Chapter 8 : Concept of Stress

Example 8.1 Page No : 158

In [1]:
			
# Variables
F = -100 			#lb
x1 = 3 			#in
y = 6 			#in
x2 = 24 			#in
x3 = 12 			#in
			
# Calculations
Force = -F
Moment = -F*(x2+x1)
Torque = -F*y
			
# Results
print  'Force = %.2f lb'%(Force)
print  'Moment =%.2f lb.in'%(Moment)
print  'Torque =%.2f lb.in'%(Torque)

Force = 100.00 lb
Moment =2700.00 lb.in
Torque =600.00 lb.in

Example 8.2 Page No : 159

In [2]:
			
# Variables
F = -5000. 			#lb
D = 250. 			#lb/ft
y1 = 4. 			#in
y2 = 2. 			#in
y3 = 5. 			#in
y4 = 3. 			#in
x = 3.   			#in
			
# Calculations
Ax = -D*y1
Ay = -F
M = (D*y1*(y2+y3+y1/2.))-F*x
			
# Results
print  'Ax = %.2f lb'%(Ax)
print  'Ay =%.2f lb'%(Ay)
print  'M =%.2f lb.in'%(M)

Ax = -1000.00 lb
Ay =5000.00 lb
M =24000.00 lb.in

Example 8.3 Page No : 160

In [1]:
import math 
			
# Variables
P = 5    			#kips
angle = 30 			#degrees
			
# Calculations
Fn = P*math.sin(math.radians(angle))
Ft = P*math.cos(math.radians(angle))
			
# Results
print  'Fn = %.2f lb'%(Fn)
print  'Ft =%.2f lb'%(Ft)

Fn = 2.50 lb
Ft =4.33 lb

Example 8.4 Page No : 162

In [3]:
import math 
			
# Variables
p = 5.   			#tons
dt = 0.75 			#in
db = 0.5 			#in
b = 0.5 			#in
h = 2.   			#in
			
# Calculations
Sc = p*2000/((math.pi/4)*(dt**2))
Sr =  p*2000/(b*h)
Sb =  p*2000/(2*(math.pi/4)*db**2)
			
# Results
print  'Stress in circular scetion = %.2f psi tension'%(round(Sc,-2))
print  'Stress in rectangular section = %.2f psi tension'%(Sr)
print  'Stress in bolt = %.2f psi tension'%(round(Sb,-2))

Stress in circular scetion = 22600.00 psi tension
Stress in rectangular section = 10000.00 psi tension
Stress in bolt = 25500.00 psi tension

Example 8.5 Page No : 168

In [7]:
			
# Variables
w = 8 			#in
wperft = 35. 			#lb/ft
A = 10.3 			#sq in
F1 = 3. 			#tons
F2 = 3. 			#tons
F3 = -8. 			#tons
F4 = -8. 			#tons
F5 = -5. 			#tons
F6 = -5. 			#tons
Pl = 12. 			#in
Pb = 12. 			#in
			
# Calculations
Sa = (F1+F2)*2000/A
Sb = -(F3+F4+F1+F2)*2000/A
Sc = -(F3+F4+F1+F2+F5+F6)*2000/A
Sp = -(F3+F4+F1+F2+F5+F6)*2000/(Pl*Pb)
			
# Results
print  'Stress in a = %.2f psi tension'%(round(Sa,-1))
print  'Stress in b = %.2f psi tension'%(round(Sb,-1))
print  'Stress in c = %.2f psi tension'%(round(Sc,-1))
print  'Stress in plate = %.f psi tension'%(Sp)

Stress in a = 1170.00 psi tension
Stress in b = 1940.00 psi tension
Stress in c = 3880.00 psi tension
Stress in plate = 278 psi tension

Example 8.6 Page No : 166

In [10]:
import math 
			
# Variables
Ns = 8000. 			#psi
Ss = 4000. 			#psi
Ws = 25000. 			#psi
angle = 30. 			#degrees
L = 4. 			#in
b = 1. 			#in
			
# Calculations
P = Ns*L*b/((math.cos(math.radians(2*angle)))**2)
P1 = 2*Ss*L*b/(math.sin(math.radians(2*angle)))
Pts = Ws*L*b
e = P1/Pts
			
# Results
if (P<P1):
    print  'P = %.2f lb'%(round(P,-3))
else:
    print  'P1 = %.2f lb'%(round(P1,-3))

print  'efficiency of the joint = %.2f '%(e)

P1 = 37000.00 lb
efficiency of the joint = 0.37

Example 8.7 Page No : 167

In [12]:
			
# Variables
T = 15000 			#psi
h1 = 3 			#in
h2 = 2.5 			#in
t = 0.25 			#in
r = 5/16. 			#in
d = 1. 			#in
			
# Calculations
P1 = T*(h1-d)*t/2.18
P2 = T*h2*t/1.7
if (P1<P2):
    print  'Safe axial load = %.f lb'%(P1)
else: 
    print  'Safe axial load = %.f lb'%(P2)

Safe axial load = 3440 lb

Example 8.8 Page No : 174

In [19]:
			
# Variables
d = 16.   			#ft
h = 24. 	    		#ft
P = 160. 			#lb/cu ft
hs1 = 8. 			#ft
hs2 = 8. 			#ft
hs3 = 8. 			#ft
Tsmax = 5000. 			#psi
			
# Calculations
SW = round(P/1728,4)
P8 = round(SW*hs1*12,2)
P16 = round(SW*(hs1+hs2)*12,1)
P24 = round(SW*(hs1+hs2+hs3)*12,1)
t8 = (P8*d*12)/(2*Tsmax)
t16 = P16*d*12/(2*Tsmax)
t24 = P24*d*12/(2*Tsmax)
			
    
# Results
print  't8 = %.2f in'%(t8)
print  't16 = %.2f in'%(t16)
print  't24 = %.2f in'%(t24)

# note : book answers are wrong. please check. 

t8 = 0.17 in
t16 = 0.34 in
t24 = 0.51 in