#Given
a_ab = 1 #inch**2, area
a_bd = 2 #inch**2
a_bc = a_bd
p = 29 #kN, load
l_ab = 2 #ft
l_bc = 1.5 #ft
l_cd = 1 #ft
#Calculations
#Internal Forces By method of Sections
p_bc = 15 #kip
p_cd = 7 #kip
p_ab=9 #kip
#Displacement
d=(p_bc*l_ab*12/(a_ab*p*10**3))+(p_cd*l_bc*12/(a_bd*p*10**3))+(p_ab*l_cd*12/(a_bc*p*10**3))
d_=p_cd*l_bc*12/(a_bd*p*10**3)
#Display
print"The displacement of B relative to C is = +%1.3f mm",round(d*10,4),"inch"
print "Displacement of B relative to C is",round(d_,5),"inch"
#Given
a_ab = 400.0 #mm**2, area
d_rod = 10.0 #mm
r_rod = d_rod/(2*1000) #radius in m
P = 80.0 #kN, load
E_st = 200*(10**9) #Pa, pressure
E_al = 70*(10**9) #Pa
l_ab = 400.0 #mm, length of ab
l_bc = 600.0 #mm length of bc
#Calculations
#Displacement
#delta =PL/AE
import math
numerator1 = P*(10**3)*(l_bc/1000.0)
denominator1 = (math.pi*r_rod**2*E_st)
delta_cb = numerator1/denominator1 #to the right
numerator2 = -P*(10**3)*(l_ab/1000.0)
denominator2 = (a_ab* 10**-6 *E_al)
delta_a = -numerator2/denominator2 #to the right
delta_c = delta_a+delta_cb
#Display
print"The displacement of C with respect to B = ",round(delta_cb,4),"m"
print"The displacement of B with respect to A = ",round(delta_a,4),"m"
print'The displacement of C relative to A = ',round(delta_c*1000,2),"mm"
#Given
d_ac = 20.0 #mm, ac diameter
r_ac = d_ac/(2*1000) #radius in m
d_bd =40.0 #mm
r_bd = d_bd/(2*1000) #radius in m
P = 90.0 #kN
E_st = 200*(10**9) #Pa
E_al = 70*(10**9) #Pa
l_af = 200.0 #mm
l_fb = 400.0 #mm
l_bd = 300.0 #mm
l_ac = l_bd
#Calculations
#Internal Force
P_ac = 60 #kN
P_bd = 30 #kN
#Displacement
import math
num1 = -(P_ac*10**3*(l_ac/1000.0))
denom1 = math.pi* r_ac**2*E_st
delta_a = -num1/denom1
delta_a = delta_a*1000
#Post BD delta = PL/AE
num2 = -(P_bd*10**3*(l_bd/1000))
denom2 = math.pi* r_bd**2*E_al
delta_b = -num2/denom2
delta_b = delta_b*1000
delta_f = delta_b + (0.184)*(l_fb/(l_af+l_fb))
#Display
print'The displacement of Post AC =',round(delta_a,3),"mm downwards"
print'The displacement of Post BD =',round(delta_b,3),"mm downwards"
print'nThe displacement of point F =',round(delta_f,3),"mm downwards"
#Given
import math
d_ab = 5 #mm, ab diameter
A = (math.pi/4)*(d_ab/1000)**2
gap = 1 #mm
P = 20 #kN, pressure
E_st = 200 #GPa
l_ac = 0.4 #m
l_cb = 0.8 #m
l_ab = l_ac+l_cb
#Calculations
#Equilibrium
# Eqn1 -Fa - Fb +P*10**3 = 0
#Compatibility
delta_ba = gap/1000.0 #in m
delta = delta_ba*(A*E_st*10**9) #delta_ba* Lac/AE
#Eqn2 (L/AE)*Fa -(Lb/AE)*Fb = delta_ba
#Solving Equations 1 and 2 by matrices
Fa=16 #KN
Fb=4.05 #KN
#Display
print"The reaction force at A = ",Fa,"kN"
print"The reaction force at B = ",Fb,"kN"
#Given
P = 9 #kip, load
E_al = 10 #ksi,
E_br = 15 # ksi
