diff options
Diffstat (limited to 'Mechanics_of_Structures_by_S_B_Junnarkar')
11 files changed, 5166 insertions, 0 deletions
diff --git a/Mechanics_of_Structures_by_S_B_Junnarkar/1-Simple_stresses_and_strains.ipynb b/Mechanics_of_Structures_by_S_B_Junnarkar/1-Simple_stresses_and_strains.ipynb new file mode 100644 index 0000000..cba56b6 --- /dev/null +++ b/Mechanics_of_Structures_by_S_B_Junnarkar/1-Simple_stresses_and_strains.ipynb @@ -0,0 +1,594 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 1: Simple stresses and strains" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.10: Chapter_1_example_10.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear ;\n", +"clc ;\n", +"a = 12;//length of each side in inches\n", +"d = 9/8;//diameter of each reinforced bar in inches\n", +"r = 3;//distance of centre from the edges in inches\n", +"p_c = 600;//in lb/in^2\n", +"n = 18;//modular ration E_s/E_c\n", +"A_s = 4*0.25*%pi*d^2;//in in^2\n", +"A_c = a^2 - A_s;//in in^2\n", +"p_s = n*p_c;//in lb/in^2\n", +"P = p_s*A_s+p_c*A_c;//safe central load in lb-wt\n", +"printf('Safe central load = %d lb-wt',P);\n", +"printf('\n Of this, the reinforcing bars carry %d lb-wt',p_s*A_s);\n", +"\n", +"//there is an error in the answer given in textbook." + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.11: Chapter_1_example_11.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear ;\n", +"clc ;\n", +"l = 8;//length in feet\n", +"d = 0.5;//diameter in inches\n", +"r = 30;//distance between two rods in inches\n", +"P = 2000;//load in lb-wt\n", +"E_s = 30*10^6;//modulus of elsticity of steel rod\n", +"E_b = 16*10^6;//modulus of elsticity of brass rod\n", +"A_s = 0.25*%pi*d^2;//section area in in^2\n", +"p_b = P/(A_s*(1+(E_s/E_b)));\n", +"p_s = (P/A_s) - p_b ;\n", +"P_b = A_s*p_b;\n", +"P_s = A_s*p_s;\n", +"printf('P_s = %.1f lb/in^2\n and P_b = %.1f lb/in^2',P_s,P_b);\n", +"x = r*P_b/P ;//\n", +"printf('\n x = %.2f inches',x);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.12: Chapter_1_example_12.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear ;\n", +"clc ; \n", +"alpha = 0.0000062 ;//co-efficient of the expansion in 'per F'\n", +"t = 100;//in F\n", +"d = 3/4;//in inches\n", +"del = 0.02;//in inches\n", +"l = 15;//in ft\n", +"E = 13000;//in tons/in^2\n", +"e = alpha*t - (del/(l*12));\n", +"p = E*e;//in tons/in^2\n", +"A = 0.25*%pi*d^2;//in in^2\n", +"P = p*A ;//in tons\n", +"printf('Tensile strain imposed by end-grips,e = %.5f',e);\n", +"printf('\n p = %.2f tons/in^2\n P = %.2f tons',p,P);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.13: Chapter_1_example_13.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"d = 1;//diameter of steel bar in inches\n", +"d1 = 3/2;//external diameter of brass tube in inches\n", +"d2 = 1;//internal diameter of brass tube in inches\n", +"t = 100;//in F\n", +"alpha_s = 0.0000062;//alpha of steel in 'per F'\n", +"alpha_b = 0.000010;//alpha of brass in 'per F'\n", +"E_s = 30*10^6;//in lb/in^2\n", +"E_b = 14*10^6;//in lb/in^2\n", +"A_s = 0.25*%pi*d^2;//section area of steel bar in in^2\n", +"A_b = 0.25*%pi*(d1^2-d2^2);//section area of brass tube in in^2\n", +"p_b = t*(alpha_b-alpha_s)*E_s/((A_b/A_s)+(E_s/E_b));\n", +"p_s = (A_b/A_s)*p_b;\n", +"printf('The stresses induced in each metal are, p_b = %d lb/in^2\n p_s = %d lb/in^2',p_b,p_s);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.14: Chapter_1_example_14.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"D = 4;//diameter of the wheel in ft\n", +"p = 6 ;//hoop stress in tons/in^2\n", +"alpha = 0.0000062;//in 'per F' \n", +"E = 13000;//in tons/in^2\n", +"d = (1/(1+(p/E)))*D*12;//internal diameter in inches\n", +"t = (D*12-d)/(d*alpha);\n", +"printf('The least temperature the tube must be heated is, t = %.1f F',t);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.15: Chapter_1_example_15.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"p = 8;//normal stress intensity in tons/in^2\n", +"theta = 35*%pi/180;//inclination of the section in degrees\n", +"P = p*cos(theta);//resultant stress intensity in tons/in^2\n", +"p_n = P*cos(theta);//normal stress intensity in tons/in^2\n", +"p_t = P*sin(theta);//tangential stress intensity in tons/in^2\n", +"p_max = 0.5*p;//maximum possible shear in tons/in^2\n", +"angle = 45;//inclination of these planes in degrees\n", +"printf('Resultant stress intensity = %.2f tons/in^2',P);\n", +"printf('\n normal stress intensity = %.2f tons/in^2',p_n);\n", +"printf('\n tangential stress intensity = %.2f tons/in^2',p_t);\n", +"printf('\n The maximum possible shear on any plane is %d tons/in^2',p_max);\n", +"printf('\n and these planes are inclined at %d degrees to the normal section.',angle);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.16: Chapter_1_example_16.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"d = 9/8;//diameter of the steel bar in inches\n", +"P = 6;//tensile load in tons\n", +"del_l = 0.0036 ;//extension of length inches\n", +"l = 8;//gauge length in inches\n", +"del_d = 0.00015;//change in diameter in inches\n", +"A = 0.25*%pi*d^2;//section area in in^2\n", +"p = P/A;//stress in tons/in^2\n", +"e = del_l/l;//strain\n", +"E = p/e;//modulus of elasticity in tons/in^2\n", +"LS = del_d/d;//lateral strain \n", +"PR = LS/e;//poisson's ratio \n", +"N = E/(2*(1+PR));//rigidity modulus in tons/in^2\n", +"K = E/(3*(1-2*PR));//bulk modulus in tons/in^2\n", +"printf('Poisson ratio 1/m = %.4f',PR);\n", +"printf('\n E = %d tons/in^2',E);\n", +"printf('\n N = %d tons/in^2',N);\n", +"printf('\n K = %d tons/in^2',K);\n", +"\n", +"//there is an error in the answer given in textbook." + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.17: Chapter_1_example_17.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"N = 2640;//rigidity modulus in tons/in^2\n", +"d = 3/8;//diameter of the rod in inches\n", +"P = 1/2;//axial pull in tons\n", +"del_d = 0.000078;//change in diameter in inches\n", +"A = 0.25*%pi*d^2;//section area in in^2\n", +"p = P/A ;//stress tons/in^2\n", +"LS = del_d/d;//lateral strain\n", +"m = p/(LS*2*N) - 1;\n", +"E = 2*N*(1 + 1/m);//modulus of elasticity in ton/in^2\n", +"PR = 1/m;//poisson's ratio \n", +"printf('Poisson ratio 1/m = %.3f',PR);\n", +"printf('\n E = %d ton/in^2',E);\n", +"\n", +"//there is an error in the answer given in textbook." + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.1: Chapter_1_example_1.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear all;\n", +"clc;\n", +"P = 5.5 ;//Axial pull in tons\n", +"E = 13000 ;//modulus of elasticity tons/in^2\n", +"l = 120 ;//length in inches\n", +"A = %pi/4 ;//Area of resisting section in^2\n", +"p = P/A ;//Intensity of stress in tons/in^2\n", +"e = p/E ;//strain\n", +"delta_l = l*e;//elongation of the bar in inches\n", +"printf('The elongation of the bar is %.4f inch',delta_l);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.2: Chapter_1_example_2.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear all;\n", +"clc;\n", +"s_p = 200;//steam pressure in lb/in^2\n", +"l = 4;//length in inches\n", +"b = 4;//breadth in inches\n", +"p = 14000;//permissible streaa in lb/in^2\n", +"P = s_p*l*b;//Pull on each bolt in lb-wt\n", +"A = P/p ;//necessary area of bolt-section\n", +"d = sqrt(4*A/%pi) ;//minimum diameter in inches\n", +"printf('The minimum diameter d of each stay bolt = %0.2f inch',d);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.3: Chapter_1_example_3.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear all;\n", +"clc;\n", +"D = 8;//external diameter in inches \n", +"d = 6;//internal diameter in inches\n", +"sigma = 36;//ultimate stress in tons/in^2\n", +"n = 6;//safety factor\n", +"A = 0.25*%pi*(D^2 - d^2);//Area of section in in^2\n", +"P = sigma*A; //crushing load for the column in tons \n", +"P_safe = P/n ;//safe load in tons\n", +"printf('Safe load = %d tons',P_safe); \n", +"//there is an error in the answer given in textbook." + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.4: Chapter_1_example_4.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear all;\n", +"clc;\n", +"sigma = 20;//ultimate sheat stress in tons/in^2\n", +"d = 1/2;//diameter of the hole in inches\n", +"t = 3/8;//thickness of the plate in inches\n", +"A = 0.25*%pi*d^2;//area of the cross-section of the punch in^2\n", +"P = %pi*d*t*sigma;//necessary force in tons\n", +"sigma_comp = P/A;//compressive stress on the punch\n", +"printf('The compressive stress of the punch = %d tons/in^2',sigma_comp);\n", +"//there is an error in the answer given in textbook." + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.5: Chapter_1_example_5.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear all;\n", +"clc;\n", +"b = 8;//width in inches\n", +"t = 3/8;//thickness in inches\n", +"l = 20;//length in feets\n", +"P = 22;//pull in tons\n", +"E = 13500;//modulus of elasticity in tons/in^2\n", +"sigma = 0.3;//poisson/s ratio\n", +"A = b*t;//in in^2\n", +"V = l*A*12;//in cub.inch\n", +"p = P/A;//in tons/in^2\n", +"e = p/E;\n", +"delta_l = e*l*12;//stretch of the bar in inches\n", +"Lateral_strain = e*sigma ;//lateral strain\n", +"del_b = b*Lateral_strain;//in inches\n", +"del_t = t*Lateral_strain;//in inches\n", +"k = e*(1-2*sigma);//(del_V)/(V)\n", +"del_V = k*V;//change in volume in cub.inch\n", +"printf('The change in volume is %.3f cub.inch',del_V);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.6: Chapter_1_example_6.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear all;\n", +"clc;\n", +"d = 7/8;//diameter of the bar in inches\n", +"l = 10;//length in feets\n", +"P = 6;;//axial pull in tons\n", +"E = 13000;//modulus of elsticity in tons/in^2\n", +"m = 4;\n", +"A = 0.25*%pi*d^2;//in in^2\n", +"V = 0.25*%pi*d^2*l*12;//volume in cub.inches\n", +"p = P/A;//in tons/in^2\n", +"e = p/E;\n", +"del_l = e*l*12;//stretchof the bar in inches\n", +"Lateral_strain = e/m ;//lateral strain\n", +"del_d = Lateral_strain*d;//Contraction in diameter in inches\n", +"printf('The Contraction in diameter is %f inches',del_d);\n", +"k = e*(1-2/m);//(del_V)/(V)\n", +"del_V = k*V;//change in volume in cub.inch\n", +"printf('\n The change in volume is %.4f cub. inch',del_V);\n", +"W = 0.5*P*del_l;;//work done in stretching the bar in in-ton\n", +"printf('\n The work done in stretching the bar is %.4f in-ton',W);\n", +"//there is an error in the answer given in textbook." + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.7: Chapter_1_example_7.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear all;\n", +"clc;\n", +"L = 24;//length of the bar in ft\n", +"d1 = 9/8;//diameter of the bar in inches\n", +"l1 = 6;//in ft\n", +"d2 = 1;//in inches\n", +"l2 = 12;//in ft\n", +"d3 = 5/4;//in inches\n", +"l3 = L-l1-l2;//in ft\n", +"P = 10000;//axial compression in lb-wt\n", +"E = 28*10^6;//modulus of elasticity in lb/in^2\n", +"A1 = 0.25*%pi*d1^2;//in in^2\n", +"A2 = 0.25*%pi*d2^2;//in in^2\n", +"A3 = 0.25*%pi*d3^2;//in in^2\n", +"p1 = P/A1 ;//in lb/in^2\n", +"e1 = p1/E;\n", +"p2 = P/A2 ;//in lb/in^2\n", +"e2 = p2/E;\n", +"p3 = P/A3 ;//in lb/in^2\n", +"e3 = p3/E;\n", +"del_l1 = e1*l1*12;//in inches\n", +"del_l2 = e2*l2*12;//in inches\n", +"del_l3 = e3*l3*12;//in inches\n", +"del_l = del_l1+del_l2+del_l3;//total change in length in ft\n", +"W = 0.5*P*del_l/12;//energy stored in the bar in ft-lbs\n", +"printf('Total change in length of the bar is %.3f inches',del_l);\n", +"printf('\n The energy stored in the bar is %.1f ft-lbs',W);\n", +"//there is an error in the answer given in textbook." + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.8: Chapter_1_example_8.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear all;\n", +"clc;\n", +"P = 1200;//axial pull in lb-wt\n", +"d1 = 1;//diameter of one end in inches\n", +"d2 = 0.5;//diameter of other end in inches\n", +"l = 10;//length of the rod in inches\n", +"E = 14*10^6;//modulus of elsticity in lb/in^2\n", +"del_l = 4*P*l/(%pi*E*d1*d2);//change in length in inches \n", +"printf('The change in length of the rod is %.4f inches',del_l);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.9: Chapter_1_example_9.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear ;\n", +"clc ;\n", +"d = 1;//diameter of the steel bar in inches\n", +"l = 12;//length of the steel bar in inches\n", +"d1 = 3/2;//external diameter in inches\n", +"d2 = 1;//internal diameter in inches\n", +"P = 5;//axial pull in tons\n", +"E_s = 30*10^6;//modulus of elasticity of steel in lb/in^2\n", +"E_b = 14*10^6;//modulus of elasticity of brass in lb/in^2\n", +"A_s = 0.25*%pi*d^2;//area of the steel section in in^2\n", +"A_b = 0.25*%pi*(d1^2-d2^2);//area of the brass section in in^2\n", +"P_b = (P/((E_s/E_b)*A_s+A_b))*A_b;//load resisted by the brass tube in tons\n", +"P_s = P-P_b;//bal;ance load resisted by the steel tube\n", +"e = (P_b/A_b)*2240/E_b ;//strain\n", +"printf('The strain e = %.4f',e);\n", +"del_l = e*l ;//extension of the bar in inches\n", +"printf('\n The extension of the bar = %.4f inches',del_l);\n", +"W = 0.5*P*del_l;//work done in stretching in inch-ton\n", +"printf('\n The work done in stretching is %.3f inch-ton',W);" + ] + } +], +"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/Mechanics_of_Structures_by_S_B_Junnarkar/10-Radial_pressure_cylindrical_and_spherical_shells.ipynb b/Mechanics_of_Structures_by_S_B_Junnarkar/10-Radial_pressure_cylindrical_and_spherical_shells.ipynb new file mode 100644 index 0000000..dfc61ef --- /dev/null +++ b/Mechanics_of_Structures_by_S_B_Junnarkar/10-Radial_pressure_cylindrical_and_spherical_shells.ipynb @@ -0,0 +1,513 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 10: Radial pressure cylindrical and spherical shells" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 10.10: Chapter_10_example_10.