)*epsillon(3,1)^2+epsillon(3,3)*epsillon(1,2)^2)\n", +"\n", +"// for epsillon_new\n", +"J11=epsillon_new(1,1)+epsillon_new(2,2)+epsillon_new(3,3)\n", +"\n", +"J22=epsillon_new(1,1)*epsillon_new(2,2)+epsillon_new(2,2)*epsillon_new(3,3)+epsillon_new(3,3)*epsillon_new(1,1)-2*(epsillon_new(1,2)^2+epsillon_new(2,3)^2+epsillon_new(3,1)^2)\n", +"\n", +"J33=epsillon_new(1,1)*epsillon_new(2,2)*epsillon_new(3,3)+2*epsillon_new(1,2)*epsillon_new(2,3)*epsillon_new(3,1)-(epsillon_new(1,1)*epsillon_new(2,3)^2+epsillon_new(2,2)*epsillon_new(3,1)^2+epsillon_new(3,3)*epsillon_new(1,2)^2)\n", +"\n", +"// Results\n", +"printf('The new strain tensor is')\n", +"disp(epsillon_new)\n", +"printf('The strain invariants of old stress tensor are J1=%0.2f J2=%.e J3=%.e \n and that of the new stress tensor are J1=%0.2f J2=%.e J3=%.e',J1,J2,J3,J11,J22,J33)\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.5: Chapter3_Example_5.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"// initialization of variables\n", +"clear\n", +"epsillon_A= 700*10^-6 \n", +"epsillon_B= 300*10^-6 \n", +"epsillon_C= 300*10^-6 \n", +"theta=45 // degrees\n", +"theta=theta*%pi/180 // radians\n", +"// calculations\n", +"epsillon_x=epsillon_A\n", +"epsillon_y=epsillon_C\n", +"gamma_xy=(epsillon_B-(epsillon_x*cos(theta)^2+epsillon_y*sin(theta)^2))/(sin(theta)*cos(theta))\n", +"epsillon_1=1/2*(epsillon_x+epsillon_y)+(1/2)*sqrt((epsillon_x-epsillon_y)^2+gamma_xy^2)\n", +"epsillon_2=1/2*(epsillon_x+epsillon_y)-(1/2)*sqrt((epsillon_x-epsillon_y)^2+gamma_xy^2)\n", +"phi=0.5*atan(gamma_xy/(epsillon_x-epsillon_y))\n", +"phi=phi*180/%pi\n", +"//results\n", +"printf('The principal strains are %.3e, %.3e',epsillon_1,epsillon_2)\n", +"printf('\n phi = %.2f degrees',phi)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.6: Chapter3_Example_6.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"// initialization of variables\n", +"clear\n", +"epsillon_A= 1000*10^-6 \n", +"epsillon_B= 720*10^-6 \n", +"epsillon_C= 600*10^-6 \n", +"th_B=120 // degrees\n", +"th_C=240 // degrees\n", +"//calculations\n", +"th_B=th_B*%pi/180\n", +"th_C=th_C*%pi/180\n", +"// we need to solve for epsillon_y and gamma_xy\n", +"// Ax=B\n", +"ep_x=epsillon_A\n", +"A=[sin(th_B)^2 sin(th_B)*cos(th_B)\n", +" sin(th_C)^2 sin(th_C)*cos(th_C)]\n", +"C=[epsillon_B-ep_x*cos(th_B)^2; epsillon_C-ep_x*cos(th_C)^2] \n", +"x=inv(A)*C\n", +"ep_y=x(1,1)\n", +"gam_xy=x(2,1)\n", +"epsillon_x=ep_x\n", +"epsillon_y=ep_y\n", +"gamma_xy=gam_xy\n", +"epsillon_1=1/2*(epsillon_x+epsillon_y)+(1/2)*sqrt((epsillon_x-epsillon_y)^2+gamma_xy^2)\n", +"epsillon_2=1/2*(epsillon_x+epsillon_y)-(1/2)*sqrt((epsillon_x-epsillon_y)^2+gamma_xy^2)\n", +"// Results\n", +"printf('The principal strains are %.3e, %.3e',epsillon_1,epsillon_2)" + ] + } +], +"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 +} diff --git a/Solid_Mechanics_by_S_M_A_Kazimi/4-STRESS_STRAIN_RELATIONS.ipynb b/Solid_Mechanics_by_S_M_A_Kazimi/4-STRESS_STRAIN_RELATIONS.ipynb new file mode 100644 index 0000000..9744fbe --- /dev/null +++ b/Solid_Mechanics_by_S_M_A_Kazimi/4-STRESS_STRAIN_RELATIONS.ipynb @@ -0,0 +1,191 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 4: STRESS STRAIN RELATIONS" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.1: Chapter4_Example_1.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"// initialization of variables\n", +"clear\n", +"E=2*10^6 // kg/cm^2\n", +"G=8*10^5 // kg/cm^2\n", +"ep=[0.001 0 -0.002\n", +" 0 -0.003 0.0005\n", +" -0.002 0.0005 0]\n", +"// calculations\n", +"nu=E/(2*G)-1\n", +"lambda=E*nu/((1+nu)*(1-2*nu))\n", +"mu=G\n", +"sigma(1,1)=2*mu*ep(1,1)+lambda*(ep(1,1)+ep(2,2)+ep(3,3))\n", +"sigma(2,2)=2*mu*ep(2,2)+lambda*(ep(1,1)+ep(2,2)+ep(3,3))\n", +"sigma(3,3)=2*mu*ep(3,3)+lambda*(ep(1,1)+ep(2,2)+ep(3,3))\n", +"tau(1,2)=2*mu*ep(1,2)\n", +"tau(1,3)=2*mu*ep(1,3)\n", +"tau(2,3)=2*mu*ep(2,3)\n", +"tau=[sigma(1,1) tau(1,2) tau(1,3)\n", +" tau(1,2) sigma(2,2) tau(2,3)\n", +" tau(1,3) tau(2,3) sigma(3,3)]\n", +"// results\n", +"printf('The lames constants are %.e and %.e kg/cm^2',lambda,mu)\n", +"printf('\n The stres tensor is')\n", +"disp(tau) \n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.2: Chapter4_Example_2.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"// initialization of variables\n", +"clear\n", +"sigma_x=1000 //kg/cm^2\n", +"sigma_y=-500 //kg/cm^2\n", +"sigma_z=0 //kg/cm^2\n", +"tau_xy=500 //kg/cm^2\n", +"E=2*10^6 // kg/cm^2\n", +"nu=0.25\n", +"//calculations\n", +"ep_x=1/E*(sigma_x-nu*(sigma_y+sigma_z))\n", +"ep_y=1/E*(sigma_y-nu*(sigma_x+sigma_z))\n", +"ep_z=1/E*(sigma_z-nu*(sigma_y+sigma_x))\n", +"J1=ep_x+ep_y+ep_z\n", +"sigma_1=(sigma_x+sigma_y)/2+sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)\n", +"sigma_2=(sigma_x+sigma_y)/2-sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)\n", +"th=1/2*atan(2*tau_xy/(sigma_x-sigma_y))\n", +"th=th*180/%pi\n", +"ep_1=1/E*(sigma_1-nu*sigma_2)\n", +"ep_2=1/E*(sigma_2-nu*sigma_1)\n", +"ep_3=-1/E*nu*(sigma_1+sigma_2)\n", +"//results\n", +"printf('The magnitude of principal strain are %.8f, %.8f, %.8f',abs(ep_1),abs(ep_2),abs(ep_3))\n", +"printf('\n and the diection is given by theta=%.2f degrees',th)\n", +"printf('\n J1 is %.6f',J1)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.3: Chapter4_Example_3.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"// initialization of variables\n", +"clear\n", +"sigma_x=1400 //kg/cm^2\n", +"tau_xy=400// kg/cm^2\n", +"ep_z=-3.6*10^-6\n", +"nu=1/4\n", +"E=2*10^8 //kg/cm^2\n", +"// calculations\n", +"sigma_y=(-ep_z*E/nu)-sigma_x\n", +"sigma_1=(sigma_x+sigma_y)/2+sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)\n", +"sigma_2=(sigma_x+sigma_y)/2-sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)\n", +"th=0.5*atan(2*tau_xy/(sigma_x-sigma_y))\n", +"th=th*180/%pi\n", +"printf('sigma_y is %d kg/cm^2',sigma_y)\n", +"printf('\n The principal stresses are %d , %d kg/cm^2',sigma_1,sigma_2)\n", +"printf('\n The direction is given by theta = %.2f degrees',th)\n", +"\n", +"// angle was given wrong in the text" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.4: Chapter4_Example_4.