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+{
+"cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 8: Combined Loadings"
+ ]
+ },
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 8.1: CL1.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clear all; clc;\n",
+"\n",
+"disp('Scilab Code Ex 8.1 : ')\n",
+"\n",
+"//Given:\n",
+"di = 1.2*1000; //m\n",
+"ri = di/2;\n",
+"t = 12; //mm\n",
+"sigma = 140; //MPa\n",
+"\n",
+"//Cylindrical Pressure Vessel:\n",
+"\n",
+"p1 = (t*sigma)/ri; //sigma = pr/t\n",
+"\n",
+"//Spherical Vessel:\n",
+"\n",
+"p2 = (2*t*sigma)/(ri); //sigma = pr/2t\n",
+"\n",
+"//Display:\n",
+"\n",
+"printf('\n\nThe maximum internal pressure the cylindrical pressure vessel can sustain = %1.1f N/mm^2',p1);\n",
+"printf('\nThe maximum internal pressure a spherical pressure vessel can sustain = %1.1f N/mm^2',p2);\n",
+"\n",
+"//----------------------------------------------------------------------END--------------------------------------------------------------------------------"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 8.2: CL2.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clear all; clc;\n",
+"\n",
+"disp('Scilab Code Ex 8.2 : ')\n",
+"\n",
+"//Given:\n",
+"P = 15000; //N\n",
+"a = 40; //mm\n",
+"b = 100; //mm\n",
+"\n",
+"//Stress Components:\n",
+"\n",
+"//Normal Force:\n",
+"A = a*b;\n",
+"sigma = P/A;\n",
+"\n",
+"//Bending Moment:\n",
+"I = (a*b^3)/12; //I = (1/12)*bh^3\n",
+"M = P*(b/2);(b/2);\n",
+"c = b/2;\n",
+"sigma_max =(M*c)/I;\n",
+"\n",
+"//Superposition:\n",
+"x = ((sigma_max-sigma)*b)/((sigma_max+sigma)+(sigma_max-sigma));\n",
+"sigma_b = (sigma_max-sigma);\n",
+"sigma_c = (sigma_max + sigma);\n",
+"\n",
+"//Display:\n",
+"\n",
+"printf('\n\nThe state of stress at B = %1.1f MPa (tensile)',sigma_b);\n",
+"printf('\nThe state of stress at C = %1.1f MPa (compressive)',sigma_c);\n",
+"\n",
+"//----------------------------------------------------------------------END--------------------------------------------------------------------------------\n",
+"\n",
+" "
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 8.3: CL3.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clear all; clc;\n",
+"\n",
+"disp('Scilab Code Ex 8.3 : ')\n",
+"\n",
+"//Given:\n",
+"ri = 600/1000; //m\n",
+"t = 12/1000; //m\n",
+"ro = ri+t;\n",
+"sp_wt_water = 10; //kN/m^3\n",
+"sp_wt_steel = 78; //kN/m^3\n",
+"l_a = 1; //m depth of point A from the top\n",
+"\n",
+"//Internal Loadings:\n",
+"v = (%pi*l_a)*(ro^2 - ri^2);\n",
+"W_st = sp_wt_steel*v;\n",
+"\n",
+"p = sp_wt_water*l_a; //Pascal's Law\n",
+"\n",
+"//Stress Components:\n",
+"\n",
+"//Circumferential Stress:\n",
+"sigma1 = (p*ri)/t;\n",
+"\n",
+"//Longitudinal Stress:\n",
+"A_st = (%pi)*(ro^2 - ri^2);\n",
+"sigma2 = W_st/A_st;\n",
+"\n",
+"//Display:\n",
+"\n",
+"\n",
+"printf('\n\nThe state of stress at A (Circumferential) = %1.1f kPa',sigma1);\n",
+"printf('\nThe state of stress at A (Longitudinal) = %1.1f kPa',sigma2);\n",
+"\n",
+"//----------------------------------------------------------------------END--------------------------------------------------------------------------------"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 8.4: CL4.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clear all; clc;\n",
+"\n",
+"disp('Scilab Code Ex 8.4 : ')\n",
+"\n",
+"//Given:\n",
+"y_c = 125/1000; //m\n",
+"x_c = 1.5; //m\n",
+"y_b = 1.5; //m\n",
+"x_b = 6; //m\n",
+"udl = 50; //kN/m\n",
+"l_udl = 2.5; //m\n",
+"l = 250/1000; //m\n",
+"width = 50/1000; //m \n",
+"\n",
+"\n",
+"//Internal Loadings:\n",
+"N = 16.45; //kN\n",
+"V = 21.93; //kN\n",
+"M = 32.89; //kNm\n",
+"\n",
+"//Stress Components:\n",
+"\n",
+"//Normal Force:\n",
+"A = l*width;\n",
+"sigma1 = N/(A*1000);\n",
+"\n",
+"//Shear Force:\n",
+"tou_c = 0;\n",
+"\n",
+"//Bending Moment:\n",
+"c = y_c;\n",
+"I = (1/12)*(width*l^3);\n",
+"sigma2 = (M*c)/(I*1000);\n",
+"\n",
+"//Superposition:\n",
