{
"metadata": {
"name": "",
"signature": "sha256:85f0dfde049627c0712f822039c348c948a05a921a2085135b06fb18242d0e33"
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"nbformat": 3,
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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 6 : Analysis of structures"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.1 Page No : 294"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Entire truss\n",
"#Applying sum(M_C) = 0\n",
"\n",
"# Given Data\n",
"E = (10.*12+5*6)/3;\t\t\t#kN\n",
"#Applying sum Fx = 0\n",
"Cx = 0.\n",
"#Applying sumFy = 0\n",
"Cy = 10.+5-E;\t\t\t#kN\n",
"\n",
"# Calculations\n",
"#At joint A\n",
"#By proportion 10kN/4 = F_AB/3 = F_AD/5\n",
"F_AB = 10./4*3;\t\t\t#kN, force in member AB\n",
"F_DA = 10./4*5;\t\t\t#kN, force in member AD\n",
"\n",
"#At joint D\n",
"F_DB = F_DA;\t\t\t#kN, force in member DB\n",
"F_DE = 2*3./5*F_DA;\t\t\t#kN, force in member DE\n",
"\n",
"#At joint B\n",
"#applying sumFy = 0\n",
"F_BE = 5./4*(-5-4./5*F_DB);\t\t\t#kN, force in member BE\n",
"#Applying sumFx = 0\n",
"F_BC = F_AB+3./5*F_DB-3./5*F_BE;\t\t\t#kN, force in member BC\n",
"#At joint E\n",
"#Applying sumFx = 0\n",
"F_EC = -5./3*(F_DE-3./5*F_BE);\t\t\t#kN, Force in member EC\n",
"\n",
"# Results\n",
"print \"The forces in member of truss are F_AB = %.1f kN T \\\n",
"\\nF_AD = %.1f kN C, \\\n",
"\\nF_DB = %.1f kN T \\\n",
"\\nF_DE = %.0f kN C \\\n",
"\\nF_BE = %.2f kN \\\n",
"\\nF_BC = %.2f kN \\\n",
"\\nF_EC = %.2f kN \"%(F_AB,F_DA,F_DB,F_DE,F_BE,F_BC,F_EC);\n",
"#Variation in answe because of round off\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The forces in member of truss are F_AB = 7.5 kN T \n",
"F_AD = 12.5 kN C, \n",
"F_DB = 12.5 kN T \n",
"F_DE = 15 kN C \n",
"F_BE = -18.75 kN \n",
"F_BC = 26.25 kN \n",
"F_EC = -43.75 kN \n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.2 Page No : 306"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Given Data\n",
"#Entire truss\n",
"v1 = 140.;\t\t\t#kn, verical force 1\n",
"v2 = 140.;\t\t\t#kN, Vertical force 2\n",
"h = 80.;\t\t\t#kN , Horizontal force\n",
"#Applying sum(M_B) = 0\n",
"J = (v1*4+v2*12+h*5)/16;\t\t\t#kN\n",
"\n",
"\n",
"# Calculations and Results\n",
"#Applying sum Fx = 0\n",
"Bx = -h;\t\t\t#kN, negative sign shows it is along negative x axis\n",
"\n",
"#Applying sumFy = 0\n",
"\n",
"By = v1+v2-J;\t\t\t#kN\n",
"\n",
"#Force in member EF\n",
"#Applying sumFy = 0\n",
"F_EF = By-v2;\t\t\t#kN, Force in member EF\n",
"print \"Force in member EF is %.0f kN Negative sign shows member is in compression \"%(F_EF);\n",
"\n",
"#Force in member GI\n",
"F_GI = (-J*4-Bx*5)/5;\t\t\t#kN Force in member GI\n",
"print \"Force in member GI is %.0f kN Negative sign shows member is in compression \"%(F_GI);\n",
"#Answer difference is because of rounding off variables\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Force in member EF is -25 kN Negative sign shows member is in compression \n",
"Force in member GI is -52 kN Negative sign shows member is in compression \n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.3 Page No : 307"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"\n",
"# Given Data\n",
"#Entire truss\n",
"vB = 1.;\t\t\t#kN, verical force at B\n",
"vD = 1.;\t\t\t#kN, verical force at D\n",
"vF = 1.;\t\t\t#kN, verical force at F\n",
"vH = 1.;\t\t\t#kN, verical force at H\n",
