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{
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"name": "",
"signature": "sha256:9e6efed33049beac69942b90d39a9e8444a663ad0d711d98275d388c059ec74c"
},
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"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter11:Additional Beam Topics"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 11.11.1, Page No:394"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable Decleration\n",
"V=1000 #Force acting on he section in lb\n",
"t=0.5 #Thickness in inches\n",
"#Dimensions\n",
"d=8 #Depth of the section in inches\n",
"wf=12 #Width of the flange in inches\n",
"wbf=8 #Width of the bottom flange in inches\n",
"\n",
"#Calculations\n",
"y_bar=((d*t*0)+wbf*t*4+wf*t*8)/(d*t+wbf*t+wf*t) #Location of Neutral Axis in inches\n",
"I=d*t*y_bar**2+t*d**3*12**-1+d*t*(d*t-y_bar)**2+wf*t*(8-y_bar)**2 #Moment of Inertia in in^4\n",
"\n",
"#Top Flange\n",
"q1=V*t*t*wf*(8-y_bar)*I**-1 #Shear flow in lb/in\n",
"#Bottom Flange\n",
"q2=V*t*t*d*y_bar*I**-1 #Shear Flow in lb/in\n",
"#Web\n",
"qB=2*q1 #Shear Flow in lb/in\n",
"qF=2*q2 #Shear Flow in lb/in\n",
"\n",
"#Max Shear Flow\n",
"qMAX=qB+V*t*(8-y_bar)**2*0.5*I**-1 #Maximum Shear Flow in lb/in\n",
"\n",
"#Result\n",
"print \"The Maximum Shear Flow is\",round(qMAX),\"lb/in\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The Maximum Shear Flow is 133.0 lb/in\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 11.11.2, Page No:395"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable Decleration\n",
"V=1000 #Shear Force in lb\n",
"#Rest ALL DATA is similar to previous problem\n",
"\n",
"#Calcualtions\n",
"I=t*wf**3*12**-1+t*d**3*12**-1 #Moment of Inertia\n",
"\n",
"#Part 1\n",
"q1=V*t*t*wf*3*I**-1 #Shear Flow in lb/in\n",
"q2=V*t*t*d*2*I**-1 #Shear FLow in lb/in\n",
"V1=2*3**-1*q1*wf #Shear force carried in lb\n",
"V2=2*3**-1*q2*d #Shear force carried in lb\n",
"\n",
"#Part 2\n",
"e=8*V2*V**-1 #Eccentricity in inches\n",
"\n",
"#Result\n",
"print \"The Shear Force carried by Flanges is\"\n",
"print \"Top Flange=\",round(V1,1),\"lb Bottom Flange=\",round(V2,1),\"lb\"\n",
"print \"The eccentricity is\",round(e,3),\"in\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The Shear Force carried by Flanges is\n",
"Top Flange= 771.4 lb Bottom Flange= 228.6 lb\n",
"The eccentricity is 1.829 in\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 11.11.3, Page No:403"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"import numpy as np\n",
"\n",
"#Variable Decleration\n",
"M=32 #Moment in kN.m\n",
"Iy=4.73*10**6 #Moment of inertia in y-axis in mm^4\n",
"Iz=48.9*10**6 #Moment of inertia in z-axis in mm^4\n",
"Sy=64.7*10**3 #Sectional Modulus in y-axis in mm^3\n",
"Sz=379*10**3 #Sectional Modulus in z-axis in mm^3\n",
"theta=16.2 #Angle between moment and z-axis in degrees\n",
"\n",
"#Calculations\n",
"#Part 1\n",
"alpha=np.arctan((Iz*Iy**-1)*tan(theta*pi*180**-1))*180*pi**-1 #Angle between NA and z-axis in degrees\n",
"\n",
"#Part 2\n",
"My=-M*np.sin(theta*pi*180**-1) #Bending Moment in y in kN.m\n",
"Mz=-M*np.cos(theta*pi*180**-1) #Bending Moment in z in kN.m\n",
