{
"cells": [
 {
		   "cell_type": "markdown",
	   "metadata": {},
	   "source": [
       "# Chapter 14: Energy Methods"
	   ]
	},
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 14.10: EM10.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clear all; clc;\n",
"\n",
"disp('Scilab Code Ex 14.10 : ')\n",
"\n",
"//Given:\n",
"m = 80*1000; //kg\n",
"v = 0.2; //m/s\n",
"l_ac = 1.5; //m\n",
"E = 200*10^9; //N/m^2\n",
"w = 0.2; //m\n",
"I = (1/12)*(w^4);\n",
"l_ab = 1000; //mm\n",
"\n",
"//Calculations:\n",
"del_Amax = sqrt((m*v^2*l_ac^3)/(3*E*I));\n",
"\n",
"P_max = (3*E*I*del_Amax)/(l_ac^3);\n",
"theta_A = (P_max*l_ac^2)/(2*E*I);\n",
"del_Amax = del_Amax*1000;\n",
"del_Bmax = del_Amax + (theta_A*l_ab);\n",
"\n",
"\n",
"//Display:\n",
"\n",
"    printf('\n\nThe maximum horizontal displacement of the post at B due to impact   = %1.1f mm',del_Bmax);\n",
"    \n",
"\n",
"//---------------------------------------------------------------------------END------------------------------------------------------------------------------\n",
"\n",
""
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 14.11: EM11.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clear all; clc;\n",
"\n",
"disp('Scilab Code Ex 14.11 : ')\n",
"\n",
"//Given:\n",
"A = 400*10^-6; //m^2\n",
"E = 200*10^6; //kN/m^2\n",
"P = 100; //kN\n",
"\n",
"//Virtual Work Equation:\n",
"\n",
"n = [0 0 -1.414 1];\n",
"N = [-100 141.4 -141.4 200];\n",
"L = [4 2.828 2.828 2];\n",
"del_cv = 0;\n",
"\n",
"for i=1:4\n",
"    del_cv = del_cv + (n(i)*N(i)*L(i))/(A*E);\n",
"end\n",
"\n",
"del_cv = del_cv*1000;\n",
"\n",
"//Display:\n",
"\n",
"    printf('\n\nThe vertical displacement of joint C of the steel truss   = %1.1f mm',del_cv);\n",
"    \n",
"\n",
"//---------------------------------------------------------------------------END------------------------------------------------------------------------------\n",
"\n",
""
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 14.12: EM12.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clear all; clc;\n",
"\n",
"disp('Scilab Code Ex 14.12 : ')\n",
"\n",
"//Given:\n",
"A = 300*10^-6; //m^2\n",
"E = 210*10^6; //kN/m^2\n",
"P = 60; //kN\n",
"F_ac = 1.25; //kN\n",
"\n",
"//Part a:\n",
"\n",
"//Virtual Work Equation:\n",
"\n",
"n = [0 1.25 0 -0.75];\n",
"N = [0 75 -60 -45];\n",
"L = [1.5 2.5 2 1.5];\n",
"del_ch = 0;\n",
"\n",
"for i=1:4\n",
"    del_ch = del_ch + (n(i)*N(i)*L(i))/(A*E);\n",
"end\n",
"\n",
"del_chA = del_ch*1000;\n",
"\n",
"//Part b:\n",
"\n",
"del_L = -6; //mm\n",
"del_chB = F_ac*del_L;\n",
"\n",
"if(del_chB<0)\n",
"    \n",
"\n",
"//Display:\n",
"   \n",
"    printf('\n\nThe horizontal displacement of joint C if a force is applied to B   = %1.3f mm',del_chA);\n",
"    printf('\nThe horizontal displacement of joint C if AC is fabricated short    = %1.1f mm',del_chB);\n",
"end\n",
"\n",
"    \n",
"\n",
"//---------------------------------------------------------------------------END------------------------------------------------------------------------------\n",
""
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 14.13: EM13.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clear all; clc;\n",
"\n",
"disp('Scilab Code Ex 14.13 : ')\n",
"\n",
