Solved Example & Practice Problems: Equilibrium of a Rigid Body in Space

Solved Examples for Understanding

Example 4.8.1 

Determine tensions is cords BD and BE which hold a rigid light member in horizontal position as shown. Assume A as ball and socket joint.

Solution: 

The unknown reactions at A can be avoided in equations by taking moment about A.

Example 4.8.2 

A plate ACED weighs 7,600 kg/m3. It is held in horizontal plane by three wires at A B and C. Find tensions in the wires. Refer Fig. 4.8.2.

Solution: 

The weight of the plate is

W = ρ × g × Volume

= 7600 × 9.81 × 0.9 × 1.2 × 10 × 10-3

⸫ W = 805.205 N

It acts through the C.G. shown in Fig. 4.8.2 (a).

Example 4.8.3

Fig. 4.8.3 shows steel pipe ABCD of length 1.8 m having 90° bend at B. The pipe weights 30 N/m and supported by three vertical wires attached to the pipe at A, C and D. Find tension in wires.

Solution: 

The weights of AB and CD are shown acting through their centres in Fig. 4.8.3 (a).

Consider moments about a line DE parallel to z-axis.

Example 4.8.4 

The uniform concrete slab has a weight of 5500 N. Determine tension in each of the three parallel supporting cables when the slab is held in horizontal plane as shown in Fig. 4.8.4.

Solution: 

Weight of slab acts at its centre

⸫ (TB) (0.6) + (5500) (0.3) = 0

Examples for Practice

Q.1

The uniform rectangular plate shown in Fig. 4.8.5 has a weight of 1000 N. Determine tension in each of the three parallel supporting cables when the plate is in the horizontal plane. 

[Ans.: TA = 250 N, TB : = 250 N, TC = 500 N] 

Q.2

A homogeneous rectangular plate of weight,500 N is held in the horizontal position by three cables as shown in Fig. 4.8.6. Find tension in the three cables.

 [Ans. : TA = 250 N, TB = 0, TC = 250 N]

Q.3

A 10 kN platform (3m × 5m) is supported vertically at A, B and C and carries 6 kN load as shown in Fig. 4.8.7. Determine reaction at each point of support.

[Ans. : RA = 3.909 kN ↑, RB = 5.818 kN ↑, RC = 6.273 kN ↑]