Structural Analysis – Conditions Common to Elastic and Plastic Methods Which condition must be satisfied by both elastic analysis and plastic (limit/upper-bound) analysis of indeterminate structures?

Introduction / Context:
Structural analysis can be performed using elastic methods (stiffness/slope-deflection) or plastic (limit state) methods. Although their assumptions differ, certain fundamental requirements must be satisfied by any admissible solution to ensure physical realism and safety.

Given Data / Assumptions:

• Indeterminate structure under static loading.
• Elastic analysis: stresses/strains within elastic range, compatibility enforced.
• Plastic analysis: considers yield and collapse mechanisms, may relax elastic compatibility locally.

Concept / Approach:

Equilibrium of forces and moments is a universal requirement. Elastic analysis also enforces compatibility and constitutive relations; plastic limit analysis replaces compatibility with yield and mechanism conditions while still maintaining global and member-wise equilibrium.

Step-by-Step Solution:

Verification / Alternative check:

Lower- and upper-bound theorems of plasticity explicitly require equilibrium (statically admissible stress field) or mechanism with yield, reinforcing its universality.

Why Other Options Are Wrong:

• Yield and mechanism conditions: specific to plastic analysis.
• Compatibility: enforced in elastic analysis; not strictly required in plastic upper-bound solutions.

Common Pitfalls:

Assuming compatibility is necessary in all methods; overlooking that limit analysis targets collapse load rather than elastic displacements.

Final Answer:

Equilibrium