GATE 2025 CE (CE2) – Question 54
A reinforced concrete beam has a support section with width of 300 mm and effective depth of 500 mm. The support section is reinforced with 3 bars of 20 mm diameter at the tension side. Two-legged vertical stirrups of 10 mm diameter and Fe415 steel at a spacing of 100 mm are provided as shear reinforcement. Assume that there is no possibility of diagonal compression failure at the section.
As per IS 456:2000, the maximum shear resisted by the vertical stirrups (in kN), as per limit state design, is ___________ (round off to one decimal place).
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Correct answer: 282.18 to 285.02
Explanation
The area of two legs of 10 mm bars is $A_{sv} = 2 \times \frac{\pi}{4} \times 10^2 = 157.08$ mm². The shear resisted by vertical stirrups is $V_{us} = \frac{0.87f_yA_{sv}d}{s_v} = \frac{0.87 \times 415 \times 157.08 \times 500}{100} = 283.6 \times 10^3$ N $= 283.6$ kN.