How the plastic redistribution works

This page explains the logic behind the New optimized plastic redistribution: what the algorithm optimizes, which rules can never be broken and how to read the results. You don't need this to use PREFAB, but it helps you understand why the solution looks the way it does.

One optimization per load combination

The redistribution is a linear optimization: PREFAB sets up the connection forces as unknowns and solves for the distribution with the lowest possible utilization. Within one load combination, the whole system is solved at once, with every element, edge connection and anchorage solved together. Each load combination is solved separately, and the combinations never affect each other.

The unknowns are the connection forces

Every edge connection is divided into 5 fixed segments, and each segment gets its own unknown force in every direction it has capacity in: shear along the edge (x'), and compression and tension perpendicular to it (y'). This split is fixed by PREFAB itself, not by the FE mesh of the FEM-Design analysis, so the resolution of the redistribution has nothing to do with how finely the model was meshed.

The 5 segments aren't equal in length: from one end of the edge to the other, they take up 1/12, 1/6, 1/2, 1/6 and 1/12 of the edge. The two end segments are the shortest, and the middle segment alone is half the edge. This puts the most resolution where force peaks typically occur, at the ends of a connection, while lumping the calmer middle into one segment. An edge crossed by an anchorage truss is the exception: it's treated as a single segment instead of 5, since the truss already fixes the load path there.

If a direction has no capacity, such as a stiffness set to 0 or a tension limit of 0, the force isn't just checked afterwards: it can't exist in the solution at all.

note

This is unrelated to the minimum edge-division number recommended elsewhere in the modelling guide. That setting is about the quality of the FE mesh in the FEM-Design analysis and has no bearing on this optimizer's own, independent segmentation.

Rules that can never be broken

Two sets of rules are absolute, and the optimizer has no freedom to bend them:

Equilibrium – every element must be in full 3D equilibrium (ΣF = 0 and ΣM = 0 around all axes) with all its loads, including self-weight with the combination's partial coefficient. This is the lower-bound (static) theorem of plasticity: the result is always a statically admissible force distribution
Friction – on detached edges, the shear force in a segment can never exceed the friction capacity, $V \le \mu \cdot C$ . No compression means no friction, and therefore no shear

What gets optimized

All other capacity checks are the target of the optimization. Every force is measured against its capacity: the minimum of the Eurocode material value and the plastic limit on the edge, the same capacities as the design checks. The optimizer then works through a strict hierarchy:

First – minimize the highest utilization anywhere in the model. This minimized maximum is the utilization PREFAB reports
Then – with the freedom left over, even out the highest utilization within each storey and along each wall plane

The second step is what makes the solution look like a sensible load take-down: an optimization problem usually has many equally good solutions, and PREFAB picks the one that also distributes the forces evenly. The hierarchy is strict: the optimizer never accepts a worse overall maximum in exchange for a nicer distribution, and the utilizations are never averaged.

Under the hood, PREFAB solves this as a single linear program per load combination rather than as two separate solves. The overall utilization has by far the largest weight in the objective, while the storey- and plane-evening terms carry a much smaller, capped weight. That gap is deliberately large enough that the optimizer could never improve the evening-out terms by giving up so much as a fraction of a percent on the overall utilization, so solving it in one pass still produces exactly the strict hierarchy described above, just without the cost of two sequential solves.

A basic example

Strip away the structural details and the redistribution is a small optimization problem you can follow by hand. Take a single edge connection carrying a shear force of $100\,\mathrm{kN}$ , split into just 2 segments instead of 5 for simplicity: segment A with a shear capacity of $80\,\mathrm{kN}$ , and segment B with a shear capacity of $40\,\mathrm{kN}$ .

A simple elastic split shares the load evenly: $50\,\mathrm{kN}$ on each segment. Segment A sits at $63\,\mathrm{\%}$ utilization, but segment B is already at $125\,\mathrm{\%}$ , over capacity, even though the connection as a whole has $120\,\mathrm{kN}$ of capacity for only $100\,\mathrm{kN}$ of load.

The optimizer instead treats $F_A$ and $F_B$ as unknowns, and searches for the split that minimizes the highest utilization:

\min \max\left(\frac{F_A}{80}, \frac{F_B}{40}\right) \quad \text{subject to} \quad F_A + F_B = 100

The lowest possible maximum utilization is reached when both segments sit at the same utilization: $F_A/80 = F_B/40$ , together with $F_A + F_B = 100$ , gives $F_A = 66.7\,\mathrm{kN}$ and $F_B = 33.3\,\mathrm{kN}$ , both segments at $83\,\mathrm{\%}$ utilization, instead of one comfortable and one overloaded. That's the whole idea, just scaled up to every segment, edge and element in the model at once.

Even split overloads segment B at 125%, while the optimized split settles both segments at 83%

Full vs Storey

Full – the whole model is optimized as one system, giving the lowest possible overall utilization
Storey – the storeys are solved one at a time from the top down, and the reactions from each storey become loads on the storey below. The capacity of the boundary toward the structure below is limited by the real capacities of the elements down there, so a storey can't lean on a boundary that can't carry the load

In the Storey option, each storey's distribution is locked before the next one is solved. It can't "look ahead" like the Full option, so the utilization is typically slightly higher, but the result reads like a classical load take-down, which is often the most intuitive. A model with less than two storeys is always solved as Full.

How to read the results

Sliding near $100\,\mathrm{\%}$ is normal – friction is a hard limit the optimizer may use to the full, not a check it tries to minimize. Seeing friction utilized at or near $100\,\mathrm{\%}$ while the compression sits comfortably low is expected behavior
Utilization above $100\,\mathrm{\%}$ is a result, not an error – if no distribution fits within the capacities, PREFAB reports the least-bad solution, e.g. $130\,\mathrm{\%}$ . Treat it like any failed design check
"No solution" means equilibrium is impossible – a combination only fails when a needed force direction has no capacity at all, or friction can't carry the required shear. PREFAB then tests each wall on its own to pinpoint the problem, and reports which element can't obtain load in which direction
Friction forces are evened out along edges – after solving, shear carried by friction is redistributed along each detached line in proportion to each segment's capacity, so the segments on a line show the same utilization

note

For what your model must contain to use the redistribution, see New optimized plastic redistribution and the checklist.

To see this logic applied to a real model in PREFAB, from setup to reading the Full result, go to ↘ basic shear handling.