For the truss shown below, the member PQ is short by 3 mm. The magnitude of vertical displacement of joint R (in mm) is ________.

This question was previously asked in

GATE CE 2014 Official Paper: Shift 1

PQ is short by 3 mm

We have to find out vertical displacement of joint R in mm

Δ_{R} = ∑u(λ)

Let in apply unit load at R as shown below

u_{PR} sin θ = \(\frac{1}{2}\)

uPQ + uPR cos θ = 0

uPQ = -u_{PR} cos θ = \(\rm -\frac{1}{2\sin\theta}\cdot \cos\theta \)

u_{PQ} = \(\rm -\frac{1}{2}\space cot\theta = \frac{-1×4/3}{2}=\frac{-2}{3}\)

Δ_{R} = u_{PQ} × λ_{PQ} = \(\rm \frac{-2}{3} (-3) = 2\) mm upwards