Chapter 3 : Center of Gravity

Example 3.1 Page No : 50

In [2]:
import math 
			
# Variables
W = 3000. 			#lb
L = 10.   			#ft
Wf1 = 1200. 			#lb
Wf2 = 1500. 			#lb
angle = 30. 			#degrees
			
# Calculations
d1 = Wf1*math.cos(angle)*L/W
d2 = Wf2*L/W
xbc = d1/math.cos(angle)
xab = d2-xbc
y = xab/math.tan(math.radians(angle))
			
# Results
print  'x  = %.2f ft'%(d2)
print  'y = %.2f ft'%(y)

x  = 5.00 ft
y = 1.73 ft

Example 3.2 Page No : 51

In [3]:
			
# Variables
W4 = 3. 			#lb
W3 = 5. 			#lb
W2 = 2. 			#lb
W1 = 6. 			#lb
x1 = 10. 			#in
x2 = 4. 			#in
z = 5. 			#in
			
# Calculations
W = W1+W2+W3+W4
x = (W1*0+W2*0+W3*x2+W4*x1)/W
z = (W1*z+W2*0+W3*0+W4*0)/W
			
# Results
print  'x  = %.2f in'%(x)
print  'z = %.2f in'%(z)

x  = 3.12 in
z = 1.88 in

Example 3.3 Page No : 52

In [4]:
			
import math 
# Variables
W1 = 3. 			#lb
W2 = 5. 			#lb
x1 = 8. 			#in
x2 = 7. 			#in
y1 = 2. 			#in
y2 = 5. 			#in
z1 = 6. 			#in
z2 = 4. 			#in
			
# Calculations
W = W1+W2
x = (W1*x1+W2*x2)/W
y = (W1*y1+W2*y2)/W
z = (W1*z1+W2*z2)/W
			
# Results
print  'x  = %.2f in'%(x)
print  'y = %.2f in'%(y)
print  'z = %.2f in'%(z)

x  = 7.38 in
y = 3.88 in
z = 4.75 in

Example 3.4 Page No : 54

In [3]:
import math 
			
# Variables
L = 9.   			#in
B = 16. 			#in
B1 = 6. 			#in
d = 2. 	    		#in
			
# Calculations
x = ((L*(B-B1)*(L/2)+(1./2)*L*B1*(L/3)-(math.pi/4)*d**2*(L/2)))/(L*(B-B1)+(1./2)*L*B1-(math.pi/4)*d**2)
y =  ((L*(B-B1)*((B-B1)/2)+(1./2)*L*B1*(B1/3+(B-B1))-(math.pi/4)*d**2*((B-B1)/2)))/(L*(B-B1)+(1./2)*L*B1-(math.pi/4)*d**2)
			
# Results
print  'x  = %.2f in to the right of y-axis'%(x)
print  'y = %.2f in above x axis'%(y)

x  = 4.14 in to the right of y-axis
y = 6.66 in above x axis

Example 3.5 Page No : 57

In [6]:
			
# Variables
Gt = 0.25 			#in
St = 0.25 			#in
Gw = 3.5 			#lb/sq ft
Sw = 10. 			#lb/sq ft
Sb = 36. 			#in
Sb1 = 18. 			#in
Sb2 = 12. 			#in
Sb3 = 6. 			#in
Sy1 = 6. 			#in
Sy2 = 12. 			#in
Sy3 = 6. 			#in
Gb = 1. 			#ft
Sh = 24. 			#in
Gh = 1. 			#ft
			
# Calculations
W = ((Sb*Sh)/(12*12)-(Gh*Gb))*Sw+(Gh*Gb)*Gw
x = ((Sb*Sh)*Sw*(Sb/24)/(12*12)-(Gh*Gb)*Sw*((Sb1+(Sb2/2))/12)+(Gh*Gb)*Gw*((Sb1+(Sb2/2))/12))/W
			
# Results
print  'centre of gravity  = %.2f ft to the right of y-axis'%(x)

centre of gravity  = 1.44 ft to the right of y-axis