GATE 2020 CE (CE2) – Question 52
The shown plane truss has hinge supports P and W and horizontal loads as shown. Taking tension positive and compression negative, find member XW force (kN), nearest integer.
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Correct answer: -31 to -29
Explanation
The overturning moment is $10(4+8+12)=240$ kN·m. With support spacing 4 m, reactions are 60 kN up at W and 60 kN down at P. Successive joint equilibrium from the unloaded top-right joint gives right-column forces 0, −10 and −30 kN in ZY, YX and XW. Thus **$F_{XW}=-30$ kN**, compression. The diagonal into W carries the remaining vertical reaction.