GATE 2021 CE (CE1) – Question 51
A simply supported 8 m beam carries a 100 kN midspan point load. Its left half has rigidity E(2I), right half EI, with E=3×10⁴ N/mm² and I=225×10⁶ mm⁴. Find downward midspan deflection in mm, rounded to integer.
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Correct answer: 100 to 130
Explanation
Use virtual work with a unit load at midspan. Each half contributes its integral of Mm/(EI); the left contribution is half the right because its inertia doubles. Consequently the deflection is 3/4 of the uniform-EI result: $\delta=\tfrac34 PL^3/(48EI)=118.5185$ mm. Rounded, **119 mm**. This is equivalent to assembling the two beam-element stiffness matrices.