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GATE 2021 MN – Question 48

Geomechanics and Ground Control · Engineering Mechanics · 2 marks · Numerical answer

A simply supported 2 m beam carries a triangular UDL increasing from zero at A to 5 kN/m at B. Find maximum bending moment in kN·m, to two decimals.

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Correct answer: 1.20 to 1.35

Explanation

Total load is 5 kN, acting at 2L/3 from A. Reactions are R(A)=5/3 and R(B)=10/3 kN. At x from A, shear is 5/3−1.25x²; zero shear gives x=√(4/3) m. Moment is(5/3)x−(5/12)x³, giving 1.2830 kN·m, or 1.28.

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