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"d = 9;// inches\n", +"p = 5000/2240;// lb/in^2\n", +"f = 8;// tons/in^2\n", +"PR = 0.3;// Poisson's ratio\n", +"//(i) Maximum principal stress hypothesis:\n", +"k_limit1 = sqrt((f + p)/(f - p));//k_limit = r1/r2\n", +"r_limit1 = k_limit1*0.5*d;//inches\n", +"printf('The outer radius in case(i), r2 = %.3f inches',r_limit1);\n", +"//(ii) Maximum principal strain:\n", +"k_limit2 = sqrt(((f/p - PR)+1)/(f/p - PR -1));\n", +"r_limit2 = k_limit2*0.5*d;// inches\n", +"printf('\n The outer radius in case(ii), r2 = %.3f inches',r_limit2);\n", +"//(iii) Maximum shear stress:\n", +"k_limit3 = sqrt(f/(2*p) /((f/(2*p)) - 1));\n", +"r_limit3 = k_limit3*0.5*d;// inches\n", +"printf('\n The outer radius in case(iii), r2 = %.3f inches',r_limit3);\n", +"//(iv) Maximum strain energy\n", +"K1 = (f^2 /p^2)/(2*((f^2 /(2*p^2)) - (1+PR)));\n", +"K2 = K1^2;\n", +"K3 = ((f^2 /(2*p^2)) - (1-PR))/((f^2 /(2*p^2)) - (1+PR));\n", +"k_limit4 = sqrt(K1+sqrt(K2-K3));\n", +"r_limit4 = k_limit4*0.5*d;// inches\n", +"printf('\n The outer radius in case(iv), r2 = %.3f inches',r_limit4);\n", +"\n", +"//there are calculation errors in the answer given in text book" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 10.11: Chapter_10_example_11.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"r1 = 0.5*6;// inches\n", +"r2 = 0.5*12;// inches\n", +"r3 = 0.5*10;// inches\n", +"p = 1500;// lb/in^2\n", +"p_f = 12000;// lb/in^2\n", +"//Initially, for the inner tube\n", +"b = -p/((1/r1^2) - (1/r3^2));\n", +"a = b/r1^2;\n", +"f_3 = (b/r1^2) +a;// lb/in^2\n", +"f_5 = (b/r3^2) +a;// lb/in^2\n", +"//for the outer tube\n", +"b1 = p/((1/r3^2)-(1/r2^2));\n", +"a1 = b1/r2^2;\n", +"f1_5 = (b1/r3^2)+a1;// lb/in^2\n", +"f1_6 = (b1/r2^2)+a1;// lb/in^2\n", +"//When the fluid pressure of 12000 lb/in^2, is admitted into the compound tube\n", +"B = p_f/((1/r1^2)-(1/r2^2));\n", +"A = B/(r2^2);\n", +"f_3_ = (B/r1^2)+A;// lb/in^2\n", +"f_5_ = (B/r3^2)+A;// lb/in^2\n", +"f_6_ = (B/r2^2)+A;// lb/in^2\n", +"printf('The hoop stresse are');\n", +"printf('\n at x = 3 inches,x = 5 inches initially on inner tube are %.1f lb/in^2.., compressive, %.1f lb/in^2..,compressive respectively',-f_3,-f_5);\n", +"printf('\n at x = 5 inches,x = 6 inches initially on outer tube are %.1f lb/in^2.., tensile, %.1f lb/in^2..,tensile respectively',f1_5,f1_6);\n", +"printf('\n at x = 3 inches,x = 5 inches and x = 6 inches due to fluid pressure are %d lb/in^2.., tensile, %d lb/in^2..,tensile, and %d lb/in^2..,tensile respectively',f_3_,f_5_,f_6_')\n", +"printf('\n at x = 3 inches,x = 5 inches finally on inner tube are %.1f lb/in^2.., tensile, %.1f lb/in^2..,tensile respectively',f_3_+f_3,f_5_+f_5);\n", +"printf('\n at x = 5 inches,x = 6 inches finally on outer tube are %d lb/in^2.., tensile, %d lb/in^2.., tensile respectively',f1_5+f_5_,f1_6+f_6_);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 10.12: Chapter_10_example_12.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"p = 1500;// lb/in^2\n", +"E = 30*10^6;// lb/in^2\n", +"f1_5 = 8318;// lb/in^2\n", +"f2_5 = 3187.5;// lb/in^2\n", +"alpha = 0.0000062;// per F\n", +"r3 = 6;// inches\n", +"del_r3 = r3*(f1_5+f2_5)/E;// inches\n", +"t = ((f1_5+f2_5)/E)/(alpha);// inches\n", +"printf('The minimum temperature to which outer tube should be heated before it can be slipped on, t = %.2f F',t);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 10.13: Chapter_10_example_13.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"r1 = 0.5*9;// inches\n", +"r2 = 0.5*3;// inches\n", +"r3 = 0.5*6;// inches\n", +"del_r3 = 0.5*0.003;// inches\n", +"E = 13000;// tons/in^2\n", +"k1 = r1/r3;\n", +"k2 = r2/r3;\n", +"a1 = (del_r3/r3)*E/((k1^2 +1)- (k2^2 +1)*(k1^2 -1)/(k2^2 -1));\n", +"a = a1*(k1^2 -1)/(k2^2 -1);\n", +"b1 = a1*r1^2;\n", +"b = a*r2^2;\n", +"p_ = (b/r3^2) -a;// tons/in^2\n", +"// for the inner tube\n", +"f_x1 = (b/r2^2) +a;// tons/in^2\n", +"f_x2 = (b/r3^2) +a;// tons/in^2\n", +"// for the outer tube\n", +"f_x3 = (b1/r3^2) +a1;// tons/in^2\n", +"f_x4 = (b1/r1^2) +a1;// tons/in^2\n", +"printf('The hoop stresses are as under:');\n", +"printf('\n For the inner tube, at x = 1/5 inches, f = %.2f tons/in^2., compressive\n at x = 3 inches, f = %.2f tons/in^2.,compressive',-f_x1,-f_x2);\n", +"printf('\n For the outer tube, at x = 3 inches, f = %.2f tons/in^2., tensile\n at x = 4.5 inches, f = %.2f tons/in^2.,tensile',f_x3,f_x4);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 10.14: Chapter_10_example_14.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"r1 = 0.5*5;// inches\n", +"p = 5000;// lb/in^2\n", +"f = 5;// tons/in^2\n", +"b = (f + p/2240)/((1/r1^3) + (2/r1^3));\n", +"a = f - (b/r1^3);\n", +"//external diameter\n", +"r = (2*b/a)^(1/3);// inches\n", +"t = r - r1;// inches\n", +"printf('The thickness of the shell required, t = %.3f inches',t);\n", +"\n", +"//the answer is approximated in the text book" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 10.1: Chapter_10_example_1.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"d = 2;// feet\n", +"p = 250;// lb/in^2\n", +"f = 12000;// lb/in^2\n", +"t_limit = p*d*12/(2*f) ;// inches\n", +"printf('The necessary thickness of metal for seamless pipe is %.2f inches',t_limit);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 10.2: Chapter_10_example_2.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"l = 8;//feet\n", +"d = 3;// feet\n", +"t = 1/2;// inches\n", +"p = 200;// lb/in^2\n", +"E = 30*10^6;// lb/in^2\n", +"PR = 0.3;// poisson's ratio\n", +"f1 = p*d*12/(2*t);// lb/in^2\n", +"f2 = p*d*12/(4*t);// lb/in^2\n", +"f_s = 0.5*(f1-f2);// lb/in^2\n", +"e1 = (f1/E)-(PR*f2/E);// lb/in^2\n", +"e2 = (f2/E)-(PR*f1/E);// lb/in^2\n", +"del_d = e1*d*12;// inches\n", +"del_l = e2*l*12;// inches\n", +"del_V = (e2+2*e1)*0.25*%pi*(12*d)^2 * l*12;// cub. inches\n", +"printf('Maximum intensity of shear stress induced = %d lb/in^2',f_s);\n", +"printf('\n del_d = %.6f inches\n del_l = %.6f inches\n del_V = %.1f cub. inches',del_d,del_l,del_V);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 10.3: Chapter_10_example_3.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"d = 30;// inches\n", +"H = 300;// feet\n", +"w = 62.5;\n", +"f = 2800;\n", +"//intensity of water pressur\n", +"p = w*H/144;// lb/in^2\n", +"t_limit = p*d/(2*f);// inches\n", +"printf('Thickness of metal required is %.4f inches',t_limit);\n", +"\n", +"//the answer is correct only, but it is approximated in the text book." + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 10.4: Chapter_10_example_4.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"d = 78;// inches\n", +"t = 3/4;// inches\n", +"n1 = 70/100;// efficiency of the longitudinal riveted joint\n", +"f = 6;// tons/in^2\n", +"n2 = 60/100;// efficiency of the circumferential riveted joint\n", +"p = f*2240/(d/(2*t*n1));//lb/in^2\n", +"p = round(p-1);\n", +"f1 = p*d/(2*t);// lb/in^2\n", +"f2 = p*d/(4*t*n2);// lb/in^2\n", +"printf('The permissible steam pressure, p = %d lb/in^2',p);\n", +"printf('\n The circumferential stress, f1 = %d lb/in^2 = %.2f tons/in^2',f1,f1/2240);\n", +"printf('\n The longitudinal stress, f2 = %d lb/in^2 = %.2f tons/in^2',f2,f2/2240);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 10.5: Chapter_10_example_5.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"d = 4;// feet\n", +"p = 200;// lb/in^2\n", +"f = 15000;// lb/in^2\n", +"n = 0.7;// efficiency\n", +"t_limit = p*d*12/(4*f*n);// inches\n", +"printf('The thickness of the plate required = %.2f inches',t_limit);\n", +"\n", +"//the answer is correct only, but it is approximated in the text book." + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 10.6: Chapter_10_example_6.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"d = 3;// feet\n", +"t = 1/4;// inches\n", +"del_V = 9;// cub. inches\n", +"E = 30*10^6;// lb/in^2\n", +"PR = 0.3;// poisson's ratio\n", +"V = (%pi/6)*(12*d)^3;// in^3\n", +"k = del_V/V;\n", +"f = k*E/(3*(1-PR));// lb/in^2\n", +"p = 4*f*t/(12*d);// lb/in^2\n", +"printf('The pressure exerted by fluid on the shell, p = %d lb/in^2',p);\n", +"\n", +"//there is a minute calculation error in the answer given in text book" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 10.7: Chapter_10_example_7.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"d = 12;// feet\n", +"t = 1/2;// inches\n", +"d1 = 1/4;// inches\n", +"p = 500;// lb/in^2\n", +"E_c = 6000;// tons/in^2\n", +"PR = 0.3;// Poisson's ratio\n", +"E_s = 13000;// tons/in^2\n", +"f_t = 8000;// lb/in^2\n", +"l = 8;\n", +"P_c = l*(%pi/64)*f_t;// lb-wt\n", +"f_c = P_c/(2*t);// lb/in^2\n", +"//bursting force per inch unit length\n", +"f_b = p*d;// lb-wt\n", +"f_p = (f_b + (l*0.049*PR*p*d/(4*t))*(E_s/E_c))/(1 + (l*0.049)*E_s/E_c);// lb/in^2 \n", +"f_w = (f_p - PR*p*d/(4*t))*E_s/E_c;// lb/in^2\n", +"printf(' Pipe Steel-wire');\n", +"printf('\n Initually, %d lb/in^2.,compr. %d lb/in^2., tensile',f_c,f_t);\n", +"printf('\n Due to p, %d lb/in^2.,tensile. %d lb/in^2., tensile',f_p,f_w);\n", +"printf('\n Finally, %d lb/in^2.,tensile. %d lb/in^2., tensile',f_p-f_c,f_w+f_t);\n", +"\n", +"//there is a calculation error in the answer given in text book" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 10.8: Chapter_10_example_8.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"d = 12;// inches\n", +"t = 3;// inches\n", +"p_x1 = 900;// lb/in^2\n", +"x1 = 0.5*d;// inches\n", +"p_x2 = 0;\n", +"x2 = 0.5*d+t;// inches\n", +"//from Lame's formulae\n", +"b = (p_x1-p_x2)/((1/x1^2)-(1/x2^2));\n", +"a = (b/x1^2)- p_x1;\n", +"f_x1 = (b/x1^2)+a;// lb/in^2\n", +"f_x2 = (b/x2^2)+a;// lb/in^2\n", +"printf('The maximum and minimum intensities of circumferential stresses are: f_6 = %d lb/in^2.,tensile\n f_9 = %d lb/in^2., tensile',f_x1,f_x2);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 10.9: Chapter_10_example_9.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"d = 5;// inches\n", +"p = 3;// tons/in^2\n", +"f = 8;// tons/in^2\n", +"x = 0.5*d;// inches\n", +"b = (p+f)/(2/x^2);\n", +"a = f-(b/x^2); \n", +"r = sqrt(b/a);//outer radius\n", +"t = r-0.5*d;//thickness\n", +"D = 2*t+d;//outer diameter\n", +"printf('The thickness of metal necessary, t = %.3f inches',t);\n", +"printf('\n the outer diameter will be, D = %.1f inches',D);\n", +"\n", +"//the answer is correct, but it is approximated in the text book." + ] + } +], +"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/Mechanics_of_Structures_by_S_B_Junnarkar/11-Riveted_joints.ipynb b/Mechanics_of_Structures_by_S_B_Junnarkar/11-Riveted_joints.ipynb new file mode 100644 index 0000000..2701980 --- /dev/null +++ b/Mechanics_of_Structures_by_S_B_Junnarkar/11-Riveted_joints.ipynb @@ -0,0 +1,421 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 11: Riveted joints" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.10: Chapter_11_example_10.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"P = 2.4;// tons\n", +"e = 18;// inches\n", +"n = 8;//no. of rivets\n", +"d = 7/8;// inches\n", +"h = 4;// inches\n", +"M = P*e;// ton-inches\n", +"d1 = 2;// \n", +"d2 = 6;//\n", +"square_r_sum = h*((0.5*h)^2 + d2^2) + h*((0.5*h)^2 + d1^2);//\n", +"r = sqrt(40);\n", +"F = M*r/square_r_sum;// tons\n", +"theta = atan(d2/d1)//radians\n", +"theta1 = theta*180/%pi// degrees\n", +"V = (P/n) + F*cos(theta);// tons\n", +"H = F*sin(theta);// tons\n", +"R = sqrt(V^2 + H^2);// tons\n", +"f_s = R/(0.25*%pi*d^2);// tons/in^2\n", +"printf('The maximum shear intensity induced at any rivet is \n f_s = %.2f tons/in^2',f_s);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.1: Chapter_11_example_1.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"t = 5/8;// inch\n", +"d = 1;// inch\n", +"p = 4;// inches\n", +"f_t = 28; //tons/in^2\n", +"f_s = 20; //tons/in^2\n", +"f_b = 40; //tons/in^2\n", +"P_t = (p-d)*t*f_t;// tons\n", +"P_s = 2*2*0.25*%pi*d^2 *f_s;// tons\n", +"P_b = 2*d*t*f_b;//tons\n", +"P = p*t*f_t;// tons\n", +"n = min(P_t,P_s,P_b)/P ;// efficiency\n", +"printf('The efficiency of the joint = %.3f or %.1f percentage',n,n*100);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.2: Chapter_11_example_2.