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"//initialization of variables\n", +"clear\n", +"C=1000/3 //kg/cm^2\n", +"sigma_x=2*C\n", +"sigma_y=4*C\n", +"tau_xy=4*C\n", +"sigma_0=4*C\n", +"sigma_1=3+C*sqrt(2)\n", +"sigma_2=3-C*sqrt(2)\n", +"sigma_3=0\n", +"tau_oct=1/3*sqrt((sigma_1-sigma_2)^2+(sigma_2-sigma_3)^2+(sigma_3-sigma_1)^2)\n", +"tau_max=sigma_1/2\n", +"taU=1.885*C\n", +"tau_y=2*C\n", +"printf('Actual tau is %.3f',taU)\n", +"printf('\n tau_max at yield is %.3f',tau_y)\n", +"printf('\n Hence yielding doesn not occur according to Von-Miles condition \n but it occurs due to Tresca condition')" + ] + } +], +"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 +} diff --git a/Solid_Mechanics_by_S_M_A_Kazimi/5-UNIAXIAL_DEFORMATIONS.ipynb b/Solid_Mechanics_by_S_M_A_Kazimi/5-UNIAXIAL_DEFORMATIONS.ipynb new file mode 100644 index 0000000..aaae3bc --- /dev/null +++ b/Solid_Mechanics_by_S_M_A_Kazimi/5-UNIAXIAL_DEFORMATIONS.ipynb @@ -0,0 +1,449 @@ +{ +"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 +} diff --git a/Solid_Mechanics_by_S_M_A_Kazimi/6-TORSION_INCLUDING_NON_CIRCULAR_SECTIONS.ipynb b/Solid_Mechanics_by_S_M_A_Kazimi/6-TORSION_INCLUDING_NON_CIRCULAR_SECTIONS.ipynb new file mode 100644 index 0000000..d0289ea --- /dev/null +++ b/Solid_Mechanics_by_S_M_A_Kazimi/6-TORSION_INCLUDING_NON_CIRCULAR_SECTIONS.ipynb @@ -0,0 +1,653 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 6: TORSION INCLUDING NON CIRCULAR SECTIONS" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.11: Chapter6_Example_11.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"//initialization of variables\n", +"clear\n", +"d=5 //cm\n", +"rpm1=300 //rpm\n", +"rpm2=30000 //rpm\n", +"s=1000 //kg/cm^2\n", +"//calcuations\n", +"T=(d/2)*%pi*10^2*s/32\n", +"hp1= 2*%pi*rpm1*T/4500\n", +"hp2=hp1*100\n", +"// results\n", +"printf('Horse power at 300 rpm and 30000 rpm are respecively %d, %d h.p.',hp1/10,hp2/10)\n", +"\n", +"// wrong/approximate answers in the text" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.12: Chapter6_Example_12.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"// initialization of variables\n", +"clear\n", +"hp=300 //h.p.\n", +"N1=30 //rpm\n", +"N2=30000 //rpm\n", +"fs=600 //kg/cm^2\n", +"// calculations\n", +"T1=4500*hp*100/(2*%pi*N1)\n", +"T2=T1/1000\n", +"D1=16*T1/(%pi*fs)\n", +"D1=D1^(1/3)\n", +"D2=16*T2/(%pi*fs)\n", +"D2=D2^(1/3)\n", +"// results\n", +"printf('Diameters required are %.1f, %.1f cm',D1,D2)\n", +"\n", +"// wrong calculations in the text" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.13: Chapter6_Example_13.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"// initialization of variables\n", +"clear\n", +"d=10 //cm\n", +"t =1 //mm\n", +"T= 100 //kg-m\n", +"L=5 //m\n", +"G=8*10^5 //kg/cm^2\n", +"\n", +"//calculations\n", +"r=d/2\n", +"fs=T*r*100/(r^2*2*%pi*L*t*10^-1)\n", +"U=fs^2/(2*G)\n", +"U1=U*(%pi*L*100)\n", +"// results\n", +"printf('Energy per unit volume = %.3f kg-cm/cm^3',U)\n", +"printf('\n Total strain energy= %d kg-cm',U1)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.14: Chapter6_Example_14.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"//initialization of variables\n", +"clear\n", +"D=10 //cm\n", +"d= 1 //cm\n", +"n=20\n", +"P=60 //kg\n", +"G=8*10^5 //kg/cm^2\n", +"//calculations\n", +"n=n-0.75*2\n", +"delta=P*n*%pi*D^3*32/(4*%pi*G)\n", +"// results\n", +"printf('The deflection is %.1f cm',delta)\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.15: Chapter6_Example_15.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"//initialization of variables\n", +"clear\n", +"// linked to 6_14\n", +"D=10 //cm\n", +"d= 1 //cm\n", +"n=20\n", +"P=60 //kg\n", +"G=8*10^5 //kg/cm^2\n", +"// calculations\n", +"m=D/d\n", +"fs=8*P*D/(d^3*%pi)\n", +"fs1=fs*(1+0.615/m+3/(4*m-4))\n", +"// results\n", +"printf('The shear stress with and without correction facor are \n respectively %d, %d kg/cm^2',fs,fs1)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.16: Chapter6_Example_16.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"//initialization of variables\n", +"clear\n", +"\n", +"// circle\n", +"D=1 //unit diameter\n", +"Ip=D^4/32\n", +"Zp=D^3/16\n", +"\n", +"//Square\n", +"s=sqrt(%pi/4)*D\n", +"Is=0.886*D^4/32\n", +"Zs=0.7383*D^3/16\n", +"\n", +"//Rectangle\n", +"a=sqrt(%pi/2)*D\n", +"b=sqrt(%pi/8)*D\n", +"Ir=0.719*D^4/32\n", +"Zr=0.616*D^3/16\n", +"\n", +"// Trianle\n", +"t=sqrt(%pi/sqrt(3))*D\n", +"It=0.725*D^4/32\n", +"Zt=0.622*D^3/16\n", +"\n", +"//Ellipse\n", +"A=D/sqrt(2)\n", +"B=D/sqrt(8)\n", +"Ie=A^3*B^3/(A^2+B^2)\n", +"Ze=A*B^2/2\n", +"\n", +"//Normalization\n", +"Is=Is/Ip\n", +"Ie=Ie/Ip\n", +"It=It/Ip\n", +"Ir=Ir/Ip\n", +"\n", +"Zs=Zs/Zp\n", +"Ze=Ze/Zp\n", +"Zt=Zt/Zp\n", +"Zr=Zr/Zp\n", +"Ip=1\n", +"Zp=1\n", +"//results\n", +"printf('Z:: Circle:Square:Ellipse:Triangle:Rectangle = %.3f : %.3f : %.3f : %.3f : %.3f',Zp,Zs,Ze,Zt,Zr)\n", +"printf('\n I:: Circle:Square:Ellipse:Triangle:Rectangle = %.3f : %.3f : %.3f : %.3f : %.3f',Ip,Is,Ie,It,Ir)\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.17: Chapter6_Example_17.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"//initialization of variables\n", +"clear\n", +"\n", +"yp=2450 //kg/cm^2\n", +"d=0.4 //cm\n", +"ys=4200 //kg/cm^2\n", +"sa=1.6 //mm\n", +"sb=7 //mm\n", +"// calculations\n", +"sa=sa/10\n", +"sb=sb/10\n", +"T1=yp*%pi*d^3/16\n", +"T2=ys*0.303*sa^2*sb\n", +"// results\n", +"printf('The maximum torque that can be transitted by the screw-driver is %.1f kg-cm',T2)\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.18: Chapter6_Example_18.