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Elastic vs plastic analysis; plastic hinge

Short answer

Elastic analysis assumes linear elasticity, uses working stresses and elastic modulus, requires compatibility and no redistribution. Plastic analysis uses ultimate load, plastic modulus, equilibrium and mechanism condition, allows moment redistribution with reserve strength. A plastic hinge is a fully yielded section rotating at constant moment Mp.

List the differences between elastic and plastic analysis. What is meant by Plastic Hinge?

Difference between elastic and plastic analysis

PointElastic analysisPlastic analysis
BasisMaterial is linearly elastic (Hooke's law); stresses stay below yieldMaterial is ductile and is stressed beyond yield; behaviour is taken as elastic-perfectly plastic
Design criterionThe stress at any point must not exceed the permissible stress (working stress method)The structure is designed to collapse only at the ultimate (factored) loads
Failure consideredFirst yield of the extreme fibreFormation of a mechanism after enough plastic hinges form
Section property usedElastic section modulus ZeZ_e; moment My=σyZeM_y = \sigma_y Z_ePlastic modulus ZpZ_p; moment Mp=σyZpM_p = \sigma_y Z_p
Indeterminate structuresNeeds compatibility conditions (deflections, settlements, EIEI)Needs only equilibrium and the yield (mechanism) condition; independent of EIEI and settlement
Moment redistributionNot considered; the moment distribution is fixed by the stiffnessesMoments are redistributed after the first hinge forms, so the reserve strength is used
SafetyFactor of safety applied to stressLoad factor applied to the collapse load
EconomyHeavier sectionsLighter and more economical sections, particularly for continuous beams and frames
ApplicabilityValid generally, including fatigue and deflection checks; simple to applyNot valid where fatigue, buckling, brittle fracture or deflection controls

Plastic hinge

A plastic hinge is a section of a beam at which the bending moment has reached the plastic moment MpM_p, so that the entire cross-section has yielded. The section can then rotate at a constant moment MpM_p, like a hinge that still transmits MpM_p. Its main points:

  • It forms at the sections of maximum moment (fixed ends, joints, under point loads).
  • A plastic hinge has a finite length (the zone where My<M≤MpM_y < M \le M_p), though it is treated as a point in analysis.
  • Unlike a real hinge, it resists rotation with the constant moment MpM_p and rotates only in the direction of the moment.
  • A structure with degree of indeterminacy rr becomes a mechanism and collapses when r+1r + 1 plastic hinges form (fewer if only part of the structure fails).

✓ Answer checked by Claude Opus 5.5 (high effort)

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