A limit‑analysis (kinematic) method for reinforced‑concrete slabs that predicts the ultimate (collapse) load and the associated collapse mechanism by idealizing the slab as rigid planar regions separated by plastic hinge lines (yield lines). The method assumes rigid‑plastic bending behaviour of the slab plate, negligible elastic strain energy except at yield lines, sufficient ductility and shear capacity in reinforcement, and determines collapse load by equating external work of applied loads to internal plastic work at the yield lines.

Principle

For an assumed admissible yield‑line mechanism, the ultimate load is found by equating external work from applied loads to internal plastic work done by rotations along yield lines; kinematic solutions provide an upper bound on true collapse load.

Demonstration

Illustrative scenario → A simply supported rectangular slab under uniform load: assume a single straight yield line across the midspan dividing two rigid panels, compute internal plastic work as Mp times yield‑line length times hinge rotation, compute external work from load times virtual displacement pattern, adjust the assumed rotation field to satisfy virtual work equality; the resulting load is the predicted collapse load for that mechanism.

Misapplication

Treating yield‑line predictions as serviceability checks or as exact crack patterns. Error: yield‑line theory predicts ultimate (limit) load and mechanism, not elastic deflections, detailed crack widths, or load redistribution before plastic hinging; using it for service‑level design misinterprets its limit‑analysis scope.

Consequence

When properly applied, it yields a rapid estimate of ultimate capacity and likely collapse mechanism useful for ultimate limit‑state design and hand checks; used without verifying model assumptions (ductility, shear capacity, absence of significant membrane action) the estimate can be nonconservative for modes excluded by the idealization.

Reversal

If membrane action, significant in‑plane forces, shear failure, or material brittleness control behaviour, the yield‑line kinematic assumption fails and the predicted mechanism and load are not representative; in such cases static lower‑bound limit analysis, detailed nonlinear finite‑element plasticity, or plate–membrane coupled models are required.

Boundary

Within: thin reinforced‑concrete slabs where bending governs ultimate behaviour and reinforcement can form plastic hinges. Boundary case: slabs with moderate membrane restraint where yield lines may form but membrane effects alter loads. Outside: deep slabs, slabs failing in shear or punching, plates dominated by membrane action, or situations needing serviceability or crack‑width predictions.

Semantic Tension

Simplicity and insight (hand‑calculable collapse mechanisms) ↔ fidelity to complex plate and reinforcement behaviour (necessitating more detailed nonlinear analysis).

Synthesis

Yield‑line theory trades detailed elastic and local failure description for a concise, mechanism‑focused upper‑bound collapse estimate; it is most valuable when used to identify possible collapse modes and check ultimate capacity, and must be combined with checks for ductility, shear, and membrane effects.