GATE 2024 CE (CE2) – Question 50
The horizontal beam PQRS shown in the figure has a fixed support at point P, an internal hinge at point Q, and a pin support at point R. A concentrated vertically downward load (V) of 10 kN can act at any point over the entire length of the beam.
[Figure: the beam with P fixed, the hinge Q at 15 m from P, the pin support R at 10 m from Q, and the free end S at 5 m beyond R.]
The maximum magnitude of the moment reaction (in kN.m) that can act at the support P due to V is ____________ (in integer).
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Correct answer: 150
Explanation
The part PQ is a cantilever fixed at P, and QRS is a beam on the hinge Q and the pin R, which passes a vertical force to PQ at Q. If the load is on PQ at the distance $x$ from P, the moment at P is $10x$, at most $10 \times 15 = 150$ kN m (with the load at Q). If the load is on QR at the distance $a$ from Q, the force passed to Q is $10\left(1 - \frac{a}{10}\right)$ downward, so the moment at P is at most $10 \times 15 = 150$ at $a = 0$. If the load is on the overhang RS, the beam QR pulls Q up (or pushes down by the ratio $\frac{b}{10}$ with $b \le 5$), which gives at most $5 \times 15 = 75$ kN m in the opposite sense. The maximum magnitude is 150 kN m.