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.∙