"vJ = 1.;\t\t\t#kN, verical force at J\n",
"vC = 5.;\t\t\t#kN, verical force at C\n",
"vE = 5.;\t\t\t#kN, verical force at E\n",
"vG = 5.;\t\t\t#kN, verical force at G\n",
"h = 8.;\t\t\t#m, height\n",
"v = 5.;\t\t\t#m, horizontal dismath.tance between successive node\n",
"\n",
"A = 12.50;\t\t\t#kN, reaction at A\n",
"L = 7.50;\t\t\t#kN, reaction at L\n",
"\n",
"# Calculations and Results\n",
"alpha = math.atan(h/3./v);\t\t\t# rad, angle made by inclined members with X axis\n",
"#alpha = alpha/math.pi*180;\t\t\t# Conversion of angle into degrees\n",
"\n",
"#Force in member GI\n",
"#Applying sum(M_H) = 0\n",
"F_GI = (L*2*v-vJ*v)/(2*v*math.tan(alpha));\t\t\t#kN Force in member GI\n",
"print \"Force in member GI is %.2f kN \"%(F_GI);\n",
"\n",
"#Force in member FH\n",
"#Applying sum(M_G) = 0\n",
"F_FH = (L*3*v-vH*v-vJ*2*v)/(-h*math.cos(alpha));\t\t\t#kN, Force in member FH\n",
"print \"Force in member FH is %.2f kN Negative sign shows member is in compression \"%(F_FH);\n",
"\n",
"#Force in member GH\n",
"be = math.atan(v/(2*v*math.tan(alpha)));\t\t\t#rad, as math.tan(be) = GI/HI\n",
"#Applying sum(M_L) = 0\n",
"F_GH = (-vH*v-vJ*2*v)/(3*v*math.cos(be));\t\t\t#kN, Force in member FH\n",
"print \"Force in member GH is %.3f kN Negative sign shows member is in compression \"%(F_GH);\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Force in member GI is 13.12 kN \n",
"Force in member FH is -13.81 kN Negative sign shows member is in compression \n",
"Force in member GH is -1.371 kN Negative sign shows member is in compression \n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.4 Page No : 319"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"#Entire truss\n",
"#Applying sum(Fy) = 0\n",
"\n",
"# Given Data\n",
"Ay = 480.;\t\t\t#N, Y component of reaction at A\n",
"#Applying sum(M_A) = 0\n",
"B = 480*100./160;\t\t\t#N, reaction at B\n",
"#Applying sum(Fx) = 0\n",
"Ax = -300.;\t\t\t#N, X component of reaction at A\n",
"\n",
"# Calculations and Results\n",
"alpha = math.atan(80./150);\t\t\t#radian\n",
"#Free body member BCD\n",
"#Applying sum(M_C) = 0\n",
"F_DE = (-480*100.-B*60)/(math.sin(alpha)*250);\t\t\t#N, Force in link DE\n",
"print \"Force in link DE is F_DE = %.0f N Negative sign shows force is compressive\"%(F_DE);\n",
"#Applying sum(Fx) = 0\n",
"Cx = F_DE*math.cos(alpha)-B;\t\t\t#N, X component of force exerted at C\n",
"#Applying sum(Fy) = 0\n",
"Cy = F_DE*math.sin(alpha)+Ay;\t\t\t#N, Y component of force exerted at C\n",
"print \"Components of force exerted at C is Cx = %.0f N and Cy = %.0f N \"%(Cx,Cy);"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Force in link DE is F_DE = -561 N Negative sign shows force is compressive\n",
"Components of force exerted at C is Cx = -795 N and Cy = 216 N \n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.5 Page No : 320"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"# Given Data\n",
"P = 18.;\t\t\t#kN, Force applied at D\n",
"AF = 3.6;\t\t\t#m, Length AF\n",
"EF = 2.;\t\t\t#m, Length EF\n",
"ED = 2.;\t\t\t#m, Length ED\n",
"DC = 2.;\t\t\t#m, Length DC\n",
"#Entire frame\n",
"\n",
"# Calculations and Results\n",
"#Applying sum(M_F) = 0\n",
"Ay = -P*(EF+ED)/AF;\t\t\t#kN, Y component of reaction at A\n",
"\n",
"#Applying sum(Fx) = 0\n",
"Ax = -P;\t\t\t#kN, X component of reaction at A\n",
"#Applying sum(Fy) = 0\n",
"F = -Ay;\t\t\t#kN, reaction at B\n",