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"t = 1/2;// inches\n", +"d1= 7/8;// inches\n", +"p1 = 5/2;// inches\n", +"d2= 9/8;// inches\n", +"p2 = 7/2;// inches\n", +"f_t = 8;// tons/in^2\n", +"f_s = 6;// tons/in^2\n", +"f_b = 10;// tons/in^2\n", +"\n", +"P_t1 = (p1-d1)*t*f_t;// tons\n", +"P_s1 = 0.25*%pi*d1^2 *f_s;// tons\n", +"P_b1 = d1*t*f_b;//tons\n", +"P1 = p1*t*f_t;// tons\n", +"n1 = min(P_t1,P_s1,P_b1)/P1 ;// efficiency\n", +"printf('The efficiency of first joint = %.2f = %d percentage',n1,n1*100);\n", +"\n", +"P_t2 = (p2-d2)*t*f_t;// tons\n", +"P_s2 = 0.25*%pi*d2^2 *f_s;// tons\n", +"P_b2 = d2*t*f_b;//tons\n", +"P2 = p2*t*f_t;// tons\n", +"n2 = min(P_t2,P_s2,P_b2)/P2 ;// efficiency\n", +"printf('\n The efficiency of second joint = %.3f = %.1f percentage\n',n2,n2*100);\n", +"\n", +"if n2 > n1 then\n", +" printf(' The second joint, with its higher efficiency, is stronger');\n", +"else\n", +" printf(' The first joint, with its higher efficiency, is stronger');\n", +"end" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.3: Chapter_11_example_3.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"t = 3/8;// inches\n", +"p2 = 7/2;// inches\n", +"f_t = 11/2;// tons/in^2\n", +"f_s = 5;// tons/in^2\n", +"f_b = 12;// tons/in^2\n", +"d = 1.2*sqrt(t);// inches\n", +"//d = 0.735, say 0.75 inches\n", +"d = 0.75;// inches\n", +"P_s = 0.25*%pi*d^2 *f_s;// tons\n", +"P_b = d*t*f_b;//tons\n", +"P_t_limit = P_s;//tons\n", +"p_limit = P_s/(t*f_t) + d;// inches\n", +"//p_limit = 1.763, take p = 1.75\n", +"p = 1.75;// inches\n", +"n = (p-d)/p;// efficiency\n", +"printf('The efficiency of the joint = %.1f percentage',n*100);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.4: Chapter_11_example_4.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"d = 7/8;// inches\n", +"t = 1/2;// inches \n", +"f_t = 6;// tons/in^2\n", +"f_s = 5;// tons/in^2\n", +"f_b = 10;// tons/in^2\n", +"p_s = 2*0.25*%pi*d^2*f_s;// tons\n", +"P_b = d*t*f_b;// tons\n", +"p_t_limit = 2*P_b/3 + d;// inches\n", +"n = (p_t_limit-d)/p_t_limit;// efficiency\n", +"printf('Pitch, p = %.3f inches',p_t_limit);\n", +"printf('\n Efficiency = %.3f or %d percentage',n,n*100);\n", +"\n", +"//the answer is approximated in the textbook." + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.5: Chapter_11_example_5.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"d = 6;// feet\n", +"p = 180;// lb/in^2\n", +"f = 6;// tons\n", +"n = 70/100;// efficiency\n", +"d1 = 1;// inches\n", +"f_s = 5;// tons/in^2\n", +"f_b = 10;// tons/in^2\n", +"t = p*d/(2*f*n);// inches\n", +"// t = 0.6889 inches, say 0.75 inches\n", +"t = 0.75;//inches\n", +"P_s = 2*0.25*%pi*d1^2*f_s;// tons\n", +"P_b = d1*t*f_b;// tons\n", +"p_limit = 2*P_b/(t*f) + d1;// inches\n", +"//p_limit = 4.33 inches, make it 4 inches\n", +"p = round(p_limit);// inches\n", +"n1 = (p-d1)/p;// efficiency\n", +"printf('Pitch = %.2f inches, make it %d inches.',p_limit,p);\n", +"printf('\n The efficiency of the joint will be %d percentage aganist the assumed value of %d percentage.',n1*100,n*100);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.6: Chapter_11_example_6.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"t = 1/2;// inches\n", +"a = 1/2;// inches\n", +"P = 42;// tons\n", +"d = 3/4;// inches\n", +"f_t = 7.5;// tons/in^2\n", +"f_s = 6;// tons/in^2\n", +"f_b = 12;// tons/in^2\n", +"P_s = 2*0.25*%pi*d^2 *f_s;// tons\n", +"P_b = d*t*f_b;// tons\n", +"n = P/min(P_s,P_b);\n", +"n = round(n+1);\n", +"b1 = P/(t*f_t) + d;// inches\n", +"b = round(b1);\n", +"e = (b-d)/b;// efficiency\n", +"f_s = (P/n)/(2*0.25*%pi*d^2) ;// tons/in^2\n", +"f_b = (P/n)/(d*t);// tons/in^2\n", +"f1 = P/(a*(b-d));// tons/in^2\n", +"f2 = (P-(P/n))/((b-2*d)*t);// tons/in^2\n", +"f3 = (P-(3*P/n))/((b-3*d)*t);// tons/in^2\n", +"f4 = (P-(6*P/n))/((b-4*d)*t);// tons/in^2\n", +"printf('The number of rivets required, n = %d',n);\n", +"printf('\n The width of the flat required, b = %.2f inches, say %d inches',b1,b);\n", +"printf('\n The efficiency of the joint = %.2f percentage',e*100);\n", +"printf('\n The actual stresses induce in the rivet are, f_s = %.2f tons/in^2\n f_b = %.2f tons/in^2',f_s,f_b);\n", +"printf('\n The tensile stress at section 11, f1 = %.3f rons/in^2',f1);\n", +"printf('\n The tensile stress at section 22, f2 = %.3f rons/in^2',f2);\n", +"printf('\n The tensile stress at section 33, f3 = %.3f rons/in^2',f3);\n", +"printf('\n The tensile stress at section 44, f4 = %.3f rons/in^2',f4);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.7: Chapter_11_example_7.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"b = 9;// inches\n", +"t = 3/4;// inches\n", +"f_t = 8;// tons/in^2\n", +"f_s = 5;// tons/in^2\n", +"f_b = 10;// tons/in^2\n", +"d = 7/8;// inches\n", +"P = (b-d)*t*f_t;// tons\n", +"P_s = 2*0.25*%pi*d^2 *f_s;// tons\n", +"P_b = d*t*f_b;// tons\n", +"n = P/min(P_s,P_b);\n", +"e = (b-d)/b;// efficiency\n", +"P1 = f_t*(b-d)*t;// tons\n", +"P2 = f_t*(b-2*d)*t+P_s;// tons\n", +"P3 = f_t*(b-3*d)*t+3*P_s;// tons\n", +"P4 = f_t*(b-3*d)*t+6*P_s;// tons\n", +"printf('The number of rivets required, n = %d',round(n+1));\n", +"printf('\n The efficiency of the joint = %.1f percentage',e*100);\n", +"printf('\n The pull at section 11, P1 = %.2f rons/in^2',P1);\n", +"printf('\n The pull at section 22, P2 = %.1f rons/in^2',P2);\n", +"printf('\n The pull at section 33, P3 = %.2f rons/in^2',P3);\n", +"printf('\n The pull at section 44, P4 = %.2f rons/in^2',P4);\n", +"if P1 == min(P1,P2,P3,P4) then\n", +" printf('\n The maximum possible pull which the flat will safely transmit is P1 = %.2f tons/in^2 at section 11',P1);\n", +"elseif P2 == min(P1,P2,P3,P4) then\n", +" printf('\n The maximum possible pull which the flat will safely transmit is P2 = %.1f tons/in^2 at section 22',P2); \n", +"elseif P3 == min(P1,P2,P3,P4) then \n", +" printf('\n The maximum possible pull which the flat will safely transmit is P3 = %.2f tons/in^2 at section 33',P3);\n", +"else\n", +" printf('\n The maximum possible pull which the flat will safely transmit is P4 = %.2f tons/in^2 at section 44',P4); \n", +"end\n", +"\n", +"//there is a minute error in the answer given textbook." + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.8: Chapter_11_example_8.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"P = 150;; //tons\n", +"t = 3/4;// inches\n", +"d = 1;// inches\n", +"f_s = 6;// tons/in^2\n", +"f_b = 12;// tons/in^2\n", +"P_s = 0.25*%pi*d^2 *f_s;// tons\n", +"P_b = t*d*f_b;// tons\n", +"n = P/min(P_s,P_b);// no. of rivets required\n", +"printf('The number of rivets required, n = %.2f, say %d',n,round(n));" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.9: Chapter_11_example_9.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"l = 50;// feet\n", +"b = 4;// feet\n", +"P = 3;// tons per foot run\n", +"t = 1/2;// inches\n", +"b1 = 4;// inches\n", +"d1 = 4;// inches\n", +"h1 = 1/2;// inches\n", +"d = 7/8;// inches\n", +"f_s = 6;// tons/in^2\n", +"f_b = 12;// tons/in^2\n", +"P_s = 2*0.25*%pi*d^2 *f_s;// tons\n", +"P_b = t*d*f_b;// tons\n", +"R = P_b;// tons\n", +"F = l*P*2/d1;// tons\n", +"p_min = R*(l-0.5*b1)/F ;// inches\n", +"printf('The minimum pitch required is p = %.2f inches, say %d inches',p_min,p_min);" + ] + } +], +"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/Mechanics_of_Structures_by_S_B_Junnarkar/12-Shafts_and_springs_in_torsion.ipynb b/Mechanics_of_Structures_by_S_B_Junnarkar/12-Shafts_and_springs_in_torsion.ipynb new file mode 100644 index 0000000..224caab --- /dev/null +++ b/Mechanics_of_Structures_by_S_B_Junnarkar/12-Shafts_and_springs_in_torsion.ipynb @@ -0,0 +1,688 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 12: Shafts and springs in torsion" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 12.10: Chapter_12_example_10.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"HP = 80;\n", +"RPM = 120;\n", +"b = 10;// feet\n", +"h = 3;// feet\n", +"F = 8000;// lb-wt\n", +"m = 4;\n", +"T = HP*33000*12/(2*%pi*RPM*2240);// ton-inches\n", +"M = F*h*(b-h)*12/(b*2240);// ton-inches\n", +"//(i) The major principal stress f1 is given by\n", +"f1 = 6;// tons/in^2\n", +"d1 = ((M+sqrt(M^2 + T^2))*16/(%pi*f1))^(1/3);// inches\n", +"\n", +"//(ii) If f_s_dash is the maximum intensity of shear stress\n", +"f_s_dash = 3;// tons/in^2\n", +"d2 = (sqrt(M^2 + T^2) * 16/(%pi*f_s_dash))^(1/3);// inches\n", +"\n", +"//(iii) If e is the major principal strain\n", +"Ee = 6;// tons/in^2\n", +"d3 = (((1-(1/m))*M + (1+(1/m))*sqrt(M^2 + T^2))*16/(%pi*Ee))^(1/3);// inches\n", +"\n", +"//(iv) If f is the direct stress which, acting alone will produce the same maximum strain energy \n", +"f = 6;// tons/in^2\n", +"d4 = ((sqrt(4*M^2 + 2*(m+1)*(T^2)/m))*16/(%pi*f))^(1/3);// inches\n", +"printf('The diameter of the shaft in different cases will be, (i) d = %.3f inches\n (ii) d = %.3f inches\n (iii) d = %.3f inches\n (iv) d = %.3f inches',d1,d2,d3,d4);\n", +"//there are round-off errors in the answers given in textbook." + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 12.11: Chapter_12_example_11.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"D = 12;// inches\n", +"d = 6;// inches\n", +"HP = 2400;\n", +"RPM = 80;\n", +"M = 40;// ton-feet\n", +"P = 25;// tons\n", +"PR = 0.3;//poisson's ratio\n", +"A = 0.25*%pi*(D^2 - d^2);// in^2\n", +"Z = (%pi/32)*(D^4 - d^4)/D;// in^3\n", +"J = (%pi/16)*(D^4 - d^4)/D;// in^3\n", +"p_0 = P/A ;// ton/in^2\n", +"p_b = M*12/Z ;// tons/in^2\n", +"f_b = p_0 + p_b;//tons/in^2\n", +"f_s = HP*33000*12/(2*%pi*RPM*2240*J);// tons/in^2\n", +"theta = 0.5*atan(2*f_s/f_b);// radians\n", +"theta1 = theta*180/%pi;// degrees\n", +"theta2 = theta1+90;//degrees\n", +"f_1 = 0.5*f_b + sqrt(f_s^2 + 0.25*f_b^2);//tons/in^2\n", +"f_2 = 0.5*f_b - sqrt(f_s^2 + 0.25*f_b^2);//tons/in^2\n", +"f = sqrt(0.25*f_b^2 + f_s^2);// tons/in^2\n", +"Ee = f_1 - PR*f_2;// tons/in^2\n", +"printf('The maximum principal stresse are f_1 = %.3f tons/in^2.,compressive \n f_2 = %.3f tons/in^2., tensile',f_1,-f_2);\n", +"printf('\n theta1 = %.1f degrees\n theta2 = %.1f degrees',theta1,theta2);\n", +"printf('\n The maximum shear intensity = %.3f tons/in^2',f);\n", +"printf('\n Maximum strain is, Ee = %.3f tons/in^2',Ee);\n", +"\n", +"//there are minute errors in the answers given in textbook." + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 12.12: Chapter_12_example_12.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"RPM = 180;\n", +"P = 10;// tons\n", +"v = 25;// feet per minute\n", +"n = 64/100;// efficiency of the crane\n", +"f = 5500;// lb/in^2\n", +"l = 10;// feet\n", +"N = 12*10^6;// lb/in^2\n", +"W = P*v*2240/n;// ft-lbs\n", +"T = W*12/(2*%pi*RPM);// lb-inches\n", +"s = (T/(0.208*f))^(1/3);// inches\n", +"theta = 7.11*T*l*12*180/(%pi*N*s^4);// degrees\n", +"printf('The size of the shaft is s = %.3f inches',s);\n", +"printf('\n The angle of the twist in the shaft for a length of %d feet, theta = %.3f degrees',l,theta);\n", +"//there is a round-off error in the answer given in textbook." + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 12.13: Chapter_12_example_13.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"d = 3/8;// inches\n", +"n = 12;//no. of complete turns\n", +"D = 4;// inches\n", +"W = 50;// lb-wt\n", +"N = 12*10^6;// lb/in^2\n", +"T = W*0.5*D;// lb-inches\n", +"f_s = T*16/(%pi*d^3);//lb/in^2\n", +"delta = 64*W*(D^3 /8)*n/(N*d^4);// inches\n", +"E = 0.5*W*delta;// inch-lbs\n", +"printf('Shear stress induced is f_s = %d lb/in^2',f_s);\n", +"printf('\n Deflection under the pull is delta = %.3f inches',delta);\n", +"printf('\n Energy stored = %.3f lb-inches',E);\n", +"\n", +"//there is a minute error in the answer given in textbook." + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 12.14: Chapter_12_example_14.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"W = 2;// tons\n", +"v = 4;// miles per hour\n", +"n = 18;// no. of coils\n", +"delta = 9;// inches\n", +"N = 6000;// tons/in^2\n", +"d = 1;// inch\n", +"D = 8;// inches\n", +"KE = 12*(W*(v*44/30)^2)/(2*32);// inch-tons\n", +"P = (delta*N*d^4)/(64*n*(0.5*D)^3);// tons\n", +"E = 0.5*P*delta;// inch-tons\n", +"m = KE/E ;// no. of springs required\n", +"printf('The number of springs required m = %d',round(m));" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 12.15: Chapter_12_example_15.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"W = 5;// cwt\n", +"n = 18;// no. of coils\n", +"delta = 9;// inches\n", +"d = 1;// inch\n", +"D = 8;// inches\n", +"N = 6000;// tons/in^2\n", +"P = (delta*N*d^4)/(64*n*(0.5*D)^3);// tons\n", +"h = (0.5*P*delta*20/W)-delta;// inches\n", +"printf('The height of drop h = %.3f inches',h);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 12.16: Chapter_12_example_16.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"s = 1/4;// inch\n", +"n = 12;// no. of coils\n", +"D = 3;// inches\n", +"f_s = 45000;// lb/in^2\n", +"N = 12*10^6;// lb/in^2\n", +"T = 0.208*f_s*s^3;// lb-inches\n", +"W = T/(0.5*D);// lb-wt\n", +"theta = 7.11*T*%pi*D*12/(N*s^4);//rdaians\n", +"delta = 0.5*D*theta;// inches\n", +"printf('Maximum possible axial load is W = %.1f lb-wt',W);\n", +"printf('\n Deflection, delta = %.3f inches',delta);\n", +"\n", +"//there is a minute error in the answer given in textbook." + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 12.17: Chapter_12_example_17.