Slab FEM analysis

Analiză FEM — Placă dreptunghiulară

Geometry & loading

Lx — span X [m]

Ly — span Y [m]

h — slab thickness [mm]

Material type

Concrete class

q — uniform load [kN/m²]

P — point load at centre [kN]

Applied at the centre of the slab; leave 0 for uniform load only.

Analysis accuracy (mesh)

Mesh: 30 × 30 = 900 elements.

Boundary conditions

Free · Pinned · Fixed

Y+

X-

SLAB

X+

Y-

Introduceți parametrii și apăsați Calculează.
Hărțile de căldură pentru deformații și momente vor apărea aici.

Tool information

What this page computes

The calculator solves a rectangular plate by the finite-element method and returns, as colour maps, the full field of internal forces and deformations: the deflection \(D_z\), the bending moments \(M_x\) and \(M_y\), the twisting moment \(M_{xy}\) and the shear forces \(V_x\), \(V_y\).

When you need finite elements for a plate

For a simple rectangular plate, edge-supported and uniformly loaded, the coefficient method is sufficient and faster. Finite elements become necessary when you go beyond those assumptions:

mixed or partial supports on the edges (some fixed, some free)
concentrated loads or non-uniform distributions
the need to see the actual distribution of the forces, not just the peak values

FEM gives the continuous field over the whole surface, so you see exactly where the maximum moments occur and how they vary between span and supports.

What the six maps tell you

\(D_z\) — the deflection; shows the most flexible zone, typically the plate centre.
\(M_x\), \(M_y\) — the bending moments in the two directions; the reinforcement (in concrete) is designed from them.
\(M_{xy}\) — the twisting moment; largest at the corners, where the plate tends to lift and where supported corners therefore need special reinforcement.
\(V_x\), \(V_y\) — the shear forces; largest along the supported edges.

Input data

Plate dimensions and thickness.
Mesh density — finer gives more accurate results, but is slower.
The support conditions of each edge (simply supported, fixed, free).
The load — uniform or concentrated.
Material properties — the modulus of elasticity, Poisson's ratio.

Assumptions and limitations

A thin plate (plate bending theory), linear-elastic behaviour.
The result depends on the mesh density; in zones with stress concentrations (corners, point loads) too coarse a mesh underestimates the peaks.
It gives the internal forces and deformations; the reinforcement design from the moments is done separately — see the concrete section.
The analysis runs on an external computation engine.

Slab moments (coefficients) — the hand method for simple rectangular slabs
Reinforced section (concrete) — designing the reinforcement from \(M_x\), \(M_y\)
Crack-width verification — the SLS check of the slab
Punching shear — for slabs supported on columns