+"sigmaC = sigma1+sigma2;\n",
+"\n",
+"//Display:\n",
+"\n",
+"\n",
+"printf('\n\nThe stress due to normal force at C = %1.2f MPa',sigma1);\n",
+"printf('\nThe stress due to shear force at C = %1.2f MPa',tou_c);\n",
+"printf('\nThe stress due to bending moment at C = %1.2f MPa',sigma2);\n",
+"printf('\nThe resultant stress at C = %1.1f MPa',sigmaC);\n",
+"\n",
+"//----------------------------------------------------------------------END--------------------------------------------------------------------------------"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 8.5: CL5.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clear all; clc;\n",
+"\n",
+"disp('Scilab Code Ex 8.5 : ')\n",
+"\n",
+"//Given:\n",
+"r = 0.75*10; //mm\n",
+"f_x =500;//N\n",
+"f_y =800;//N\n",
+"l1 = 8*10; //mm\n",
+"l2 = 10*10; //mm\n",
+"l3 = 14*10; //mm\n",
+"\n",
+"//Stress Components:\n",
+"\n",
+"//Normal Force:\n",
+"A1 = (%pi*r^2);\n",
+"sigma1 = f_x/A1; //stress = P/A\n",
+"\n",
+"//Shear Force:\n",
+"y_bar = (4*r)/(3*%pi);\n",
+"A2 = A1/2;\n",
+"Q = y_bar*A2; //Q = yA\n",
+"V = f_y;\n",
+"I = (1/4)*(%pi*r^4);\n",
+"t = 2*r;\n",
+"tou_a = (V*Q)/(I*t); //Shear = VQ/It\n",
+"\n",
+"//Bending Moment:\n",
+"M_y = f_x*l3;\n",
+"c = r;\n",
+"sigma_A = (M_y*c)/I; \n",
+"\n",
+"//Torsional Moment:\n",
+"T = f_y*l3;\n",
+"J = (0.5*%pi*r^4); \n",
+"tou_A = (T*c)/J;\n",
+"\n",
+"//Resultant:\n",
+"res_normal= sigma1+sigma_A;\n",
+"res_shear = tou_a+tou_A;\n",
+"\n",
+"//Display:\n",
+"\n",
+"printf('\n\nThe stress due to normal force at A = %1.2f MPa',sigma1);\n",
+"printf('\nThe stress due to shear force at A = %1.2f MPa',tou_a);\n",
+"printf('\nThe stress due to bending moment at A = %1.2f MPa',sigma_A);\n",
+"printf('\nThe stress due to torsional moment at A = %1.2f MPa',tou_A);\n",
+"printf('\nThe resultant normal stress component at A = %1.2f MPa',res_normal);\n",
+"printf('\nThe resultant shear stress component at A = %1.2f MPa',res_shear);\n",
+"\n",
+"//------------------------------------------------------------------------END------------------------------------------------------------------------------"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 8.6: CL6.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"clear all; clc;\n",
+"\n",
+"disp('Scilab Code Ex 8.6 : ')\n",
+"\n",
+"//Given:\n",
+"P = 40; //kN\n",
+"l_ab = 0.4; //m\n",
+"l_bc = 0.8; //m\n",
+"\n",
+"//Stress Components:\n",
+"\n",
+"//Normal Force:\n",
+"A = l_ab*l_bc;\n",
+"sigma = P/A;\n",
+"\n",
+"//Bendng Moments:\n",
+"M_x = P*l_ab/2;\n",
+"cy = l_ab/2;\n",
+"Ix = (1/12)*(l_bc*l_ab^3); //I = (1/12)*(bh^3)\n",
+"sigma_max_1 = (M_x*cy)/Ix; //sigma = My/I\n",
+"\n",
+"M_y = P*l_bc/2;\n",
+"cx = l_bc/2;\n",
+"Iy = (1/12)*(l_ab*l_bc^3); //I = (1/12)*(bh^3)\n",
+"sigma_max_2 = (M_y*cx)/Iy; //sigma = My/I\n",
+"\n",
+"//Superposition:\n",
+"stress_A = -sigma + sigma_max_1 + sigma_max_2;\n",
+"stress_B = -sigma - sigma_max_1 + sigma_max_2;\n",
+"stress_C = -sigma - sigma_max_1 - sigma_max_2;\n",
+"stress_D = -sigma + sigma_max_1 - sigma_max_2;\n",
+"\n",
+"e = abs((stress_B*l_ab)/(stress_A-stress_B));\n",
+"h = abs((stress_B*l_bc)/(stress_A-stress_B));\n",
+"\n",
+"//Display:\n",
+"\n",
+"\n",
+"printf('\n\nThe normal stress at corner A = %1.0f kPa',stress_A);\n",
+"printf('\nThe normal stress at corner B = %1.0f kPa',stress_B);\n",
+"printf('\nThe normal stress at corner C = %1.0f kPa',stress_C);\n",
+"printf('\nThe normal stress at corner D = %1.0f kPa',stress_D);\n",
+"printf('\nThe line of zero stress along AB = %1.4f m',e);\n",
+"printf('\nThe line of zero stress along AD = %1.3f m',h);\n",
+"\n",
+"//------------------------------------------------------------------------END------------------------------------------------------------------------------\n",
+"\n",
+"\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
+}
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