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"d = 3/8;// inches\n", +"n = 12;//no. of complete turns\n", +"D = 4;// inches\n", +"W = 50;// lb-wt\n", +"N = 12*10^6;// lb/in^2\n", +"E = 30*10^6;// lb/in^2\n", +"M = 75;// lb-inches\n", +"I = (%pi/64)*d^4;// in^4\n", +"Z = 2*I/d;// in^3\n", +"f = M/Z ;// lb/in^2\n", +"phi = M*%pi*D*12/(E*I);// radians\n", +"n_ = (phi/(2*%pi)) + n;// increase in no. of turns\n", +"printf('The bending stress is f = %d lb/in^2',f);\n", +"printf('\n n_new = %.5f turns',n_);\n", +"\n", +"//there are minute errors in the answers given in textbook." + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 12.18: Chapter_12_example_18.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"d = 3/8;// inches\n", +"n = 12;//no. of complete turns\n", +"D = 4;// inches\n", +"W = 50;// lb-wt\n", +"N = 12*10^6;// lb/in^2\n", +"alpha = 15*%pi/180;// degrees\n", +"E = 30*10^6;// lb/in^2\n", +"T = W*0.5*D*cos(alpha);// lb-inches\n", +"M = W*0.5*D*sin(alpha);// lb-inches\n", +"J = %pi*d^4 /32;// in^4\n", +"I = %pi*d^4 /64;// in^4\n", +"delta = 64*W*((D/2)^3)*n*sec(alpha)*((cos(alpha)^2)/N + (2*sin(alpha)^2)/E)/d^4 ;// inches\n", +"f = 32*W*0.5*D*sin(alpha)/(%pi*d^3) ;// lb/in^2\n", +"f_s = T*16/(%pi*d^3);// lb/in^2\n", +"f_1 = 0.5*f + sqrt(f_s^2 + 0.25*f^2);// lb/in^2\n", +"f_2 = 0.5*f - sqrt(f_s^2 + 0.25*f^2);// lb/in^2\n", +"f_s_dash = sqrt(f_s^2 + 0.25*f^2);// lb/in^2\n", +"printf('Deflection, delta = %.3f inches',delta);\n", +"printf('\n f = %d lb/in^2\n f_s = %d lb/in^2',f,f_s);\n", +"printf('\n The maximum intensity of shear stress = %d lb/in^2',f_s_dash);\n", +"\n", +"//there are calculation errors in the answers given in textbook" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 12.19: Chapter_12_example_19.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"d = 3/8;// inches\n", +"n = 12;//no. of complete turns\n", +"D = 4;// inches\n", +"M = 75;// lb-inches\n", +"N = 12*10^6;// lb/in^2\n", +"alpha = 15*%pi/180;// degrees\n", +"E = 30*10^6;// lb/in^2\n", +"phi_dash = (64/d^4)*M*0.5*D*n*sec(alpha)*((2*(cos(alpha))^2)/E + ((sin(alpha))^2)/N);// radians\n", +"DELTA = 64*M*((0.5*D)^2)*n*sin(alpha)*((1/N) - (2/E))/d^4;// inches\n", +"printf('Angle of rotation phi_dash = %.4f radians or %.2f degrees',phi_dash,phi_dash*180/%pi);\n", +"printf('\n The axial deflection = %.4f inches',DELTA);\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 12.1: Chapter_12_example_1.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"d = 3;//inches\n", +"HP = 120;//horse power\n", +"RPM = 180;\n", +"l = 25;//feet\n", +"N = 12*10^6;// lb/in^2\n", +"T = 33000*HP/(2*%pi*RPM);// lb-feet\n", +"f_s = 16*T*12/(%pi*d^3);// lb/in^2\n", +"theta = f_s*l*12/(0.5*d*N);// radian\n", +"printf('The maximum intensity of shear stress induced is f_s = %.d lb/in^2',f_s);\n", +"printf('\n The angle of twist in degrees is theta = %.2f',theta*180/%pi);\n", +"//there is a minute error in the answer given in textbook." + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 12.2: Chapter_12_example_2.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"D = 2;// inches\n", +"N = 150;// RPM\n", +"f_s = 9000;// lb/in^2\n", +"M_r = f_s*(%pi/16)*D^3;// lb-inches\n", +"HP = M_r*2*%pi*N/(12*33000);//\n", +"printf('H.P transmitted is %.2f',HP);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 12.3: Chapter_12_example_3.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"HP = 80;\n", +"N = 200;// RPM\n", +"m = 30/100;\n", +"f = 12000;// lb/in^2\n", +"T = HP*33000/(2*%pi*N);// lb-feet\n", +"T_max = (1+m)*T;// lb-feet\n", +"D = (T_max*12*16/(%pi*f))^(1/3);// inches\n", +"printf('Suitable diameter is D = %.3f inches',D);\n", +"\n", +"//the answer is approximated in the textbook." + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 12.4: Chapter_12_example_4.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"HP = 750;\n", +"N = 90;// RPM\n", +"m = 40/100;\n", +"f = 12000;// lb/in^2\n", +"t = 1;// inch\n", +"T = HP*33000/(2*%pi*N);// lb-inches\n", +"T_max = (1+m)*T;// lb-inches\n", +"//On solving (4*t)D^3 - (6*t^2)D^2 +(4*t^3 -(16*M/f*%pi))D -t^4 = 0, we get D\n", +"D = 7.6;//inches\n", +"d = D - 2;//inches\n", +"printf('A shaft % d inches external diameter and %d inches internal diameter will be satisfactory.',round(D),round(d));\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 12.5: Chapter_12_example_5.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"RPM = 180;// RPM\n", +"HP = 130;\n", +"f = 9000;// lb/in^2\n", +"alpha = 1;//degree\n", +"l = 10;// feet\n", +"N = 6000;// tons/in^2\n", +"T = 33000*HP/(2*%pi*RPM);// lb-feet\n", +"D1 = (16*T*12/(f*%pi))^(1/3);// inches\n", +"D2 = (T*12*l*12*32*alpha*180/(%pi*N*%pi*2240))^(1/4);// inches\n", +"if D1 > D2 then\n", +" printf('D = %d inches will be suitable for the shaft',round(D1));\n", +"else\n", +" printf('D = %d inches will be suitable for the shaft',round(D2));\n", +"end" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 12.6: Chapter_12_example_6.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"HP = 3000;\n", +"RPM = 60;\n", +"f = 12000;//lb/in^2\n", +"rho = 480;//lb. per sq. foot\n", +"k = 3/4;// k = d/D \n", +"T = HP*33000*12/(2*%pi*RPM);// lb-inches\n", +"D1 = (T*16/(f*%pi))^(1/3);//inches\n", +"D2 = (T/((1+k^2)*(1-k^2)*%pi*f/16))^(1/3);//inches\n", +"d = k*D2;// inches\n", +"w1 = 0.25*%pi*D1^2 *rho/144 ;// lb-wt\n", +"w2 = 0.25*%pi*(D2+d)*(D2-d)*rho/144 ;// lb-wt\n", +"w = w1-w2;// lb-wt\n", +"n = (w/w1)*100;\n", +"printf('The saving in weight per foot run is w = %d lb-wt',w);\n", +"printf('\n Percentage saving is %.2f',n);\n", +"\n", +"//there is a minute error in the answer given in textbook." + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 12.7: Chapter_12_example_7.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"l1 = 3;// feet\n", +"d1 = 1;// feet\n", +"l2 = 9;// feet\n", +"M = 200;// lb-wt\n", +"l = 9;// inches\n", +"N = 12*10^6;// lb/in^2\n", +"k = l2/l1;\n", +"T1 = M/(1+k);// lb-feet\n", +"T2 = k*T1;// lb-feet\n", +"f_s = T2*12/(%pi/16);// lb/in^2\n", +"theta = f_s*l/(0.5*d1*N);// radians\n", +"printf('T1 = %d lb-feet\n T2 = %d lb-feet',T1,T2);\n", +"printf('\n f_s = %d lb/in^2',f_s);\n", +"printf('\n theta = %.5f radian\n = %.4f degrees',theta,theta*180/%pi);\n", +"//there is a minute error in the answer given in twxtbook" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 12.8: Chapter_12_example_8.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"D = 5;// inches\n", +"HP = 120;\n", +"RPM = 150;\n", +"b = 5;// inches\n", +"h = 1;//inch\n", +"n = 6;// no. of bolts\n", +"d = 3/4;// inches\n", +"T = HP*33000*12/(2*%pi*RPM);// lb-inches\n", +"f_s = T*16/(%pi*27);\n", +"f_k = T/(b*h*2*d);\n", +"f_b = T/(n*0.25*%pi*d^2 * b);// lb-inches\n", +"printf('f_s = %d lb/in^2\n f_k = %d lb/in^2\n f_b = %d lb/in^2',f_s,f_k,f_b);\n", +"//there are errors given in the answers given in the textbook" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 12.9: Chapter_12_example_9.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"d = 4;//inches\n", +"T = 30;// ton-inches\n", +"M = 20;//ton-inches\n", +"m = 1/0.3;\n", +"f_s = 16*T/(%pi*d^3);// tons/in^2\n", +"f_b = 32*M/(%pi*d^3);// tons/in^2\n", +"theta = 0.5*atan(T/M);// radians\n", +"theta1 = theta*180/%pi;\n", +"theta2 = theta1+90;\n", +"f1 = 0.5*f_b + sqrt(f_s^2 + 0.25*f_b^2);// tons/in^2\n", +"f2 = 0.5*f_b - sqrt(f_s^2 + 0.25*f_b^2);// tons/in^2\n", +"Ee = f1 - (f2/m);// tons/in^2\n", +"f = sqrt(f1^2 + f2^2 - 2*f1*f2/m);// tons/in^2\n", +"printf('Maximum strain is Ee = %.3f tons/in^2',Ee);\n", +"printf('\n Maximum strain energy is f = %.3f tons/in^2',f);" + ] + } +], +"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/Mechanics_of_Structures_by_S_B_Junnarkar/13-Elements_of_reinforced_concrete.ipynb b/Mechanics_of_Structures_by_S_B_Junnarkar/13-Elements_of_reinforced_concrete.ipynb new file mode 100644 index 0000000..8958851 --- /dev/null +++ b/Mechanics_of_Structures_by_S_B_Junnarkar/13-Elements_of_reinforced_concrete.ipynb @@ -0,0 +1,306 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 13: Elements of reinforced concrete" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 13.1: Chapter_13_example_1.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"b = 10;//inches\n", +"d = 1;//inches\n", +"h = 20;//inches\n", +"r = 2;//inches\n", +"M_r = 500000;//lb-inches\n", +"m = 15;\n", +"A_r = 4*0.25*%pi*d^2;//in^2\n", +"h_eff = h-r;//inches\n", +"K = m*A_r/(b*h_eff);//inches\n", +"n1 = sqrt((K)^2+(2*K))-K;\n", +"n = n1*h_eff;//inches\n", +"a = h_eff-(n/3);//inches\n", +"c = 2*M_r/(b*n*a);//lb/in^2\n", +"t = (h_eff-n)*m*c/n;//lb/in^2\n", +"printf('The stress induced in the concrete and steel, t = %d lb/in^2',t);\n", +"//there is a minute error in the answer given in textbook." + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 13.2: Chapter_13_example_2.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"b = 8;//inches\n", +"d = 7/8;//inches\n", +"h = 18;//inches\n", +"r = 2;//inches\n", +"c = 750;//lb/in^2\n", +"t_limit = 18000;//lb/in^2\n", +"m = 8;\n", +"h_eff = 16;//inches\n", +"m = 18;\n", +"A_t = 3*0.25*%pi*d^2;//in^2\n", +"K = m*A_t/(b*h_eff);//inches\n", +"n1 = sqrt((K)^2+(2*K))-K;\n", +"n = n1*h_eff;//inches\n", +"a = h_eff - (n/3);//inches\n", +"t = m*c*(h_eff-n)/n;//lb/in^2\n", +"\n", +"if t<t_limit then\n", +" t = t;\n", +"else\n", +" t = t_limit;\n", +"end\n", +"\n", +"M_r = t*A_t*a;// lb/inches\n", +"W = M_r*8/(12*h_eff);//lb-wt\n", +"printf('The distance of the N.A from the top edge, n = %.3f inches.',n);\n", +"printf('\n The safe moment of inertia is, t = %d lb/in^2.',t);\n", +"printf('\n Unifromly distributed load over the beam, W = %d lb-wt. or %d lb. per foot run',W,W/16.011);\n", +"\n", +"//there are calculation errors given in the answer in textbook." + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 13.3: Chapter_13_example_3.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"function Z = quadratic(d,M_c,c_limit,b)\n", +" n = poly(0,'n');\n", +" p = n^2-(d*3)*n + M_c*3/(0.5*c_limit*b);\n", +" Z = roots(p);\n", +"endfunction\n", +"b = 12;//inches\n", +"h = 22;//inches\n", +"r = 2;//inches\n", +"W = 1500;//lb per foot run\n", +"d = h-r;//feet\n", +"l = 20;//inches\n", +"c_limit = 700;// lb/in^2\n", +"m = 15;\n", +"M_c = W*20*l*b/8;// lb-inches\n", +"Z = quadratic(d,M_c,c_limit,b);\n", +"n = round(Z(2));\n", +"t = m*c_limit*(d-n)/n;// lb/in62\n", +"A_t = 0.5*c_limit*b*n/t;// in^2\n", +"printf('Area of steel reinforcement required is, A_t = %d in^2',A_t);\n", +"printf('\n Corresponding stress in steel is, t = %d lb/in^2',t);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 13.4: Chapter_13_example_4.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"m = 15;\n", +"t = 18000;// lb/in^2\n", +"c = 700;// lb/in^2\n", +"b = 12;;// inches\n", +"M = 900000;//bending moment lb/inches\n", +"k1 = 1/((t/(m*c))+1);//k = n/d\n", +"k2 = 1-k1/3;//k2 = a/d\n", +"p = 0.5*c*k1/(t);\n", +"d = sqrt(M/(0.5*c*b*k1*k2));//inches\n", +"A_t = p*b*d;// sq.inches\n", +"A_t_previous = 0.25*%pi*(7/8)^2;//section area with diameter 7/8 inches\n", +"n = A_t/A_t_previous;\n", +"printf('Effective deapth is d = %.2f inches',d);\n", +"printf('\n A_t = %.3f sq.inches',A_t);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 13.5: Chapter_13_example_5.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"l = 20;//feet\n", +"W = 500;// lb per foot run\n", +"c = 750;// lb/in^2\n", +"t = 18000;// lb/in^2\n", +"m = 15;\n", +"BM_max = W*l*l*12/8 ;// lb-inches\n", +"//by making the effective deapth d twice the width b\n", +"d = (BM_max/(126*0.5))^(1/3);//inches\n", +"b = 0.5*d;//inches\n", +"//necessary reinforcement is 0.8% of concrete section\n", +"A_t = 0.008*b*d;// in^2\n", +"printf('d = %.2f inches\n b = %.2f inches',d,b);\n", +"printf('\n A_t = %.3f in^2',A_t);\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 13.6: Chapter_13_example_6.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"W = 180;// lb per sq.foot\n", +"l = 10;// feet\n", +"b = 12;//inches\n", +"c = 750;// lb/in^2\n", +"m = 15;\n", +"M = W*l*l*12/8;//lb-inches\n", +"d_new = sqrt(M/(126*b));//inches\n", +"A_t = 0.8*b*d_new/100;//in^2\n", +"//using 3/8 inch rods \n", +"d1 = 3/8;//inches\n", +"A1 = 0.25*%pi*(d1)^2;//in^2 \n", +"r1 = A1*b/A_t;//inch\n", +"//using 1/2 inch rods \n", +"d2 = 1/2;//inches\n", +"A2 = 0.25*%pi*(d2)^2;//in^2 \n", +"r2 = A2*b/A_t;//inches\n", +"printf('d = %.3f inches',d_new);\n", +"printf('\n A_t = %.3f in^2',A_t);\n", +"printf('\n Using %.3f inch rods, spacing centre to centre will be %.2f inches',d1,r1);\n", +"printf('\n Using %.2f inch rods, spacing centre to centre will be %.1f inches',d2,r2);\n", +"//there are round-off errors in the answer given in textbook" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 13.7: Chapter_13_example_7.