From 476705d693c7122d34f9b049fa79b935405c9b49 Mon Sep 17 00:00:00 2001 From: prashantsinalkar Date: Tue, 14 Apr 2020 10:19:27 +0530 Subject: Initial commit --- Mechanics_Of_Material_by_J_M_Gere/3-Torsion.ipynb | 313 ++++++++++++++++++++++ 1 file changed, 313 insertions(+) create mode 100644 Mechanics_Of_Material_by_J_M_Gere/3-Torsion.ipynb (limited to 'Mechanics_Of_Material_by_J_M_Gere/3-Torsion.ipynb') diff --git a/Mechanics_Of_Material_by_J_M_Gere/3-Torsion.ipynb b/Mechanics_Of_Material_by_J_M_Gere/3-Torsion.ipynb new file mode 100644 index 0000000..54bb7ee --- /dev/null +++ b/Mechanics_Of_Material_by_J_M_Gere/3-Torsion.ipynb @@ -0,0 +1,313 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 3: Torsion" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.10: evaluation_of_the_strain_energy_for_different_cases.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"Ta = 100 ; // Torque in N-m at A\n", +"Tb = 150; // Torque in N-m at B\n", +"L = 1.6 ; // Length of shaft in meter\n", +"G = 80e09 ; // Modulus of elasticity\n", +"Ip = 79.52e-09; // polar moment of inertia in m4\n", +"Ua = ((Ta^2)*L)/(2*G*Ip) // Strain energy at A\n", +"disp('joule',Ua,'Torque acting at free end')\n", +"Ub = ((Tb^2)*L)/(4*G*Ip) // Strain energy at B\n", +"disp('joule',Ub,'Torque acting at mid point')\n", +"a = (Ta*Tb*L)/(2*G*Ip) // dummy variabble\n", +"Uc = Ua+a+Ub ; // Strain energy at C\n", +"disp('joule',Uc,'Total torque')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.11: Evaluation_of_the_strain_energy_of_a_hollow_shaft.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"t = 480 ; // Torque of constant intensity\n", +"L = 144 ; // Length of bar\n", +"G = 11.5e06; // Modulus of elasticity in Psi\n", +"Ip = 17.18 ; // Polar moment of inertia\n", +"U = ((t^2)*(L^3))/(G*Ip*6) // strain energy in in-lb\n", +"disp('in-lb',U,'The strain energu for the hollow shaft is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.1: Calculation_of_maximum_shear_stress_and_permissible_torque_in_the_bar.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"d = 1.5; // diameter of bar in inch\n", +"L = 54 ; // Length of bar in inch\n", +"G = 11.5e06 ; // modulus of elasticity in psi \n", +"// Part (a)\n", +"T = 250 ; // torque\n", +"t_max = (16*T*12)/(%pi*(d^3)); // maximum shear stress in bar\n", +"Ip = (%pi*(d^4))/32 ; // polar miment of inertia \n", +"f = (T*12*L)/(G*Ip) ; // twist in radian\n", +"f_ = (f*180)/%pi ; // twist in degree\n", +"disp('psi',t_max,'Maximum shear stress in the bar is ')\n", +"disp('degree',f_,'Angle of twist is')\n", +"//Part (b)\n", +"t_allow = 6000 ; // allowable shear stress\n", +"T1 = (%pi*(d^3)*t_allow)/16; //allowable permissible torque in lb-in\n", +"T1_ = T1*0.0831658 ; //allowable permissible torque in lb-ft\n", +"f_allow = (2.5*%pi)/180 ; // allowable twist in radian\n", +"T2 = (G*Ip*f_allow)/L; // allowable stress via a another method\n", +"T2_ = T2*0.0831658; //allowable permissible torque in lb-ft\n", +"T_max = min(T1_,T2_); // minimum of the two\n", +"disp('lb-ft',T_max,'Maximum permissible torque in the bar is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.2: Calculation_of_required_diameter_for_solid_and_hollow_shaft.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"T = 1200 ; // allowable torque in N-m\n", +"t = 40e06 ; // allowable shear stress in Pa\n", +"f = (0.75*%pi)/180 ; // allowable rate of twist in rad/meter\n", +"G = 78e09; // modulus of elasticity\n", +"// Part (a) : Solid shaft\n", +"d0 = ((16*T)/(%pi*t))^(1/3)\n", +"Ip = T/(G*f) ; // polar moment of inertia\n", +"d01 = ((32*Ip)/(%pi))^(1/4); // from rate of twist definition\n", +"disp('m',d0,'The required diameter of the solid shaft is ')\n", +"// Part (b) : hollow shaft\n", +"d2 = (T/(0.1159*t))^(1/3) ; // Diamater of hollow shaft in meter\n", +"// The above equation comes from solving the following four equation \n", +"// t1 = 0.1*d2 ; thickness of shaft\n", +"// d1 = d2-(2*t1) ; // diameter of inner radius\n", +"// Ip = (%pi/32)*((d2^4)-(d1^4)); // Polar moment of inertia\n", +"// r = d2/2\n", +"// t = (T*r)/Ip ; // allowable shear stress\n", +"d2_ = (T/(0.05796*G*f))^(1/4) ; // Another value of d2 by definition of theta(allow), f = T/(G*Ip)\n", +"d1 = 0.8*d2_ ; // because rate of twist governs the design\n", +"disp('m',d2,'The required diameter of the hollow shaft is ')\n", +"// Part (c) : Ratio of diameter and weight\n", +"r1 = d2_/d01 ; // diameter ratio\n", +"r2 = ((d2_^2)-(d1^2))/(d01^2) ; // Weight Ratio\n", +"disp(r1,'Ratio of the diameter of the hollow and solid shaft is')\n", +"disp(r2,'Ratio of the weight of the hollow and solid shaft is')\n", +"\n", +"\n", +"\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.4: EX3_4.