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"//initialization of variables\n", +"clear\n", +"b=5 //cm\n", +"h=10 //cm\n", +"tL=3 //mm\n", +"tl=1.5 //mm\n", +"T=100 //kg-cm\n", +"// calculations\n", +"tl=tl/10\n", +"fs=T*100/(2*b*h*tl)\n", +"// results\n", +"printf('The maximum stress is %.1f kg/cm^2',fs)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.19: Chapter6_Example_19.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"//initialization of variables\n", +"clear\n", +"b=5 //cm\n", +"h=10 //cm\n", +"tL=3 //mm\n", +"tl=1.5 //mm\n", +"T=100 //kg-cm\n", +"// calculations\n", +"D=2*(b+h)/%pi\n", +"AR=b*h\n", +"AC=%pi*D^2/4\n", +"r=AC/AR\n", +"// results\n", +"printf('The ratio is 1:%.2f',r)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.20: Chapter6_Example_20.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"//initialization of variables\n", +"clear\n", +"G=8*10^5 //kg/cm^2\n", +"//part (a)\n", +"T =20 //kg-m\n", +"t1=0.9 //cm\n", +"t2=0.5 //cm\n", +"b1=6.8 //cm\n", +"b2=14.2 //cm\n", +"I0=1/3*(2*b1*t1^3+b2*t2^3)\n", +"Zt=I0/max(t1,t2)\n", +"fs=T*100/Zt\n", +"Phi=T*100/(G*I0)\n", +"printf('part (a)')\n", +"printf('\n The maximum shear stress and twist rate are respectively \n %d kg/cm^2, %.2e radians/cm ',fs,Phi)\n", +"\n", +"//part (b)\n", +"t1=1 //cm\n", +"t2=1 //cm\n", +"b1=10 //cm\n", +"b2=9 //cm\n", +"I0=1/3*(b1*t1^3+b2*t2^3)\n", +"Zt=I0/max(t1,t2)\n", +"fs=T*100/Zt\n", +"Phi=T*100/(G*I0)\n", +"printf('\n part (b)')\n", +"printf('\n The maximum shear stress and twist rate are respectively \n %d kg/cm^2, %.2e radians/cm ',fs,Phi)\n", +"\n", +"//part (c)\n", +"t1=0.76 //cm \n", +"t2=0.48 //cm\n", +"b1=8 //cm\n", +"b2=14.04 //cm\n", +"I0=1/3*(2*b1*t1^3+b2*t2^3)\n", +"Zt=I0/max(t1,t2)\n", +"fs=T*100/Zt\n", +"Phi=T*100/(G*I0)\n", +"printf('\n part (c)')\n", +"printf('\n The maximum shear stress and twist rate are respectively \n %d kg/cm^2, %.2e radians/cm ',fs,Phi)\n", +"\n", +"//part(d)\n", +"t=1 //cm \n", +"b=19 //cm\n", +"I0=1/3*t^3*b\n", +"Zt=I0/t\n", +"fs=T*100/Zt\n", +"Phi=T*100/(G*I0)\n", +"printf('\n part (d)')\n", +"printf('\n The maximum shear stress and twist rate are respectively \n %d kg/cm^2, %.2e radians/cm ',fs,Phi)\n", +"\n", +"// Twist rate: answers differ by a scale of 10. wrong answers in the text" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.21: Chapter6_Example_21.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"// initialization of variables\n", +"clear\n", +"D=5 //cm\n", +"d=2 //cm\n", +"t_y=3000 //kg/cm^2\n", +"// calculations\n", +"R=D/2 \n", +"r=d/2 \n", +"Tep=2*%pi*R^3*t_y/3-%pi*r^3*t_y/6\n", +"t_er=2*Tep/(%pi*R^3)\n", +"t_er1=t_er*r/R\n", +"prs=t_y-t_er1\n", +"nrs=t_er-t_y\n", +"// results\n", +"printf('Maximum +ve residual stress occurs at %d cm radius and is equal to \n %d kg/cm^2',r,prs)\n", +"printf('\n Maximum -ve residual stress occurs at %d cm radius and is equal to \n %d kg/cm^2',R,-nrs)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.3: Chapter6_Example_3.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"// initialization o variables\n", +"clear\n", +"p=5 //cm\n", +"D=10 //cm\n", +"d=2 //mm\n", +"T= 10 //kgm\n", +"ss= 785 //kg/cm^2\n", +"// calculations\n", +"P= 2*T/(%pi*D^2)\n", +"P=P*5*100\n", +"// results\n", +"printf('Force per rivet is %.1f kg',P)\n", +"printf('\n The diameter of rivet, using a permissible stress of %d kg/cm^2 = 0.227 cm',ss)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.4: Chapter6_Example_4.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"// initialization of variables\n", +"clear\n", +"D=5 //cm\n", +"Y=3500 //kg/cm^2\n", +"\n", +"//part (a)\n", +"Ta=350 //kg-m\n", +"tau=Y/2\n", +"Ip=Ta*D*100/(2*tau)\n", +"d1=Ip*32/%pi\n", +"d1=(D^4-d1)^(1/4)\n", +"\n", +"//part (b)\n", +"Tb= 700 //kg-m\n", +"Ip=Tb*D*100/(2*tau)\n", +"d2=Ip*32/%pi\n", +"d2=(D^4-d2)\n", +"T=tau*%pi*(D^4)*2/(32*D)\n", +"// results\n", +"printf('The maximum diameter corresponding to the case a is %.2f cm',d1)\n", +"printf('\n Since the daimeter for the case (b) is coming out to be negative, \n The maximum torque transmitted is %.d kg-m',T/100)\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.5: Chapter6_Example_5.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", +"E= 2*10^6 //kg/cm^2\n", +"nu= 0.25\n", +"l= 60 //m\n", +"L=150 //cm\n", +"d=0.5 //cm\n", +"dd=10 //cm\n", +"D=180 //cm\n", +"//calculations\n", +"K=(l*100/(A*E))+(L*D/2*D*32*2*(1+nu)/(E*%pi*dd^4*2))\n", +"P=d/K\n", +"// results\n", +"printf('The weight of the students that entered the length is %d kg',P)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.6: Chapter6_Example_6.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"// initialization of variables\n", +"clear\n", +"// linked to 6_5\n", +"A=3 //cm^2\n", +"E= 2*10^6 //kg/cm^2\n", +"nu= 0.25\n", +"l= 60 //m\n", +"L=150 //cm\n", +"d=0.5 //cm\n", +"dd=10 //cm\n", +"D=180 //cm\n", +"//calculations\n", +"K=(l*100/(A*E))+(L*D/2*D*32*2*(1+nu)/(E*%pi*dd^4*2))\n", +"P=d/K\n", +"Ts=P/A\n", +"fs=dd*D*P*32/(%pi*4*dd^4)\n", +"\n", +"// results\n", +"printf('The tensile stress is %.1f kg/cm^2',Ts)\n", +"printf('\n Maximum shear stress is %.1f kg/cm^2',fs)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.7: Chapter6_Example_7.