"//Given:\n",
"del_T = 60; //degree celcius\n",
"alpha = 12*10^-6; //per degree celcius\n",
"E = 200*10^6; //kN/m^2\n",
"A = 250*10^-6; //m^2\n",
"L = 4; //m\n",
"\n",
"//Virtual Work Equation:\n",
"n = 1.155; //kN\n",
"N = -12; //kN\n",
"\n",
"del_bh = (n*N*L)/(A*E) + (n*alpha*del_T*L);\n",
"del_bh = del_bh*1000;\n",
"\n",
"//Display:\n",
"\n",
"printf('\n\nThe horizontal displacement of joint B of the truss   = %1.2f mm',del_bh);\n",
"\n",
"//---------------------------------------------------------------------END--------------------------------------------------------------------------------------------"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 14.16: EM16.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clear all; clc;\n",
"\n",
"disp('Scilab Code Ex 14.16 : ')\n",
"\n",
"//Given:\n",
"I = 175.8*10^-6; //m^4\n",
"E = 200*10^6; //kN/m^2\n",
"Ra = 1;//kN\n",
"l_ab = 3; //m\n",
"l_bc = 6; //m\n",
"\n",
"\n",
"//Virtual Work Equation:\n",
"m1 = -1; //*x1\n",
"M1 = -2.5; //*x1^3\n",
"m2 = -0.5; //*x2\n",
"\n",
"x10 = 0;\n",
"x11 = l_ab;\n",
"I1 = integrate('m1*M1*(x1^4)','x1',x10,x11);\n",
"\n",
"x20 = 0;\n",
"x21 = l_bc;\n",
"I2 = integrate('m2*123.75*(x2^2)','x2',x20,x21);\n",
"\n",
"x20 = 0;\n",
"x21 = l_bc;\n",
"I3 = integrate(' -m2*22.5*(x2^3)','x2',x20,x21);\n",
"\n",
"In = I1 + I2 + I3;\n",
"del_A = (In)/(E*I);\n",
"del_A = del_A*1000;\n",
"\n",
"\n",
"//Display:\n",
"\n",
"    printf('\n\nThe displacement of point A of the steel beam   = %1.1f mm',del_A);\n",
"    \n",
"//---------------------------------------------------------------------------END------------------------------------------------------------------------------\n",
"\n",
""
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 14.17: EM17.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clear all; clc;\n",
"\n",
"disp('Scilab Code Ex 14.17 : ')\n",
"\n",
"//Given:\n",
"E = 210*10^3; //N/mm^2\n",
"P = 40*10^3;//N\n",
"A_ab = 1250; //mm^2\n",
"A_ac = 625; //mm^2\n",
"A_cd = 1250; //mm^2\n",
"A_bc = 625; //mm^2\n",
"\n",
"N_by_P = [0 0 1.67 -1.33];\n",
"L = [4000 3000 5000 4000];\n",
"A = [A_ab A_bc A_ac A_cd];\n",
"N = zeros(4);\n",
"sum = 0;\n",
"\n",
"\n",
"for i =1:4\n",
"    N(i) = N_by_P(i)*P;\n",
"    num(i) = N(i)*N_by_P(i)*L(i);\n",
"   \n",
"end\n",
"\n",
"for i = 1:4\n",
"    sum = sum + (num(i)/(A(i)*E)); //By Castigliano's Second theorem.\n",
"end\n",
"\n",
"del_ch = sum;\n",
"\n",
"//Display:\n",
"    printf('\n\nThe horizontal displacement of joint C of the steel truss   = %1.2f mm',sum);\n",
"    \n",
"//---------------------------------------------------------------------------END------------------------------------------------------------------------------\n",
"\n",
""
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 14.18: EM18.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clear all; clc;\n",
"\n",
"disp('Scilab Code Ex 14.18 : ')\n",
"\n",
"//Given:\n",
"E = 200*10^6; //kN/m^2\n",
"P = 0;//N\n",
"A = 400*10^-6; //m^2\n",
"\n",
"N_by_P = [0 0 -1.414 1];\n",
"L = [4 2.828 2.828 2];\n",
"N = [-100 141.4 -141.4 200];\n",
"sum = 0;\n",
"\n",
"\n",
"for i =1:4\n",
"    num(i) = N(i)*N_by_P(i)*L(i); \n",
"end\n",
"\n",
"for i = 1:4\n",
