III-RESULTANT OF NON-CONCURRENT FORCES
R2 = Rx2 + Ry
2
Rx =∑Fx
Ry =∑Fy
∑M = Rd
θ=tan-1 𝑅𝑦𝑅𝑥
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
m O2m
5kN
7kN
7kN
30˚
60˚x
y
1
1
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
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
The resultant of the three forces is a force R that passes through point B. Determine R and F.
The resultant of the belt tensions and the couple C is a force R acting through point O. Determine C and R.
The resultant of the force system shown is a 50-N m counterclockwise couple. Find P, Q and C.∙
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