# Chapter 2 : Force System : Components, Resultants, Equivalence¶

## Example 2.3 Page No : 21¶

In [4]:
import math

# Variables
f1 = 20. 			#lb
f2 = 40. 			#lb
alpha = 30. 			#degrees

# Calculations
R = math.sqrt(f1**2+f2**2+2*f1*f2*math.cos(math.radians(alpha)))
angle = math.degrees(math.asin((f2*math.sin(math.radians(180-alpha)))/(R)))

# Results
print  'R  = %.1f lb'%(R)
print  'angle = %.1f degrees'%(angle)

R  = 58.2 lb
angle = 20.1 degrees


## Example 2.4 Page No : 22¶

In [8]:
import math

# Variables
fx = 100. 			#lb
f1 = 200. 			#lb
f2 = 100. 			#lb
f3 = 50. 			#lb
a1 = 30. 			#degrees
a2 = 45. 			#degrees
a3 = 60. 			#degrees

# Calculations
Rx = fx+f1*math.cos(math.radians(a1))-f2*math.cos(math.radians(a2))-f3*math.cos(math.radians(a3))
Ry = f1*math.sin(math.radians(a1))+f2*math.sin(math.radians(a2))-f3*math.sin(math.radians(a3))
R = math.sqrt(Rx**2+Ry**2)
angle = math.degrees(math.atan(Ry/Rx))

# Results
print  'R  = %.f lb'%(R)
print  'angle = %.1f degrees'%(angle)

R  = 218 lb
angle = 35.7 degrees


## Example 2.5 Page No : 25¶

In [10]:
import math

# Variables
f1 = 100. 			#lb
f2 = 200. 			#lb
x1 = 2.
x2 = -3.
y1 = 3.
y2 = 5.
z1 = 4.
z2 = -2.

# Calculations
d1 = math.sqrt(x1**2+y1**2+z1**2)
d2 = math.sqrt(x2**2+y2**2+z2**2)
f1x = f1*x1/d1
f1y = f1*y1/d1
f1z = f1*z1/d1
f2x = f2*x2/d2
f2y = f2*y2/d2
f2z = f2*z2/d2
Rx = f1x+f2x
Ry = f1y+f2y
Rz = f1z+f2z
R = math.sqrt(Rx**2+Ry**2+Rz**3)
I1 = Rx/R
I2 = Ry/R
I3 = Rz/R

# Results
print  'R  = %d lb'%(R)
print  'I1 = %.3f '%(I1)
print  'I2 = %.3f '%(I2)
print  'I3 = %.3f '%(I3)

# note : rounding off error would be there for R.

R  = 227 lb
I1 = -0.264
I2 = 0.956
I3 = 0.041


## Example 2.6 Page No : 27¶

In [4]:
import math

# Variables
F = 100. 			#lb
x1 = 6. 			#in
x2 = 8. 			#in
x3 = 2. 			#in

# Calculations
xab = math.sqrt(x1**2+x2**2)
d = x3*x1/xab
M1 = F*d
Fx = F*x2/xab
Fy = F*x1/xab
M2 = Fy*xab-Fx*x1
M3 = Fy*x3

# Results
print  'M1  = %.f lb.in'%(M1)
print  'M2 = %.f lb.in'%(M2)
print  'M3 = %.f lb.in'%(M3)

M1  = 120 lb.in
M2 = 120 lb.in
M3 = 120 lb.in


## Example 2.7 Page No : 30¶

In [5]:
import math

# Variables
Fy1 = 2. 			#kips
Fy2 = 5. 			#kips
Fy3 = 10. 			#kips
Fy4 = 3. 			#kips
L = 5.   			#ft

# Calculations
Ry = Fy1+Fy2+Fy3+Fy4
x = (Fy1*L+Fy2*2*L+Fy3*3*L+Fy4*4*L)/Ry

# Results
print  'Ry = %.2f kips'%(Ry)
print  'x = %.1f ft to the right of O'%(x)

Ry = 20.00 kips
x = 13.5 ft to the right of O


## Example 2.8 Page No : 30¶

In [11]:
import math

# Variables
Fx1 = -15. 			#lb
Fx2 = 55. 			#lb
Fy1 = 70. 			#lb
Fy2 = -40. 			#lb
x1 = 4. 			#in
x2 = 3. 			#in
x3 = 5. 			#in
y1 = 4. 			#in
y2 = 2. 			#in

# Calculations
Rx = Fx1+Fx2
Ry = Fy1+Fy2
R = math.sqrt(Rx**2+Ry**2)
angle = math.degrees(math.atan(Ry/Rx))

# Results
print  'R = %.2f lb'%(R)
print  'angle = %.1f degrees'%(angle)

R = 50.00 lb
angle = 36.9 degrees


## Example 2.9 Page No : 32¶

In [8]:
import math

# Variables
Fy = 200. 			#lb
Fx = 100. 			#lb
y = 3. 	    		#in
x = 6.   			#in

# Calculations
M = Fy*x-Fx*y

# Results
print  'Moment = %.2f lb in'%(M)

Moment = 900.00 lb in