"    sum = sum + (num(i)/(A*E)); //By Castigliano's Second theorem.\n",
"end\n",
"\n",
"del_ch = sum*1000;\n",
"\n",
"//Display:\n",
"  printf('\n\nThe vertical displacement of joint C of the steel truss   = %1.1f mm',del_ch);\n",
"    \n",
"//---------------------------------------------------------------------------END------------------------------------------------------------------------------\n",
"\n",
""
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 14.1: EM1.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clear all; clc;\n",
"\n",
"disp('Scilab Code Ex 14.1 : ')\n",
"\n",
"//Given:\n",
"sigma_y = 310; //N/mm^2\n",
"db =18; //mm\n",
"rb = db/2;\n",
"Ab = %pi*(rb^2);\n",
"E = 210*10^3; //N/mm^2\n",
"da1 = 20; //mm\n",
"ra1 = da1/2;\n",
"Aa1 = %pi*(ra1^2);\n",
"La1 = 50;//mm\n",
"La2= 6; //mm\n",
"da2 =18; //mm\n",
"ra2 = da2/2;\n",
"Aa2 = %pi*(ra2^2);\n",
"Lb = 56; //mm\n",
"\n",
"\n",
"//Bolt A:\n",
"P_max = sigma_y*Ab;\n",
"Uia = (P_max^2/(2*E))*(La1/Aa1 + La2/Aa2); //Ui = (N^2L)/(2AE)\n",
"Uia = Uia/1000;\n",
"\n",
"//Bolt B:\n",
"Uib = (P_max^2/(2*E))*(Lb/Ab);\n",
"Uib = Uib/1000;\n",
"\n",
"//Display:\n",
"    printf('\n\nThe greatest amount of strain energy absorbed by bolt A    = %1.3f J',Uia);\n",
"    printf('\nThe greatest amount of strain energy absorbed by bolt B    = %1.3f J',Uib);\n",
"    \n",
" //-------------------------------------------------------------------------END---------------------------------------------------------------------------------"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 14.21: EM21.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clear all; clc;\n",
"\n",
"disp('Scilab Code Ex 14.21 : ')\n",
"\n",
"//Given:\n",
"I = 125*10^-6; //m^4\n",
"E = 200*10^6; //kN/m^2\n",
"Rc = 5;//kN\n",
"l_ac = 6; //m\n",
"l_cb = 4; //m\n",
"\n",
"\n",
"//Castigliano's Second Theorem:\n",
"m = 0.4/9;\n",
"\n",
"x10 = 0;\n",
"x11 = l_ac;\n",
"I11 = integrate('4.4*(x1^2)','x1',x10,x11);\n",
"I12 = integrate('-m*(x1^4)','x1',x10,x11);\n",
"I1 = I11 + I12;\n",
"\n",
"x20 = 0;\n",
"x21 = l_cb;\n",
"I21 = integrate('6*0.6*(x2^2)','x2',x20,x21);\n",
"I22 = integrate('18*0.6*(x2)','x2',x20,x21);\n",
"I2 = I21+I22;\n",
"\n",
"In = I1 + I2 ;\n",
"del_cv = (In)/(E*I);\n",
"del_cv = del_cv*1000;\n",
"\n",
"\n",
"//Display:\n",
"\n",
"    printf('\n\nThe vertical displacement of point C of the steel beam   = %1.1f mm',del_cv);\n",
"    \n",
"//---------------------------------------------------------------------------END------------------------------------------------------------------------------\n",
"\n",
""
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 14.5: EM5.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clear all; clc;\n",
"\n",
"disp('Scilab Code Ex 14.5 : ')\n",
"\n",
"//Given:\n",
"G = 75*10^9; //N/m^2\n",
"ro = 80/1000; //m\n",
"t = 15/1000; //m\n",
"ri = ro - t;\n",
"l1 = 750/1000; //m\n",
"l2 = 300/1000; //m\n",
"T1 = 40; //Nm\n",
"T2 =15; //Nm\n",
"\n",
"//Calculations:\n",
"\n",
"J = (%pi/2)*(ro^4 - ri^4);\n",
"\n",
"//Eqn 14-22\n",
"U1 = (T1^2*l1)/(2*G*J); \n",
"U2 = (T2^2*l2)/(2*G*J);\n",
"Ui = U1 + U2;\n",
"Ui = Ui*10^6; //in micro Joule\n",
"\n",
"//Display:\n",
"\n",
"   printf('\n\nThe strain energy stored in the shaft    = %1.0fX10^-6 J',Ui);\n",
