Among common dished heads used on pressure vessels, which head form is inherently the strongest for a given diameter and thickness?

Introduction / Context:
Pressure vessel end closures include hemispherical, elliptical (2:1), and torispherical (flanged and dished) heads. Their strength and thickness requirements vary because of differences in stress distribution under internal pressure. Selecting the correct head type can significantly reduce required thickness and weight at a given design pressure.

Given Data / Assumptions:

• Same nominal diameter and material.
• Heads designed for the same internal pressure using basic membrane stress principles.

Concept / Approach:
A sphere is the ideal geometry for equal biaxial membrane stresses, producing the lowest maximum stress for a given thickness and pressure. Hemispherical heads therefore require the least thickness compared with elliptical and torispherical heads of the same diameter. Elliptical heads are stronger than torispherical but weaker than hemispherical; torispherical heads are typically the most economical to fabricate but need higher thickness for the same pressure.

Step-by-Step Solution:

Verification / Alternative check:
ASME code formulas for required thickness show the smallest t for hemispherical heads at equal conditions, confirming superior strength.

Why Other Options Are Wrong:

• Elliptical and torispherical have regions of higher stress (crown/knuckle) and need more thickness.
• “None of these” contradicts established design relationships.

Common Pitfalls:
Equating “strongest” with “cheapest.” Torispherical is often cheaper to fabricate despite needing more thickness.

Final Answer:
Hemispherical head