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GATE 2024 CE (CE2) – Question 20

Concrete Structures · Design and detailing of beams and slabs · 1 mark · Multiple choice

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 $l_x$ and $l_y$, respectively. The design moments for the reinforcements along the x and y directions are $M_{ux}$ and $M_{uy}$, respectively. By using Rankine-Grashoff method, the ratio $M_{ux}/M_{uy}$ is proportional to

  1. $l_x/l_y$
  2. $l_y/l_x$
  3. $(l_x/l_y)^2$
  4. $(l_y/l_x)^2$

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Correct answer: (D) $(l_y/l_x)^2$

Explanation

The load is shared in proportion to $\frac{l_y^4}{l_x^4 + l_y^4}$ in the x-direction and $\frac{l_x^4}{l_x^4 + l_y^4}$ in the y-direction. The moments are $M_{ux} = \frac{w_xl_x^2}{8}$ and $M_{uy} = \frac{w_yl_y^2}{8}$. Then $\frac{M_{ux}}{M_{uy}} = \frac{l_y^4l_x^2}{l_x^4l_y^2} = \left(\frac{l_y}{l_x}\right)^2$.