Solved Example & Practice Problems: Equivalent Force Systems

Solved Examples for Understanding

Example 3.8.1 

Resolve the 500 N force acting along OO' shown in Fig. 3.8.1 into two components along a) A-B and C-D b) C-D and E-F c) A-B and G-H.

Solution: 

a) Let the two components be FAB and FCD as shown in Fig. 3.8.1 (a).

Here we are replacing one system of forces consisting of a single 500 N force by another system consisting of two forces.

b) The two equivalent force systems are as shown in Fig. 3.8.1 (b).

c) The two equivalent force systems are as shown in Fig. 3.8.1 (c).

Example 3.8.2 

Replace the 1000 N force acting at A by two forces - a vertical force at B and a force at C. Refer Fig. 3.8.2.

Solution: 

The first force system consisting of a single 1000 N force at A is to be replaced by another force system as shown in Fig. 3.8.2 (a).

• Assume force at B to be upward and the force at C to be in first quadrant with components Fx and Fy.

1000 sin 60 = FB + Fy     ... (1)

• Moments of the two systems can be equated about any point but if moments are equated about B or C, one of the values can be directly obtained.

Example 3.8.3 

Replace the force and couple acting on the rectangular plate shown in Fig. 3.8.3 by two forces – a horizontal force at B and another force at D.

Solution: 

The equivalent force system is shown in Fig. 3.8.3 (a).

Example 3.8.4 

Determine the resultant of the force system acting on triangular plate ABC shown in Fig. 3.8.4. Replace this force system by three forces acting along the sides of the triangular plate.

Solution : 

• Let the resultant of given force system be R1. The two 40 N forces acting at B and C are in opposite directions and hence cancel each other.

• As the force is vertical, it will intersect the horizontal axis AC at a distance 'x' from A as shown in Fig. 3.8.4 (a). Using Varignon's theorem at A,

• Consider the equivalent force system consisting of three forces F1, F2 and F3 acting along the sides of the triangular plate as shown in Fig. 3.8.4 (b).

Examples for Practice

Q.1

Resolve the 1000 N force acting along OO' in Fig. 3.8.5 into two components along

a) A – A and B - B

b) B – B and C - C

Q.2

Replace the 1000 N force acting at A by two forces a horizontal force at C and a force at B. Refer Fig. 3.8.6.