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"l = 12;//feet\n", +"w = 150;// lb per sq.foot\n", +"//Live load\n", +"LL = w*l;//lb-wt\n", +"//Dead Load assuming the slab thickness to be 6 inches\n", +"t = 6;//inches\n", +"DL = t*l*12;//lb-wt\n", +"//total load\n", +"W = LL+DL;//lb-wt\n", +"M = W*l*12/10;//lb-inches\n", +"d = sqrt(M/(12*126));\n", +"printf('d = %.3f inches',d);\n", +"//With about an inch to cover the slab will be 6 inch thick\n", +"A_t = 0.8*l*d/100;// in^2\n", +"//using 1/2 inch rods \n", +"d1 = 1/2;//inches\n", +"A1 = 0.25*%pi*(d1)^2;//in^2 \n", +"r1 = A1*l/A_t;//inches\n", +"printf('\n Per foot width of slab, A_t = %.4f in^2',A_t);\n", +"printf('\n Using %.2f inch rods, spacing centre to centre will be %.3f inches',d1,r1);\n", +"//there are minute calculation errors in the answer given in textbook." + ] + } +], +"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/Mechanics_of_Structures_by_S_B_Junnarkar/2-Principal_planes_and_principal_stresses.ipynb b/Mechanics_of_Structures_by_S_B_Junnarkar/2-Principal_planes_and_principal_stresses.ipynb new file mode 100644 index 0000000..7e00202 --- /dev/null +++ b/Mechanics_of_Structures_by_S_B_Junnarkar/2-Principal_planes_and_principal_stresses.ipynb @@ -0,0 +1,233 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 2: Principal planes and principal stresses" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.1: Chapter_2_example_1.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"p_1 = 5;//principal stress in tons/in^2\n", +"p_2 = 5/2;//principal stress in tons/in^2\n", +"theta = 50*%pi/180;//angle in degrees\n", +"p_n = p_1*cos(theta)^2+p_2*sin(theta)^2;//normal stress intensity\n", +"p_t = (p_1-p_2)*sin(theta)*cos(theta);//tangential stress intensity\n", +"p = sqrt((p_1*cos(theta))^2+(p_2*sin(theta))^2);//resultant intensity of stress\n", +"alpha = atan((p_2*sin(theta))/(p_1*cos(theta)));//in radians\n", +"alpha = alpha*180/%pi;//in degrees\n", +"printf('Normal stress intensity p_n = %.2f tons/in^2',p_n);\n", +"printf('\n Tangential stress intensity p_t = %.2f tons/in^2',p_t);\n", +"printf('\n Resultant stress intensity p = %.2f tons/in^2',p);\n", +"printf('\n angle alpha p_n = %.2f degrees',alpha);\n", +"\n", +"//there is an error in the answer given in text book" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.3: Chapter_2_example_3.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"d = 3/4 ;//inches\n", +"P = 2;//tons\n", +"Q = 0.5;//tons\n", +"m = 4;\n", +"A = 0.25*%pi*d^2;//in^2\n", +"p = P/A ;//tons/in^2\n", +"q = Q/A;//tons/in^2\n", +"theta = 0.5*atan(2*q/p);//radians\n", +"theta1 = theta*180/%pi;//degrees\n", +"theta2 = theta1+90;//degrees\n", +"printf('The inclination of principal planes to the axis of the bolt will be %.2f degress and %.2f degrees respectively',theta1,180-theta2);\n", +"printf('\n The inclination of maximum shear planes to the axis of the bolt will be %.2f degress and %.2f degrees respectively',theta1+45,180-theta2-45);\n", +"p_1 = 0.5*p+sqrt(0.25*p^2+q^2);//tons/in^2\n", +"p_2 = 0.5*p-sqrt(0.25*p^2+q^2);//tons/in^2\n", +"p_max = 0.5*(p_1-p_2);//tons/in^2\n", +"p_s = p_1-(p_2/m);//tons/in^2 \n", +"printf('\n The principal stresse are given by p_1 = %.2f tons/in^2.,tensile\n p_2 = %.2f tons/in^2\n p_2 = %.2f tons/in^2 .,compressive',p_1,p_2,-p_2);\n", +"printf('\n Maximum shear stress is p_max = %.2f tons/in^2',p_max);\n", +"printf('\n The stress which acting alone will produce the same maximum strain is given by, %.2f tons/in^2',p_s);\n", +"\n", +"//there is an error in the answer given in text book" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.4: Chapter_2_example_4.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"q = 2;//tons/in^2\n", +"p = 5;//tons/in^2\n", +"p_dash = 2;//tons/in^2\n", +"theta = 0.5*atan(2*q/(p-p_dash));//radians\n", +"theta1 = theta*180/%pi;//degrees\n", +"theta2 = theta1+90;//degrees\n", +"p_1 = 0.5*(p+p_dash)+sqrt(q^2 + 0.25*(p-p_dash)^2);//tons/in^2\n", +"p_2 = 0.5*(p+p_dash)-sqrt(q^2 + 0.25*(p-p_dash)^2);//tons/in^2\n", +"q_max = 0.5*(p_1-p_2);//tons/in^2\n", +"printf('The principal stresses are p_1 = %d tons/in^2 .,tensile\n p_2 = %d tons/in^2., tensile',p_1,p_2);\n", +"printf('\n The maximum shear stress is %.1f tons/in^2., the planes offering it being inclined at %.2f degrees and %.2f degrees \n to the plane having the normal stress intensity of %d tons/in^2.',q_max,theta1+45,theta2+45,p);\n", +"//there is an error in the answer given in text book" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.5: Chapter_2_example_5.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"p_res = 6;//tons/in^2\n", +"p_dash = 4;//tons/in^2\n", +"theta = 30*%pi/180;//degrees\n", +"p_n = 4;//tons/in^2\n", +"p = p_res*cos(theta);//tons/in^2\n", +"q = p_res*sin(theta);//tons/in^2\n", +"L = 2*q/(p-p_dash);\n", +"theta = 0.5*atan(2*q/(p-p_dash));\n", +"theta1 = theta*180/%pi;//degrees\n", +"theta2 = theta1+90;//degrees\n", +"p_1 = 0.5*(p+p_dash)+sqrt(q^2 + 0.25*(p-p_dash)^2);//tons/in^2\n", +"p_2 = 0.5*(p+p_dash)-sqrt(q^2 + 0.25*(p-p_dash)^2);//tons/in^2\n", +"p_max = 0.5*(p_1-p_2);//tons/in^2\n", +"printf('Theta1 = %.2f degrees and Theta2 = %.2f degrees',theta1,theta2);\n", +"printf('\n p_1 = %.2f tons/in^2.,tensile\n p_2 = %.2f tons/in^2.,tensile',p_1,p_2);\n", +"printf('\n The maximum shear intensity will be %.2f tons/in^2 across the planes of maximum shear.',p_max);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.6: Chapter_2_example_6.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"p_1 = 7;//tons/in^2\n", +"p_2 = 4;//tons/in^2\n", +"p_3 = 3;//tons/in^2\n", +"m = 4;\n", +"E = 13000;//tons/in^2\n", +"e_1 = (p_1/E)+(p_2/(m*E))-(p_3/(m*E));\n", +"e_2 = (p_2/E)+(p_1/(m*E))+(p_3/(m*E));\n", +"e_3 = (p_3/E)-(p_1/(m*E))+(p_2/(m*E));\n", +"printf('e_1 = %.6f, tensile\n e_2 = %.4f, compressive\n e_3 = %.6f, tensile',e_1,e_2,e_3);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.7: Chapter_2_example_7.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"a = 2;//inches\n", +"l = 6;//inches\n", +"E = 13000;//tons/In^2\n", +"m = 1/0.3;\n", +"P = 20;//tons\n", +"p_1 = P/a^2;//tons/in^2\n", +"p_2 = p_1/(2*(m-1));//tons/in^2\n", +"e_1 = (5-0.6*p_2)/E;//tons/in^2\n", +"del_l = e_1*l;//inches\n", +"printf('The contraction in the length del_l = %.5f inches',del_l);" + ] + } +], +"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/Mechanics_of_Structures_by_S_B_Junnarkar/3-Impact_or_shock_loading_.ipynb b/Mechanics_of_Structures_by_S_B_Junnarkar/3-Impact_or_shock_loading_.ipynb new file mode 100644 index 0000000..05509b0 --- /dev/null +++ b/Mechanics_of_Structures_by_S_B_Junnarkar/3-Impact_or_shock_loading_.ipynb @@ -0,0 +1,230 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 3: Impact or shock loading " + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.1: Chapter_3_example_1.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"d = 3/2;//inches\n", +"l = 10;;//feet\n", +"P = 8;//tons\n", +"E = 13500;//tons/in^2\n", +"A = 0.25*%pi*d^2;//in^2\n", +"p = 2*P/A;// tons/in^2\n", +"e = p/E;\n", +"del_l = e*l*12;//inches\n", +"W = P*del_l;//inch-ton\n", +"printf('The maximum instantaneous stress produced is, p = %.2f tons/in^2',p);\n", +"printf('\n The corresponding strain is e = %.6f \n del_l = %.2f inches',e,del_l);\n", +"printf('\n The work done on the rod and stored by it is %.2f inch-ton.',W);\n", +"\n", +"//there is an error in the answer given in text book" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.2: Chapter_3_example_2.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"l = 6;//feet\n", +"d = 1;//inches\n", +"h = 4;//inches\n", +"E = 30*10^6;//lb/in^2\n", +"A = 0.25*%pi*d^2;//in^2\n", +"P = 50;//lb\n", +"p = (P/A)+sqrt((P^2/A^2)+(2*E*P*h)/(A*l*12));\n", +"e = p/E;\n", +"del_l = e*l*12//inches\n", +"printf('Maximum instantaneous stress produced is p = %d lb/in^2',p);\n", +"printf('\n Maximum instantaneous extension produced is del_l = %.3f lb/in^2',del_l);\n", +"\n", +"//there is an error in the answer given in text book" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.3: Chapter_3_example_3.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"l = 10;//feet\n", +"d = 5/4;//inches\n", +"p = 8;//tons/in^2\n", +"E = 13000;//tons/in^2\n", +"A = 0.25*%pi*d^2;//in^2\n", +"e = p/E;\n", +"del_l = e*l*12;//inches\n", +"W = 0.5*p^2*A*l*12/E;// inch-ton\n", +"h = W*10-del_l;//inches\n", +"printf('Instantaneous elongation is del_l = %.3f inches',del_l);\n", +"printf('\n Height of the drop is h = %.2f inches',h);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.4: Chapter_3_example_4.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"w = 4;//tons\n", +"v = 2;//miles per hour\n", +"l = 150;//feet\n", +"d = 3/2;//inches\n", +"E = 13000;// tons/in^2\n", +"g = 32;// ft/sec^2\n", +"A = 0.25*%pi*d^2;// in^2\n", +"KE = w*(v*17.6)^2/(2*g*12);// inch-tons\n", +"p = sqrt(KE*(2*E)/(A*l*12));// tons/in^2\n", +"del_l = p*l*12/E;// inches\n", +"printf('Maximum instantaneous stress produced is p = %.2f tons/in^2',p);\n", +"printf('\n Maximum instantaneous extension produced is del_l = %d inch',del_l);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.5: Chapter_3_example_5.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"d = 2;//inches\n", +"l = 8;//feet\n", +"U = 50;// ft-lbs\n", +"E = 28*10^6;// lb/in^2\n", +"V = 0.25*%pi*d^2*l*12;// in^3\n", +"p = sqrt(2*U*12*E/V);// lb/in^2\n", +"e = p/E;\n", +"del_l = e*l*12;// inches\n", +"printf('Maximum instantaneous stress produced is p = %d lb/in^2',p);\n", +"printf('\n Maximum instantaneous extension produced is del_l = %.4f inches',del_l);\n", +"//there is an error in the answer given in text book" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.6: Chapter_3_example_6.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"l = 12;//feet\n", +"d1_A = 1;//inch\n", +"d2_A = 2;//inches\n", +"l1_A = 4;//inches\n", +"l2_A = 8;//inches\n", +"d1_B = 1;//inch\n", +"d2_B = 2;//inches\n", +"l1_B = 8;//inches\n", +"l2_B = 4;//inches\n", +"p_A = 15/2;// tons/in^2\n", +"p_B = sqrt((2/3)*p_A^2);// tons/in^2\n", +"r1 = (9*%pi/8)/(3*%pi/4);//ratio of energies if both bars are allowed to reach the proof stress\n", +"V_A = 0.25*%pi*d1_A^2*l1_A+ 0.25*%pi*d2_A^2*l2_A;// in^3\n", +"V_B = 0.25*%pi*d1_B^2*l1_B+ 0.25*%pi*d2_B^2*l2_B;// in^3\n", +"r2 = ((3/16)*p_B^2)/((1/12)*p_B^2);//ratio of enrgies\n", +"printf('Maximum instantaneous stress produced is p_B = %.2f tons/in^2',p_B);\n", +"printf('\n Ratio of energies stored if both bars are allowed to reach the proof stress is r1 = %.2f ',r1);\n", +"printf('\n Ratio of energies stored at the same stress per unit volume, is r2 = %.2f ',r2);" + ] + } +], +"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/Mechanics_of_Structures_by_S_B_Junnarkar/5-Beams_and_Bending_2.ipynb b/Mechanics_of_Structures_by_S_B_Junnarkar/5-Beams_and_Bending_2.ipynb new file mode 100644 index 0000000..d28a2aa --- /dev/null +++ b/Mechanics_of_Structures_by_S_B_Junnarkar/5-Beams_and_Bending_2.ipynb @@ -0,0 +1,1004 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 5: Beams and Bending 2" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.11: Chapter_5_example_11.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"b = 6;// inches\n", +"d = 12;// inches\n", +"t1 = 7/8;// inch\n", +"t2 = 1/2;// inch\n", +"I_xx = (1/12)*(b*d^3 - (b-t2)*(d-2*t1)^3);// in^4\n", +"Z1 = I_xx/b;// in ^3\n", +"A = 2*b*t1 + 0.5*(d-2*t1);// in^2\n", +"b = sqrt(A/2);// inches\n", +"d = 2*b;// inches\n", +"Z2 = (1/6)*b*d^2;// in^3\n", +"k = Z1/Z2 ;\n", +"printf('The ratio of strengths Z1/Z2 = %.2f ',k);\n", +"\n", +"//there is an error in the answer given in text book" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.12: Chapter_5_example_12.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"A = 15.625;// in^2\n", +"Z1 = 61.75;// in^3\n", +"Z2 = 14.63;// in^3\n", +"d = sqrt(4*A/%pi);// inches\n", +"Z3 = (%pi/32)*d^3;// in^3\n", +"R1 = Z1/Z3;\n", +"R2 = Z2/Z3;\n", +"printf('If the strength of the solid circular section is taken as unity,\n that of the rectangular section is %.2f and of the I-section it is %.2f.',R2,R1);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.13: Chapter_5_example_13.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"D = 8;// inches\n", +"B = 3;// inches\n", +"t1 = 1/2;// inch\n", +"t2 = 3/8;// inch\n", +"b = B-t2;// inches\n", +"d = D-2*t1;// inches\n", +"a1 = t1*B;// in^2\n", +"x1 = 0.5*B;// inches\n", +"a2 = t2*(D-2*t1);// in^2\n", +"x2 = 0.5*t2;// inches\n", +"a3 = B*t1;// in^2\n", +"x3 = 0.5*B;// inches\n", +"a = a1+a2+a3;// in^2\n", +"P = (a1*x1+a2*x2+a3*x3)/(a1+a2+a3);// inches\n", +"I_xx = (1/12)*(B*D^3 - b*d^3);// in^4\n", +"I_AB = (1/3)*t1*B^3 + (1/3)*d*t2^3 + (1/3)*t1*B^3;// in^4\n", +"I_yy = I_AB - a*P^2;// in^4\n", +"printf('Position of the c.g of the section P = %.3f inches',P);\n", +"printf('\n I_xx = %.2f in^4\n I_yy = %.3f in^4',I_xx,I_yy);\n", +"//there is an error in the answer given in text book" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.14: Chapter_5_example_14.