h = 1.5 #ft
ri = 1 #inch
ro = 2 #inch
#Calculations
import math
A = (math.pi*(ro**2 -ri**2))
Ai = math.pi*ri**2
#Equilibrium Eqn1 F_al +F_br = P
#Compatibility
coeff_F_br = (A*E_al)/(Ai*E_br)
#Eqn2 F_al- (coeff_F_br*F_br) = 0
#Solving equations 1 and 2 using matrices
Fal=6
Fbr=3
avg_stress_al = Fal/A
avg_stress_br = Fbr/Ai
avg_stress_al = avg_stress_al/1000
avg_stress_br = avg_stress_br/1000
#Display
print"The axial force experienced by Al = ",Fal,"ksi"
print"The axial force experienced by Brass = ",Fbr,"ksi"
print'The average normal stress in Al = ',round(avg_stress_al*1000,3),"ksi"
print'The average normal stress in Al Brass = ',round(avg_stress_br*1000,3),"ksi"
#Given
P = 15 #kN. load
a_ab = 50 #mm**2, area
a_ef =a_ab
a_cd = 30 #mm**2, area
l_ef = 0.5 #m, ef length
l_ce = 0.4 #m
l_ac = 0.4 #m
#Calculations
#In the y direction F_a +F_c +F_e = P
#of moments -F_a(l_ac)+ P(l_ac/2) +F_e(l_ce) = 0
#Compatibility equation for displacemnts
coeff_Fc = (1/a_cd) #coefficient of Fc
coeff_Fa = (0.5/a_ab) #coefficient of Fc
coeff_Fe = (0.5/a_ef) #coefficient of Fc
#Solving the 3 Equations
F_a=9.52
F_b=3.46
F_c=2.02
#Display
print"The force in rod AB = ",F_a,"kN"
print'The force in rod CD = ',F_b,"kN"
print'The force in rod EF = ',F_c,"kN"
#Given
r_o = 0.5 #inch, outside radius
r_i = 0.25 #inch, inside radius
l = 3 #inch
one_turn =20 #threads per inch
#calculations
import math
a_t = (math.pi)*(r_o**2 - r_i**2) #Area of thread
a_b = (math.pi*(r_i**2))# Area of bolt
# In Y direction F_b - F_t = 0
#Compatibility
half_turn = one_turn/2.0
#Solving the two simultaneous equations for F_b and F_t
F_b =11.22 #kip
F_t = F_b
stress_b = F_b/a_b
stress_t = F_t/a_t
F_b = F_b/1000.0
F_t = F_t/1000.0
#Display
print'The stress in the bolt ',round(stress_b,1),"ksi"
print'The stress in the screw ',round(stress_t,1),"ksi"
#Given
import math
l_ab = 800 + 400 #mm, ab length
P = 20 #kN, load
d = 5/1000.0 #m, diameter
area = (math.pi/4.0)*d**2 #Cross sectional area
l_bbdash = 1/1000.0 #m
E = 200.0 #GPa
#Calculations
#Compatibility
delta_p = (P*10**3*0.4)/(area*E*10**9) #delta = PL/AE
delta_b = delta_p-l_bbdash
F_b = (delta_b*area*E*10**9)/(l_ab/1000.0)
F_b = F_b/1000.0
#Equilibrium
F_a = P - F_b
#Display
print"The reaction at A ",round(F_a,2),"kN"
print'The reaction at B',round(F_b,2),"kN"
#Given
T1 = 60 #degree celcius
T2 = 120 #degress celcius
l_ab = 0.5 #m
area =l_ab**2 #m**2
alpha = 6.6*10**-6 # per degree celcius
E = 29*10**6 #kPa
#Equilibrium
#F_a = F_b = F
del_T = T2-T1
F = alpha*del_T*area*E #Thermal Stress Formula
avg_normal_comp_stress = (F*10**-3)/area # sigma = F/A
#Display
print"The force at A and B = ",F/1000,"kip"
