GATE 2022 AR — Architecture – Question 63
The beam diagram shows supports W and Y 4 m apart, a 1 m overhang YZ, 20 kN/m UDL over WY and 120 kN downward at Z. Section X–X is 2 m from W. Taking sagging positive and hogging negative, find moment at X–X in kN·m to one decimal.
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Correct answer: -20.0 to -20.0
Explanation
Taking moments about W:4R(Y)=80×2+120×5=760, so R(Y)=190 kN. Vertical equilibrium gives R(W)=200−190=10 kN. At X, the left-side segment gives M=10×2−20×2²/2=20−40=−20.0 kN·m. The negative sign indicates hogging.