GATE 2026 ME – Question 49
A simply supported beam is subjected to an external point load P as shown in the figure below. The beam has a rectangular cross-section of 20 mm $\times$ 45 mm. A is a pin support and B is a roller support. The shear stress developed at point C, lying on the neutral axis of the beam, is 3 MPa. Neglecting the mass of the beam, the magnitude of the applied load is ________ kN (*rounded off to 1 decimal place*).
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 2.98 to 3.02
Explanation
The beam spans $1 + 1 + 3 = 5$ m with the load at 2 m from A. The reaction at A is $R_A = P \times \frac{3}{5} = 0.6P$, and this is the shear force at C. For a rectangular section, the shear stress at the neutral axis is $\tau = \frac{3V}{2A}$ with $A = 20 \times 45 = 900$ mm$^2$. With $\tau = 3$ MPa, $V = \frac{2 \times 3 \times 900}{3} = 1800$ N. So $0.6P = 1800$ and $P = 3000$ N, which is 3.0 kN.