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"// initialization of variables\n", +"clear\n", +"F=500 //kg\n", +"k=25 //kg/cm\n", +"dd=15 //cm\n", +"ss=3500 //kg/cm^2\n", +"L=2 //m\n", +"G=8*10^5 //kg/cm^2\n", +"// calculations\n", +"x=sqrt(%pi*G/(25*L*32*100))\n", +"d=x*16*(F+dd*k)/(ss*%pi)\n", +"x2=x*d^2\n", +"// results\n", +"printf('d=%.2f cm',d)\n", +"printf('\n x=%.2f cm',x2)\n", +"\n", +"// Text: not exact\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 +} diff --git a/Solid_Mechanics_by_S_M_A_Kazimi/7-BEAMS_AND_BENDING.ipynb b/Solid_Mechanics_by_S_M_A_Kazimi/7-BEAMS_AND_BENDING.ipynb new file mode 100644 index 0000000..efc25c9 --- /dev/null +++ b/Solid_Mechanics_by_S_M_A_Kazimi/7-BEAMS_AND_BENDING.ipynb @@ -0,0 +1,569 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 7: BEAMS AND BENDING" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.10: Chapter7_Example_10.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"//initialization of variables\n", +"clear\n", +"Ys=17000 //kg/cm^2\n", +"E=2*10^6 //kg/cm^2\n", +"d1=1 //mm\n", +"d=1 //cm\n", +"//calculations: 1 cm\n", +"R=E*d/(2*Ys)\n", +"M=Ys*%pi*d^3/32\n", +"// results\n", +"printf('%d cm daimeter wire:',d)\n", +"printf('\n Minimum radius = %.2f cm',R)\n", +"printf('\n Bending Moment = %.2f kg-cm',M)\n", +"// calculations: 1 mm\n", +"R1=R/(d1*10)\n", +"M1=M/(d1*1000)\n", +"// results\n", +"printf('\n %d mm daimeter wire:',d1)\n", +"printf('\n Minimum radius = %.2f cm',R1)\n", +"printf('\n Bending Moment = %.2f kg-cm',M1)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.11: Chapter7_Example_11.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"//initialization of variables\n", +"clear\n", +"t=0.5 //cm\n", +"s=2 //m\n", +"p1=7.5 //cm\n", +"p2=10 //cm\n", +"d=p2/2\n", +"str=1650 //kg/cm^2\n", +"// calculations\n", +"// ab\n", +"IxX=p1*t^3/12+t*p1*d^2\n", +"// bc\n", +"alpha=atan(3/4)\n", +"Ixx=t*(p1+d)^3/12\n", +"Iyy=0\n", +"Ixy=0\n", +"Iuu=Ixx*cos(alpha)^2+Iyy*sin(alpha)^2-Ixy*sin(2*alpha)\n", +"Ixx=Iuu+IxX\n", +"IXX=Ixx*100/(2*p1)\n", +"Z=IXX/(d+t/2)\n", +"w=str*Z*8/(s^2*100)\n", +"w=w/1000\n", +"//Results\n", +"printf('w = %.1f tonne/m',w)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.12: Chapter7_Example_12.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"//initialization of variables\n", +"clear\n", +"wb=10 //cm\n", +"wh=20 //cm\n", +"sb=0.5 //cm\n", +"sh=10 //cm\n", +"s=6 //m\n", +"fs=1650 //kg/cm^2\n", +"fw=150 //kg/cm^2\n", +"Es=2*10^6 //kg/cm^2\n", +"Ew=12*10^4 //kg/cm^2\n", +"\n", +"//calculations\n", +"// Method 1\n", +"as=2*fs/(21*Es)\n", +"aw=2*fw/(20*Ew)\n", +"a=min(as,aw)\n", +"ss=a*Ew*wh/2\n", +"//Moment resistance of steel portion\n", +"F=(fs+1573)/2*sb*sh\n", +"k=sb/3*(fs+2*1573)/(fs+1573)\n", +"Ms=2*F*(10.5-k)\n", +"//Moment resistance of wooden portion\n", +"F=ss*wb*wb/2\n", +"Mw=2*(F*(wb-wb/3))\n", +"M=Ms+Mw\n", +"//Total udl supported\n", +"W=M*8/(s*100)\n", +"\n", +"//Results\n", +"printf('Using method 1')\n", +"printf('\n W = %d kg',W)\n", +"\n", +"//Method 2\n", +"nE=Es/Ew\n", +"nf=fs/fw\n", +"Is=2*(0+sb*sh*10.25^2)\n", +"Iw=0.6*wh^3/12\n", +"I=Is+Iw\n", +"W=fs*I*8/(s*100*10.5)\n", +"\n", +"//Results\n", +"printf('\n Using method 2')\n", +"printf('\n W = %d kg',W)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.13: Chapter7_Example_13.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"//initialization of variables\n", +"clear\n", +"p=6 //mm\n", +"Ixx=2375 //cm^4\n", +"Es=2*10^6 //kg/cm^2\n", +"EAl=0.667*10^6 //kg/cm^2\n", +"d1=10.6 //cm\n", +"d2=10 //cm\n", +"// calculations\n", +"I1=2*(0+p/10*10*10.3^2)\n", +"I2=Ixx*EAl/Es\n", +"I=I1+I2\n", +"n=I/I2\n", +"// results\n", +"printf('stiffness ratio = %.2f ',n)\n", +"n1=Es*d1/(d2*EAl)\n", +"printf('\n Stress ration = %.2f ',n1)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.14: Chapter7_Example_14.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"//initilization of new variables\n", +"clear\n", +"wt=0.8 //cm\n", +"ft=1.4 //cm\n", +"w=10 //cm\n", +"y=20 //cm\n", +"// Sigma_y: yield stress is not given explicitly\n", +"k1=wt*(40-2*ft)/2\n", +"Zp=(14*19.3+k1*9.3)*2\n", +"If=2*(w*ft^3/12+w*ft*19.3^2)\n", +"Iw=wt*(40-2*ft)^3/12\n", +"I=Iw+If\n", +"Z=I/y\n", +"sf=Zp/Z\n", +"//Results\n", +"printf('shape factor = %.2f ',sf)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.15: Chapter7_Example_15.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"//initilization of new variables\n", +"clear\n", +"wt=0.8 //cm\n", +"ft=1.4 //cm\n", +"w=10 //cm\n", +"y=20 //cm\n", +"T=750 //T==750*sigma_y\n", +"// calculations\n", +"MpF=ft*w*(40-2*ft)\n", +"c1=((40-2*ft)/2)^2-(T-MpF)/wt\n", +"c=sqrt(3*c1)\n", +"// results\n", +"printf('Elastic core of %.1f cm depth is present',2*c)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.17: Chapter7_Example_17.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"//initialization of new variables\n", +"clear\n", +"P=2000 //kg\n", +"a=4 //cm\n", +"b=1 //cm\n", +"d=7 //cm\n", +"r=3 //cm\n", +"// calculations\n", +"A=(a+b)/2*d\n", +"xbar=(a+b*2)*d/(r*(a+b))\n", +"rbar=r+xbar\n", +"I=b*d^3/12+r*d^3/12\n", +"Ixx=I-A*2.8^2\n", +"e=Ixx/(rbar*A)\n", +"f1=P*5.8*(xbar-0.62)/(A*0.62*r)\n", +"f2=P*5.8*(-d+2.18)/(A*0.62*(5.18+d-2.18))\n", +"str=P/A\n", +"Str_i=f1+str\n", +"Str_o=-f2-str\n", +"//Results\n", +"printf('stress at the inner side of the hook = %.1f kg/cm^2 (tensile)',Str_i)\n", +"printf('\n stress at the outer side of the hook = %.1f kg/cm^2 (compressive)',Str_o)\n", +"// approximations involved in the text" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.20: Chapter7_Example_20.