The GATE Grind

GATE 2022 AE – Question 22

Structures · Flight vehicle structures: torsion, bending and shear of thin-walled sections, loads on aircraft · 1 mark · Multiple choice

The closed thin-walled rectangular channel shown in figure (i) is opened by introducing a sharp cut at the center of the bottom edge, as shown in figure (ii). Which one of the following statements is correct?

source diagram and its labels are reproduced in the attached image.
  1. Centroids of (i) and (ii) coincide while shear centers do not
  2. Shear centers of (i) and (ii) coincide while centroids do not
  3. Both centroids and shear centers of (i) and (ii) coincide
  4. Neither centroids nor shear centers of (i) and (ii) coincide

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Show answer and explanation

Correct answer: (A) Centroids of (i) and (ii) coincide while shear centers do not

Explanation

An infinitesimal slit removes negligible area, preserving the centroid. It changes the closed shear-flow path to an open section, moving the shear center.