print'The average normal compressive stress = ',avg_normal_comp_stress,"ksi"
#Given
area_sleeve = 600*10**-6 #m**2, area
area_bolt = 400*10**-6 #m**2, area
T1 = 15 #degree celcius
T2 = 80 #degree celcius
alpha_bolt = 12*10**-6 #per degree celcius
alpha_sleeve = 23*10**-6 #per degree celcius
l = 0.15 #m
E_bolt = 200*10**9 #N/m**2
E_sleeve = 73.1*10**9 #N/m**2
#Equilibrium
#F_s = F_b
#Compatibility
del_T = T2 - T1
delb_T = alpha_bolt*del_T*l
delb_F = l/(area_bolt*E_bolt)
dels_T = alpha_sleeve*del_T*l
dels_F = l/(area_sleeve*E_sleeve)
#delb_T + F_b*delb_F = dels_T + F_s*dels_F
F_b = (dels_T-delb_T)/(delb_F+dels_F)
F_b = F_b/1000 #in kN
F_s= F_b
#Display
print"The force experienced by sleeve and bolt, Fs=Fb ",round(F_s,1),"kN"
#Given
yiel = 250 #MPa, yield stress
r = 4 #mm, radius
width = 40 #mm
thick = 2 #mm
#a)
r_h = r/(width - (2*r))
w_h = width/(width - (2*r))
K = 1.75
area = (thick*(width - (2*r))*10**-6)
P_y = (yiel*10**6*area)/K
P_y = P_y/1000.0
#b)
P_p = (yiel*10**6*area)
P_p = P_p/1000.0
#Display
print"The maximum load P that does not cause the steel to yield ",round(P_y,2),"kN"
print'The maximum load that the bar can support ',P_p,"kN"
#Given:
P = 60 #KN, load
sigmaY= 420 #MPa, bending stress
E = 70*10**6 #MPa
l1 = 0.1 #m
l2 = 0.3 #m
r=0.005 #m
#Maximum Normal Stress:
#r_h = 6/20.0
#w_h = 40/20.0
#K = 1.6
#from sec 4.4
Fa=45
Fb=15
sigmaAC=(Fa/1000.0)/((math.pi)*r**2)
sigmaCB=(Fb/1000.0)/((math.pi)*r**2)
Fay=sigmaY*10**3*(math.pi)*r**2
Fb=P-Fay
if sigmaAC>sigmaY:
print"Calculate sigmaAC again"
else:
print"It is OK"
sigmaAC_=sigmaY
sigmaCB_=Fb/1000.0/((math.pi)*r**2)
if sigmaCB_<sigmaY:
print"It is OK"
else:
print"Calculate sigmaAC again"
dL=Fb*l2/(((math.pi)*r**2)*E)
epsilonCB=dL/l2
epsilonAC=dL/l1
epsilonY=sigmaY*10**6/(E*10**3)
sigmaACr=-sigmaAC_+sigmaAC
sigmaCBr=sigmaCB_-sigmaCB
#Display:
print"Residual stress in AC is",round(sigmaACr,0),"MPa"
print"Residual stress in CB is",round(sigmaCBr,0),"MPa"
#Given
weight = 3.0 #kip, weight
l_ab = 20.0 #ft, length
l_ac= 20.03 #ft
area = 0.05 #inch**2, area
sigmaY=50 #ksi
#calculations
strain_ab = (l_ac-l_ab)/l_ab
max_strain = 0.0017
stress_ab = (350*strain_ab)/max_strain
F_ab = stress_ab*area
E_st = 350/max_strain
del1 = l_ab/(area*10**-6*E_st*10**3)
del2 = l_ac/(area*10**-6*E_st*10**3)
T_ab=sigmaY*area
T_ac = weight-T_ab #kip
stress_in_ab = (T_ab*10**3)/area
stress = (T_ac)/area
strain_ac = (stress*max_strain)/50.0
elong_ac = strain_ac*l_ac #m
elong_ab = (l_ac-l_ab)+elong_ac #m
#Display
print'The force experienced by wire AB = ',T_ab,"kip"
print'The force experienced by wire AC = ',T_ac,"kip"
print'The elongation in wire AB = ',round(elong_ab,4),"ft"
print'The elongation in wire AC = ',round(elong_ac,5),"ft"