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"b = 6;// inches\n", +"d = 4;// inches\n", +"t = 5/8;// inch\n", +"a1 = d*t;// in^2\n", +"y1 = d/2;// inches\n", +"a2 = (b-t)*t;// in^2\n", +"y2 = t/2;// inch\n", +"a = a1+a2;// in^2\n", +"J = (a1*y1+a2*y2)/(a1+a2);// inches\n", +"I_AB = (1/3)*t*d^3 + (1/3)*(b-t)*t^3;// in^4\n", +"I_xx = I_AB - a*J^2;// in^4\n", +"I_yy = (1/12)*t*b^3 + (1/12)*(d-t)*t^3;// in^4\n", +"printf('The position of the c.g is J = %.2f inches',J);\n", +"printf('\n I_xx = %.2f in^4\n I_yy = %.2f in^4',I_xx,I_yy);\n", +"\n", +"\n", +"//14(a)\n", +"H = 18;// feet\n", +"l = 10;// feet\n", +"w = 3/2;// cwt/ per .sq. foot\n", +"y_c = 2.97;// inches\n", +"y_t = 1.03;// inches\n", +"W = (3/40)*(w*l);// tons\n", +"BM_max = W*l*12/8;// ton-inches\n", +"M_r = BM_max;// ton-inches\n", +"f_c = M_r*y_c/I_xx ;// tons/in^2\n", +"f_t = M_r*y_t/I_xx ;// tons/in^2\n", +"printf('\n\n Maximum stresses induced are f_c = %.2f tons/in^2\n f_t = %.2f tons/in^2',f_c,f_t);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.15: Chapter_5_example_15.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"b = 5;// inches\n", +"d = 4;// inches\n", +"t = 1/2;// inches\n", +"a1 = b*t;// in^2\n", +"x1 = t/2;// inches\n", +"y1 = b/2;// inches\n", +"a2 = (d-t)*t;// in^2\n", +"y2 = t/2;// inch\n", +"x2 = t + 0.5*(d-t);// inches\n", +"x_bar = (a1*x1+a2*x2)/(a1+a2);// inches\n", +"y_bar = (a1*y1+a2*y2)/(a1+a2);// inches\n", +"I_AB = (1/3)*t*b^3 + (1/3)*(d-t)*t^3;// in^4\n", +"I_xx = I_AB - (a1+a2)*y_bar^2;// in^4\n", +"I_yy = (1/3)*t*d^3 + (1/3)*(b-t)*t^3 - (a1+a2)*x_bar^2;// in^4\n", +"printf('The position of c.g is x_bar = %.3f inches, y_bar = %.2f inches',x_bar,y_bar);\n", +"printf('\n I_xx = %.3f in^4\n I_yy = %.2f in^4',I_xx,I_yy);\n", +"\n", +"\n", +"\n", +"//Example 15(a)\n", +"l = 12;// feet\n", +"y_c = y_bar;//inches\n", +"y_t = b - y_c;//inches\n", +"f_t_max = 7;// tons/in^2\n", +"f_c = y_c*f_t_max/y_t;// tons/in^2\n", +"M_r = f_t_max*I_xx/y_t;// ton-inches\n", +"W = M_r/(l*12/8);// tons\n", +"printf('\n \n Total uniformly distribute load over the span is W = %.2f tons',W);\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.16: Chapter_5_example_16.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"b1 = 6;//inches\n", +"d1 = 1;//inch\n", +"b2 = 9;//inches\n", +"d2 = 1;//inch\n", +"b3 = 10;//inches\n", +"d3 = 2;//inch\n", +"a1 = b3*d3;// in^2\n", +"y1 = d3/2;// inches\n", +"a2 = b2*d2;// in^2\n", +"y2 = d3 + b2/2;// inches\n", +"a3 = b1*d1;// in^2\n", +"y3 = b2+d3+d1/2;// inches\n", +"y_bar = (a1*y1+a2*y2+a3*y3)/(a1+a2+a3);//inches\n", +"I_AB = (1/3)*b3*d3^3 + (1/12)*d2*b2^3 +b2*(d3+b2/2)^2 + (1/12)*b1*d1^3 + b1*(b2+d3+d1/2)^2;// in^4\n", +"I_xx = I_AB - (a1+a2+a3)*y_bar^2;// in^4\n", +"I_yy = (1/12)*(d3*b3^3 + b2*d2^3 +d1*b1^3);// in^4\n", +"printf('The c.g of the section is y_bar = %.3f inches',y_bar);\n", +"printf('\n I_xx = %.2f in^4\n I_yy = %.2f in^4',I_xx,I_yy);\n", +"\n", +"//Example 16(a)\n", +"l = 20;// feet\n", +"y_t = y_bar;// inches\n", +"y_c = d1+b2+d3-y_t;// inches\n", +"f_t = 1.5;// tons/in^2\n", +"f_c = y_c*f_t/y_t;// tons/in^2\n", +"M_r = f_c*I_xx/y_c;// ton-inches\n", +"W = M_r*8/(l*12);// tons\n", +"w = W/l;// ton per foot run\n", +"printf('\n\n Load required is w = %.2f ton per foot run',w);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.17: Chapter_5_example_17.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"b = 12;// inches\n", +"d = 6;// inches\n", +"h = 14;// inches\n", +"t = 1/2;// inch\n", +"A = 12.94;// in^2\n", +"//section moment of inertia\n", +"I_xx_s = 315.3;// in^4\n", +"I_yy_s = 22.27;// in^4\n", +"\n", +"I_xx = 2*I_xx_s + 2*((1/12)*h*(2*t)^3 + h*2*t*(d+t)^2);// in^4\n", +"I_yy = 2*(I_yy_s + A*(d/2)^2) + 2*((1/12)*2*t*h^3);// in^4\n", +"printf('I_xx = %.2f in^4\n I_yy = %.2f in^4',I_xx,I_yy);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.18: Chapter_5_example_18.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"b = 15;// inches\n", +"d = 15/2;// inches\n", +"h = 16;// inches\n", +"t = 1/2;// inch\n", +"P = 0.935;// inches\n", +"A = 12.33;// in^2\n", +"//section moment of inertia\n", +"I_xx_s = 377;// in^4\n", +"I_yy_s = 14.55;// in^4\n", +"\n", +"I_xx = 2*I_xx_s + 2*((1/12)*h*(2*t)^3 + h*2*t*(d+t)^2);// in^4\n", +"I_yy = 2*(I_yy_s + A*(d/2 + P)^2) + 2*((1/12)*2*t*h^3);// in^4\n", +"printf('I_xx = %.2f in^4\n I_yy = %.2f in^4',I_xx,I_yy);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.19: Chapter_5_example_19.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"b1 = 16;// inches\n", +"d1 = 6;// inches\n", +"b2 = 9;// inches\n", +"d2 = 7;// inches\n", +"A = 14.71;// in^2\n", +"I_xx1 = 618.09;// in^4\n", +"I_yy1 = 22.47;// in^4\n", +"I_xx2 = 208.13;// in^4\n", +"I_yy2 = 40.17;// in^4\n", +"I_xx = I_xx1 + 2*I_yy2;// in^4\n", +"I_yy = I_yy1 + 2*(I_xx2 + A*(b2/2 + 0.5*0.4)^2);// in^4\n", +"k_xx = sqrt(I_xx/(3*A));// inches\n", +"k_yy = sqrt(I_yy/(3*A));// inches\n", +"printf('I_xx = %.2f in^4\n I_yy = %.2f in^4\n k_xx = %.2f inches\n k_yy = %.2f inches',I_xx,I_yy,k_xx,k_yy);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.1: Chapter_5_example_1.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"b = 6;// inches \n", +"t = 1/2;// inch\n", +"R = 40;// feet\n", +"E = 13000;// tons/in^2\n", +"y = t/2;// inch\n", +"f = (E/(R*12))*(y);// tons/in^2\n", +"printf('The maximum intensity of stress induced is f = %.2f tons/in^2',f);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.20: Chapter_5_example_20.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"b1 = 7/2;// inches\n", +"d1 = 7/2;// inches\n", +"t1 = 3/8;// inches\n", +"l = 18;// inches\n", +"I_xx1 = 2.80;// in^4\n", +"I_yy1 = 2.80;// in^4\n", +"J = 1;// inch\n", +"A = 2.49;// in^2\n", +"I_xx = 4*(I_xx1 + A*(l/2 - J)^2);// in^4\n", +"k_xx = sqrt(I_xx/(4*A));// inches\n", +"printf('I_xx = %.2f in^4\n k_xx = %.1f inches',I_xx,k_xx);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.21: Chapter_5_example_21.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"b1 = 12;// inches\n", +"d1 = 4;// inches\n", +"A = 9.21;// in^2\n", +"I_xx1 = 200.1;// in^4\n", +"P = 1.055;// inches\n", +"I_yy1 = 12.12;// in^4\n", +"I_xx = 2*I_xx1;\n", +"//for equal strength I_xx = I_yy\n", +"x = 2*(sqrt(((I_xx/2)-I_yy1)/A) - P);// in^4\n", +"printf('x = %.2f inches',x);\n", +"\n", +"//answer is corrct only, but it is approximated in the text book." + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.22: Chapter_5_example_22.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"d =10;// inches\n", +"b = 8;// inches\n", +"t1 = 1;// inch\n", +"t2 = 0.6;// inch\n", +"I = (1/12)*(b*d^3 - (b-t2)*b^3);// in^4\n", +"//(i) Resistance to M\n", +"R1 = integrate('(t2/I)*y^2','y',-4,4);\n", +"//(ii) Resistance to F\n", +"R2 = integrate('(4/I)*(25-y^2)','y',4,5);\n", +"printf('The moment of resistance offered by the flanges is %.3fM. The flanges take up %.1f percentage of the B.M.,\n the web resisting only %.1f percentage of the B.M',1-R1,(1-R1)*100,R1*100);\n", +"printf('\n The shear borne by the web is %.4fF. The web thus takes up %.2f percentage of the shear force.,\n the flanges resisting only %.2f percentage of the shear force',(1-2*R2),(1-2*R2)*100,2*R2*100);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.23: Chapter_5_example_23.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"b = 14;// inches\n", +"d = 6;// inches\n", +"t1 = 0.7;// inch\n", +"t2 = 0.4;// inch\n", +"F = 20;// tons\n", +"I = (1/12)*(d*b^3 - (d-t2)*(b-2*t1)^3);// in^4\n", +"q = F*t1*0.5*(0.5*b + (0.5*b-t1))/I;// ton/in^2\n", +"q_max = (F/(I*t2))*(d*t1*0.5*(0.5*b + (0.5*b-t1)) + t2*(0.5*b-t1)*(0.5*b-t1)*0.5);// tons/in^2\n", +"printf('The maximum intensity of shear stress is q_max = %.2f tons/in^2',q_max);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.24: Chapter_5_example_24.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"b = 4;// inches\n", +"d = 13/2;// inches\n", +"t = 1/2;// inch\n", +"a = 4;// inches\n", +"F = 10;// tons\n", +"a1 = b*t;// in^2\n", +"y1 = t/2;// inch\n", +"a2 = (d-t)*t;// in^2\n", +"y2 = t+0.5*(d-t);// inches\n", +"y_bar = (a1*y1+a2*y2)/(a1+a2);// inches\n", +"I_AB = (1/3)*b*t^3 + (1/12)*t*(d-t)^3 + (b-2*t)*(b-t)^2;// in^4\n", +"I_xx = I_AB - (a1+a2)*y_bar^2;// in^4\n", +"q = (F/(b*I_xx))*b*t*(y_bar-0.5*t);// ton/in^2\n", +"q_max = (F/(t*I_xx))*(b*t*(y_bar-0.5*t) + 0.5*t*(y_bar-t)*(y_bar-t));// tons/in^2\n", +"printf('The maximum intensity of shear stress at the N.A is q_max = %.2f tons/in^2',q_max);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.25: Chapter_5_example_25.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"function [p1, p2,theta] = func(p,q)\n", +" p1 = 0.5*p + sqrt(q^2 + 0.25*p^2);\n", +" p2 = 0.5*p - sqrt(q^2 + 0.25*p^2);\n", +" theta = 0.5*atan(2*q/p) * 180/%pi;\n", +"endfunction\n", +"b = 5;// inches\n", +"d = 12;// inches\n", +"F = 4800 ;// lb-wt\n", +"M = 192000;// lb-inches\n", +"I = (1/12)*b*d^3;// in^4\n", +"\n", +"//At 6 inches above the N.A\n", +"p6 = M*6/I ; // lb/in^2\n", +"q6 = 0;\n", +"[p1_6,p2_6,theta6] = func(p6,q6);\n", +"\n", +"//At 4 inches above the N.A\n", +"p4 = M*4/I;// lb/in^2\n", +"q4 = (F/(I*b))*b*(0.5*d-4)*b;\n", +"[p1_4,p2_4,theta4] = func(p4,q4);\n", +"\n", +"//At 2 inches above the N.A\n", +"p2 = M*2/I;// lb/in^2\n", +"q2 = (F/(I*b))*b*(0.5*d-2)*4;\n", +"[p1_2,p2_2,theta2] = func(p2,q2);\n", +"\n", +"//At the N.A\n", +"p = 0;//\n", +"q = F*b*0.5^3*d^2/(I*b);// lb/in^2\n", +"p1 = q;// lb/in^2\n", +"p2 = -q;// lb/in^2\n", +"\n", +"printf('At 6 inches above the N.A, p1 = %d lb/in^2., compressive, and p2 = %d ',p1_6,p2_6);\n", +"printf('\n At 4 inches above the N.A, p1 = %.1f lb/in^2., compressive, and p2 = %.2f lb/in^2 .,tensile\n theta1 = %.2f degrees \n theta2 = %.2f degrees',p1_4,-p2_4,theta4,theta4+90);\n", +"printf('\n At 2 inches above the N.A, p1 = %.2f lb/in^2., compressive, and p2 = %.2f lb/in^2.,tensile\n theta1 = %.2f degrees \n theta2 = %.2f degrees',p1_2,-p2_2,theta2,theta2+90);\n", +"printf('\n At the N.A, p1 = %d lb/in^2., compressive, and p2 = %d.,tensile ',p1,-p2);\n", +"\n", +"//there is an error in the answer given in text book" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.26: Chapter_5_example_26.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"b = 10;// inches\n", +"d = 8;// inches\n", +"t1 = 1;// inch\n", +"t2 = 0.6;// inch\n", +"M = 500;// ton-inches\n", +"F = 25;// tons\n", +"I = (1/12)*(d*b^3 - (d-t2)*d^3);// in^4\n", +"\n", +"//At the top\n", +"p = M*b/(2*I);// tons/in^2\n", +"q = 0;\n", +"p1 = p;// tons/in^2\n", +"p2 = 0;\n", +"printf('At the top, principal stresses are \n p1 = %.2f tons/in^2\n p2 = %d tons/in^2',p1,p2);\n", +"\n", +"//In the web, 4 inches from the N.A\n", +"p = M*d/(2*I);// tons/in^2\n", +"q = F*d*t1*0.5*(d+t1)/(I*t2);// tons/in^2\n", +"theta = 0.5*atan(2*q/p);\n", +"theta1 = theta*180/%pi;\n", +"theta2 = theta1+90;\n", +"p1 = 0.5*p + sqrt(q^2 + 0.25*p^2);// tons/in^2\n", +"p2 = 0.5*p - sqrt(q^2 + 0.25*p^2);// tons/in^2\n", +"printf('\n In the web, 4 inches from the N.A.:\n The principal stresse are p1 = %.2f tons/in^2.,compressive\n p2 = %.2f tons/in^2.,tensile\n theta1 = %.1f degrees\n theta2 = %.1f degrees',p1,-p2,theta1,theta2);\n", +"\n", +"//At the N.A\n", +"p = 0;\n", +"q = (F/(I*t2))*(d*t1*0.5*(d+t1) + t2*0.5*d*2*t1);\n", +"p1 = q;// tons/in^2\n", +"p2 = -q;//tons/in^2\n", +"printf('\n The principal stresse across the diagonal are %.2f tons/in^2., compressive on one plane and %.2f tons/in^2., tensile on the other.',q,q);\n", +"\n", +"//there is an error in the answer given in text book" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.27: Chapter_5_example_27.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"W = 10;// tons\n", +"l = 16;// feet\n", +"f = 15/2;// tons/in^2\n", +"//section modulus required\n", +"SM = W*l*12/(8*f);// in^3\n", +"//for this section modulus \n", +"l1 = 12;// inches\n", +"b1 = 5;// inches\n", +"t1 = 0.55;// inches\n", +"t2 = 0.35;// inches\n", +"I_xx = 220;// in^4\n", +"F_max = 5;// tons\n", +"q_max = (F_max/(I_xx*t2))*(F_max*t1*(0.5*l1-0.5*t1) + t2*0.5*(0.5*l1-t1)^2);// tons/in^2\n", +"printf('The maximum intensity of shear stress is q_max = %.2f tons/in^2',q_max);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.28: Chapter_5_example_28.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"b = 9/2;// inches\n", +"D = 12;// inches\n", +"d = 10;// inches\n", +"t = 1/2;// inches\n", +"f_w = 1000;// lb/in^2\n", +"m = 18;//m = E_s/E_w\n", +"f_t = m*d*f_w/D ;// lb/in^2\n", +"M_w = f_w*(1/6)*2*b*D^2;// lb-inches\n", +"M_s = f_t*(1/6)*t*d^2;// lb-inches\n", +"M = M_w + M_s;// lb-inches\n", +"printf('Skin stresse in steel plate is, M_s = %d lb-inches\n The total moment of resistance is M = %d lb-inches',M_s,M);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.2: Chapter_5_example_2.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"d = 14;// inches\n", +"I = 442.57;//inch units\n", +"f = 8;// tons/in^2\n", +"E = 13000;// tons/in^2\n", +"R = E*d/(2*f);// inches\n", +"M_r = f*(I/(d/2));// ton-inches\n", +"printf('The radius to which it should be bent is R = % d inches or %.1f feet',R,R/12);\n", +"printf('\n The moment of resistance is M_r = %.1f ton-inches',M_r);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.3: Chapter_5_example_3.