Plane frames in a 3D solver

When to use the 2D Frame and 2D Truss model types, why a flat structure in a 3D model is a mechanism, and how to restrain it.

Modeling 4 min read

A project's model type decides how many dimensions it has. 2D Frame and 2D Truss keep everything in the XZ plane, with three or two degrees of freedom per node, and a structure in them cannot move out of plane. For a portal frame or a roof truss on its own, that is the simplest correct model.

In a 3D project every node has six degrees of freedom, and a portal frame drawn in the XZ plane is a 3D structure that happens to be flat. With nothing holding it out of plane it is a mechanism. The rest of this page is about that case: a plane structure inside a model that needs the third dimension.

The symptom

A frame that is stable in the plane you drew it in stops with a singular stiffness matrix. The pre-solve model check names the free motion: translation in the out-of-plane direction, or rotation about an in-plane axis, at nodes with nothing restraining them that way.

Pinned bases are the usual culprit. A pin restrains three translations, so the frame cannot slide out of plane at its feet. Nothing stops it rotating about the line joining the two bases and falling over sideways like a hinged gate. In a plane-frame program that motion does not exist. Here it does.

A portal drawn in the XZ plane on pinned bases (left) can rotate about the line joining its feet, so the stiffness matrix is singular even though the frame is stable in its own plane. Holding u_y, θ_x and θ_z at the bases (right) removes the motion without touching the in-plane result.

The three ways to restrain it

1. Restrain the out-of-plane degrees of freedom at the supports

For a portal frame in the global XZ plane, restrain $u_{y}$ , $θ_{x}$ and $θ_{z}$ at every base. The frame now cannot move in Y or rotate about X or Z at its feet. With the frame's own stiffness this is usually enough for a single frame.

It works because fixing $θ_{x}$ at the bases stops the gate rotation: each column stands as an out-of-plane cantilever from its base, and the rafter ties the two together. The real structure is held by purlins and bracing, not base fixity, so the out-of-plane results (which you are not reading) are meaningless. If the model check still reports a free motion, method 2 is more robust.

2. Restrain the out-of-plane degrees of freedom at every node

Fix $u_{y}$ , $θ_{x}$ and $θ_{z}$ at every node in the frame. This is exactly what a 2D program does implicitly, so it is the exact equivalent. The in-plane behaviour ( $u_{x}$ , $u_{z}$ , $θ_{y}$ ) is untouched, and the reactions in the restrained directions are zero under in-plane loading: a useful check that the model really is planar.

The properties panel applies a support to the whole selection, so this is one operation on all the nodes. See Supports and releases.

3. Model what actually holds it

A real portal frame is one of a row, tied by purlins and side rails and braced in one or two bays. The out-of-plane restraint exists in the members you left out. Adding the purlins as beams and the bracing as bars, as the steel hall example does, gives a model with no artificial restraint. The purlins' restraint of the rafter is then also there for the stability analysis to see.

This is the right answer when out-of-plane behaviour matters: wind on the gable, the buckling length of the rafter, a crane surge. For a quick in-plane check of one frame it is more model than the question needs.

Which one to use

Question	Method
In-plane forces and moments in one frame	2 — restrain every node, it cannot go wrong
Quick check, supports only	1 — and read the model check's answer
Sway and buckling of the rafter	3 — the purlins are the restraint, model them
Wind on the gable, or any out-of-plane load	3 — nothing else carries it
Modal analysis of the frame	3, or 2 if only in-plane modes are wanted — the first mode of an unrestrained plane frame is out of plane

What the artificial restraints do to the results

In the plane, nothing, provided every load is in the plane too. A load with an out-of-plane component is carried by the restraints instead of the structure, and its reaction appears at whichever nodes you restrained.

State in the report that the frame was analysed in its plane with out-of-plane motion restrained. It is the first assumption a reviewer will look for.

Trusses

A planar truss modelled in 3D can move out of plane: restrain $u_{y}$ at its nodes, or use the 2D Truss model type, which has no out-of-plane freedom to restrain. Its rotations need nothing: bars carry no rotational stiffness, and the solver locks rotations no member holds. See Bars, beams and trusses.

Grillages and floor plates

The other flat structure is horizontal: a grillage of beams, or a slab, in the XY plane. Its rigid-body motions are translation in X and Y and rotation about Z, and a model whose supports are all vertical-only has all three free. Restrain the in-plane translations somewhere: at one column base in both directions and at another in one, for a statically determinate set that attracts no thermal or in-plane force, or at every support if the real structure is held that way.

The rule is the same as for frames. Six global directions; each must be restrained somewhere; the pre-solve check tells you which one is not.

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