GATE CE 2023 Set 2 — Question 16
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Structural Engineering → Determinate Structures & Energy Methods → Method of Superposition
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Question
When a simply-supported elastic beam of span and flexural rigidity ( is the modulus of elasticity and is the moment of inertia of the section) is loaded with a uniformly distributed load per unit length, the deflection at the mid-span is . If the load on one half of the span is now removed, the mid-span deflection ________.
Correct answer
(A) reduces to Δ₀/2
Solution
By the principle of superposition, the deflection at the mid-span due to a uniformly distributed load (UDL) over the entire span () is the sum of the deflections at the mid-span due to a UDL over the left half () and a UDL over the right half (). Due to the symmetry of the simply-supported beam and the loading, the mid-span deflection caused by a UDL on the left half is exactly equal to the mid-span deflection caused by a UDL on the right half. Let be the mid-span deflection due to load on the left half and be the mid-span deflection due to load on the right half. Since by symmetry:Therefore, if the load on one half of the span is removed, the mid-span deflection reduces to .
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