This document discusses calculating the resultant force of non-concurrent forces. It provides the equations to calculate the x and y components of the resultant force and the moment. It then provides examples of calculating the resultant force and point of application for different force systems acting on structures.

1. III-RESULTANT OF NON-CONCURRENT FORCES
R2 = Rx
2 + Ry
2
Rx =∑Fx
Ry =∑Fy
∑M = Rd
θ=tan-1

2. Sample Problems
Ex1. Replace the force system by a single force
resultant and specify its coordinate point of
application (x,0) on the x-axis.
3m
O
2m
5kN
7kN
7kN
30˚
60˚
x
y
1
1

3. Ex2. Replace the loading system acting on the post by
a single resultant force and specify its point of
application on the post measured from point O.
1m
3m
2m
O
45˚
3
3
4
4
20N
70N
40N
60N

4. Ex3. Determine the resultant of the three forces
acting on the dam shown in the figure and locate its
intersection with the base AB. For a good design, the
intersection should occur within the middle third of
the base. Does it?
W=24000 lb
P=6000 lbA=10000 lb
7 ft
6 ft
4 ft
18 ftA B

5. The resultant of the three forces is a force R that
passes through point B. Determine R and F.

6. The resultant of the belt tensions and the
couple C is a force R acting through point O.
Determine C and R.

7. The resultant of the force system shown is a 50-
N∙m counterclockwise couple. Find P, Q and C.