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"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 1 : Stress, Axial loads and Safety concepts"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.1 page number 24"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"import math\n",
"d_bolt = 20.0 #mm,diameter,This is not the minimum area\n",
"d_bolt_min = 16.0 #mm This is at the roots of the thread \n",
"#This yealds maximum stress \n",
"A_crossection = (math.pi)*(d_bolt**2)/4 #mm*2\n",
"A_crossection_min = (math.pi)*(d_bolt_min**2)/4 #mm*2 ,This is minimum area which yeilds maximum stress\n",
"load = 10.0 #KN\n",
"BC = 1.0 #m\n",
"CF = 2.5 #m\n",
"contact_area = 200*200 # mm*2 , The contact area at c\n",
"\n",
"#caliculations \n",
"#Balancing forces in the x direction:\n",
"# Balncing the moments about C and B:\n",
"Fx = 0 \n",
"R_cy = load*(BC+CF) #KN , Reaction at C in y-direction\n",
"R_by = load*(CF) #KN , Reaction at B in y-direction\n",
"#Because of 2 bolts\n",
"stress_max = (R_by/(2*A_crossection_min))*(10**3) # MPA,maximum stess records at minimum area\n",
"stress_shank = (R_by/(2*A_crossection))*(10**3) # MPA\n",
"Bearing_stress_c = (R_cy/contact_area)*(10**3) #MPA, Bearing stress at C\n",
"\n",
"print\"The bearing stress at C is \",(Bearing_stress_c) ,\"MPA\"\n",
"print\"The maximum normal stress in BD bolt is: \",round(stress_max),\"MPA\"\n",
"print\"The tensile strss at shank of the bolt is: \",round(stress_shank),\"MPA\"\n",
"\n",
"\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The bearing stress at C is 0.875 MPA\n",
"The maximum normal stress in BD bolt is: 62.0 MPA\n",
"The tensile strss at shank of the bolt is: 40.0 MPA\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.2 page number 26"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given \n",
"load_distributed = 20 #KN/m*2, This is the load distributed over the pier\n",
"H = 2 # m, Total height \n",
"h = 1 #m , point of investigation \n",
"base = 1.5 #m The length of crossection in side veiw \n",
"top = 0.5 #m ,The length where load is distributed on top\n",
"base_inv = 1 #m , the length at the point of investigation \n",
"area = 0.5*1 #m ,The length at a-a crossection \n",
"density_conc = 25 #KN/m*2\n",
"#caliculation of total weight \n",
"\n",
"v_total = ((top+base)/2)*top*H #m*2 ,The total volume \n",
"w_total = v_total* density_conc #KN , The total weight\n",
"R_top = (top**2)*load_distributed #KN , THe reaction force due to load distribution \n",
"reaction_net = w_total + R_top\n",
"\n",
"#caliculation of State of stress at 1m \n",
"v_inv = ((top+base_inv)/2)*top*h #m*2 ,The total volume from 1m to top\n",
"w_inv = v_inv*density_conc #KN , The total weight from 1m to top\n",
"reaction_net = w_inv + R_top #KN\n",
"Stress = reaction_net/area #KN/m*2\n",
"print\"The total weight of pier is\",w_total,\"KN\"\n",
"print\"The stress at 1 m above is\",Stress,\"MPA\"\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The total weightof pier: 25.0 KN\n",
"The stress at 1 m above is 28.75 MPA\n"
]
}
],
"prompt_number": 12
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.3 page number 27"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"from math import pow\n",
"d_pins = 0.375 #inch\n",
"load = 3 #Kips\n",
"AB_x = 6 #inch,X-component\n",
"AB_y = 3 #inch,Y-component \n",
"BC_y = 6 #inch,Y-component\n",
"BC_x = 6 #inch,X-component\n",
"area_AB = 0.25*0.5 #inch*2 \n",
"area_net = 0.20*2*(0.875-0.375) #inch*2 \n",
"area_BC = 0.875*0.25 #inch*2 \n",
"area_pin = d_pins*2*0.20 #inch*2 \n",
"area_pin_crossection = 3.14*((d_pins/2)**2)\n",
"#caliculations\n",
"\n",
"slope = AB_y/ AB_x #For AB\n",
"slope = BC_y/ BC_x #For BC\n",
"\n",
"#momentum at point C:\n",
"F_A_x = (load*AB_x )/(BC_y + AB_y ) #Kips, F_A_x X-component of F_A\n",
"\n",
"#momentum at point A:\n",
"F_C_x = -(load*BC_x)/(BC_y + AB_y ) #Kips, F_C_x X-component of F_c\n",
"\n",
"#X,Y components of F_A\n",
"F_A= (pow(5,0.5)/2)*F_A_x #Kips\n",
"F_A_y = 0.5*F_A_x #Kips\n",
"\n",
"#X,Y components of F_C \n",
"F_C= pow(2,0.5)*F_C_x #Kips\n",
"F_C_y = F_C_x #Kips\n",
"\n",
"T_stress_AB = F_A/area_AB #Ksi , Tensile stress in main bar AB\n",
"stress_clevis = F_A/area_net #Ksi ,Tensile stress in clevis of main bar AB\n",
"c_strees_BC = F_C/area_BC #Ksi , Comprensive stress in main bar BC\n",
"B_stress_pin = F_C/area_pin #Ksi , Bearing stress in pin at C\n",
"To_stress_pin = F_C/area_pin_crossection #Ksi , torsion stress in pin at C\n",
"\n",
"print\"Tensile stress in main bar AB:\",round(T_stress_AB,2),\"Ksi\"\n",
"print\"Tensile stress in clevis of main bar AB:\",round(stress_clevis,2),\"Ksi\"\n",
"print\"Comprensive stress in main bar BC:\",round(-c_strees_BC,2),\"Ksi\"\n",