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"d = 16;// inches\n", +"I = 618;// inch units\n", +"l = 24;// feet\n", +"f = 15/2;// tons/in^2\n", +"Z = I/(d/2);// inch-units\n", +"M_r = f*Z;// ton-inches\n", +"//If the load is uniformly spread over its span,BM = W*l/8\n", +"W1 = 8*M_r/(12*l);//tons\n", +"//If the load is concentrated at the centre,BM = W*l/4\n", +"W2 = 4*M_r/(12*l);//tons\n", +"printf('If the load is uniformly spread over its span, then W is given by \n W = %.1f tons\n = %.3f ton per foot run',W1,W1/l);\n", +"printf('\n If the load is concentrated at the centre, then W is given by\n W = %.2f tons',W2);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.4: Chapter_5_example_4.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"d = 20;// inches\n", +"I = 1673;// inch units\n", +"W = 3/4;// ton per foot run\n", +"f = 8;// tons/in^2\n", +"Z = I/(d/2);// inch-units\n", +"M_r = f*Z;// ton-inches\n", +"l = sqrt(M_r*32/(3*12));//feet\n", +"printf('The maximum permissible span for this beam is l = %.2f feet',l);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.5: Chapter_5_example_5.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"function [M,f]=func(W,l,d,b,Z)\n", +" M = 0.5*W*d - (W/l)*d*b;\n", +" f = M*12/Z;\n", +"endfunction\n", +"b = 6;// inches\n", +"d = 12;// inches\n", +"l = 16;// feet\n", +"W = 6000;// lb-wt\n", +"Z = (1/6)*b*d^2;\n", +"d1 = 2;// feet\n", +"d2 = 4;// feet\n", +"d3 = 6;// feet\n", +"d4 = 8;// feet\n", +"b1 = 1// feet\n", +"b2 = 2;// feet\n", +"b3 = 3;// feet\n", +"b4 = 4;// feet\n", +"[M2,f2] = func(W,l,d1,b1,Z);\n", +"[M4,f4] = func(W,l,d2,b2,Z);\n", +"[M6,f6] = func(W,l,d3,b3,Z);\n", +"[M8,f8] = func(W,l,d4,b4,Z);\n", +"printf('At %d feet,M2 = %d lb-feet and f2 = %.1f lb/in^2\n At %d feet,M4 = %d lb-feet and f4 = %d lb/in^2 \n At %d feet,M4 = %d lb-feet and f6 = %.1f lb/in^2\n At %d feet,M4 = %d lb-feet and f8 = %d lb/in^2\n',d1,M2,f2,d2,M4,f4,d3,M6,f6,d4,M8,f8);\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.6: Chapter_5_example_6.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"w = 160;// lb. per sq. foot\n", +"b = 3;// inches\n", +"d = 9;// inches\n", +"l = 15;// feet\n", +"f = 1200;// lb. per sq. inch\n", +"Z = (1/6)*b*d^2;// in^3\n", +"M_r = f*Z;// lb-inches\n", +"x = M_r/(w*l^2*12/8);// feet\n", +"printf('x = %.1f feet',x);\n", +"\n", +"//The answer is correct only, but it is approximated in the text book" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.7: Chapter_5_example_7.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"l = 20;// feet\n", +"b = 9;// inches\n", +"h = 10;// feet\n", +"w = 120;// lb. per cub. foot\n", +"f = 1100;// lb/in^2\n", +"W = w*(3/4)*l*h;// lb-wt\n", +"BM_max = W*l*12/8;// lb-inches\n", +"//assumnig d = 2b\n", +"b = (6*BM_max/(f*4))^(1/3);// inches\n", +"d = 2*b;// inches\n", +"printf('b = %.2f inches\n d = %.2f inches',b,d);\n", +"printf('\n A section %d X %d will therfore do.',b,d);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.8: Chapter_5_example_8.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"B = 5;// inches\n", +"D = 12;// inches\n", +"t1 = 0.55;// inches\n", +"t2 = 0.35;// inches\n", +"f = 15/2;// tons/in^2\n", +"l = 16;// feet\n", +"b = B-t2;// inches\n", +"d = D-2*t1;// inches\n", +"I_xx = (B*D^3 - b*d^3)/12;// in^4\n", +"Z = I_xx/6;// in^3\n", +"M_r = f*Z;// ton-inches\n", +"W = M_r/(l*12/8);// tons\n", +"w = W/l;// ton per foot run\n", +"printf('W = %.2f tons\n w = %.2f ton per foot run',W,w);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.9: Chapter_5_example_9.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"D = 19.5;// inches\n", +"d = 18;// inches\n", +"l = 30;// feet\n", +"t1 = 3/4;// inch\n", +"rho1 = 450;// lb. per cub. foot\n", +"rho2 = 62.5;// lb. per cub. foot\n", +"A = 0.25*%pi*(D^2 - d^2);// sq. in\n", +"DW = rho1*l*A/144;// lb-wt\n", +"WW = rho2*0.25*%pi*(D-d)^2*l;// lb-wt\n", +"W = DW+WW;// lb-wt\n", +"BM_max = W*l*0.0004467202*12/8;// ton-inches\n", +"I_xx = (%pi/64)*(D^4 - d^4);// in^4\n", +"Z_xx = I_xx/(0.5*d+t1);// ton/in^2\n", +"f = BM_max/Z_xx;// ton/in^2\n", +"printf('The maximum stress f = %.3f ton/in^2',f);\n", +"\n", +"//there is an error in the answer given in text book" + ] + } +], +"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/Mechanics_of_Structures_by_S_B_Junnarkar/6-Beams_and_bending_3.ipynb b/Mechanics_of_Structures_by_S_B_Junnarkar/6-Beams_and_bending_3.ipynb new file mode 100644 index 0000000..b01ed51 --- /dev/null +++ b/Mechanics_of_Structures_by_S_B_Junnarkar/6-Beams_and_bending_3.ipynb @@ -0,0 +1,363 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 6: Beams and bending 3" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.10: Chapter_6_example_10.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"b = 18;// inches\n", +"d = 6;// inches\n", +"l = 16;// feet\n", +"W = 2;// tons\n", +"h = 1/2;// inches\n", +"I_xx = 841.76;// in^4\n", +"E = 13000;// tons/in^2\n", +"P = W + sqrt(2*W*h*48*E*I_xx/(l*12)^3 + 2*W);// tons\n", +"M_max = P*l*12/4;// ton-inches\n", +"Z = 2*I_xx/b ;// in^3\n", +"f = M_max/Z ;// tons/in^2\n", +"delta = P*(l*12)^3 /(48*E*I_xx);// inches\n", +"printf('The maximum instantaneous deflection delta = %.4f inches\n and stress induced, f = %.3f tons/in^2',delta,f);\n", +"//there is an error in the answer given in text book" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.11: Chapter_6_example_11.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"l = 3;// feet\n", +"b = 3;// inches\n", +"t = 3/8;// inches\n", +"W = 1500;// lb.\n", +"f = 12;// tons/in^2\n", +"E = 30*10^6;// tons/in^2\n", +"M_max = W*l*12/4 ;// lb-inches\n", +"M_r = f*(1/6)*b*t^2 *2240;// lb-inches\n", +"n = M_max/M_r ;// no. of plates\n", +"n = round(n+1);\n", +"f = M_max/(n*(1/6)*b*t^2);// lb/in^2\n", +"R = E/(2*f/t) ;// inches\n", +"delta = (l*12)^2 /(8*R);// inches\n", +"printf('Number of plates required, n = %d',n);\n", +"printf('\n The central deflection, delta = %.4f inch.',delta);\n", +"printf('\n The initial radius to which the plates must be bent, R = %.3f inches',R);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.1: Chapter_6_example_1.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"l = 5;// feet\n", +"W = 150;// lb\n", +"w = 120;// lb. per foot run\n", +"l1 = 3;// feet\n", +"b = 3;// inches\n", +"d = 6;// inches\n", +"E = 1.5*10^6;// lb/in^2\n", +"I = (1/12)*b*d^3;// in^4\n", +"y_B1 = (W*l^3)/(3*E*I);// feet\n", +"y_B2 = (w*l1*l1^3)/(8*E*I) + (l-l1)*(w*l1*l1^2)/(6*E*I);// feet\n", +"y_B = (12^3)*(y_B1+y_B2);// inches\n", +"printf('The deflection at the free end = %.4f inches',y_B);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.3: Chapter_6_example_3.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"b = 4;// inches\n", +"d = 9;// inches\n", +"l = 12;// feet\n", +"y_c = 1/4;// inches\n", +"E = 1.5*10^6;// lb/in^2\n", +"I = (1/12)*b*d^3;// in^4\n", +"W = y_c*384*E*I/(5*12^3*l^3);// inches\n", +"printf('Uniform distributed load, the beam should carry is, W = %d lb-wt',W);\n", +"\n", +"//there is an error in the answer given in text book" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.4: Chapter_6_example_4.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"d = 6;// feet\n", +"l = 60;// feet\n", +"f = 15/2;// tons/in^2\n", +"E = 13000;// tons/in^2\n", +"k1 = 2*f/(12*d);// k1 = M_r/I \n", +"k2 = k1/(l*12/8);//k2 = W/I\n", +"y_c = (5/384)*k2*l^3 *12^3 /E;// inches\n", +"//If the giredr is of constant deapth and uniform strength, it bends to an arc of a circle of radius R \n", +"R = E*d*12/(2*f);// inches\n", +"delta = (l*12)^2 /(8*R);// inches\n", +"printf('The deflection for a uniformly distributed load on it is,delta = %.2f inches',delta);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.5: Chapter_6_example_5.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"f = 8;//tons/in^2\n", +"E = 12800;// tons/in^2\n", +"k1 = 1/480;//central deflection = k = delta/l\n", +"k2 = (5/24)*(f/E)/k1 ;//k2 = d/l = deapth to span ratio\n", +"printf('The ratio of deapth to span, d/l = %f ',k2);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.6: Chapter_6_example_6.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"w = 550;// lb. per foot run\n", +"f = 1000;// lb/in^2\n", +"l = 20;// feet\n", +"d_limit = 15;// inches\n", +"E = 1.5*10^6;// lb/in^2\n", +"//central ddeflection\n", +"delta = (1/2);// inches\n", +"d = (5/24)*(f/E)*20*12/(1/(2*20*12));// inches\n", +"M = w*l*l*12/8;// lb-inches\n", +"b = M/(f*(1/6)*d^2);// inches\n", +"printf('A section with d = %d inches, b = %d inches will do.',round(d),round(b));\n", +"f1 = (1/(2*20*12))*(d_limit/(l*12))*E/(5/24);// lb/in^2\n", +"b = M/(f1*(1/6)*d_limit^2);// inches\n", +"printf('\n If the deapth of section is limited to %d inches, then \n f = %.1f lb/in^2\n b = %.1f inches',d_limit,f1,b);\n", +"\n", +"//tha answer is correct only, but it is approximated in the text book." + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.7: Chapter_6_example_7.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"l = 20;// feet\n", +"b = 4;// feet\n", +"W = 5;// tons\n", +"d = 12;// inches\n", +"h = 5;// inches\n", +"I_xx = 220;// in^4\n", +"E = 13000;// tons/in^2\n", +"a = l-b;// feet\n", +"//for maximum deflection\n", +"x = sqrt((a^2 + 2*a*b)/3);// feet\n", +"y_max = x*12^3 *((a^2 + 2*a*b) - x^2)/(6*E*I_xx);// inches\n", +"//for deflection at the centre\n", +"x1 = 0.5*l;// inches\n", +"y_x1 = x1*12^3 *((a^2 + 2*a*b) - x1^2)/(6*E*I_xx);// inches\n", +"printf('The position of maximum deflection occurs at x = %.2f feet\n The maximum deflection is, y_max = %.4f inches',x,y_max);\n", +"printf('\n The deflection at the centre, y_%d = %.4f inches',x1,y_x1);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.8: Chapter_6_example_8.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"d = 12;// inches\n", +"h = 5;// inches\n", +"l = 20;// feet\n", +"E = 13000; //tons/in^2\n", +"I_xx = 220;// in^4\n", +"W = 4;// tons\n", +"W1 = 3;// tons\n", +"a = 15;// feet\n", +"b = l-a;// feet\n", +"a1 = 16;// feet \n", +"b1 = l-a1;// feet\n", +"K1 = (-2*W1*b1*l)/(W1*b1-W*b);\n", +"K2 = (W*b*a^2 + 2*a*W*b^2 + 2*W1*b1*l^2 - W1*b1*a1^2 -2*W1*a1*b1^2 +W1*b1*l^2)/(3*(W1*b1 - W*b));\n", +"x = -0.5*K1 + sqrt(-K2 + 0.25*K1^2);// feet\n", +"x1 = l-x;// feet\n", +"y_max = W*b*x*1728*(a^2 +2*a*b -x^2)/(6*E*I_xx*l) + W1*b1*x1*1728*(a1^2 +2*a1*b1 -x1^2)/(6*E*I_xx*l);// inches\n", +"printf('The position of the maximum deflection is, x = %.2f feet.',x);\n", +"printf('\n And the maximum deflection is, y_max = %.4f inches.',y_max);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.9: Chapter_6_example_9.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"b = 18;// inches\n", +"d = 7;// inches\n", +"w1 = 1;// ton per foot run\n", +"w2 = 3;// ton per foot run\n", +"I_xx = 1149;// in^4\n", +"E = 13000;// tons/in^2\n", +"R_A = 0.5*b + (b/3);// tons\n", +"R_B = 0.5*b + (2*b/3);// tons\n", +"//integrating M = E*I*y'', to get E*I*y' and making y' = 0;, we get maximu deflection\n", +"x = 9.18;// by trial and error method\n", +"y_derivative = -R_A*0.5*x^3 + x^4 /6 +0.5*(2/3)*(1/b)*(1/4)*x^5 + 469.8;\n", +"y = -R_A*0.5*x^3 /3 + x^4 /24 +0.5*(2/3)*(1/b)*(1/(4*5))*x^5 + 469.8*x;\n", +"y_max = y;// inches\n", +"printf('The position of maximum deflection from the end A, x = %.2f inches and \n Maximum deflection, y_max = %.4f inches',x,y_max*12^3 /(E*I_xx));" + ] + } +], +"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/Mechanics_of_Structures_by_S_B_Junnarkar/8-Direct_and_bending_stresses.ipynb b/Mechanics_of_Structures_by_S_B_Junnarkar/8-Direct_and_bending_stresses.ipynb new file mode 100644 index 0000000..d1f879c --- /dev/null +++ b/Mechanics_of_Structures_by_S_B_Junnarkar/8-Direct_and_bending_stresses.ipynb @@ -0,0 +1,381 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 8: Direct and bending stresses" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.10: Chapter_8_example_10.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"h = 20;// feet\n", +"b = 4;// feet\n", +"d = 12;// feet\n", +"h1 = 18;// feet\n", +"//density of masonary\n", +"rho_m = 140;// lb-ft^3\n", +"//density of water\n", +"rho_w = 62.5;// lb-ft^3\n", +"W = rho_m*0.5*(b+d)*h;// lb-wt\n", +"//to locate its line of action divide the dam section into a rectangle and a triangle \n", +"x1 = b/2;//feet\n", +"a1 = b*h;// sq. feet\n", +"a2 = 0.5*(d-b)*h;// sq. feet\n", +"x2 = b+((d-b)/3);// feet\n", +"x_bar = (a1*x1+a2*x2)/(a1+a2);// feet\n", +"P = rho_w*h1^2/2;// lb-wt\n", +"z = x_bar + (h1/3)*(P/W);// feet\n", +"e = z - d/2;// feet\n", +"p_0 = W/d;// lb/ft^2\n", +"M = W*e;// lb-feet\n", +"Z = 1*d^2*1/6;// ft^3\n", +"p_b = M/Z;// lb-ft^2\n", +"p_max = p_0 + p_b;// lb-ft^2\n", +"p_min = p_0 - p_b;// lb-ft^2\n", +"printf('p_max = %.1f lb/ft^2., compressive at B.\n p_min = %.1f lb/ft^2., compressive at A.',p_max,p_min);\n", +"\n", +"//there is an error in the answer given in text book" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.1: Chapter_8_example_1.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"d = 6;//inches\n", +"b = 3/4;//inch\n", +"P = 18;//tons\n", +"e = 1/8;//inch\n", +"A = b*d;//sq.in\n", +"M = P*e;//ton-in\n", +"Z = (1/6)*b*d^2;//in^3\n", +"p_0 = P/A;// tons/in^2\n", +"p_b = M/Z;// ton/in^2\n", +"p_max = p_0+p_b;// tons/in^2\n", +"p_min = p_0-p_b;// tons/in^2\n", +"printf('p_max = %.1f tons/in^2.,tensile\n p_min = %.1f tons/in^2.,tensile',p_max,p_min);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.2: Chapter_8_example_2.