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diff --git a/Mechanics_of_Materials_by_Pytel_and_Kiusalaas/Chapter05_1.ipynb b/Mechanics_of_Materials_by_Pytel_and_Kiusalaas/Chapter05_1.ipynb new file mode 100755 index 00000000..dd430e74 --- /dev/null +++ b/Mechanics_of_Materials_by_Pytel_and_Kiusalaas/Chapter05_1.ipynb @@ -0,0 +1,560 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:d010557f61cf332fc38fdfe2d2ac6c4c0f491cf23de08424aa98b7c064b49092" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 05:Stresses in Beams" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.5.1, Page No:142" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "import matplotlib.pyplot as plt\n", + "\n", + "#Variable Decleration\n", + "b=0.12 #Breadth of the CS of the beam in m\n", + "h=0.2 #Depth of the CS of the beam in m\n", + "BM_max=16*10**3 #Maximum Bending Moment in N.m\n", + "c=0.1 #Distance of the centroid of the CS from the bottom fibre in m\n", + "y1=0.025 #Distance in m\n", + "BM=9.28*10**3 #Bending Moment in kN.m\n", + "\n", + "#Calculations\n", + "#Preliminary Calculations\n", + "I=b*h**3*12**-1 #Moment of Inertia in m^4\n", + "\n", + "#Part 1\n", + "sigma_max=(BM_max*c)/(I) #Maximum bending stress in the beam in Pa\n", + "\n", + "#Part 2\n", + "#Plot variables\n", + "x_plot=[0.00000001,c,c+0.000000011,c+c]\n", + "y_plot=[sigma_max,0,0,sigma_max]\n", + "\n", + "#Part 3\n", + "y=h*0.5-y1 #Distance of point at which BM is 9.8kN.m\n", + "sigma=(BM*y)/I #Bending Stress in Pa\n", + "\n", + "#Result\n", + "print \"The Bending Stress at maximum Bending Moment in the beam is\",sigma_max*10**-6,\"MPa\"\n", + "print \"The Bending Stress in part 3 is\",-sigma*10**-6,\"MPa\"\n", + "print \"The plot for stress distribution is given below\"\n", + "\n", + "plt.plot(y_plot,x_plot)\n", + "plt.ylabel(\"Distance from top fibre in m\")\n", + "plt.xlabel(\"Stress in MPa\")\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The Bending Stress at maximum Bending Moment in the beam is 20.0 MPa\n", + "The Bending Stress in part 3 is -8.7 MPa\n", + "The plot for stress distribution is given below\n" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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D0X2Oh1n/SRmM3YDXJW3OH08Cdpb02pgLdoCD0VscD7P+kDIYy8luoLQxf/wLwC2S3tfW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\nYII=\n", + "text": [ + "<matplotlib.figure.Figure at 0x10b690cd0>" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.5.2, Page No:143" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable Decleration\n", + "wf=6 #Width of the top flange in inches\n", + "df=0.8 #Depth of the top flange in inches\n", + "dw=8 #Depth of the web portion in inches\n", + "ww=0.8 #Width of the web portion in inches\n", + "Ra=1600 #Reation at point A in lb\n", + "Rb=3400 #Reaction at point B in lb\n", + "w=400 #Load on the beam in lb/ft\n", + "M_4=3200 #Moment at x=4 ft in lb.ft\n", + "M_10=4000 #Moment at x=10 ft in lb.ft\n", + "\n", + "#Calculations\n", + "#Preliminary Calculations\n", + "#Area computation\n", + "A1=dw*ww #Area of the web portion in sq.in\n", + "A2=wf*df #Area of the top flange in sq.in\n", + "y1=dw*0.5 #Centroid from the bottom of the web portion in inches\n", + "y2=dw+df*0.5 #Centroid from the bottom of the flange portion in inches\n", + "\n", + "#y_bar computation\n", + "y_bar=(A1*y1+A2*y2)/(A1+A2) #centroid of the section in inches from the bottom\n", + "\n", + "#Moment of Inertia computation\n", + "I=(ww*dw**3*12**-1)+(A1*(y1-y_bar)**2)+(wf*df**3*12**-1)+(A2*(y2-y_bar)**2) #Moment of inertia in in^4\n", + "\n", + "#Maximum Bending Moment\n", + "c_top=dw+df-y_bar #distance of top fibre in inches\n", + "c_bot=y_bar #Distance of bottom fibre in inches\n", + "\n", + "#Stress at x=4 ft\n", + "sigma_top=-(12*M_4*c_top)*I**-1 #Stress at top fibre in psi\n", + "sigma_bot=12*M_4*c_bot*I**-1 #Stress at bottom fibre in psi\n", + "\n", + "#Stress at x=10 ft\n", + "sigma_top2=M_10*12*c_top*I**-1 #Stress at the top fibre in psi\n", + "sigma_bot2=-M_10*12*c_bot*I**-1 #Stress at the bottom fibre in psi\n", + "\n", + "#Maximum values\n", + "sigma_t=max(sigma_bot,sigma_bot2,sigma_top,sigma_top2) #Maximum values for stress in tension\n", + "sigma_c=min(sigma_top,sigma_top2,sigma_bot,sigma_bot2) #Maximum