"print\"Bearing stress in pin at C:\",round(-B_stress_pin,2),\"Ksi\"\n",
"print\"torsion stress in pin at C:\",round(To_stress_pin,2),\"Ksi\"\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Tensile stress in main bar AB: 17.89 Ksi\n",
"Tensile stress in clevis of main bar AB: 11.18 Ksi\n",
"Comprensive stress in main bar BC: 12.93 Ksi\n",
"Bearing stress in pin at C: 18.86 Ksi\n",
"torsion stress in pin at C: -25.62 Ksi\n"
]
}
],
"prompt_number": 35
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.4 page number 38"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"strength_steel = 120 #Ksi\n",
"factor = 2.5\n",
"F_C = 2.23 #Ksi\n",
"\n",
"#caliculations\n",
"\n",
"stress_allow = strength_steel/factor #Ksi\n",
"A_net = F_C/strength_steel #in*2 , \n",
"#lets adopt 0.20x0.25 in*2 and check wether we are correct or not? \n",
"\n",
"A_net_assumption = 0.25*0.20 #in*2 , this is assumed area which is near to A_net\n",
"stress = 2.23/A_net_assumption #Ksi\n",
"factor_assumed = strength_steel/stress \n",
"\n",
"if factor_assumed > factor :\n",
" print \"The factor\",factor,\"is less than assumed factor\",round(factor_assumed,1),\"so this can be considered\"\n",
"else:\n",
" print \"The assumed factor\",factor, \"is more than assumed factor\",factor_assumed,\"factor_assumed\"\n",
" \n",
" \n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The factor 2.5 is less than assumed factor 2.7 so this can be considered\n"
]
}
],
"prompt_number": 36
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.6 page number 35"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"mass = 5 #Kg\n",
"frequency = 10 #Hz\n",
"stress_allow = 200 #MPa\n",
"R = 0.5 #m\n",
"\n",
"#caliculations \n",
"from math import pi\n",
"w = 2*pi*frequency #rad/sec\n",
"a = (w**2)*R #m*2/sec\n",
"F = mass*a #N\n",
"A_req = F/stress_allow #m*2 , The required area for aloowing stress\n",
"print\"The required size of rod is:\",round(A_req,2),\"m*2\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The required size of rod is: 49.35 m*2\n"
]
}
],
"prompt_number": 40
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.7 page number 45"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"D_n = 5.0 #kips, dead load\n",
"L_n_1 = 1.0 #kips ,live load 1\n",
"L_n_2 = 15 #kips ,live load 2\n",
"stress_allow = 22 #ksi\n",
"phi = 0.9 #probalistic coefficients\n",
"y_stress = 36 #ksi,Yeild strength\n",
"#According to AISR \n",
"\n",
"#a\n",
"p_1 = D_n + L_n_1 #kips since the total load is sum of dead load and live load\n",
"p_2 = D_n + L_n_2 #kips, For second live load\n",
"\n",
"Area_1 = p_1/stress_allow #in*2 ,the allowable area for the allowed stress\n",
"Area_2 = p_2/stress_allow #in*2\n",
"print \"the allowable area for live load\",L_n_1,\"is\",round(Area_1,3),\"in*2\"\n",
"print \"the allowable area for live load\",L_n_2,\"is\",round(Area_2,3),\"in*2\"\n",
"\n",
"#b\n",
"#area_crossection= (1.2*D_n +1.6L_n)/(phi*y_stress)\n",
"\n",
"area_crossection_1= (1.2*D_n +1.6*L_n_1)/(phi*y_stress) #in*2,crossection area for first live load\n",
"area_crossection_2= (1.2*D_n +1.6*L_n_2)/(phi*y_stress) #in*2,crossection area for second live load\n",
"print \"the crossection area for live load\",L_n_1,\"is\",round(area_crossection_1,3),\"in*2\"\n",
"print \"the crossection area for live load\",L_n_2,\"is\",round(area_crossection_2,3),\"in*2\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"the allowable area for live load 1.0 is 0.273 in*2\n",
"the allowable area for live load 15 is 0.909 in*2\n",
"the crossection area for live load 1.0 is 0.235 in*2\n",
"the crossection area for live load 15 is 0.926 in*2\n"
]
}
],
"prompt_number": 46
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.8 page number 51"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"A_angle = 2 #in*2 \n",
"stress_allow = 20 #ksi, The maximum alowable stress\n",
"F = stress_allow*A_angle #K, The maximum force\n",
"AD = 3 #in, from the figure\n",
"DC = 1.06 #in, from the figure\n",
"strength_AWS = 5.56 # kips/in,Allowable strength according to AWS\n",
"\n",
"#caliculations \n",
"#momentum at point \"d\" is equal to 0\n",
"R_1 = (F*DC)/AD #k,Resultant force developed by the weld\n",
"R_2 = (F*(AD-DC))/AD #k,Resultant force developed by the weld\n",
"\n",
"l_1 = R_1/strength_AWS #in,Length of the Weld 1\n",
"l_2 = R_2/strength_AWS #in,Length of the Weld 2\n",
" \n",
"print \"Length of the Weld 1:\",round(l_1,2),\"in\"\n",
"print \"Length of the Weld 2:\",round(l_2,2),\"in\" \n",
" \n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Length of the Weld 1: 2.54 in\n",
"Length of the Weld 2: 4.65 in\n"
]
}
],
"prompt_number": 52
},
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"cell_type": "code",
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