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"//initialization of new variables\n", +"clear\n", +"t=1 //cm\n", +"a=40 //cm\n", +"A=236\n", +"// calculations\n", +"ybar=a*t*0.5+(50-1)*4*0.5/(a*t+(50-1)*4)\n", +"y1bar=1.25*a-ybar\n", +"IAA=a*t^3/3+(50-1)^3*4/12+(50-1)*4*25.5^2\n", +"Io=IAA-A*ybar^2\n", +"//part (1)\n", +"r=y1bar/ybar\n", +"// results\n", +"printf('Ratio of maximum bending stress in the stem and flange')\n", +"printf('\n Ratio = %.2f',r)\n", +"//part(2)\n", +"// calculations\n", +"r=(2/3*388*29.56)-(2/3*160*20.44)-(228*20.44)\n", +"r=r/(2*2/3*388*29.56)\n", +"// results\n", +"printf('\n Ratio of S.F in flange to total S.F')\n", +"printf('\n Ratio = %.2f percent',r*100)\n", +"// part (3)\n", +"// calculations\n", +"r=359*200/Io\n", +"// results\n", +"printf('\n Ratio of maximum shear stress in the flange to average sher stress in the stem')\n", +"printf('\n Ratio = %.2f ',r)\n", +"//part (4)\n", +"// calculations\n", +"s=10 //m\n", +"r=r/0.922\n", +"sigma=1650 //kg/cm^2\n", +"shear=945 //kg/cm^2\n", +"wsh=2*200*shear/(r*s)\n", +"wsi=8*Io*sigma/(s^2*10*29.56)\n", +"w=min(wsh,wsi)\n", +"// results\n", +"printf('\n Maximum u.d.l. = %d kg/m ',w)\n", +"\n", +"//wrong moment of Inertia (Io) in the text and hence part (3) and part (4) are wrong" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.21: Chapter7_Example_21.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"//initialization of new variables\n", +"clear\n", +"a=30 //cm\n", +"t=2.5 //cm\n", +"S=15 //cm\n", +"s=5 //Tonne\n", +"// calculations\n", +"I=a*a^3-25*25^3\n", +"I=I/12\n", +"tau_zx=s*1000*27.5*t*25/(4*35000*t)\n", +"FA=S*t*tau_zx\n", +"tau_xy=s*1000*a*t*27.5/(4*35000*t)\n", +"FB=tau_xy*t*S\n", +"//Results\n", +"printf('case A \n F = %d kg',FA)\n", +"printf('\n case B \n F= %d kg',FB)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.23: Chapter7_Example_23.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"//initialization of variables\n", +"clear\n", +"h=40 //cm\n", +"b=10 //cm\n", +"t1=1.4 //cm\n", +"t2=0.8 //cm\n", +"Ixx=13989.5 //cm^4\n", +"//calculations\n", +"e=b^2*h^2*t1/(4*Ixx)*(1-t1/h-t1/b+t1^2/(b*h))*(1-t1/h)\n", +"//Results\n", +"printf('Shear center: \n e = %.2f cm',e)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.2: Chapter7_Example_2.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"//initialization of variables\n", +"clear\n", +"s=3 //m\n", +"n=60\n", +"p=50 //kg\n", +"// calculations\n", +"W=n*p\n", +"Rc=W*2/s\n", +"Rb=W-Rc\n", +"dx = 0.001;\n", +"x = 0:dx:s\n", +"n = s/dx +1;\n", +"for i = 1:n\n", +" Sx(i) = -Rb + Rc*x(i)^2/6;\n", +" Mx(i) = Rb*x(i) - Rc*x(i)^3 /18;\n", +"end\n", +"//Results\n", +"figure(1);plot(x,Sx);title('Shear force diagram');xlabel('X (in m)');ylabel('Shear force (in kg)');\n", +"figure(2);plot(x,Mx);title('Bending Moment diagram');xlabel('X (in m)');ylabel('Bending Moment (in kg-m)');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.33: Chapter7_Example_33.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"//initialization of new variables\n", +"clear\n", +"L=50 //cm\n", +"k=15 //cm\n", +"I=200 //cm^4\n", +"II=40 //cm^4\n", +"d=30 //cm\n", +"Pd=40 //cm\n", +"E=0.6667*10^6 //kg/cm^2\n", +"//calculations\n", +"delta=(100*10/2*16.33+L*d*35+L*k/2*25+d*k/2*45)\n", +"delta1=delta/E\n", +"//Results\n", +"printf('deflection = %.2f mm',delta1*10^1)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.8: Chapter7_Example_8.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"//initialization of new variables\n", +"clear\n", +"b=10075 //mm\n", +"h=10 //mm\n", +"p1=7.5\n", +"p2=9\n", +"//part (a)\n", +"ybar=1*p1*0.5+1*p2*5.5\n", +"ybar=ybar/16.5\n", +"xbar=1*p1*0.5+1*p1*4.75\n", +"xbar=xbar/16.5\n", +"printf('part (a)')\n", +"printf('\n Centroid coordinates (x,y) = (%.2f, %.2f) cm',xbar,ybar)\n", +"\n", +"//part (b)\n", +"Ixx=p1*1^3/12+p1*1*(3.23-0.5)^2+1*p2^3/12+p2*1*(5.5-3.23)^2\n", +"Iyy=1*p1^3/12+p1*1*(3.75-2.43)^2+p2*1^3/12+p2*1*(2.43-0.5)^2\n", +"Ixy=p1*1.32*2.73+9*(-1.93)*(-2.27)\n", +"printf('\n part (b)')\n", +"printf('\n Moment of Areas: \n Ixx = %.1f cm^4 \n Iyy = %.1f cm^4 \n Ixy=%.1f cm^4',Ixx,Iyy,Ixy)\n", +"\n", +"//part (c)\n", +"alpha=0.5*atan(2*Ixy/(Iyy-Ixx))\n", +"alpha=alpha*180/%pi\n", +"printf('\n part (c)')\n", +"printf('\n Direction of principal axes:')\n", +"printf('\n alpha = %.2f degrees',alpha)\n", +"\n", +"//part (d)\n", +"Iuu=(Ixx+Iyy)/2+sqrt((Iyy-Ixx)^2/4+Ixy^2)\n", +"Ivv=(Ixx+Iyy)/2-sqrt((Iyy-Ixx)^2/4+Ixy^2)\n", +"printf('\n part (d)')\n", +"printf('\n Iuu = %.2f cm^4 \n Ivv = %.2f cm^4',Iuu,Ivv)" + ] + } +], +"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 +} diff --git a/Solid_Mechanics_by_S_M_A_Kazimi/8-STABILITY_OF_EQUILIBRIUM_COLUMNS.ipynb b/Solid_Mechanics_by_S_M_A_Kazimi/8-STABILITY_OF_EQUILIBRIUM_COLUMNS.ipynb new file mode 100644 index 0000000..ad4e00e --- /dev/null +++ b/Solid_Mechanics_by_S_M_A_Kazimi/8-STABILITY_OF_EQUILIBRIUM_COLUMNS.ipynb @@ -0,0 +1,264 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 8: STABILITY OF EQUILIBRIUM COLUMNS" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.1: Chapter8_Example_1.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"// initialization of variables\n", +"clear\n", +"L=5 //m\n", +"D=20 //cm\n", +"t=1 //cm\n", +"E=2*10^6 //kg/cm^2\n", +"I=2502 //cm^4\n", +"L=5*100 //cm\n", +"// calculations\n", +"P=E*I/(4*L^2)\n", +"// results\n", +"printf('The maximal axial load taken is %.1f Tonne',P/100)\n", +"printf('\n for both ends pinned, P=%.1f Tonne',P*4/100)\n", +"printf('\n for both ends fixed, P=%.1f Tonne',P*16/100)\n", +"printf('\n for one end fixed, one pinned, P=%.1f Tonne',P*4*2.13/100)\n", +"\n", +"// Evaluation of critical load (P) in the text is wrong" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.2: Chapter8_Example_2.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"//initialization of variables\n", +"clear\n", +"E=2*10^6 //kg/cm^2\n", +"sigma_y=2600 //kg/cm^2\n", +"I=2502 //cm^4\n", +"L=500 //cm\n", +"A=59.7 //cm^2\n", +"L_tcr=L/sqrt(I/A)\n", +"\n", +"printf('The actual critical length ratio is %.1f',L_tcr)\n", +"//case (b)\n", +"L_cr=sqrt(E*%pi^2/sigma_y)\n", +"printf('\n case (b)')\n", +"printf('\n The critical length ratio is %.1f',L_cr)\n", +"\n", +"//case (a)\n", +"L_cr=sqrt(E*%pi^2/(4*sigma_y))\n", +"printf('\n case (a)')\n", +"printf('\n The critical length ratio is %.1f',L_cr)\n", +"\n", +"//case (c)\n", +"L_cr=sqrt(4*E*%pi^2/sigma_y)\n", +"printf('\n case (c)')\n", +"printf('\n The critical length ratio is %.1f',L_cr)\n", +"\n", +"// case (d)\n", +"L_cr=sqrt(2.05*E*%pi^2/sigma_y)\n", +"// Results\n", +"printf('\n case (d)')\n", +"printf('\n The critical length ratio is %.1f',L_cr)\n", +"printf('\n Only in case (a) actual ratio is more than critical ratio and material \n remains elastic For cases (b), (c) and (d) critical length ratio is \n much higher and hence the material yelds before crippling loads are reached')\n", +"\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.3: Chapter8_Example_3.