Springs – energy at limiting load: What is the name of the strain energy stored in a spring when it is loaded up to the greatest load that causes no permanent set?

Introduction / Context:
Besides load capacity, springs are often characterized by how much elastic energy they can store and release without damage. The correct term for the maximum recoverable energy at the elastic limit is frequently used in design reports and acceptance criteria.

Given Data / Assumptions:

• Spring is deflected only within the elastic range (no plastic deformation).
• The 'greatest load with no permanent set' equals the proof load.
• Strain energy refers to the recoverable elastic energy stored due to deformation.

Concept / Approach:
Energy stored up to the elastic limit (or proof point) and fully recoverable upon unloading is called proof resilience. For a linear spring, energy U = 0.5 * P * delta at the proof load, where P is the proof load and delta is the corresponding elastic deflection.

Step-by-Step Solution:
Recognize that the question asks for an energy term, not a force or a stress.At the limiting elastic load, the spring stores maximum recoverable energy.The proper term for this maximum recoverable energy is 'proof resilience.'Therefore, choose 'proof resilience' as the answer.

Verification / Alternative check:
Compare with 'modulus of resilience,' which is energy per unit volume for the material; in contrast, proof resilience refers to the total elastic energy stored by the spring at the proof load.

Why Other Options Are Wrong:

• Stiffness: a rate (force per unit deflection), not energy.
• Proof stress: a stress value at yield/proof point; again, not energy.
• Proof load: the limiting load itself, not the energy at that load.
• Modulus of resilience: material energy density, not the spring's total stored energy at proof.

Common Pitfalls:
Mixing up system-level quantities (load, energy) with material-level properties (stress, modulus of resilience); assuming any energy term at maximum load is 'modulus of resilience' rather than the correct 'proof resilience.'

Final Answer:
proof resilience