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-{
- "metadata": {
- "name": ""
- },
- "nbformat": 3,
- "nbformat_minor": 0,
- "worksheets": [
- {
- "cells": [
- {
- "cell_type": "heading",
- "level": 1,
- "metadata": {},
- "source": [
- "Chapter 1: Tension Comprssion and Shear"
- ]
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 1.1, page no. 9"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\"\"\"\n",
- "Find compressive stress and strain in the post\n",
- "\"\"\"\n",
- "\n",
- "import math\n",
- "\n",
- "#initialisation\n",
- "\n",
- "d_1 = 4 # inner diameter (inch)\n",
- "d_2 = 4.5 #outer diameter (inch)\n",
- "P = 26000 # pressure in pound\n",
- "L = 16 # Length of cylinder (inch)\n",
- "my_del = 0.012 # shortening of post (inch)\n",
- "\n",
- "#calculation\n",
- "A = (math.pi/4)*((d_2**2)-(d_1**2)) #Area (inch^2)\n",
- "s = P/A # stress\n",
- "\n",
- "print \"compressive stress in the post is \", round(s), \"psi\"\n",
- "\n",
- "e = my_del/L # strain\n",
- "\n",
- "print \"compressive strain in the post is %e\" %e"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "compressive stress in the post is 7789.0 psi\n",
- "compressive strain in the post is 7.500000e-04\n"
- ]
- }
- ],
- "prompt_number": 5
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 1.2, page no. 10"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\"\"\"\n",
- "formula for maximum stress & calculating maximum stress\n",
- "\"\"\"\n",
- "\n",
- "import math \n",
- "\n",
- "#initialisation\n",
- "W = 1500 # weight (Newton)\n",
- "d = 0.008 #diameter(meter) \n",
- "g = 77000 # Weight density of steel\n",
- "L = 40 # Length of bar (m)\n",
- "\n",
- "#calculation\n",
- "\n",
- "A = (math.pi/4)*(d**2) # Area\n",
- "s_max = (1500/A) + (g*L) # maximum stress\n",
- "\n",
- "#result\n",
- "print \"Therefore the maximum stress in the rod is \", round(s_max,1), \"Pa\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Therefore the maximum stress in the rod is 32921551.8 Pa\n"
- ]
- }
- ],
- "prompt_number": 16
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 1.3. page no. 26"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\"\"\"\n",
- "calculating change in lenght of pipe, strain in pipe, increase in diameter & increase in wall thickness\n",
- "\"\"\"\n",
- "\n",
- "import math \n",
- "\n",
- "#initialisation\n",
- "d1 = 4.5 # diameter in inch\n",
- "d2 = 6 # diameter in inch\n",
- "A = (math.pi/4)*((d2**2)-(d1**2)) # Area\n",
- "P = 140 # pressure in K\n",
- "s = -P/A # stress (compression)\n",
- "E = 30000 # young's modulus in Ksi\n",
- "e = s/E # strain\n",
- "\n",
- "#calculation\n",
- "\n",
- "# Part (a)\n",
- "my_del = e*4*12 # del = e*L \n",
- "print \"Change in length of the pipe is\", round(my_del,3), \"inch\"\n",
- "\n",
- "# Part (b)\n",
- "v = 0.30 # Poissio's ratio\n",
- "e_ = -(v*e)\n",
- "print \"Lateral strain in the pipe is %e\" %e_\n",
- "\n",
- "# Part (c)\n",
- "del_d2 = e_*d2 \n",
- "del_d1 = e_*d1\n",
- "print \"Increase in the inner diameter is \", round(del_d1,6), \"inch\"\n",
- "\n",
- "# Part (d)\n",
- "t = 0.75\n",
- "del_t = e_*t\n",
- "print \"Increase in the wall thicness is %f\" %del_t, \"inch\"\n",
- "del_t1 = (del_d2-del_d1)/2 \n",
- "print \"del_t1 = del_t\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Change in length of the pipe is -0.018 inch\n",
- "Lateral strain in the pipe is 1.131768e-04\n",
- "Increase in the inner diameter is 0.000509 inch\n",
- "Increase in the wall thicness is 0.000085 inch\n",
- "del_t1 = del_t\n"
- ]
- }
- ],
- "prompt_number": 7
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 1.4, page no. 35"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\"\"\"\n",
- "calculate average shear stress and compressive stress\n",
- "\"\"\"\n",
- "\n",
- "import math \n",
- "\n",
- "#initialisation\n",
- "d = 0.02 # diameter in m\n",
- "t = 0.008 # thickness in m\n",
- "A = math.pi*d*t # shear area\n",
- "P = 110000 # prassure in Newton\n",
- "\n",
- "#calculation\n",
- "A1 = (math.pi/4)*(d**2) # Punch area\n",
- "t_aver = P/A # Average shear stress \n",
- "\n",
- "\n",
- "print \"Average shear stress in the plate is \", t_aver, \"Pa\"\n",
- "s_c = P/A1 # compressive stress\n",
- "print \"Average compressive stress in the plate is \", s_c, \"Pa\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Average shear stress in the plate is 218838046.751 Pa\n",
- "Average compressive stress in the plate is 350140874.802 Pa\n"
- ]
- }
- ],
- "prompt_number": 37
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Eample 1.5, page no. 36"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\"\"\"\n",
- "calculate bearing stress, shear stress in pin,\n",
- "bearing stress between pin and gussets,\n",
- "shear stress in anchor bolts\n",
- "\"\"\"\n",
- "\n",
- "import math \n",
