Energy methods – Definition of proof resilience for springs\n\nThe strain energy stored in a spring under the maximum permissible load without permanent set is known as what?

Introduction / Context:
Energy storage in elastic members is crucial in shock absorption and vibration isolation. Springs are designed to store strain energy up to an elastic limit without plastic deformation.

Given Data / Assumptions:

• Spring is loaded up to its maximum allowable (proof) load in the elastic range.
• No permanent deformation is permitted at the proof load.
• Material obeys Hooke’s law up to that load.

Concept / Approach:
Proof resilience is the maximum strain energy that a material or spring can store per unit volume (for materials) or in total (for springs) without permanent set. For a linear spring: U = (1/2) * F * δ at the elastic limit.

Step-by-Step Solution:
Identify the proof (maximum elastic) load F_proof.Determine the corresponding deflection δ_proof from the load–deflection relation.Compute stored energy: U_proof = (1/2) * F_proof * δ_proof.Interpretation: This is the spring’s proof resilience.

Verification / Alternative check:
For material specimens, the area under the stress–strain curve up to elastic limit equals modulus of resilience (per unit volume). For a spring, the analogous total energy at the elastic limit is termed proof resilience.

Why Other Options Are Wrong:
Impact energy relates to sudden loads, not necessarily elastic limit; proof stress is a stress value; modulus of resilience is per unit volume of material, not total spring energy; toughness covers energy to fracture, including plasticity.

Common Pitfalls:
Confusing proof resilience with modulus of resilience; exceeding elastic limit in design assumptions.

Final Answer:
proof resilience