GATE CE 2024 Set 2 — Question 20
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Structural Engineering → Slabs, Columns & Prestressed → Two-Way Slabs
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Question
A simply supported, uniformly loaded, two-way slab panel is torsionally unrestrained. The effective span lengths along the short span (x) and long span (y) directions of the panel are and , respectively. The design moments for the reinforcements along the x and y directions are and , respectively. By using Rankine-Grashoff method, the ratio is proportional to
Correct answer
(D) (l_y/lₓ)²
Solution
According to the Rankine-Grashoff theory for two-way slabs, the load shared in the and directions ( and ) are inversely proportional to the fourth power of their respective spans to ensure equal deflection at the center:The design moments for a simply supported slab are given by:Taking the ratio:Thus, the ratio is proportional to .
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