Dished heads: for better strength, the knuckle radius of a torispherical head should meet a minimum. The provided knuckle radius should be not less than which criterion?

Introduction / Context:
Torispherical (dished) heads have a crown with a toroidal knuckle that blends into the shell. The knuckle radius strongly influences stress concentration at the junction; larger radii generally reduce peak stresses and improve fatigue and buckling resistance.

Given Data / Assumptions:

• Geometric parameters: inside diameter D, thickness t.
• We consider common code practice for minimum knuckle radius.
• Goal: avoid excessive stress concentration at the knuckle.

Concept / Approach:
Design rules typically require the knuckle radius r to be at least a certain fraction of diameter and also a multiple of thickness. Using a “whichever is larger” rule ensures sufficient radius across sizes and thicknesses, preventing an undersized radius in thick or large heads.

Step-by-Step Solution:

Verification / Alternative check:
This rule matches common design handbooks and reduces local membrane and bending stresses in the knuckle region compared with smaller radii.

Why Other Options Are Wrong:

• 6% of I.D. or 3t alone: may be non-conservative for certain sizes.
• Whichever is smaller: unsafe because it can permit too tight a radius.
• Fixed value: does not scale with geometry.

Common Pitfalls:
Misreading “less than” vs “not less than”; ignoring the thickness criterion for small-diameter but thick heads.

Final Answer:
Either (a) or (b), whichever is larger