Question

if a thin-walled cylindrical pressure vessel with radius r and wall thickness t has internal pressure p, would we expect failure according to the criterion of absolute maximum shear stress with a material of yield strength sy and a safety factor sf? by what factor might we multiply thickness to ensure safety?

Answer 1

To determine if a thin-walled cylindrical pressure vessel will fail according to the criterion of absolute maximum shear stress, calculate the maximum shear stress and compare it to the yield strength multiplied by the safety factor.

If failure is expected, the thickness of the vessel can be multiplied by a factor greater than 1 to ensure safety.

Step-by-step explanation:

According to the criterion of absolute maximum shear stress, a thin-walled cylindrical pressure vessel with internal pressure may fail if the maximum shear stress exceeds the yield strength of the material.

To determine if failure is expected, we need to calculate the maximum shear stress and compare it to the yield strength multiplied by the safety factor. The formula to calculate the maximum shear stress is:

σ_max = p * r / t

Where σ_max is the maximum shear stress, p is the internal pressure, r is the radius of the vessel, and t is the wall thickness of the vessel.

If σ_max is greater than the yield strength (sy) multiplied by the safety factor (sf), then failure is expected. To ensure safety, the thickness of the vessel can be multiplied by a factor greater than 1.