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"d = 0.03 ; // diameter of the shaft in meter\n", +"T2 = 450 ; // Torque in N-m\n", +"T1 = 275 ; //\n", +"T3 = 175 ; //\n", +"Lbc = 0.5 ; // Length of shaft in meter\n", +"Lcd = 0.4 ; // Length of shaft in meter\n", +"G = 80e09 ; // Modulus of elasticity\n", +"Tcd = T2-T1 ; // torque in segment CD\n", +"Tbc = -T1 ; // torque in segment BC\n", +"tcd = (16*Tcd)/(%pi*(d^3)); // shear stress in cd segment\n", +"disp('Pa',tcd,'Shear stress in segment cd is')\n", +"tbc = (16*Tbc)/(%pi*(d^3)); // shear stress in bc segment\n", +"disp('Pa',tbc,'Shear stress in segment bc is')\n", +"Ip = (%pi/32)*(d^4); // Polar monent of inertia\n", +"fbc = (Tbc*Lbc)/(G*Ip); // angle of twist in radian\n", +"fcd = (Tcd*Lcd)/(G*Ip); // angle of twist in radian\n", +"fbd = fbc + fcd ; // angle of twist in radian\n", +"disp('radian',fbd,'Angles of twist in section BD')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.6: Calculation_of_various_stress_and_strain_in_circular_tube.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"d1 = 0.06 ; // Inner diameter in meter\n", +"d2 = 0.08 ; // Outer diameter in meter\n", +"r = d2/2; // Outer radius\n", +"G = 27e09 ; // Modulus of elasticity\n", +"T = 4000 ; // Torque in N-m\n", +"Ip = (%pi/32)*((d2^4)-(d1^4)); // Polar moment of inertia\n", +"t_max = (T*r)/Ip ; // maximum shear stress\n", +"disp('Pa',t_max,'Maximum shear stress in tube is ')\n", +"s_t = t_max ; // Maximum tensile stress\n", +"disp('Pa',s_t,'Maximum tensile stress in tube is ')\n", +"s_c = -(t_max); // Maximum compressive stress\n", +"disp('Pa',s_c,'Maximum compressive stress in tube is ')\n", +"g_max = t_max / G ; // Maximum shear strain in radian\n", +"disp('radian',g_max,'Maximum shear strain in tube is ')\n", +"e_t = g_max/2 ; // Maximum tensile strain in radian\n", +"disp('radian',e_t,'Maximum tensile strain in tube is ')\n", +"e_c = -g_max/2 ; // Maximum compressive strain in radian\n", +"disp('radian',e_c,'Maximum compressive strain in tube is ')\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.7: Calculation_of_the_required_diameter_d_of_the_shaft.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"H = 40 ; // Power in hp\n", +"s = 6000 ; // allowable shear stress in steel in psi\n", +"// Part (a)\n", +"n = 500 ; // rpm\n", +"T = ((33000*H)/(2*%pi*n))*(5042/420); // Torque in lb-in\n", +"d = ((16*T)/(%pi*s))^(1/3); // diameter in inch\n", +"disp('inch',d,'Diameter of the shaft at 500 rpm')\n", +"// Part (b)\n", +"n1 = 3000 ; // rpm\n", +"T1 = ((33000*H)/(2*%pi*n1))*(5042/420); // Torque in lb-in\n", +"d1 = ((16*T1)/(%pi*s))^(1/3); // diameter in inch\n", +"disp('inch',d1,'Diameter of the shaft at 3000 rpm')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.8: Calculation_of_maximum_shear_stress_tmax_in_the_shaft_and_the_angle_of_twist.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"d = 0.05 ; // diameter of the shaft\n", +"Lab = 1 ; // Length of shaft ab in meter\n", +"Lbc = 1.2 ; // Length of shaft bc in meter\n", +"Pa = 50000; // Power in Watt at A\n", +"Pb = 35000; // Power in Watt at B\n", +"Ip = (%pi/32)*(d^4) ; // Polar moment of inertia\n", +"Pc = 15000; // Power in Watt at C\n", +"G = 80e09; // Modulus of elasticity\n", +"f = 10 ; // frequency in Hz \n", +"Ta = Pa/(2*%pi*f) // Torque in N-m at A\n", +"Tb = Pb/(2*%pi*f) // Torque in N-m at B\n", +"Tc = Pc/(2*%pi*f) // Torque in N-m at B\n", +"Tab = Ta ; // Torque in N-m in shaft ab\n", +"Tbc = Tc ; // Torque in N-m in shaft bc\n", +"tab = (16*Tab)/(%pi*(d^3)) ; // shear stress in ab segment\n", +"fab = (Tab*Lab)/(G*Ip); // angle of twist in radian\n", +"tbc = (16*Tbc)/(%pi*(d^3)); // shear stress in ab segment\n", +"fbc = (Tbc*Lbc)/(G*Ip); // angle of twist in radian\n", +"fac = (fab+fbc)*(180/%pi); // angle of twist in degree in segment ac\n", +"tmax = Tab; // Maximum shear stress\n", +"disp('Nm',tmax,'The maximum shear stress tmax in the shaft')\n", +"disp('degree',fac,'Angle of twist in segment AC')" + ] + } +], +"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 +} -- cgit