Question

A rod AD of length 40 cm is suspended from point D as shown in figure. If it has a weight of 25 N and also supports a load of 40N,find the tension in the cable using the method of virtual work.Take AC=30 cm.

Given : Length of rod AD=40cm=0.4m
AC=0.3m
W=25N
Load on rod AD=40N
To find : Tension in the cable

Answer 1

Assume rod AD have a small virtual angular displacement 𝛿θ in the clockwise direction T is the tension in the cable

Assume A be the origin and AX be the X-axis
Reaction forces HA and VA do not do any virtual work

Sr. no.	Active force	Co-ordinate of the point of action along the force	Virtual displacement
1.	W = 25N	0.2sinθ	𝛿yB=0.2cosθ 𝛿θ
2.	40 N	0.3sinθ	𝛿yC=0.3cosθ 𝛿θ
3.	T	0.4sinθ	𝛿yD=0.4cos θ𝛿θ

By using the principle of virtual work

, 𝛿U=0

-25 x 𝛿yB -40 x 𝛿yC +T x 𝛿yD=0

T x 𝛿yD = 25 x 𝛿yB + 40 x 𝛿yC

T x (0.4cos θ𝛿θ) = 25 x (0.2cosθ 𝛿θ) + 40 x (0.3cosθ 𝛿θ) Dividing by cosθ 𝛿θ and solving
T=42.5N
Tension in the cable=42.5N