values for stress in compression\n", + "\n", + "#Result\n", + "print \"The maximum values of stress are\"\n", + "print \"Maximum Tension=\",round(sigma_t),\"psi at x=4ft\"\n", + "print \"Maximum Compression=\",round(-sigma_c),\"psi at x=10ft\"\n", + "\n", + "#NOTE:Answer is differing becuase of the decimal accuracy\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The maximum values of stress are\n", + "Maximum Tension= 2583.0 psi at x=4ft\n", + "Maximum Compression= 3229.0 psi at x=10ft\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.5.3, Page No:145" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable Decleration\n", + "L=4 #Length of each section in ft\n", + "h_ab=4 #Thickness of the front section in inches\n", + "h_bd=6 #Thickness of the back section in inches\n", + "P=2000 #Point load acting at point A in lb\n", + "M_B=8000 #Moment at 4ft in lb.ft\n", + "M_D=16000 #Moment at x=8ft in lb.ft\n", + "b=2 #Breadth in inches\n", + "\n", + "#Calculations\n", + "S_ab=b*h_ab**2*6**-1 #Sectional Modulus of section AB in in^3\n", + "S_bd=b*h_bd**2*6**-1 #Sectional Modulus of section BD in in^3\n", + "sigma_B=12*M_B*S_ab**-1 #Maximum bending stress in psi\n", + "sigma_D=12*M_D*S_bd**-1 #Maximum bending stress in psi\n", + "\n", + "#Maximum stress\n", + "sigma_max=max(sigma_B,sigma_D) #Maximum stress in psi\n", + "\n", + "#Result\n", + "print \"Comparing the two results we find that the maximum stress is\"\n", + "print \"Sigma_max=\",round(sigma_max),\"psi\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Comparing the two results we find that the maximum stress is\n", + "Sigma_max= 18000.0 psi\n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.5.4, Page No:146" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable Decleration\n", + "M=15000 #Maximum bending moment in absolute values in lb.ft\n", + "S=42 #Sectional Modulus in in^3\n", + "\n", + "#Calculations\n", + "sigma_max=M*12*S**-1 #Maximum stress in the section in psi\n", + "\n", + "#Result\n", + "print \"The maximum Bending Stress in the section is\",round(sigma_max),\"psi\"\n", + "\n", + "#NOTE:The answer differs due to decimal point accuracy" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The maximum Bending Stress in the section is 4286.0 psi\n" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.5.5, Page No:157" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable Decleration\n", + "M_max=60*10**3 #Maximum Bending Moment in kN.m\n", + "sigma_w=120*10**6 #Maximum Bending Stress allowed in Pa\n", + "M_max_2=61.52*10**3 #max bending moment computed in N.m\n", + "\n", + "#Section details\n", + "mass=38.7 #Mass in kg/m\n", + "g=9.81 #Acceleration due to gravity in m/s^2\n", + "S=549*10**3 #Sectional modulus of the section in mm^3\n", + "\n", + "#Calculations\n", + "S_min=M_max*sigma_w**-1*10**9 #Minimum Sectional Modulus required in mm^3\n", + "\n", + "#We selecet section W310x39\n", + "w0=mass*g*10**-3 #Weight of the beam in kN/m\n", + "sigma_max=M_max_2*S**-1*10**3 #Maximum stress in MPa\n", + "\n", + "#Result\n", + "print \"The section chosen is W310x39 with maximum stress as\",round(sigma_max,1),\"MPa\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The section chosen is W310x39 with maximum stress as 112.1 MPa\n" + ] + } + ], + "prompt_number": 25 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.5.6, Page No:166" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable Decleration\n", + "V_max=24 #Maximum Shear in kN\n", + "b=0.160 #Width of the beam in m\n", + "h=0.240 #Depth of the beam in m\n", + "\n", + "#Calculations\n", + "I=b*h**3*12**-1 #Moment of Inertia of the beam in m^4\n", + "\n", + "#Part 1\n", + "Q=b*(h*3**-1)**2 #First moment of Area m^3\n", + "tau_max=(V_max*Q)*(I*b)**-1 #Maximum Shear Stress in glue in kPa\n", + "\n", + "#Part 2\n", + "tau_max_2=(3.0/2.0)*(V_max/(b*h)) #Shear Stress in kPa\n", + "Q_1=b*h*0.5*h*0.25 #First moment about NA in m^3\n", + "tau_maxx=(V_max*Q_1)/(I*b) #Shear stress in kPa\n", + "\n", + "#Result\n", + "print \"The Results agree in both parts\"\n", + "print \"The maximum stress is\", round(tau_max_2),\"kPa\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The Results agree in both parts\n", + "The maximum stress is 938.0 