GATE 2026 CE (CE2) – Question 51
A simply-supported rectangular reinforced concrete beam has a width 250 mm and an overall depth 600 mm. The effective span of the beam is 6.23 m. The beam carries a live load of 5 kN/m and super imposed dead load of 5 kN/m, in addition to its own weight. The unit weight of reinforced concrete is 25 kN/m$^3$. Consider the load factor of 1.5 for all stated loads.
The design bending moment (in kN-m) for the limit state of collapse is ______ (*rounded off to two decimal places*).
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Correct answer: 99.56 to 100.56
Explanation
The self weight is $0.25 \times 0.6 \times 25 = 3.75$ kN/m. The total service load is $3.75 + 5 + 5 = 13.75$ kN/m and the factored load is $w_u = 1.5 \times 13.75 = 20.625$ kN/m. The design moment is $M_u = \frac{w_uL^2}{8} = \frac{20.625 \times 6.23^2}{8} = 100.06$ kN·m.