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🔩 Plastic Collapse Challenge

Elastic design stops at first yield. Plastic design keeps going: the section yields, forms a hinge, redistributes moment to its neighbours, and the beam carries on until enough hinges form to turn it into a mechanism. Push the load up and watch the hinges appear one by one — and notice where the propped cantilever's sagging hinge actually lands.

Beam

Support condition

Span L 6.0 m

Plastic modulus Z 1500 cm³

Load

Applied UDL w 30 kN/m

Live Result

—

Load Factor λ

—

Collapse Load (kN/m)

Plastic moment M_p—

Mechanism coefficient (w_cL²/M_p)—

Hinges needed for a mechanism—

🎯 Goal: size the beam so λ ≥ 1.5. Then switch to "Propped cantilever" and read the hinge position — it lands at 0.414L, not midspan.

Powered by exact plastic limit analysis (engine/plastic-collapse.js). The fixed-fixed collapse load was verified before publishing by two independent methods — the kinematic virtual-work approach and static equilibrium of the collapse moment diagram — which agree exactly. The propped cantilever uses its exact coefficient 6+4√2 ≈ 11.657 with the hinge at √2−1 ≈ 0.4142L, rather than the midspan approximation that many textbooks quietly substitute. Scope: compact sections with full lateral restraint (no LTB), rigid-plastic material, small deflections (no P-Δ).

Method

Limit analysisUpper-bound kinematic theorem — at collapse, internal work at the plastic hinges equals external work of the load (Baker/Horne/Heyman; Neal).

Exact resultsSimple: 8Mp/L². Propped: (6+4√2)Mp/L², hinge at √2−1. Fixed: 16Mp/L².

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