kPa\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.5.7, Page No:167" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable Decleration\n", + "I=310 #Moment of inertia in in^4\n", + "V=160 #Shear Force in kips\n", + "#Dimension defination\n", + "tf=0.515 #Thickness of flange in inches\n", + "de=11.94 #Effective depth in inches\n", + "tw=0.295 #Thickness of web in inches\n", + "wf=8.005 #Width of lange in inches\n", + "\n", + "#Calculations\n", + "#Part 1\n", + "Q=wf*tf*(de-tf)*0.5 #First moment about NA in inch^3\n", + "tau_min=(V*Q*10**2)/(I*tw) #Minimum shear stress in web in psi\n", + "\n", + "#Part 2\n", + "A_2=(de*0.5-tf)*tw #Area in in^3\n", + "y_bar_2=0.5*(de*0.5-tf) #Depth in inches\n", + "\n", + "Q_2=Q+A_2*y_bar_2 #First Moment in inches^3\n", + "\n", + "tau_max=(V*Q_2*10**2)/(I*tw) #Maximum Shear Stress in psi\n", + "\n", + "#Part 3\n", + "V_web=10.91*tw*(tau_min+((2*3**-1)*(tau_max-tau_min))) #Shear in the web in lb\n", + "perV=(V_web/V)*100 #Percentage shear force in web in %\n", + "t_max_final=V*10**3/(10.91*tw)\n", + "\n", + "#result\n", + "print \"The final shear stress in the web portion is\",round(t_max_final),\"psi\"\n", + "#NOTE:Answer differs due to deciaml point accuracy" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The final shear stress in the web portion is 49713.0 psi\n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.5.8, Page No:168" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable Decleration\n", + "I=547 #Moment of inertia in inches^4\n", + "d=8.9 #NA deoth in inches\n", + "V=12 #Shear Force in kips\n", + "h=7.3 #Depth of NA\n", + "b=2 #Width in inches\n", + "t=1.2 #Thickness in inches\n", + "h2=7.5 #Depth in inches\n", + "\n", + "#Calculations\n", + "#Shear Stress at NA\n", + "Q=(b*h)*(h*0.5) #First Moment about NA in in^3\n", + "tau=(V*10**3*Q)/(I*b) #Shear stress at NA in psi\n", + "\n", + "#Shear Stress at a-a\n", + "Q_1=(t*h2)*(d-h2*0.5) #First moment about NA in in^3\n", + "tau1=(V*Q_1)/(I*t) #Shear Stress in psi\n", + "\n", + "#Result\n", + "print \"Comparing two stresses\"\n", + "print \"The maximum stress is\",round(max(tau,tau1)),\"psi\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Comparing two stresses\n", + "The maximum stress is 585.0 psi\n" + ] + } + ], + "prompt_number": 24 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.5.10, Page No:175" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable Decleration\n", + "sigma_w=1000 #Working Stress in Bending in psi\n", + "tau_w=100 #Working stress in shear in psi\n", + "#Dimensions\n", + "b_out=8 #Width in inches\n", + "h=10 #Depth in inches\n", + "b_in=6 #Width in inches\n", + "\n", + "#Calculations\n", + "I=((b_out*h**3)-(b_in*b_out**3))*12**-1 #Moment of inertia in in^4\n", + "#Design for shear\n", + "Q=(b_out*h*0.5*0.25*h)-(b_in*b_out*0.5*0.25*b_out) #First Moment about NA in in^3\n", + "\n", + "#Largest P\n", + "P=(tau_w*I*2)/(1.5*Q) #P in shear in lb\n", + "\n", + "#Design for bending\n", + "P1=(sigma_w*I)/(60*5) #P in bending in lb\n", + "\n", + "#Result\n", + "print \"The maximum allowable P value is\",round(min(P,P1)),\"lb\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The maximum allowable P value is 1053.0 lb\n" + ] + } + ], + "prompt_number": 33 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.5.11, Page No:182" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable Decleration\n", + "A=2630 #Area in mm^2\n", + "y_bar=536.6 #Neutral Axis depth from top in mm\n", + "tau_w=100 #Allowable stress in MPa\n", + "sigma_b_w=280 #Allowable bending stress in MPa\n", + "d=0.019 #Diameter of the rivet in m\n", + "t_web=0.01 #Thickness of the web in m\n", + "I=4140 #Moment of inertia in m^4\n", + "V=450 #Max shear allowable in kN\n", + "\n", + "#Calculations\n", + "Q=A*y_bar #first moment in mm^3\n", + "Fw=(pi*d**2)*tau_w*10**6 #Allowable force in N\n", + "Fw_2=d*t_web*sigma_b_w*10**6*0.5 #Allowable force in N\n", + "e=Fw_2*I*(V*10**3*Q*10**-3)**-1 #Allowable spacing in m\n", + "\n", + "#Result\n", + "print \"The maximum spacing allowed is\",round(e*1000,1),\"mm\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The maximum spacing allowed is 173.4 mm\n" + ] + } + ], + "prompt_number": 6 + } + ], + "metadata": {} + } + ] +}
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