"\n",
"print \"Components of force exerted at A is Ax = %.0f kN and Ay = %.0f kN \"%(Ax,Ay);\n",
"print \"Force exerted at F is F = %.0f kN \"%(F);\n",
"#Free body member BE\n",
"#Applying sum(Fx) = 0\n",
"#B = E, and as it is 2 force member\n",
"By = 0;\n",
"Ey = 0;\n",
"\n",
"#Member ABC\n",
"#Applying sum(Fy) = 0\n",
"Cy = -Ay;\t\t\t#kN, Y component of force exerted at C\n",
"#Applying sum(M_C) = 0\n",
"B = (Ay*AF-Ax*(DC+ED+EF))/(ED+DC);\t\t\t#kN, Force in link DE\n",
"print \"Force exerted at B is B = %.0f kN \"%(B);\n",
"#Applying sum(Fx) = 0\n",
"Cx = -Ax-B;\t\t\t#kN, X component of force exerted at C\n",
"\n",
"print \"Components of force exerted at C is Cx = %.0f kN and Cy = %.0f kN \"%(Cx,Cy);\n",
"print \"Negative signs shows forces are in negative direction\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Components of force exerted at A is Ax = -18 kN and Ay = -20 kN \n",
"Force exerted at F is F = 20 kN \n",
"Force exerted at B is B = 9 kN \n",
"Components of force exerted at C is Cx = 9 kN and Cy = 20 kN \n",
"Negative signs shows forces are in negative direction\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.6 Page No : 320"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math \n",
"from numpy.linalg import solve\n",
"\n",
"# Given Data\n",
"P = 3.;\t\t\t#kN, Horizontal Force applied at A\n",
"AB = 1.;\t\t\t#m, perpendicular dismath.tance between A and B\n",
"BD = 1.;\t\t\t#m, perpendicular dismath.tance between D and B\n",
"CD = 1.;\t\t\t#m, perpendicular dismath.tance between C and D\n",
"FC = 1.;\t\t\t#m, perpendicular dismath.tance between C and F\n",
"EF = 2.4;\t\t\t#m, perpendicular dismath.tance between E and F\n",
"#Entire frame\n",
"\n",
"# Calculations\n",
"#Applying sum(M_E) = 0\n",
"Fy = P*(AB+BD+CD+FC)/EF;\t\t\t#kN, Y component of reaction at F\n",
"\n",
"\n",
"#Applying sum(Fy) = 0\n",
"Ey = -Fy;\t\t\t#kN, Y component of reaction at E\n",
"\n",
"#Free body member ACE\n",
"#Applying sum(Fy) = 0, and sum(M_E) = 0 we get 2 equation\n",
"A = [[-AB/math.sqrt(AB**2+EF**2) ,CD/math.sqrt(CD**2+EF**2) ] , [ -EF/math.sqrt(AB**2+EF**2)*(AB+BD+CD+FC) , -EF/math.sqrt(CD**2+EF**2)]];\t\t\t# Matrix of coefficients\n",
"B = [[Ey],[-P*(AB+BD+CD+FC)]];\t\t\t# Matrix B\n",
"X = solve(A,B);\t\t\t#kN Solution matrix\n",
"F_AB = X[0];\t\t\t#kN, Forec inmember AB\n",
"F_CD = X[1];\t\t\t#kN, Forec inmember CD\n",
"Ex = -P-EF/math.sqrt(AB**2+EF**2)*F_AB-EF/math.sqrt(CD**2+EF**2)*F_CD;\t\t\t#kN, X component of force exerted at E\n",
"#Free body : Entire frame\n",
"#Applying sum(F_X) = 0\n",
"Fx = -P-Ex;\t\t\t#kN, X component of force exetered at F\n",
"print \"Components of force exerted at F is Fx = %.1f kN and Fy = %.0f kN \"%(Fx,Fy);\n",
"print \"Force in member AB is F_AB = %.1f kN \"%(F_AB);\n",
"print \"Force in member CD is F_CD = %.1f kN \"%(F_CD);\n",
"print \"Components of force exerted at E is Ex = %.1f kN and Ey = %.1f kN \"%(Ex,Ey);\n",
"\n",
"print \"Negative signs shows forces are in negative direction\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Components of force exerted at F is Fx = -2.4 kN and Fy = 5 kN \n",
"Force in member AB is F_AB = 5.2 kN \n",
"Force in member CD is F_CD = -7.8 kN \n",
"Components of force exerted at E is Ex = -0.6 kN and Ey = -5.0 kN \n",
"Negative signs shows forces are in negative direction\n"
]
}
],
"prompt_number": 7
}
],
"metadata": {}
}
]
}