"\n",
"sigma_max=My*Sy**-1+Mz*Sz**-1 #Largest Bedning Stress in MPa\n",
"\n",
"#Result\n",
"print \"The angle between the Neutral Axis and Z-Axis is\",round(alpha,1),\"degrees\"\n",
"print \"The maximum Bending Moment is\",abs(round(sigma_max*10**6)),\"MPa\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The angle between the Neutral Axis and Z-Axis is 71.6 degrees\n",
"The maximum Bending Moment is 219.0 MPa\n"
]
}
],
"prompt_number": 24
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 11.11.4, Page No:403"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable Decleration\n",
"A=4.75 #Area in inches^2\n",
"Iy_dash=6.27 #Moment of inertia in in^4\n",
"Iz_dash=17.4 #Moment of inertia in in^4\n",
"ry=0.87 #Radius of Gyration in inches\n",
"tan_theta=0.44\n",
"P=1 #Force in kips\n",
"L=48 #Length in inches\n",
"y_dash_B=-4.01 #Y coordinate of point B in inches\n",
"z_dash_B=-0.487 #Z coordinate of point B in inches\n",
"\n",
"#Calcualtions\n",
"theta=np.arctan(tan_theta) #Angle in radians\n",
"Iy=A*ry**2 #Moment of inertia in y in in^4\n",
"Iz=Iy_dash+Iz_dash-Iy #Moment of inertia in y in in^4\n",
"\n",
"#Part 1\n",
"alpha=arctan(Iz*Iy**-1*tan_theta)*180*pi**-1 #Angle in radians\n",
"beta=alpha-(theta*180*pi**-1) #Angle in degrees\n",
"\n",
"#Part 2\n",
"M=P*L*4**-1 #Moment in kip.in\n",
"My=M*np.sin(theta) #Moment in y in kip.in\n",
"Mz=M*np.cos(theta) #Moment in z in kip.in\n",
"\n",
"y_B=y_dash_B*np.cos(theta)+z_dash_B*np.sin(theta) #Y coordinate in inches\n",
"z_B=z_dash_B*np.cos(theta)-y_dash_B*np.sin(theta) #Z coordinate in inches\n",
"\n",
"#Maximum Bending Stress\n",
"sigma_max=My*z_B*Iy**-1-Mz*y_B*Iz**-1 #Maximum Bedning Stress in ksi\n",
"\n",
"#Result\n",
"print \"The angle of inclination of the Neutral axis to the z-axis is\",round(beta,1),\"degrees\"\n",
"print \"The maximum Bedning Stress is\",round(sigma_max,2),\"ksi\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The angle of inclination of the Neutral axis to the z-axis is 44.1 degrees\n",
"The maximum Bedning Stress is 3.69 ksi\n"
]
}
],
"prompt_number": 45
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 11.11.5, Page No:412"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable Decleration\n",
"A1=4 #Area in in^2\n",
"A2=6 #Area in in^2\n",
"r1=7.8 #Radius in inches\n",
"r2=14.8 #Radius in inches\n",
"t=0.5 #Thickness in inches\n",
"d=4 #Depth in inches\n",
"sigma_w=18 #Maximum allowable stress in kips\n",
"\n",
"#Calculations\n",
"A=A1+A2 #Area in in^2\n",
"r_bar=(A1*(r1+t)+A2*(r2+d))*(A1+A2)**-1 #Centroidal Axis in inches\n",
"#Simplfying the computation\n",
"a=(r1+2*t)/r1\n",
"b=r2/(r1+t*2)\n",
"integral=d*math.log(a)+2*t*math.log(b) #\n",
"R=A/integral #Radius of neutral Surface in inches\n",
"\n",
"#Maximum Stress\n",
"#Answers are in variable terms hence not computable\n",
"\n",
"P=sigma_w/0.7847 #Maximum Allowable load in kips\n",
"\n",
"#Result\n",
"print \"The maximum allowable load is\",round(P,1),\"kips\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The maximum allowable load is 22.9 kips\n"
]
}
],
"prompt_number": 58
}
],
"metadata": {}
}
]
}
|