"    \n",
"//-------------------------------------------------------------------------END-------------------------------------------------------------------------------------------\n",
"    "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 14.6: EM6.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clear all; clc;\n",
"\n",
"disp('Scilab Code Ex 14.6 : ')\n",
"\n",
"//Given:\n",
"l_ab = 1; //m\n",
"l_bc = 2; //m\n",
"N_ab = 11.547*1000; //N\n",
"Nb = 20*1000; //N\n",
"Nc = -23.094*1000; //N\n",
"N_ac = -20*1000; //N\n",
"A = 100/(1000^2); //mm^2\n",
"E = 200*10^9; //N/m^2\n",
"P = 20*10^3;//N\n",
"\n",
"//Eqn 14-26\n",
"P_by_2 = P/2;\n",
"l_ac = sqrt(l_bc^2 - l_ab^2);\n",
"del = 0;\n",
"\n",
"N2= [N_ab^2 Nc^2 N_ac^2];\n",
"L = [l_ab l_bc l_ac];\n",
"\n",
"for i = 1:3\n",
"    del = del + (N2(i)*L(i))/(2*A*E);\n",
"end\n",
"\n",
"del_bh = del/P_by_2;\n",
"del_bh = del_bh*1000;\n",
"\n",
"//Display:\n",
"\n",
"printf('\n\nThe horizontal displacement at point B   = %1.2fmm',del_bh);\n",
"    \n",
"//-------------------------------------------------------------------------END-------------------------------------------------------------------------------------------\n",
"    "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 14.8: EM8.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clear all; clc;\n",
"\n",
"disp('Scilab Code Ex 14.8 : ')\n",
"\n",
"//Given:\n",
"ro = 60; //mm\n",
"ri = 50; //mm\n",
"E = 70; //kN/mm^2\n",
"W = 600; //kN\n",
"L = 240; //mm\n",
"h = 0;\n",
"\n",
"//Part a:\n",
"\n",
"A = (%pi)*(ro^2 - ri^2);\n",
"del_st= (W*L)/(A*E);\n",
"\n",
"//Part b:\n",
"\n",
"del_max = del_st*(1 + sqrt(1 + 2*(h/del_st)));\n",
"\n",
"//Display:\n",
"\n",
"  printf('\n\nThe maximum displacement at the top of the pipe for gradually applied load   = %1.4f mm',del_st);\n",
"    printf('\nThe maximum displacement at the top of the pipe for suddenly applied load    = %1.4f mm',del_max);\n",
"\n",
"//---------------------------------------------------------------------------END------------------------------------------------------------------------------"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 14.9: EM9.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clear all; clc;\n",
"\n",
"disp('Scilab Code Ex 14.9 : ')\n",
"\n",
"//Given:\n",
"W = 6000; //N\n",
"h = 50; //mm\n",
"E = 210*1000; //N/mm^2\n",
"L = 5000; //mm\n",
"I = 87.3*10^6; //mm^2\n",
"\n",
"//Calculations:\n",
"\n",
"del_st = (W*L^3)/(48*E*I);\n",
"del_max = del_st*(1 + sqrt(1 + 2*(h/del_st)));\n",
"\n",
"c = 252/2;\n",
"sigma_max = (12*E*del_max*c)/(L^2);\n",
"\n",
"//Display:\n",
"\n",
"     printf('\n\nThe maximum bending stress in the steel beam   = %1.2f N/mm^2',sigma_max);\n",
"    printf('\nThe maximum deflection in the beam             = %1.3f mm',del_max);\n",
"\n",
"//---------------------------------------------------------------------------END------------------------------------------------------------------------------"
   ]
   }
],
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		   "help_links": [
			{
			 "text": "MetaKernel Magics",
			 "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
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