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"//initialzation of variables\n", +"clear\n", +"h=3.5 //m\n", +"A=22.4 //cm^2\n", +"r=7.08 //cm\n", +"E=2*10^6 //kg/cm^2\n", +"Q=1/2\n", +"// calculations\n", +"h=h*100\n", +"Q1=(Q*h/r)^2\n", +"s_cr=E*%pi^2/Q1\n", +"// results\n", +"printf('The critical stress is %d kg/cm^2',s_cr)\n", +"printf('\n This is much higher than yield stress for the material, \n so the column will fail by yielding')\n", +"\n", +"// rounding off errors in the text" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.4: Chapter8_Example_4.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"//initialization of variables\n", +"clear\n", +"r_min=1.17 //cm\n", +"A=17.21 //cm^2\n", +"Q=1/2\n", +"h=3.5 //m\n", +"E=2*10^6 //kg/cm^2\n", +"h=h*100\n", +"// calculations\n", +"Q1=(Q*h/r_min)^2\n", +"s_cr=E*%pi^2/Q1\n", +"P_cr=s_cr*A\n", +"// results\n", +"printf('The crippling load is %d kg',P_cr)\n", +"\n", +"// wrong calculations given in the text" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.5: Chapter8_Example_5.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"//initialization of variables\n", +"clear\n", +"L=2.5 //m\n", +"A=6.02 //cm^2\n", +"Q1=105\n", +"s=796.5 //kg/cm^2\n", +"// calculations\n", +"P=2*A*s\n", +"printf('The safe load is %d kg',P)\n", +"// Results\n", +"// wrong calculations in the text" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.6: Chapter8_Example_6.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"//initialization of variables\n", +"clear\n", +"h=3.5 //m\n", +"r_xx=7.08 //cm\n", +"A=24.38 //cm^2\n", +"Q=0.5\n", +"Q1=Q*h*100/r_xx\n", +"\n", +"//Permissible load by secent formula\n", +"P=1231.28*2*A\n", +"printf('Permissible load by secent formula: %d kg',P)\n", +"\n", +"//Permissible load by Rankine-Gordon formula\n", +"P=1260/(1+(24.75^2/18000))*2*A\n", +"printf('\n Permissible load by Rankine-Gordon formula: %d kg',P)\n", +"\n", +"//Permissible load by parabolic formula\n", +"P=(1050-0.0233*Q1^2)*2*A\n", +"printf('\n Permissible load by parabolic formula: %d kg',P)\n", +"\n", +"//Permissible load by straight-line formula\n", +"P=(1120-Q1*4.8)*2*A\n", +"printf('\n Permissible load by parabolic formula: %d kg',P)\n", +"\n", +"// Rounding off errors in the text\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 +} diff --git a/Solid_Mechanics_by_S_M_A_Kazimi/9-COMBINED_STRESSES.ipynb b/Solid_Mechanics_by_S_M_A_Kazimi/9-COMBINED_STRESSES.ipynb new file mode 100644 index 0000000..bdc1414 --- /dev/null +++ b/Solid_Mechanics_by_S_M_A_Kazimi/9-COMBINED_STRESSES.ipynb @@ -0,0 +1,707 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 9: COMBINED STRESSES" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.10: Chapter9_Example_10.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"//initialization of variables\n", +"clear\n", +"b=2 //cm\n", +"h=2 //cm\n", +"T=2000 //kg-cm\n", +"V=250 //kg\n", +"M=2000 //kg-cm\n", +"// calculations\n", +"Mmax=M*6/(b*h*b)\n", +"Vmax=3*V/(2*b*h)\n", +"Zt=0.208*b^2*h\n", +"Tmax=T/(Zt)\n", +"\n", +"sigma=Mmax\n", +"printf('points A,B,')\n", +"printf('\n sigma=%d kg/cm^2 (tension)',sigma)\n", +"printf('\n points C,D,')\n", +"printf('\n sigma=%d kg/cm^2 (cmpression)',sigma)\n", +"tau=Vmax+Tmax\n", +"printf('\n point E')\n", +"printf('\n tau=%.2f kg/cm^2 shear',tau)\n", +"tau=Vmax-Tmax\n", +"printf('\n tau=%.2f kg/cm^2 shear',tau)\n", +"// at G\n", +"sigma_x=sigma\n", +"sigma_y=0\n", +"tau_xy=Tmax\n", +"sigma_1=(sigma_x+sigma_y)/2+sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)\n", +"sigma_2=(sigma_x+sigma_y)/2-sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)\n", +"// results\n", +"printf('\n at point G')\n", +"printf('\n sigma_1 = %d kg/cm^2 (tension)',sigma_1)\n", +"printf('\n sigma_2 = %d kg/cm^2 (compression)',sigma_2)\n", +"\n", +"// Question was asked only to find out at A,B,C,D,E,F and G" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.11: Chapter9_Example_11.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"//initialization of variables\n", +"clear\n", +"w=10 //cm\n", +"s=2.8 //m\n", +"P=1 //tonne\n", +"Ft=1.4 //cm\n", +"Wt=0.8 //cm\n", +"Ix=13989.5 //cm^4\n", +"Z=699.5 //cm^3\n", +"// calculations\n", +"BM= 2.8 \n", +"T=P*1000*8.21\n", +"SF=P*1000\n", +"BS=BM*10^5/(Z)\n", +"sigmaXA=BS*18.6/20\n", +"K=w*Ft*19.3+18.6*Wt*9.3\n", +"tau_xy_C=SF/(Ix*Wt)*K\n", +"tau_xy_A=tau_xy_C*(w*Ft*19.3)/K \n", +"tau_xy_B=tau_xy_A*0.5*Wt/w\n", +"sigmaXB=sigmaXA*19.3/20\n", +"\n", +"tau_max=3*Ft*8210/(w*Ft^3+37.2*Wt^3)\n", +"tau_A=3*Wt*8210/(w*Ft^3+37.2*Wt^3)\n", +"\n", +"//For point A\n", +"Shear=tau_xy_A-tau_A\n", +"sigma_x=sigmaXA\n", +"sigma_y=0\n", +"tau_xy=Shear\n", +"sigma_1=(sigma_x+sigma_y)/2+sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)\n", +"sigma_2=(sigma_x+sigma_y)/2-sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)\n", +"\n", +"printf('For point A')\n", +"printf('\n Total shear= %.1f kg/cm^2 ',Shear)\n", +"printf('\n Bending stress = %d kg/cm^2 (Compr.)',sigma_x)\n", +"printf('\n Principal stresses are %d (tension), %d (comp.) kg/cm^2 ',sigma_1,sigma_2)\n", +"\n", +"//For point B\n", +"printf('\n FOr point B')\n", +"printf('\n Bending shear stress is %.2f k/cm^2',tau_xy_B)\n", +"sigmaXB=BS*19.3/20\n", +"sigma_x=sigmaXB\n", +"sigma_y=0\n", +"tau_xy=tau_max\n", +"sigma_1=(sigma_x+sigma_y)/2+sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)\n", +"sigma_2=(sigma_x+sigma_y)/2-sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)\n", +"printf('\n Principal stresses are %d (tension), %d (comp.) kg/cm^2 ',sigma_1,sigma_2)\n", +"\n", +"// Answers in the text are approximations" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.12: Chapter9_Example_12.