GATE 2026 AR — Planning – Question 44
An RCC stair flight has 10 steps, each 150 mm rise and 300 mm tread, over a 75 mm waist slab. Width is 1500 mm. Steel is 0.75% of total RCC volume and density 7800 kg/m³. Find reinforcement mass in kg, to two decimals.
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Correct answer: 38.00 to 44.00
Explanation
Ten triangular step prisms have volume 10×½×0.30×0.15×1.5=0.3375 m³. Sloping waist length is 10√(0.30²+0.15²)=3.35410 m; slab volume is 3.35410×0.075×1.5=0.377336 m³. Total RCC is 0.714836 m³. Steel mass is 0.714836×0.0075×7800≈41.82 kg. Waist thickness is normal to the slope, as drawn.