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GATE 2026 CE (CE1) – Question 13

Solid Mechanics · Simple stress and strain relationships · 1 mark · Multiple choice

A thin-walled spherical gas balloon of radius $R$ and wall thickness $t$ ($t \ll R$) is subjected to an internal (gauge) pressure $p$. The maximum tensile and shear stresses in the balloon wall are, respectively:

  1. Zero and $pR/2t$
  2. $pR/2t$ and Zero
  3. $pR/2t$ and $pR/4t$
  4. $pR/4t$ and Zero

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Correct answer: (C) $pR/2t$ and $pR/4t$

Explanation

In a thin spherical shell the stress is the same in every direction in the wall, $\sigma = \frac{pR}{2t}$. In the plane of the wall the Mohr circle collapses to a point, so the in-plane shear is zero. Including the thickness direction, where the stress is almost zero, the largest shear stress is half of the tensile stress, $\frac{pR}{4t}$.