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"d1 = 12;//inches\n", +"t = 1;//inch\n", +"d2 = d1-2*t;//inches\n", +"P = 5;//tons\n", +"e = 12;//inch\n", +"A = 0.25*%pi*(d1^2-d2^2);//sq.in\n", +"M = P*e;//ton-in\n", +"Z = %pi*(d1^4-d2^4)/(32*d1);//in^3\n", +"p_0 = P/A;// tons/in^2\n", +"p_b = M/Z;// ton/in^2\n", +"p_max = p_0+p_b;// tons/in^2\n", +"p_min = p_0-p_b;// tons/in^2\n", +"printf('p_max = %.4f ton/in^2.,cmopressive\n p_min = %.4f ton/in^2.,\n i.e., %.4f ton/in^2., tensile',p_max,p_min,-p_min);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.3: Chapter_8_example_3.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"l = 6;//inches\n", +"b = 4;//inches\n", +"d = 1/2;//inch\n", +"P = 10;//tons\n", +"r = 1.5;//inches\n", +"A = 4.771;// in^2\n", +"J = 0.968;// inches\n", +"I_xx = 6.07;// in^4\n", +"I_yy = 8.64;// in^4\n", +"e = r-J;// inches\n", +"M = P*e;// ton-inches\n", +"y_t = J;//inches \n", +"y_c = b-y_t;//inches\n", +"//compressive\n", +"p_c = M*y_c/I_xx;// tons/in^2\n", +"//tensile\n", +"p_t = M*y_t/I_xx;// tons/in^2\n", +"//compressive\n", +"p_0 = P/A ;// tons/in^2\n", +"p_max = p_0+p_c;// tons/in^2\n", +"p_min = p_0-p_t;// tons/in^2\n", +"printf('p_max = %.3f tons/in^2.,compressive\n p_min = %.3f tons/in^2.,compressive',p_max,p_min);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.4: Chapter_8_example_4.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"b = 5;//inches\n", +"t = 1/2;//inch\n", +"P = 12;//tons\n", +"d = 1/2;//inch\n", +"r = 3/2;//inch\n", +"A = (b-d)*t;// in^2\n", +"p_0 = P/A;// tons/in^2\n", +"a1 = b*d;// in^2\n", +"x1 = 0;\n", +"a2 = d*t;// in^2\n", +"x2 = -3/2;\n", +"e = (a1*x1-a2*x2)/(a1-a2);//inches\n", +"M = P*e;// ton-inches\n", +"y_c = a1-e;// inches\n", +"y_t = a1+e;// inches\n", +"I_yy = (t*b^3)/12 - ((t*d^3)/12 + 0.5*d*r^2);// in^4\n", +"I_GG = I_yy - (a1-a2)*(e^2);// in^4\n", +"p_c = M*y_c/I_GG;// tons/in^2\n", +"p_t = M*y_t/I_GG;// tons/in^2\n", +"p_max = p_0 + p_t;// tons/in^2\n", +"p_min = p_0 - p_c;// tons/in^2\n", +"printf('p_max = %.1f tons/in^2., tensile\n p_min = %.2f tons/in^2., tensile',p_max,p_min);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.5: Chapter_8_example_5.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"h = 20;// feet\n", +"b = 12;// feet\n", +"d = 4;// feet\n", +"p = 30;// lb. per sq.foot\n", +"rho = 140;// lb. per cubic foot\n", +"p_0 = rho*h;// lb-ft^2\n", +"P = p*b*h;// lb-wt\n", +"M = P*h/2;//lb-ft\n", +"Z = b*d^2/6;// ft^3\n", +"p_b = M/Z;// lb/ft^2\n", +"p_max = p_0 + p_b;// lb/ft^2\n", +"p_min = p_0 - p_b;// lb/ft^2\n", +"printf('p_max = %d lb/ft^2., compressive\n p_min = %d lb/ft^2., compressive',p_max,p_min);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.6: Chapter_8_example_6.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"h = 80;// feet\n", +"p = 28;// lb. per sq.foot\n", +"rho = 126;// lb. per cubic foot\n", +"p_0 = rho*h/2240;// tons-ft^2\n", +"p_max = 7;// tons/ft^2\n", +"d = 4;// feet\n", +"p_b = p_max - p_0;// tons/ft^2\n", +"D = sqrt(3*p*h^2 /(2*p_b*2240) +sqrt(d^4 + (3*p*h^2 /(2*p_b*2240))^2));// feet\n", +"t = 0.5*(D-d);// feet\n", +"printf('The necessary thickness is, t = %d feet',round(t));" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.7: Chapter_8_example_7.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"h = 60;//feet\n", +"rho = 130;// lb. per cubic foot\n", +"D = 12;//feet\n", +"d = 5;//feet\n", +"P_h = 24;// lb. per sq. foot\n", +"p_0 = rho*h;// lb-ft^2\n", +"P = P_h*D*h;// lb-wt\n", +"M = P*h/2;// lb-feet\n", +"Z = %pi*(D^4 - d^4)/(32*D);//lb-ft^3\n", +"p_b = M/Z;// lb/ft^2\n", +"p_max = p_0 + p_b;// lb/ft^2\n", +"p_min = p_0 - p_b;// lb/ft^2\n", +"printf('p_max = %d lb/ft^2., compressive\n p_min = %d lb/ft^2., compressive',p_max,p_min);\n", +"\n", +"//there is an error in the answer given in text book" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.8: Chapter_8_example_8.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"h = 120;// feet\n", +"d = 5;// feet\n", +"h1 = 49;// feet\n", +"p = 42;// lb. per square foot\n", +"c = 0.6;\n", +"//p = k*sqrt(x)\n", +"k = p/sqrt(h1);\n", +"M = integrate('18*x^(3/2)','x',0,120);\n", +"printf('Bending moment at the foot of the chimney is, M = %d lb-ft',M);\n", +"//there is an error in the answer given in text book" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.9: Chapter_8_example_9.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"h = 100;// feet\n", +"d = 4;// feet\n", +"p = 50;// lb. per square foot\n", +"c = 2/3;\n", +"M = integrate('(100*x/3)*(10-(6*x/100))','x',0,100);\n", +"printf('Bending moment at the foot of the chimney is, M = %d lb-feet',M);" + ] + } +], +"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/Mechanics_of_Structures_by_S_B_Junnarkar/9-Columns_and_struts_of_uniform_section.ipynb b/Mechanics_of_Structures_by_S_B_Junnarkar/9-Columns_and_struts_of_uniform_section.ipynb new file mode 100644 index 0000000..4280c6a --- /dev/null +++ b/Mechanics_of_Structures_by_S_B_Junnarkar/9-Columns_and_struts_of_uniform_section.ipynb @@ -0,0 +1,433 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 9: Columns and struts of uniform section" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.10: Chapter_9_example_10.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"e = 7/4;// inches\n", +"E = 13000;// tons/in^2\n", +"p = 5;// tons/in^2\n", +"y_c = 6;// inches\n", +"l = 20;// feet\n", +"A = 38.38;// in^2\n", +"k = sqrt(11.78);// inches\n", +"I = 11.78;// in^4\n", +"p_e = (%pi)^2 *E*k^2 /(l*12)^2;// tons/in^2\n", +"//from Perry's formula\n", +"p_0 = 0.5*((p_e*1.2*e*y_c/k^2)+p_e+p)-sqrt((0.5*((p_e*1.2*e*y_c/k^2)+p_e+p))^2 - p_e*p);// tons/in^2\n", +"P = p_0*A;// tons\n", +"printf('The safe load, P = %.2f tons',P);\n", +"\n", +"//there is a minute calculation error in the answer given in text book" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.11: Chapter_9_example_11.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"b1 = 10;// inches\n", +"d1 = 6;// inches\n", +"b2 = 12;// inches\n", +"d2 = 1/2;// inches\n", +"l = 16;// feet\n", +"A_s = 11.77;// in^2\n", +"I_xxs = 204.80;// in^4\n", +"I_yys = 21.76;// in^4\n", +"A = A_s + 2*b2*d2;// in^2\n", +"I_yy = I_yys + 2*(1/12)*d2*b2^3;// in^4\n", +"k = sqrt(I_yy/A);// inches\n", +"//from the Perry-Robertson formula\n", +"n = 0.003*l*12/k;\n", +"p_e = 13000*%pi^2/((l*12)/k)^2 ;// tons/in^2\n", +"f = 18;// tons/in^2\n", +"x = 0.5*(f+p_e*(1+n));\n", +"p_0 = x - sqrt(x^2 - f*p_e);// tons/in^2\n", +"P = p_0*A;// tons\n", +"P_safe = P/2.36;// tons\n", +"printf('The safe load, P = %.1f tons',P_safe);\n", +"\n", +"//there is a minute calculation error in the answer given in text book" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.1: Chapter_9_example_1.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"// n =l/k\n", +"n1 = 40;\n", +"n2 = 60;\n", +"n3 = 80;\n", +"n4 = 100;\n", +"n5 = 120;\n", +"n6 = 140;\n", +"n7 = 160;\n", +"n8 = 180;\n", +"n9 = 200;\n", +"E = 13000;// tons/in^2\n", +"//m = P/A\n", +"m1 = 4*%pi^2 *E/n1^2;// tons per sq. inch\n", +"m2 = 4*%pi^2 *E/n2^2;// tons per sq. inch\n", +"m3 = 4*%pi^2 *E/n3^2;// tons per sq. inch\n", +"m4 = 4*%pi^2 *E/n4^2;// tons per sq. inch\n", +"m5 = 4*%pi^2 *E/n5^2;// tons per sq. inch\n", +"m6 = 4*%pi^2 *E/n6^2;// tons per sq. inch\n", +"m7 = 4*%pi^2 *E/n7^2;// tons per sq. inch\n", +"m8 = 4*%pi^2 *E/n8^2;// tons per sq. inch\n", +"m9 = 4*%pi^2 *E/n9^2;// tons per sq. inch\n", +"printf('l/k : %d %d %d %d %d %d %d %d %d\n P/A: %d %.1f %.1f %.2f %.2f %.1f %.2f %.2f %.2f',n1,n2,n3,n4,n5,n6,n7,n8,n9,m1,m2,m3,m4,m5,m6,m7,m8,m9);\n", +"//there is a minute error in the answer given in text book" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.2: Chapter_9_example_2.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"d = 1;// inches\n", +"t = 1/8;// inches\n", +"l = 10;// feet\n", +"E = 13500;// tons/in^2\n", +"D = d+2*t;// inches\n", +"I = (%pi/64)*(D^4 - d^4);// in^4\n", +"P = 20.25*E*I/(12*l)^2 ;// tons\n", +"printf('The collapsing load, P = %.2f tons',P);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.3: Chapter_9_example_3.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"b = 10;// inches\n", +"d = 6;//inches\n", +"l = 15;// feet\n", +"A = 11.77;// in^2\n", +"I_xx = 204.80;// in^4\n", +"I_yy = 21.76;// in^4\n", +"f_c = 21;// tons/in^2\n", +"a = 1/7500;\n", +"n = 3;//factor of safety\n", +"k = sqrt(I_yy/A);// radius of gyration\n", +"P = f_c*A/(1+(a/2)*(l*12/k)^2);// tons\n", +"P_s = P/n;// safe load\n", +"printf('The safe axial load = %.3f tons',P_s);\n", +"\n", +"//there is a minute calculation error in the answer given in text book" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.4: Chapter_9_example_4.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"l = 16;// feet\n", +"F = 30;// tons\n", +"n = 8;// factor of safety\n", +"k = 0.8;//k = d/D\n", +"f_c = 36;// tons/in^2\n", +"a = 1/1600;\n", +"r = 0.25*%pi*(1-k^2);//r = A/D^2\n", +"P = n*F;// tons\n", +"D1 = sqrt(P/(f_c*r*2) +sqrt((P/(f_c*r))*((a/4)*(l*12)^2)/((1+k^2)/16) + (P/(f_c*r*2))^2));// inches\n", +"D = round(D1);// inches\n", +"d = k*D;// inches\n", +"t = (D-d)/2;// inches\n", +"printf('The internal diameter d = %.1f inches',d);\n", +"printf('\n The thickness of the metal will be %.2f inches',t);\n", +"// the answer is correct only, but it is approximated in the text book" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.5: Chapter_9_example_5.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"l = 5;// feet\n", +"b = 5/2;// inches\n", +"d = 5/2;// inches\n", +"h = 1/4;// inches\n", +"n = 3;// factor of safety\n", +"A = 1.19;// in^2\n", +"k = 0.49;// minimum radius of gyration\n", +"f_c = 21;// lb/in^2\n", +"a = 1/7500;\n", +"P = f_c*A/(1+(a/2)*((l*12)^2)/k^2);// tons\n", +"P_safe = P/n;// tons\n", +"printf('The safe axial load = %.2f tons',P_safe);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.6: Chapter_9_example_6.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"b1 = 10;// inches\n", +"d1 = 7/2;// inches\n", +"r = 9/2;// inches\n", +"b2 = 12;// inches\n", +"d2 = 1/2;// inches\n", +"l = 20;// feet\n", +"n = 4;// factor of safety\n", +"A_s = 7.19;// in^2\n", +"I_xx1 = 109.42;// in^4\n", +"I_yy1 = 7.42;// in^4\n", +"d = 0.97;// inches\n", +"f_c = 21;// lb/in^2\n", +"a = 1/7500;\n", +"A = 2*A_s + 4*b2*d2;// in^2\n", +"I_xx = 2*I_xx1 + 2*((1/12)*b2*(2*d2)^3 + b2*(r+2*d2)^2);// in^4\n", +"I_yy = 2*(1/12)*(2*d2)*b2^3 + 2*(I_yy1 + A_s*(0.5*r+d)^2);// in^4\n", +"k = sqrt(min(I_xx,I_yy)/A);// minimum radius of gyration\n", +"P = f_c*A/(1+ a*((l*12)^2/k^2));// tons\n", +"P_safe = P/n;// tons\n", +"printf('The safe axial load = %d tons',round(P_safe));" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.7: Chapter_9_example_7.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"m = 4;// no. of angles\n", +"b = 7/2;// inches\n", +"d = 7/2;// inches\n", +"h = 3/8;// inches\n", +"s = 18;// inches\n", +"l = 30;// feet\n", +"n = 3;// factor of safety\n", +"A = 2.49;// in^2\n", +"J = 1;// inches\n", +"I_xxs = 2.80;// in^4\n", +"I_yys = I_xxs;// in^4\n", +"//from the chapter V. \n", +"I = 648.64;// in^4\n", +"k = sqrt(65.2);// in^2\n", +"f_c = 21;// lb/in^2\n", +"a = 1/7500;\n", +"P = m*f_c*A/(1+a*((l*12)^2)/k^2);// tons\n", +"P_safe = P/n;// tons\n", +"printf('The safe axial load = %.1f tons',P_safe);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.8: Chapter_9_example_8.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"D = 7;// inches\n", +"t = 3/4;// inches\n", +"l = 16;// feet\n", +"P = 12;// tons\n", +"e = 3/4;// inches\n", +"E = 6000;// tons/in^2\n", +"d = D-2*t;// inches\n", +"A = 0.25*%pi*(D^2 - d^2);// in^2\n", +"I = (%pi/64)*(D^4 - d^4);// in^4\n", +"p_0 = P/A;// tons/in^2\n", +"Z = 2*I/D;// in^3\n", +"M = P*e*sec(0.25*l*12*sqrt(P/(E*I)));// ton-inches\n", +"p_b = M/Z;// tons/in^2\n", +"p_max = p_0+p_b;// tons/in^2\n", +"p_min = p_0-p_b;// tons/in^2\n", +"//if tension is just on the point being induced in the section, p_b = p_0\n", +"e = p_0*t*Z/M;// inches\n", +"printf('Stress intensities, p_max = %.3f tons/in^2.,compressive\n p_min = %.3f tons/in^2., compressive',p_max,p_min);\n", +"printf('\n Maximum possible eccentricity, e = %.2f inches',e);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.9: Chapter_9_example_9.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear;\n", +"clc;\n", +"P = 80;// tons\n", +"p_max = 5;// tons/in^2\n", +"E = 13000;// tons/in^2\n", +"A = 38.38;// in^2\n", +"I_yy = 451.94;// in^4\n", +"y_c = 6;// inches\n", +"l = 20;// inches\n", +"k = sqrt(I_yy/A);// inches\n", +"Z_yy = I_yy/y_c;// in^3\n", +"p_0 = P/A;// tons/in^2\n", +"p_b = p_max-p_0;// tons/in^2\n", +"M_max = p_b*Z_yy;// ton-inches\n", +"e = M_max/(P*sec(0.5*l*12*sqrt(P/(E*I_yy))));//inches\n", +"printf('The maximum possible eccentricity, e = %.2f inches',e);" + ] + } +], +"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 +} |