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GATE 2022 CE (CE1) – Question 13

Solid Mechanics · Transformation of stress, Mohr circle · 1 mark · Multiple choice

The hoop stress at a point on the surface of a thin cylindrical pressure vessel is computed to be 30.0 MPa. The value of maximum shear stress at this point is

  1. 7.5 MPa
  2. 15.0 MPa
  3. 30.0 MPa
  4. 22.5 MPa

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Correct answer: (B) 15.0 MPa

Explanation

For a thin closed cylindrical vessel, longitudinal stress is half the hoop stress: $\sigma_L=15$ MPa. The three principal stresses at the surface are approximately 30, 15 and 0 MPa.

The **absolute** maximum shear is $(\sigma_{max}-\sigma_{min})/2=(30-0)/2=\mathbf{15}$ MPa, **B**. The in-plane value 7.5 MPa omits the zero radial principal stress.