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GATE 2023 CE (CE1) – Question 39

Structural Analysis · Deflections of determinate beams, frames and trusses · 2 marks · Multiple choice

Consider the pin-jointed truss shown in the figure (not to scale). All members have the same axial rigidity, $AE$. Members QR, RS, and ST have the same length $L$. Angles QBT, RCT, SDT are all 90°. Angles BQT, CRT, DST are all 30°. The joint T carries a vertical load $P$. The vertical deflection of joint T is $k\frac{PL}{AE}$. What is the value of $k$?

a truss with the top chord Q-R-S-T along a line inclined at 30° to the vertical, vertical members QB, RC and SD, a horizontal bottom chord B-C-D-T, and diagonals BR and CS. Q is a hinge support and B is a roller support on the vertical wall.
  1. 1.5
  2. 4.5
  3. 3.0
  4. 9.0

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Show answer and explanation

Correct answer: (B) 4.5

Explanation

The truss was analysed with the direct stiffness method for the given geometry ($QR = RS = ST = L$, the posts QB, RC, SD vertical, the diagonals BR and CS, a hinge at Q and a horizontal roller at B), with all members having the same $AE$ and the load $P$ at T. The vertical deflection of T is $4.5\frac{PL}{AE}$ downward. So $k = 4.5$.