# Chapter 4 : Equilibrium¶

## Example 4.3 Page No : 71¶

In [1]:
import math
from numpy import linalg

# Variables
W = 100. 			#lb
a1 = 30. 			#degrees
a2 = 45. 			#degrees

# Calculations
b =[[0],[W]]
c = linalg.solve(A,b)
Tbc = c[0]
Tab = c[1]

# Results
print  'Tbc = %.1f lb'%(Tbc)
print  'Tab =%.1f lb'%(Tab)

Tbc = 89.7 lb
Tab =73.2 lb


## Example 4.4 Page No : 72¶

In [2]:
import math

# Variables
W1 = 7000. 			#lb
W2 = 1000. 			#lb
W3 = 3000. 			#lb
x1 = 6. 			#in
x2 = 9. 			#in
x3 = 10. 			#in
x4 = 5. 			#in

# Calculations
Rb = (W1*x1+W2*(x1+x2)+W3*(x1+x2+x3))/(x1+x2+x3+x4)
Ra = W1+W2+W3-Rb

# Results
print  'Rb = %.1f lb'%(Rb)
print  'Ra = %.1f lb'%(Ra)

Rb = 4400.0 lb
Ra = 6600.0 lb


## Example 4.5 Page No : 74¶

In [3]:
import math

# Variables
Fc = 500. 			#lb
Fd = 1000. 			#lb
xc = 2. 			#in
xd = 8. 			#in
y = 6.   			#in

# Calculations
Ay = Fc+Fd
Bx = (Fc*xc+Fd*xd)/y
Ax = Bx
A = math.sqrt(Ax**2+Ay**2)

# Results
print  'A = %.f lb'%(A)
print  'B = %.f lb'%(Bx)

A = 2121 lb
B = 1500 lb


## Example 4.6 Page No : 75¶

In [4]:

# Variables
W = -300. 			#lb
r = 4. 			#in
x1 = 2. 			#ft
x2 = 3. 			#ft
x3 = 1. 			#ft
y1 = 1. 			#ft
x4 = 3. 			#in

# Calculations
F = -W*r/(y1*12)
By = -W*x1/(x1+x2)
Bz = -F*(x1+x2+x3+(x4/12))/(x1+x2)
Ay = -W-By
Az = -F-Bz

# Results
print  'Ay  = %.2f lb'%(Ay)
print  'By = %.2f lb'%(By)
print  'Az = %.2f lb'%(Az)
print  'Bz = %.2f lb'%(Bz)
print  'F = %.2f lb'%(F)

Ay  = 180.00 lb
By = 120.00 lb
Az = 25.00 lb
Bz = -125.00 lb
F = 100.00 lb


## Example 4.7 Page No : 77¶

In [5]:
import math

# Variables
W = 500. 			#lb
r = 4. 			#in
Lx = 3. 			#in
Ly = 12. 			#in
Lz = 4. 			#in

# Calculations
Tbd = W*(math.sqrt((-Lx)**2+(-Ly)**2+(-Lz)**2))/Ly
Tcd = Lx*Tbd/(math.sqrt((-Lx)**2+(-Ly)**2+(-Lz)**2))

Tbd = 542 lb