Mechanical property definition — what does stiffness mean? Choose the correct definition of stiffness for an engineering material in the context of mechanics of materials and structural design.

Introduction / Context:
Stiffness, strength, and toughness are distinct mechanical concepts often conflated by beginners. Correctly identifying stiffness is crucial for sizing members against deflection limits in civil, mechanical, and aerospace applications where serviceability matters as much as ultimate strength.

Given Data / Assumptions:

• Small-strain, linear-elastic regime for metals and common engineering materials.
• Standard definitions from mechanics of materials.

Concept / Approach:
Stiffness quantifies a material or component's resistance to elastic deformation under applied load. At the material level, high stiffness corresponds to a high Young's modulus E (and shear modulus G for shear). At the structural level, stiffness depends on both material moduli and geometry (e.g., EI for bending, GA for shear, EA for axial). Strength, by contrast, is the stress level at which yielding or fracture occurs; toughness relates to energy absorption before fracture.

Step-by-Step Solution:

Verification / Alternative check:
Comparing steel and aluminium beams of identical geometry shows steel deflects less under the same load because steel has a higher E; this is a stiffness difference even if both remain safely below yield.

Why Other Options Are Wrong:

• Fracture due to impact: that is impact strength or toughness (Charpy/Izod), not stiffness.
• Resisting forces without yielding: that describes strength (yield or ultimate), not stiffness.
• None of the above / permanent set only: ignores the elastic definition and confuses plastic deformation with elastic response.

Common Pitfalls:
Using high strength alloys expecting lower deflection without considering modulus; assuming heat treatment that raises strength also raises stiffness (E changes little with heat treatment for metals).

Final Answer: