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diff --git a/Strength_of__Materials_by_Dr.R.K.Bansal/chapter4.ipynb b/Strength_of__Materials_by_Dr.R.K.Bansal/chapter4.ipynb new file mode 100644 index 00000000..1bf2c1be --- /dev/null +++ b/Strength_of__Materials_by_Dr.R.K.Bansal/chapter4.ipynb @@ -0,0 +1,675 @@ +{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:08a19915ea28ff1c8eacb09b86820e50e5a6bce0905af69520d3a90c0261cd74"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 4:Strain Energy and Impact Loading"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Problem 4.1,page no.145"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Given\n",
+ "#Variable declaration\n",
+ "P=60*10**3 #Load in N\n",
+ "d=4*10 #diameter in mm\n",
+ "L=5*10**3 #Length of rod in mm\n",
+ "E=2e5 #Young's Modulus in N/sq.mm\n",
+ "\n",
+ "\n",
+ "#Calculation\n",
+ "A=(math.pi/4)*d**2 #Area in sq.mm\n",
+ "V=int(A*L) #Volume of rod in cubic.mm\n",
+ "#case (ii):stress in the rod\n",
+ "sigma=round(P/A,3) #stress in N/sq.mm\n",
+ "\n",
+ "#case (i):stretch in the rod\n",
+ "x=round((sigma/E)*L,2) #stretch or extension in mm\n",
+ "\n",
+ "#case (iii):strain energy absorbed by the rod\n",
+ "U=round((sigma**2/(2*E)*V),-1)*1e-3 #strain energy absorbed by the rod in Nm\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print \"stress in the rod =\",sigma,\"N/mm^2\"\n",
+ "print \"stretch in the rod =\",x,\"mm\"\n",
+ "print \"strain energy absorbed by the rod =\",U,\"N-m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "stress in the rod = 47.746 N/mm^2\n",
+ "stretch in the rod = 1.19 mm\n",
+ "strain energy absorbed by the rod = 35.81 N-m\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Problem 4.3,page no.146"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Given\n",
+ "#Variable declaration\n",
+ "A=10*10**2 #Area of bar in sq.mm\n",
+ "L=3*10**3 #Length of bar in mm\n",
+ "x=1.5 #Extension due to suddenly applied load in mm\n",
+ "E=2e5 #Young's Modulus in N/sq.mm\n",
+ "\n",
+ "#Calculation\n",
+ "sigma=int(x*E/L) #Instantaneous stress due to sudden load in N/sq.mm \n",
+ "P=int((sigma*A)/2*1e-3) #Suddenly applied load in kN\n",
+ "\n",
+ "#Result\n",
+ "print \"Instantaneous stress produced by a sudden load =\",sigma,\"N/mm^2\"\n",
+ "print \"Suddenly applied load =\",P,\"kN\" "
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Instantaneous stress produced by a sudden load = 100 N/mm^2\n",
+ "Suddenly applied load = 50 kN\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Problem 4.4,page no.147"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Given\n",
+ "#Variable declaration\n",
+ "L=2*10**3 #Length in mm\n",
+ "d=50 #Diameter in mm\n",
+ "P=100*10**3 #Suddenly applied load in N\n",
+ "E=200e3 #Young's Modulus in N/sq.mm\n",
+ "\n",
+ "#Calculation\n",
+ "A=(math.pi/4)*d**2 #Area in sq.mm\n",
+ "sigma=round(2*P/A,2) #Instantaneous stress induced in N/sq.mm\n",
+ "dL=(sigma*L)/E #Elongation in mm\n",
+ "\n",
+ "#Result\n",
+ "print \"Instantaneous stress induced =\",sigma,\"N/mm^2\"\n",
+ "print \"Instantaneous elongation =\",dL,\"mm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Instantaneous stress induced = 101.86 N/mm^2\n",
+ "Instantaneous elongation = 1.0186 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Problem 4.5,page no.147"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Given\n",
+ "#Variable declaration\n",
+ "A=700 #Area in sq.mm\n",
+ "L=1.5*10**3 #Length of a metal bar in mm\n",
+ "sigma=160 #Stress at elastic limit in N/sq.mm\n",
+ "E=2e5 #Young's Modulus in N/sq.mm\n",
+ "\n",
+ "\n",
+ "#Calculation\n",
+ "V=A*L #Volume of bar in sq.mm\n",
+ "Pr=(sigma**2/(2*E)*V)*1e-3 #Proof resilience in N-m\n",
+ "P=int(sigma*A/2*1e-3) #Suddenly applied load in kN\n",
+ "P1=int(sigma*A*1e-3) #gradually applied load in kN\n",
+ "\n",
+ "#Result\n",
+ "print \"Proof resilience =\",Pr,\"N-m\"\n",
+ "print \"Suddenly applied load =\",P,\"kN\"\n",
+ "print \"Gradually applied load =\",P1,\"kN\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Proof resilience = 67.2 N-m\n",
+ "Suddenly applied load = 56 kN\n",
+ "Gradually applied load = 112 kN\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Problem 4.9,page no.154"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Given\n",
+ "#Variable declaration\n",
+ "P=10*10**3 #Falling weight in N\n",
+ "h=30 #Falling height in mm\n",
+ "L=4*10**3 #Length of bar in mm\n",
+ "A=1000 #Area of bar in sq.m\n",
+ "E=2.1e5 #Young's modulus in N/sq.mm\n",
+ "\n",
+ "#Calculation\n",
+ "sigma=float(str((P/A)*(1+(math.sqrt(1+((2*E*A*h)/(P*L))))))[:5])\n",
+ "delL=round(sigma*L/E,3)\n",
+ "\n",
+ "#Result \n",
+ "print \"Instantaneous elongation due to falling weight =\",delL,\"mm\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Instantaneous elongation due to falling weight = 3.575 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Problem 4.10,page no.155"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#Given\n",
+ "#Variable declaration\n",
+ "P=100 #Impact load in N\n",
+ "h=2*10 #Height in mm\n",
+ "L=1.5*1000 #Length of bar in mm\n",
+ "A=1.5*100 #Area of bar in sq.mm\n",
+ "E=2e5 #Modulus of elasticity in N/sq.mm\n",
+ "\n",
+ "#Calculation\n",
+ "V=A*L #Volume in mm^3\n",
+ "#case(i):Maximum instantaneous stress induced in the vertical bar\n",
+ "sigma=round((P/A)*(1+(math.sqrt(1+((2*E*A*h)/(P*L))))),2)\n",
+ "#case(ii):Maximum instantaneous elongation\n",
+ "delL=round(sigma*L/E,3)\n",
+ "#case(iii):Strain energy stored in the vertical rod\n",
+ "U=round(sigma**2/(2*E)*V*1e-3,3)\n",
+ "\n",
+ "#Result\n",
+ "print \"NOTE:The answer in the book for instantaneous stress is incorrect.The correct answer is,\"\n",
+ "print \"Maximum instantaneous stress =\",sigma,\"N/mm^2\"\n",
+ "print \"Maximum instantaneous elongation =\",delL,\"mm\"\n",
+ "print \"Strain energy =\",U,\"N-m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "NOTE:The answer in the book for instantaneous stress is incorrect.The correct answer is,\n",
+ "Maximum instantaneous stress = 60.3 N/mm^2\n",
+ "Maximum instantaneous elongation = 0.452 mm\n",
+ "Strain energy = 2.045 N-m\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Problem 4.11,page no.155"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#Given\n",
+ "#Variable declaration\n",
+ "delL=2.1 #Instantaneous extension in mm\n",
+ "L=3*10**3 #Length of bar in mm\n",
+ "A=5*100 #Area of bar in mm\n",
+ "h=4*10 #Height in mm\n",
+ "E=2e5 #Modulus of elasticity in N/sq.mm\n",
+ "\n",
+ "#Calculation\n",
+ "V=A*L #Volume of bar in mm^3\n",
+ "\n",
+ "#case(i):Instantaneous stress induced in the vertical bar\n",
+ "sigma=int(E*delL/L) \n",
+ "\n",
+ "#case(ii):Unknown weight\n",
+ "P=round(((sigma**2)/(2*E)*V)/(h+delL),1) \n",
+ "\n",
+ "#Result\n",
+ "print\"Instantaneous stress =\",sigma,\"N/mm^2\"\n",
+ "print\"Unknown weight =\",P,\"N\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Instantaneous stress = 140 N/mm^2\n",
