Thick-walled cylinder under internal pressure p: The circumferential (tangential) stress is tensile while the radial stress is compressive across the thickness. Is this statement correct?

Introduction / Context:
Pressurized cylinders (gun barrels, pressure vessels, pipes) exhibit non-uniform stress fields. Distinguishing tangential (hoop) and radial stresses is crucial in thick-cylinder design using Lame’s equations.

Given Data / Assumptions:

• Internal pressure p acts; external pressure may be zero unless stated.
• Thick cylinder theory (Lame) applies; elastic, isotropic material.
• Ends closed; plane strain in axial direction if long.

Concept / Approach:
In a thick tube:sigma_theta (hoop) is tensile and highest near the inner radius.sigma_r (radial) is compressive, equal to −p at the inner surface and reduces in magnitude toward the outer surface (often to zero if external pressure is zero).

Step-by-Step Solution:

Verification / Alternative check:
Plotting sigma_r across thickness shows negative values increasing toward zero; sigma_theta always positive for internal pressure only, confirming the statement.

Why Other Options Are Wrong:
“Incorrect” contradicts thick-cylinder solutions.Dependence on external pressure alone is false; sign pattern holds for p_ext = 0.Truth limited to a surface is incorrect; the sign trend holds throughout thickness.

Common Pitfalls:
Using thin-cylinder formulas; confusing sign conventions; assuming radial stress is tensile at the outer surface without external pressure.

Final Answer:

Correct