- "\n",
- "#initialisation\n",
- "\n",
- "P = 12.0 # Pressure in K\n",
- "t = 0.375 # thickness of wall in inch\n",
- "theta = 40.0 # angle in degree\n",
- "d_pin = 0.75 # diameter of pin in inch\n",
- "t_G = 0.625 # thickness of gusset in inch\n",
- "t_B = 0.375 #thickness of base plate in inch\n",
- "d_b = 0.50 # diameter of bolt in inch\n",
- "\n",
- "#calculation\n",
- "\n",
- "#Part (a)\n",
- "s_b1 = P/(2*t*d_pin) # bearing stress\n",
- "print \"Bearing stress between strut and pin\", round(s_b1,1), \"ksi\"\n",
- "\n",
- "#Part (b)\n",
- "t_pin = (4*P)/(2*math.pi*(d_pin**2)) # average shear stress in the \n",
- "print \"Shear stress in pin is \", round(t_pin,1), \"ksi\"\n",
- "\n",
- "# Part (c)\n",
- "s_b2 = P/(2*t_G*d_pin) # bearing stress between pin and gusset\n",
- "print \"Bearing stress between pin and gussets is\", s_b2, \"ksi\"\n",
- "\n",
- "# Part (d)\n",
- "s_b3 = (P*math.cos(math.radians(40))/(4*t_B*d_b)) # bearing stress between anchor bolt and base plate\n",
- "print \"Bearing stress between anchor bolts & base plate\", round(s_b3,1), \"ksi\"\n",
- "\n",
- "# Part (e)\n",
- "t_bolt = (4*math.cos(math.radians(40))*P)/(4*math.pi*(d_b**2)) # shear stress in anchor bolt\n",
- "print \"Shear stress in anchor bolts is\", round(t_bolt,1), \"ksi\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Bearing stress between strut and pin 21.3 ksi\n",
- "Shear stress in pin is 13.6 ksi\n",
- "Bearing stress between pin and gussets is 12.8 ksi\n",
- "Bearing stress between anchor bolts & base plate 12.3 ksi\n",
- "Shear stress in anchor bolts is 11.7 ksi\n"
- ]
- }
- ],
- "prompt_number": 39
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 1.7, page no. 42"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\"\"\"\n",
- "determine stress at various parts\n",
- "\"\"\"\n",
- "\n",
- "import math\n",
- "\n",
- "#initialisation\n",
- "b1 = 1.5 # width of recmath.tangular crosssection in inch\n",
- "t = 0.5 # thickness of recmath.tangular crosssection in inch\n",
- "b2 = 3.0 # width of enlarged recmath.tangular crosssection in inch\n",
- "d = 1.0 # diameter in inch\n",
- "\n",
- "#calculation\n",
- "\n",
- "# Part (a)\n",
- "s_1 = 16000 # maximum allowable tensile stress in Psi\n",
- "P_1 = s_1*t*b1 \n",
- "print \"The allowable load P1 is\", P_1, \"lb\"\n",
- "\n",
- "# Part (b)\n",
- "s_2 = 11000 # maximum allowable tensile stress in Psi\n",
- "P_2 = s_2*t*(b2-d) \n",
- "print \"allowable load P2 at this section is\", P_2, \"lb\"\n",
- "\n",
- "#Part (c)\n",
- "s_3 = 26000 # maximum allowable tensile stress in Psi\n",
- "P_3 = s_3*t*d \n",
- "print \"The allowable load based upon bearing between the hanger and the bolt is\", P_3, \"lb\"\n",
- "\n",
- "# Part (d)\n",
- "s_4 = 6500 # maximum allowable tensile stress in Psi\n",
- "P_4 = (math.pi/4)*(d**2)*2*s_4 \n",
- "print \"the allowable load P4 based upon shear in the bolt is\", round(P_4), \"lb\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The allowable load P1 is 12000.0 lb\n",
- "allowable load P2 at this section is 11000.0 lb\n",
- "The allowable load based upon bearing between the hanger and the bolt is 13000.0 lb\n",
- "the allowable load P4 based upon shear in the bolt is 10210.0 lb\n"
- ]
- }
- ],
- "prompt_number": 42
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 1.8, page no. 46"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\"\"\"\n",
- "calculating the cross sectional area \n",
- "\"\"\"\n",
- "\n",
- "import math \n",
- "\n",
- "#initialisation\n",
- "R_ah = (2700*0.8 + 2700*2.6)/2 # Horizontal component at A in N\n",
- "R_ch = R_ah # Horizontal component at C in N\n",
- "R_cv = (2700*2.2 + 2700*0.4)/3 # vertical component at C in N\n",
- "R_av = 2700 + 2700 - R_cv # vertical component at A in N\n",
- "R_a = math.sqrt((R_ah**2)+(R_av**2))\n",
- "R_c = math.sqrt((R_ch**2)+(R_cv**2))\n",
- "Fab = R_a # Tensile force in bar AB\n",
- "Vc = R_c # Shear force acting on the pin at C\n",
- "s_allow = 125000000 # allowable stress in tension \n",
- "t_allow = 45000000 # allowable stress in shear\n",
- "\n",
- "#calculation\n",
- "Aab = Fab / s_allow # required area of bar \n",
- "Apin = Vc / (2*t_allow) # required area of pin\n",
- "\n",
- "\n",
- "print \"Required area of bar is %f\" %Apin, \"m^2\"\n",
- "d = math.sqrt((4*Apin)/math.pi) # diameter in meter\n",
- "print \"Required diameter of pin is %f\" %d, \"m\""
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Required area of bar is 0.000057 m^2\n",
- "Required diameter of pin is 0.008537 m\n"
- ]
- }
- ],
- "prompt_number": 9
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [],
- "language": "python",
- "metadata": {},
- "outputs": []
- }
- ],
- "metadata": {}
- }
- ]
-} \ No newline at end of file
generated by cgit (git 2.34.1) at 2024-12-20 11:55:43 +0000