Restrained slab panel — moments and beam loads

What this calculator does

It solves a rectangular slab panel supported on all four edges by the tabulated coefficient method, and carries the result through to the end:

• moments in the span and over the supports, in both directions, for the nine support cases
• design spans, from the clear spans plus the support
• balancing of the support moment with the adjacent panel
• loads transferred to the perimeter beams, in kN/m

Where the coefficients come from

EN 1992-1-1 gives no coefficient table for slabs. It only requires the analysis to be appropriate (§5.1.1), so every program borrows a table from somewhere. These are from BS 8110-1:1997, Table 3.14 — rectangular panels supported on four sides with provision for torsion at the corners.

The source is stated explicitly, on the page and in the calculation report. A coefficient table without a provenance is a number nobody can check.

The nine cases

The cases are named after the discontinuous edges — those where the slab does not continue into the next panel, so no hogging moment can develop. An interior panel has all four edges continuous; a corner panel has two adjacent edges discontinuous; an isolated slab has all four.

The distinction is not cosmetic: between case 1 (interior) and case 9 (four edges discontinuous), the short-span sagging moment rises from \(0.024\) to \(0.055 \cdot p \, l_x^2\) — more than double.

The trap: both moments use \(l_x^2\)

\(m_{sx} = \beta_{sx} \, p \, l_x^2 \qquad m_{sy} = \beta_{sy} \, p \, l_x^2\)

The second one also uses the short span, not \(l_y\). That is the table's convention, and it is the easiest mistake to make: using \(l_y^2\) in the second overstates the long-span moment by \((l_y/l_x)^2\) — on a 1:2 panel, by a factor of four.

Design span

The calculation does not use the clear span but the design span: the distance between support centrelines, capped at the clear span plus the slab thickness (§5.3.2.2). In practice the smaller of the beam width and the slab thickness is added. On a thin slab carried by wide beams, the cap does bite.

Balancing with the adjacent panel

On a shared edge, two neighbouring panels give different moments — each computed with its own span and its own support case. The average is taken, and the difference lost is added to the span of the panel that gives way.

Without this step, the support reinforcement would be designed for a value the adjacent panel cannot balance, and the span moment would be understated.

Loads on the beams

The panel area is split by 45° lines from the corners: beams on the short edges take a triangle, those on the long edges a trapezoid. The peak is the same for both, \(p \, l_x / 2\).

The page gives three values per beam, and they are not interchangeable:

• the total [kN] — for equilibrium checks
• the average = total/span [kN/m] — for reactions and columns
• the moment-equivalent [kN/m] — for designing the beam

The last is larger than the average, because the load is concentrated towards midspan. For a triangle it works out at exactly \(\tfrac{2}{3}\) of the peak. Designing the beam with the average errs on the unsafe side.

Input data

• Support case — which edges are continuous and which are not
• Clear spans \(l_x\) and \(l_y\), with \(l_y\) the long side, plus the beam widths and the slab thickness
• Loads \(g_k\) (additional, excluding self-weight — that is added from \(h\)) and \(q_k\), with the partial factors
• The adjacent panel's support moment, if there is one

Assumptions and limits

• Rectangular panel of constant thickness, supported on all edges, with the corners held down. Slabs with openings, irregular shapes or flat slabs on columns need finite elements.
• Uniformly distributed load; the method does not apply to concentrated loads.
• Above \(k = 2\) the slab effectively spans one way; the coefficients are capped on the last row, but a one-way strip calculation is more appropriate.
• The output is moments, not deflections or crack widths — those are checked separately.
• The coefficients assume elastic behaviour with limited redistribution; yield-line analysis gives different values.

Related calculations

• Slab analysis (finite element) — for arbitrary shapes and supports
• RC section — designing the reinforcement from these moments
• Beam serviceability — cracking and deflection of the beams the slab loads
• Crack width — serviceability check of the slab