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GATE 2022 CE (CE1) – Question 16

Solid Mechanics · Simple bending theory, flexural and shear stresses, shear centre · 1 mark · Multiple choice

Consider the cross-section of a beam made up of thin uniform elements having thickness t(t≪a) shown in the figure. The (x, y) coordinates of the points along the center-line of the cross-section are given in the figure. The coordinates of the shear center of this cross-section are:

Thin-walled open T section with unequal horizontal arms meeting the vertical web at y=3a. See the attached source image.
  1. $x=0,y=3a$
  2. $x=2a,y=2a$
  3. $x=-a,y=2a$
  4. $x=-2a,y=a$

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Correct answer: (A) $x=0,y=3a$

Explanation

Each thin branch of this open T section carries shear flow along its own centre-line. All three branch centre-lines meet at the web–flange intersection.

Their resultant therefore passes through that intersection without a torque. This identifies the shear centre even though the flange arms are unequal. The intersection is $(x,y)=\mathbf{(0,3a)}$, **A**.