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"//initialization of variables\n", +"clear\n", +"b=10 //cm\n", +"h=10 //cm\n", +"P=5 //tonne\n", +"e=1 //cm\n", +"E=12*10^4 //kg/cm^2\n", +"str=130 // kg/cm^2\n", +"n=3\n", +"L=2 //m\n", +"// calculations\n", +"L=L*100 //cm\n", +"Pcr=%pi^2*E*b*h^3/(12*L^2)\n", +"Pcr=Pcr/1000\n", +"Smax=-P*1000/(b*h)-(P*1000*1*5*12/10^4)*1/(1-(n*P/Pcr))\n", +"// results\n", +"printf('permissible stress = %d kg/cm^2',str)\n", +"printf('\n develoed stress = %.1f kg/cm^2',Smax)\n", +"printf('\n Since it is below the permissible stress, the design is safe')\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.13: Chapter9_Example_13.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"//initializatio of variables\n", +"clear\n", +"// linked to 9.13\n", +"b=10 //cm\n", +"h=10 //cm\n", +"P=5 //tonne\n", +"e=1 //cm\n", +"E=12*10^4 //kg/cm^2\n", +"str=130 // kg/cm^2\n", +"n=3\n", +"L=2 //m\n", +"// calculations\n", +"L=L*100 //cm\n", +"Pcr=%pi^2*E*b*h^3/(12*L^2)\n", +"Pcr=Pcr/1000\n", +"Smax=-P*1000/(b*h)-(P*1000*1*5*12/10^4)*1/(1-(n*P/Pcr))\n", +"Smax=abs(Smax)\n", +"\n", +"rr=b*h^3/(12*100)\n", +"Smax_se=P*1000/(b*h)*(1+e*5/rr*sec(%pi/2*sqrt(n*P/Pcr)))\n", +"Perror=(Smax-Smax_se)/Smax\n", +"Perror=Perror*100\n", +"Perror=abs(Perror)\n", +"// results\n", +"printf('Using secent formula, stress obtained is %d kg/cm^2',Smax_se)\n", +"printf('\n hence, the percentage error %.2f',Perror)\n", +"// approximate answees in the text" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.14: Chapter9_Example_14.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"//initialization of variables\n", +"clear\n", +"P=400 //kg/m\n", +"L=10 //m\n", +"F=10 //tonne\n", +"n=3\n", +"Ixx=5943.1 //cm^4\n", +"A=52.03 //cm^2\n", +"rx=10.69 //cm\n", +"E=2*10^6 //kg/cm^2\n", +"// calculations\n", +"Pcr=%pi^2*E*Ixx/((L*100)^2)\n", +"Pcr=Pcr/1000\n", +"e=P*L^2/(8*F*1000)\n", +"g=e*12.5*100/rx^2\n", +"Smax=F*1000/A*(1+g*1/(1-n*(F/Pcr)))\n", +"// results\n", +"printf('The maximum stress developed is %d kg/cm^2',Smax)\n", +"\n", +"// approximate calculations involved in the text book" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.15: Chapter9_Example_15.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"//initialization of variables\n", +"clear\n", +"// linked to 9_14\n", +"// calculations\n", +"P=400 //kg/m\n", +"L=10 //m\n", +"F=10 //tonne\n", +"n=3\n", +"Ixx=5943.1 //cm^4\n", +"A=52.03 //cm^2\n", +"rx=10.69 //cm\n", +"E=2*10^6 //kg/cm^2\n", +"Pcr=%pi^2*E*Ixx/((L*100)^2)\n", +"Pcr=Pcr/1000\n", +"e=P*L^2/(8*F*1000)\n", +"g=e*12.5*100/rx^2\n", +"Smax=F*1000/A*(1+g*1/(1+n*(F/Pcr)))\n", +"// results\n", +"printf('The maximum stress developed is %d kg/cm^2',Smax)\n", +"\n", +"// approximate answer in the text" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.1: Chapter9_Example_1.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"//initialization of variables\n", +"clear\n", +"//case (a)\n", +"A=72.9 //cm^2\n", +"Iy=633 //cm^4\n", +"Ix=1199 //cm^4\n", +"t=24/(5*Ix)+13.5/(5*Iy)\n", +"r=1/(A*t)\n", +"printf('case (a) \n r = %.3f cm',r)\n", +"// case (b)\n", +"t=24/(5*Ix)-13.5/(5*Iy)\n", +"r=1/(A*t)\n", +"printf('\n case (b) \n r = %.1f cm',r)\n", +"//case (c)\n", +"t=-24/(5*Ix)+13.5/(5*Iy)\n", +"r=1/(A*t)\n", +"printf('\n case (a) \n r = %.1f cm',r)\n", +"printf('\n So the load is to be placed on the leg OD, at a distance of %.1f cm from O',r )\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.3: Chapter9_Example_3.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"//initialization of variables\n", +"clear\n", +"b=14 //cm\n", +"d=20 //cm\n", +"rx=8.46 //cm\n", +"ry=2.99 //cm\n", +"// calculations\n", +"ex=2*rx^2/d\n", +"ey=2*ry^2/b\n", +"h=2*ex\n", +"w=2*ey\n", +"// results\n", +"printf('for steel height=%.3f cm and width=%.3f cm',h,w)\n", +"// ISHB 225\n", +"b=22.5 //cm\n", +"d=22.5 //cm\n", +"rx=9.8 //cm\n", +"ry=4.96 //cm\n", +"// calculations\n", +"ex=2*rx^2/d\n", +"ey=2*ry^2/b\n", +"h=2*ex\n", +"w=2*ey\n", +"// results\n", +"printf('\n for an ISHB height=%.3f cm and width=%.3f cm',h,w)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.4: Chapter9_Example_4.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"//initialization of variables\n", +"clear\n", +"t=280 //kg/cm^2\n", +"c=840 //kg/cm^2\n", +"xbar=7.5 //cm from AB\n", +"A=210 //cm^2\n", +"// calculations\n", +"e=50+xbar //cm\n", +"Iyy=7433 //cm^2\n", +"k=(1/210+e*xbar/Iyy)\n", +"P=t/k\n", +"k1=(-1/210+e*(xbar+5)/Iyy)\n", +"P1=c/k1\n", +"P_safe=min(P1,P)\n", +"// results\n", +"printf('The safe load is %d kg',P_safe)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.5: Chapter9_Example_5.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"//initialization of the variables\n", +"clear\n", +"s=1.6 //m\n", +"s1=4 //m\n", +"pi=28 //degrees\n", +"w=16 //kg/m^2\n", +"p=100 //kg/m^2\n", +"pl=20 //cm\n", +"pb=10 //cm\n", +"r=500 //kg/m^3\n", +"// calculations\n", +"pi=pi*%pi/180 //radians\n", +"W=w*s+(r*pl*pb/(100*100))\n", +"P=p*s\n", +"L=P+W*cos(pi)\n", +"Mx=L*s1^2*100/8\n", +"sigma_1=Mx*6/(pb*pl^2)\n", +"My=W*sin(pi)*s1^2*100/8\n", +"sigma_2=My*6/(pl*pb^2)\n", +"sigma=sigma_1+sigma_2\n", +"// results\n", +"printf('Due to bending in the noth the planes, D experiences maximum \n compression of %.2f kg/cm^2 and B has maximum tension of %.2f kg/cm^2',sigma,sigma)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.6: Chapter9_Example_6.