Question

A thin walled cylindrical vessel of wall thickness 't' and diameter 'd' is filled with gas to a gauge pressure of p, the maximum shear stress on the pressure wall will be

• A. $$\frac{pd}{4t}+\frac p2$$
• B. $$\frac{pd}{8t}+\frac p2$$
• C. $$\frac{pd}{8t}$$
• D. $$\frac{pd}{4t}$$

Answer 1

Answer:

$$\frac{pd}{8t}$$

The maximum shear stress on the pressure wall of a thin walled cylindrical vessel filled with gas at gauge pressure p, with wall thickness t and diameter d is pd/8t. This is the in- plane shear stress, which ignores the third principal stress. The longitudinal stress is pd/4t and the hoop stress is 2pd/4t. The maximum shear stress formula is $(\sigma_{h} - \sigma_{L}) / 2$ where $\sigma_{h}$ is hoop stress and $\sigma_{L}$ is longitudinal stress.