Solved Example & Practice Problems: Resultant of General Non-concurrent Force System

Solved Examples for Understanding

Example 3.13.1 

Find resultant force and moment at origin. Refer Fig. 3.13.1.

Solution: 

The required co-ordinates are A (0, 100, 150), C (80, 100, 0), D (0, 100, 0), G (80, 0, 0), E (0, 0, 150)

Example 3 13 2 

Force P1 = 10 N acts from A (3,2,-1) to B (8, 5,3) and force P2 = 5N acts from B to C(-2, 11, 5). Compute a) resultant of the forces b) moment of resultant about point (1, 1, 1). c) components of resultant along line BE where point E has co-ordinates (5,8.3)

Solution: 

Component of resultant along

Example 3.13.3 

A machine component is subjected to the forces as shown in Fig. 3.13.2 each of which is parallel to one of the co-ordinate axes. Replace these forces by an equivalent force couple system at origin 'O'.

Solution: 

Example 3.13.4 

A 20-kg ladder (Fig. 3.13.3) used to reach high shelves in a store room is supported by two flanged wheels A and B mounted on a rail and by an unflanged wheel Cresting against a rail fixed to the wall. An 80-kg man stands on the ladder and leans to the right. The line of action of the combined weight W of the man and ladder intersects the floor at point D. Detremine the reactions at A, B and C.

Solution: 

The free body diagram of ladder is shown in Fig. 3.13.3 (a).

Examples for Practice

Q.1

Determine resultant of four forces shown in Fig. 3.13.4 and resultant couple system at the origin (F2 = 20 √2 N).

Q.2

Three forces F1 = 20 N, F2 = 10 N and F3 = 20 N act on a bent pipe as shown in Fig. 3.13.5. Replace the system by a force couple system at the origin.