GATE CE 2026 Set 1 — Question 13
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Structural Engineering → Stress, Strain & Beams → Principal Stresses & Planes
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Question
A thin-walled spherical gas balloon of radius and wall thickness () is subjected to an internal (gauge) pressure . The maximum tensile and shear stresses in the balloon wall are, respectively:
Correct answer
(B) (pR)/(2t) and Zero
Solution
For a thin-walled spherical pressure vessel with internal pressure , radius , and thickness :
1.Principal Stresses: The principal stresses in the plane of the shell are equal in all directions:
The third principal stress (radial stress) is at the outer surface (since ).2.Maximum Tensile Stress: The maximum tensile stress is the largest principal stress:
3.Maximum Shear Stress:
- In-plane maximum shear stress:
- Absolute maximum shear stress:
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