+ "Unknown weight = 1745.8 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Problem 4.13,page no.157"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#Given\n",
+ "#Variable declaration\n",
+ "d=12 #Diameter of bar in mm \n",
+ "delL=3 #Increase in length in mm\n",
+ "W=8000 #Steady load in N\n",
+ "P=800 #Falling weight in N\n",
+ "h=8*10 #Vertical distance in mm\n",
+ "E=2e5 #Young's modulus in N/sq.mm\n",
+ "\n",
+ "#Calculation\n",
+ "A=round((math.pi/4)*d**2,1) #Area of bar in sq.mm\n",
+ "L=round(E*A*delL/W,1) #Length of the bar in mm\n",
+ "sigma=round(round(P/A,4)*float(str(1+(math.sqrt(1+round((2*E*A*h)/(P*L),2))))[:7]),4) \n",
+ "sigma=float(str(sigma)[:7]) #Stress produced by the falling weight in N/sq.mm\n",
+ "\n",
+ "#Result\n",
+ "print \"Stress produced by the falling weight =\",sigma,\"N/mm^2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Stress produced by the falling weight = 170.578 N/mm^2\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Problem 4.14,page no.158"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#Given\n",
+ "#Variable declaration\n",
+ "d=12.5 #Diameter of the rod in mm\n",
+ "delL=3.2 #Increase in length in mm\n",
+ "W=10*1000 #Steady load in N\n",
+ "P=700 #Falling load in N\n",
+ "h=75 #Falling height in mm\n",
+ "E=2.1e5 #Young's modulus in N/sq.mm\n",
+ "\n",
+ "#Calculation\n",
+ "A=round((math.pi/4)*d**2,2) #Area of rod in sq.mm \n",
+ "L=round(E*A*delL/W,1) #Length of the rod in mm\n",
+ "sigma=round((P/A)*(1+(math.sqrt(1+((2*E*A*h)/(P*L))))),2) #Stress produced by the falling weight in N/mm^2\n",
+ "\n",
+ "#Result\n",
+ "print \"NOTE:The given answer for stress is wrong.The correct answer is,\"\n",
+ "print \"Stress = %.2f N/mm^2\"%sigma"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "NOTE:The given answer for stress is wrong.The correct answer is,\n",
+ "Stress = 153.42 N/mm^2\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Problem 4.15,page no.159"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Given\n",
+ "#Variable declaration\n",
+ "L=1.82*1000 #Length of rod in mm\n",
+ "h1=30 #Height through which load falls in mm\n",
+ "h2=47.5 #Fallen height in mm\n",
+ "sigma=157 #Maximum stress induced in N/sq.mm\n",
+ "E=2.1e5 #Young's modulus in N/sq.mm\n",
+ "\n",
+ "#Calculation\n",
+ "U=sigma**2/(2*E) #Strain energy stored in the rod in N-m\n",
+ "delL=sigma*L/E #Extension of the rod in mm\n",
+ "Tot_dist=h1+delL #Total distance in mm\n",
+ "\n",
+ "#case(i):Stress induced in the rod if the load is applied gradually\n",
+ "sigma1=round((U/Tot_dist)*L,1)\n",
+ "\n",
+ "#case(ii):Maximum stress if the load had fallen from a height of 47.5 mm\n",
+ "sigma2=round((sigma1)*(1+(math.sqrt(1+((2*E*h2)/(sigma1*L))))),2)\n",
+ "\n",
+ "#Result\n",
+ "print \"Stress induced in the rod = %.1f N/mm^2\"%sigma1\n",
+ "print \"NOTE:The given answer for stress(2nd case) in the book is wrong.The correct answer is,\"\n",
+ "print \"Maximum stress if the load has fallen = %.2f N/mm^2\"%sigma2"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Stress induced in the rod = 3.4 N/mm^2\n",
+ "NOTE:The given answer for stress(2nd case) in the book is wrong.The correct answer is,\n",
+ "Maximum stress if the load has fallen = 196.48 N/mm^2\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Problem 4.17,page no.162"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Given\n",
+ "#Variable declaration\n",
