Slabs and walls as plates: finite element meshing explained

Beams and columns are lines; slabs and walls are surfaces. A slab supported on four sides carries load in two directions at once, and a wall acts like a deep beam standing on end. To analyse them, Struxt3D uses the finite element method: each slab and wall is cut into small shell elements. This tutorial explains what plates do, how the mesh works, and how to read and use plate results.

#One-way and two-way action

A slab supported on two opposite edges bends like a wide beam: one-way action. A slab supported on all four sides spreads load in both directions: two-way action, and it is much more efficient.

#Worked example: the same 6 m slab, two ways

A slab panel 6 m × 6 m carrying q = 10 kN/m²:

• Supported on two edges (one-way): m = qL²/8 = 10 × 6² / 8 = 45 kN·m/m.
• Simply supported on four edges (two-way, Timoshenko's plate tables): m_max = 0.0479 q a² = 0.0479 × 10 × 36 = 17.2 kN·m/m in each direction.

Two-way action cuts the moment by more than half. That is why plate analysis matters: treating every slab as one-way strips wastes reinforcement, while ignoring where the load really goes (towards the stiffer, shorter direction, and towards the columns in a flat slab) can leave weak spots.

#The plate results

Plate results are given per metre width, in the element's local axes:

Result	Unit	Meaning
mx, my	kN·m/m	Bending moments that need bars running along x and along y.
mxy	kN·m/m	Twisting moment: largest near corners, it wants bars at 45° — in practice provided by adding to both directions.
nx, ny, nxy	kN/m	Membrane (in-plane) forces: the main action in walls, and diaphragm forces in floors.
vx, vy	kN/m	Transverse shear, highest near supports and columns (punching).

#Wood–Armer: from moments to reinforcement

Bars run in two directions, x and y, but the principal moments can point anywhere. The Wood–Armer method gives design moments for the x and y bars that are always safe, by adding the twisting moment:

Example: m_x = 20, m_y = 8, m_xy = 6 kN·m/m gives bottom design moments of 26 and 14 kN·m/m. The top values (14 and 2) are positive, so no top steel is needed there. Struxt3D applies Wood–Armer per face and direction, for bending and for membrane tension (walls), in every combination.

#The analysis mesh

The finite element model replaces each slab or wall by a grid of four-node quadrilateral shells. Struxt3D's shells combine a membrane (in-plane) part and a bending part (the MITC4 formulation, which avoids the "locking" that makes thin plates too stiff), so the same element serves a floor bending under gravity and a wall resisting wind in its plane.

#Model versus mesh

In Struxt3D you never edit the mesh. The model is what you build — nodes, whole members, panels — and the mesh is made from it for every analysis. Members stay one piece in the model (so their design and connections see a whole beam), and the mesh splits them at every node along them and wherever shells attach.

#How fine is the mesh?

A finer mesh follows peaks more closely, but the solving time grows quickly — roughly with the square of the number of nodes on one floor. Struxt3D chooses the element size from the panel areas: fine enough for at least about two shells across a bay, coarse enough to keep the analysis to seconds (never below 0.5 m). This is accurate for design moments across the bays; very local peaks (right over a column, at a re-entrant corner) are smoothed.

#Structural panels and cladding

Not every surface in a model is a plate. Struxt3D distinguishes:

• Structural panels — floors, roofs, decks, walls and plates — analysed as shells, with self-weight from their thickness and the slab material.
• Cladding — non-structural walls and roof sheeting on sheds and frames. They carry no stiffness; each passes its loads (wind, finishes) to the members along its edges, each edge taking the triangle between it and the panel's centre.
• Panels on the ground — rafts with a subgrade modulus get a soil spring under every mesh node (see supports).

#Try it in Struxt3D

1. Open the Flat slab building template.
2. In How is it held and loaded?, the Slabs and walls group sets the thickness of each kind of panel (for example Floor slabs, 80–1500 mm). The note names the slab material.
3. Switch to the Full interface and choose View › Show analysis mesh to see the shells and the split members.
4. Run the analysis and pick Slab moment (kN·m/m): the Wood–Armer design moment, the larger of |M_x| + |M_xy| and |M_y| + |M_xy|. Look for the peaks over the columns and at midspan.
5. Run the design (F6) and pick Slab reinforcement (mm²/m). The Slabs & plates table lists the bar meshes: B bottom, T top, x / y directions.

#Summary

• Two-way slabs carry load far more efficiently than one-way strips.
• Plate results are per metre: m_x, m_y, the twisting m_xy, membrane and shear forces.
• Wood–Armer turns them into safe design moments for x and y bars.
• The mesh is made from the model for each analysis; you edit the model, not the mesh.