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GATE 2023 CE (CE2) – Question 16

Structural Analysis · Principle of superposition, virtual work and Castigliano theorem · 1 mark · Multiple choice

When a simply-supported elastic beam of span L and flexural rigidity EI (E is the modulus of elasticity and I is the moment of inertia of the section) is loaded with a uniformly distributed load w per unit length, the deflection at the mid-span is $\Delta_0=5wL^4/(384EI)$. If the load on one half of the span is now removed, the mid-span deflection ______.

  1. reduces to $\Delta_0/2$
  2. reduces to a value less than $\Delta_0/2$
  3. reduces to a value greater than $\Delta_0/2$
  4. remains unchanged at $\Delta_0$

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Correct answer: (A) reduces to $\Delta_0/2$

Explanation

**Use superposition and symmetry.** Split the full-span UDL into a load on the left half and a load on the right half.

- The beam is symmetric about the mid-span, so a UDL on the left half and a UDL on the right half each produce **the same deflection at mid-span**.
- By superposition, the two deflections add up to the full-load value:
$$\Delta_{left}+\Delta_{right}=\Delta_0\;\Rightarrow\;\Delta_{left}=\Delta_{right}=\frac{\Delta_0}2 .$$

Removing the load from one half therefore leaves exactly one of those two parts, so the mid-span deflection **reduces to $\Delta_0/2$** (option A).