GATE 2022 CE (CE1) – Question 53
A reinforced concrete beam with rectangular cross section (width = 300 mm, effective depth = 580 mm) is made of M30 grade concrete. It has 1% longitudinal tension reinforcement of Fe 415 grade steel. The design shear strength for this beam is 0.66 N/mm2. The beam has to resist a factored shear force of 440 kN. The spacing of two-legged, 10 mm diameter vertical stirrups of Fe 415 grade steel is __________mm. (round off to the nearest integer)
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Correct answer: 101
Explanation
Concrete carries $V_c=\tau_cbd=0.66(300)(580)=114840$ N. The stirrups must carry $V_{us}=440000-114840=325160$ N.
For two 10 mm legs, $A_{sv}=2\pi10^2/4=157.080$ mm². Use $V_{us}=0.87f_yA_{sv}d/s$: $s=0.87(415)(157.080)(580)/325160=101.16$ mm. **Answer: 101 mm**.