The GATE Grind

GATE 2021 ME (ME1) – Question 61

Mechanics of Materials · Bending and shear stresses, shear centre · 2 marks · Numerical answer

An overhanging beam PQR is subjected to uniformly distributed load 20 kN/m as shown in the figure. The maximum bending stress developed in the beam is _____ MPa (round off to one decimal place).

Beam PQR supported at P,Q, with PQ=2000 mm and QR=1000 mm, carrying 20 kN/m throughout; section is 24 mm wide and 100 mm deep. See the attached source image.

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: 248.75 to 251.25

Explanation

Reactions are RQ=45 kN and RP=15 kN. On PQ, zero shear occurs at x=15/20=0.75 m, where positive moment is 5.625 kNm. The overhang produces moment −20(1)²/2=−10 kNm at Q, the larger magnitude.

Section modulus is $Z=24(100)^2/6=40000$ mm³. Thus maximum stress is $10^7/40000=\mathbf{250.0}$ MPa.