Question

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

• A. 7.5 MPa
• B. 15.0 MPa
• C. 30.0 MPa
• D. 22.5 MPa

Hint:

In thin-walled pressure vessels, the maximum shear stress is half of the hoop stress. This relation is important in designing safe pressure vessels.

Answer 1

The Correct Option is A

For a thin cylindrical pressure vessel, the relationship between hoop stress (\(\sigma_h\)) and maximum shear stress (\(\tau_{max}\)) is given by: \[ \tau_{max} = \frac{\sigma_h}{2} \] Given that the hoop stress at the point is 30.0 MPa, we can substitute this value into the equation: \[ \tau_{max} = \frac{30.0}{2} = 15.0 \text{ MPa} \] Thus, the value of the maximum shear stress at this point is 15.0 MPa, which corresponds to option (A).