+ "L=4*10**3 #Length of bar in mm\n",
+ "A=2000 #Area of bar in sq.mm\n",
+ "P1=3000 #Falling weight in N(for 1st case)\n",
+ "h1=20*10 #Height in mm(for 1st case)\n",
+ "P2=30*1000 #Falling weight in N(for 2nd case)\n",
+ "h2=2*10 #Height in mm(for 2nd case)\n",
+ "E=2e5 #Young's modulus in N/sq.mm\n",
+ "\n",
+ "#Calculation\n",
+ "V=A*L #Volume of bar in mm^3\n",
+ "\n",
+ "#case(i):Maximum stress when a 3000N weight falls through a height of 20cm\n",
+ "sigma1=round(((math.sqrt((2*E*P1*h1)/(A*L)))),1)\n",
+ "\n",
+ "#case(ii):Maximum stress when a 30kN weight falls through a height of 2cm\n",
+ "sigma2=round((P2/A)*(1+(math.sqrt(1+((2*E*A*h2)/(P2*L))))),2)\n",
+ "\n",
+ "#Result\n",
+ "print\"Maximum stress induced(when a weight of 3000N falls through a height of 20cm)=\",sigma1,\"N/mm^2\"\n",
+ "print\"Maximum stress induced(when a weight of 30kN falls through a height of 2cm)=\",sigma2,\"N/mm^2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Maximum stress induced(when a weight of 3000N falls through a height of 20cm)= 173.2 N/mm^2\n",
+ "Maximum stress induced(when a weight of 30kN falls through a height of 2cm)= 188.85 N/mm^2\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Problem 4.18,page no.163"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from __future__ import division\n",
+ "import math\n",
+ "\n",
+ "#Given \n",
+ "#Variable declaration\n",
+ "A=6.25*100 #Area in sq.mm\n",
+ "W=10*10**3 #Load in N\n",
+ "V=(40/60) #Velocity in m/s\n",
+ "L=10000 #Length of chain unwound in mm\n",
+ "E=2.1e5 #Young's modulus in N/sq.mm\n",
+ "g=9.81 #acceleration due to gravity\n",
+ "\n",
+ "#Calculation\n",
+ "K_E=round(((W/g)*(V**2))/2,1)*1e3 #K.E of the crane in N mm\n",
+ "sigma=round(math.sqrt(K_E*E*2/(A*L)),2) #Stress induced in the chain in N/sq.mm\n",
+ "\n",
+ "#Result\n",
+ "print \"Stress induced in the chain due to sudden stoppage =\",sigma,\"N/mm^2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Stress induced in the chain due to sudden stoppage = 123.37 N/mm^2\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Problem 4.19,page no.164"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Given\n",
+ "#Variable declaration\n",
+ "W=60*10**3 #Weight in N\n",
+ "V=1 #Velocity in m/s\n",
+ "L=15*10**3 #Free length in mm\n",
+ "A=25*100 #Area in sq.mm\n",
+ "E=2e5 #Young's modulus in N/sq.mm\n",
+ "g=9.81 #acceleration due to gravity\n",
+ "\n",
+ "#Calculation\n",
+ "K_E=((W/g)*(V**2))/2*1e3 #Kinetic Energy of the cage in N mm\n",
+ "sigma=round(math.sqrt(K_E*E*2/(A*L)),2) #Maximum stress in N/sq.mm\n",
+ "\n",
+ "#Result\n",
+ "print\"Maximum stress produced in the rope =\",sigma,\"N/mm^2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Maximum stress produced in the rope = 180.61 N/mm^2\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Problem 4.20,page no.166"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Given \n",
+ "#Variable declaration\n",
+ "tau=50 #Shear stress in N/sq.mm\n",
+ "C=8e4 #Modulus of rigidity in N/sq.mm\n",
+ "\n",
+ "#Calculation\n",
+ "ste=(tau**2)/(2*C) #Strain energy per unit volume in N/sq.mm\n",
+ "\n",
+ "#Result\n",
+ "print\"Strain energy per unit volume =\",ste,\"N/mm^2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Strain energy per unit volume = 0.015625 N/mm^2\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [],
+ "language": "python",
+ "metadata": {},
+ "outputs": []
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file |