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"//initialization of the problems\n", +"clear\n", +"s=1.6 //m\n", +"s1=4 //m\n", +"pi=28 //degrees\n", +"w=16 //kg/m^2\n", +"p=100 //kg/m^2\n", +"pl=20 //cm\n", +"pb=10 //cm\n", +"r=500 //kg/m^3\n", +"Zx=54.8 //cm^3\n", +"Zy=3.9 //cm^3\n", +"// calculations\n", +"pi=pi*%pi/180 //radians\n", +"W=w*s+8.1\n", +"P=p*s\n", +"L=P+W*cos(pi)\n", +"Mx=L*s1^2*100/8\n", +"sigma_1=Mx/Zx\n", +"My=W*sin(pi)*s1^2*100/8\n", +"sigma_2=My/Zy\n", +"sigma=sigma_1+sigma_2\n", +"// results\n", +"printf('Maximum stresses are %d kg/cm^2, tension or compression',sigma)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.7: Chapter9_Example_7.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"//initialization of variables\n", +"clear\n", +"s=1.6 //m\n", +"s1=4 //m\n", +"pi=28 //degrees\n", +"w=16 //kg/m^2\n", +"p=100 //kg/m^2\n", +"pl=20 //cm\n", +"pb=10 //cm\n", +"r=500 //kg/m^3\n", +"sg=5 //cm\n", +"E=12*10^4\n", +"pi=pi*%pi/180 //radians\n", +"// calculations\n", +"W=w*s+(r*pl*pb/(100*100))\n", +"P=p*s\n", +"L=P+W*cos(pi)\n", +"Mx=L*s1^2*100/8\n", +"sigma_1=Mx*6/(pb*pl^2)\n", +"My=W*sin(pi)*s1^2*100/8\n", +"sigma_2=My*6/(pl*pb^2)\n", +"st=sigma_1*sg/10\n", +"Ts=st-sigma_2\n", +"ez=Ts/E\n", +"// results\n", +"printf('The strain gauge, aligned to the z axis will give compression strain of %.1e',ez)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.8: Chapter9_Example_8.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"//initialization of variables\n", +"clear\n", +"P=3 //tonne/m\n", +"s=6 //m\n", +"l=50 //cm\n", +"b=20 //cm\n", +"k=0.5 //m\n", +"//calculations\n", +"R=P*s/2\n", +"sf=R-k*P\n", +"bm=R*k-P*k^2/2\n", +"tau_xy=1.5*sf*1000/(l*b)\n", +"tau_max=tau_xy\n", +"str=bm*s*10^5/(b*l*l)\n", +"\n", +"// consider the line a-a\n", +"\n", +"sigma_x=str*12.5/25\n", +"sigma_y=0\n", +"tau_xy=tau_xy*(1-(12.5/25)^2)\n", +"\n", +"sigma_1=(sigma_x+sigma_y)/2+sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)\n", +"sigma_2=(sigma_x+sigma_y)/2-sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)\n", +"\n", +"printf('For the line a-a the bending stress and shearing stress are \n respectively %.2f kg/cm^2, %.2f kg/cm^2 ',sigma_x,tau_xy)\n", +"printf('\n The principal stresses are %.2f kg/cm^2 (tension) %.2f kg/cm^2 (compression) ',sigma_1,sigma_2)\n", +"\n", +"//consider the line c-c\n", +"printf('\n For the line c-c the bending stress and shearing stress are \n respectively %.2f kg/cm^2, %.2f kg/cm^2 ',sigma_x,tau_xy)\n", +"printf('\n The principal stresses are %.2f kg/cm^2 (compression) %.2f kg/cm^2 (tension) ',sigma_2,sigma_1)\n", +"\n", +"//for the line b-b\n", +"tau_xy=tau_max\n", +"sigma_x=0\n", +"sigma_y=0\n", +"sigma_1=(sigma_x+sigma_y)/2+sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)\n", +"sigma_2=(sigma_x+sigma_y)/2-sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)\n", +"// results\n", +"printf('\n For the line b-b the bending stress and shearing stress are \n respectively %.2f kg/cm^2, %.2f kg/cm^2 ',sigma_x,tau_xy)\n", +"printf('\n The principal stresses are %.2f kg/cm^2 (tension) %.2f kg/cm^2 (compression) ',sigma_1,sigma_2)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.9: Chapter9_Example_9.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"//initialization of variables\n", +"clear\n", +"P=3 //tonne/m\n", +"s=6 //m\n", +"l=50 //cm\n", +"b=20 //cm\n", +"k=0.5 //m\n", +"//calculations\n", +"R=P*s/2\n", +"sf=R-k*P\n", +"bm=R*k-P*k^2/2\n", +"tau_xy=1.5*sf*1000/(l*b) //max shear stress\n", +"tau_max=tau_xy \n", +"str=bm*s*10^5/(b*l*l) //max bending stress\n", +"\n", +"// consider the line a-a\n", +"\n", +"sigma_x=str*12.5/25\n", +"sigma_y=0\n", +"tau_xy=tau_xy*(1-(12.5/25)^2)\n", +"\n", +"sigma_1=(sigma_x+sigma_y)/2+sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)\n", +"sigma_2=(sigma_x+sigma_y)/2-sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)\n", +"\n", +"theta=1/2*atan(2*tau_xy/(sigma_x-sigma_y))\n", +"sigma_p=sigma_1/cos(theta)\n", +"P=sigma_p*2*l*b/(3*1000)\n", +"printf('A prestressing force of %.2f Tonne must be applied to balance the tension at a-a',P)\n", +"\n", +"//At bottom point D or C\n", +"pre_str=P*2*1000/(l*b)\n", +"net=str-pre_str\n", +"printf('\n At bottom point D or C')\n", +"printf('\n Net tension = %.2f kg/cm^2 ',net)\n", +"\n", +"//consider the line b-b\n", +"pre_str=P\n", +"sigma_x=pre_str\n", +"sigma_y=0\n", +"tau_xy=tau_max\n", +"sigma_1=(sigma_x+sigma_y)/2+sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)\n", +"sigma_2=(sigma_x+sigma_y)/2-sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)\n", +"printf('\n At section b-b')\n", +"printf('\n pre-stress=%.2f kg/cm^2',pre_str)\n", +"printf('\n principal stresses are %.2f, %.2f kg/cm^2 ',sigma_1,sigma_2)\n", +"\n", +"//for the line c-c\n", +"sigma_x=str*12.5/25\n", +"sigma_y=0\n", +"tau_xy=tau_xy*(1-(12.5/25)^2)\n", +"sigma_1=(sigma_x+sigma_y)/2+sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)\n", +"sigma_2=(sigma_x+sigma_y)/2-sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)\n", +"pre_str=pre_str/2\n", +"net=sigma_1+pre_str\n", +"sigma_x=net\n", +"sigma_y=0\n", +"sigma_1=(sigma_x+sigma_y)/2+sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)\n", +"sigma_2=(sigma_x+sigma_y)/2-sqrt((1/2*(sigma_x-sigma_y))^2+tau_xy^2)\n", +"// results\n", +"printf('\n At section c-c')\n", +"printf('\n the direct stress is %.2f kg/cm^2',net)\n", +"printf('\n pre-stress = %.2f kg/cm^2',pre_str)\n", +"printf('\n principal stresses are %.2f, %.2f kg/cm^2 ',sigma_1,sigma_2)\n", +"\n", +"// wrong calculations in the thext for some parts\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 +} |