Resultant of General Non-concurrent Force System

Resultant of General Non-concurrent Force System

A non-concurrent general force system can be reduced to a single resultant force and a couple moment at a specified point. The magnitude and direction of resultant force can be obtained as in concurrent force system. The resultant couple moment about the specified point can be obtained by algebraically adding all the couple moments about that point.

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).