Dealing with multiple point loads on a composite slab

Whilst placing concentrated loads on composite slabs is not particularly recommended, we are seeing more and more situations where multiple, sometimes quite significant, loads are placed on a slab. Dr Graham Couchman from SCI discusses how composite slabs support concentrated loads, how software designs these slabs, and highlights issues to be taken into account when numerous such loads are present on a given area of slab. He also reminds designers about the need to explicitly consider the transverse reinforcement, normally mesh (fabric), that is needed to distribute a load, and the confusion that has arisen over the definition of a load that is sufficiently small to not warrant this check given in EN 1994-1-1¹.

Why are concentrated loads a concern?

A composite slab supports loads because it has resistance to moment, shear etc. The moment resistance is achieved by the axial force in some of the concrete in compression balancing the axial force in the steel decking in tension, forming a couple. The axial force in the decking is governed by the mechanical shear interaction between the steel and concrete, up to the point at which the steel yields. For typical deck geometries, steel grades and spans the deck does not reach yield and shear interaction dictates the moment resistance.

Shear interaction is achieved through the embossments that are rolled into the deck, and the shape of the re-entrant parts of its profile. This means that the force that can be transferred between steel and concrete is a function of the contact area between the two, therefore for a given width force transfer increases with distance into the span. The moment resistance of the slab increases to a maximum at mid-span. This is analogous to a composite beam, except in the latter case force transferred increases as each stud is ‘passed’, working away from the support. With an off-centre concentrated load the maximum applied moment, which may also be off-centre depending on relative sizes of coincident concentrated and uniform loading, must be compared with the resistance at the same point in the span (not the maximum resistance). Near a support this resistance could be considerably less than the maximum resistance at mid-span.

A second concern when considering concentrated loads, although this may be more theoretical than practical, is that shear interaction values are determined from tests, and these tests only ever consider unform loading. It is assumed that the interaction that can be achieved per unit contact area will not vary as a function of the type of loading.

How are concentrated loads supported?

The first thing to remember when considering their behaviour is that composite slabs are assumed to be one-way spanning. This is not an unreasonable assumption given the ribs run in one direction only. However, they do still clearly have some stiffness in the orthogonal direction. When a concentrated load is placed on a slab it is assumed to distribute laterally over a width that comprises the stiff bearing width, plus the width achieved by 45 degree distribution through the concrete, plus an additional width due to the transverse stiffness of the slab (see Figure 1, which is a reproduction of EN 1994-1-1 Figure 9.4). The later depends on where in the span the load is placed. All this is quantified in EN 1994-1-1 clause 9.4.3.

For bending and longituinal shear, for simple spans (EN 1994-1-1 Eq. 9.2):

For vertical shear (EN 1994-1-1 Eq. 9.4):

L_p is the distance of the centre of the load from the nearest support.
L is the span length.
b_m is the stiff bearing width.
b_em is the effective width of the longitudinal strip carrying the load.

Not stated, but the effective widths defined in EN 1994 are maximum values – the load should not be considered to be supported by a greater width when verifying the various resistances (bending, longitudinal shear and vertical shear). This is what a designer would normally want, as it places the least demand on the slab in the direction of span. The rules also assume a certain (unstated but typical) transverse stiffness for the slab. If the slab had less transverse stiffness than this unstated value, the effective widths defined by EN 1994-1-1 could not be achieved. In the extreme one can imagine a slab that had no transverse stiffness and therefore could not resist transverse bending – the load would simply be carried on a longitudinal strip of width defined by the stiff bearing width plus 45 degree distribution through the concrete.

A method for determining the magnitude of transverse moment present in the longitudinal strip, and therefore how much transverse reinforcement is needed to support a given load, is defined in AD450². AD477³ takes this further, and introduces the idea of reducing the width of a longitudinal strip down to the minimum that will still support the load spanning between end supports, in order to reduce transverse demands. The principle is easy to understand, but the implementation can get complex so SCI has produced a Tedds module⁴ that does it for you. It should also be noted that the EN 1994 allowance to assume nominal mesh is sufficient when concentrated loads do not exceed certain limits (9.4.3(5)) has long been misunderstood (including by SCI, with an incorrect explanation given in P359⁵) and should not be relied upon. Recent investigations into the origin of this rule revealed it only applies to slabs that are far different from many designed in the UK (for example the mesh is assumed to be laid directly on the decking, and only one concentrated load may be present in what may be rather a large area of slab).

What does design software do?

It is important to understand that composite slab design software relies on the one-way spanning characteristic to simply design a 1 m strip of slab. A clue is the fact that input values do not ask for the ‘width’ of slab, only the span. If there are concentrated loads present on a floor plate, a designer will consider the region(s) where those loads are applied. For its 1 m strip, the software will take into account any uniform load that is present, plus whatever proportion of the concentrated load is acting on the strip (so although the input may define a concentrated load P as present, if the EN 1994 rules distribute that load over say 2 m then only 0.5 P acts on the 1 m strip designed by the software).

What about overlapping loads?

The fact that a given concentrated load may be carried by a longitudinal strip that has a width in excess of the 1 m designed by software gets complicated if you have adjacent – side-by-side – concentrated loads. Although not present on the line of slab the designer assumed to be most critical they could still affect it (Figure 2 b). For a typical slab spanning 3 m, the EN 1994 rules tell us that a concentrated load placed at mid-span will be carried by a strip of width around 2 m. If you had two adjacent loads 1 m apart, the critical 1 m strip would be centred about the mid-point between the loads (not about a line on which one of the loads was present), and subject to both loads. Failure to take this into account, and instead design a strip that one of the loads was directly applied to, could result in a significantly under designed slab. To avoid this some side calculations may be needed to increase the level of load used as a software input.
We can also envisage more complex situations where adjacent loads well into the span (so with significant effective width) overlap on a strip between their points of application, but there are other loads, on the same adjacent lines, near the support that will not overlap because they have a smaller effective width. It then becomes less easy to predict which is the most critical strip, and more than one case may need to be designed.

Conclusions

It seems that composite slabs are more-and-more being used in situations where there are numerous concentrated loads present. It is therefore more important than ever that designers using slab design software have a good understanding of how composite slabs behave, particularly the way they support concentrated loads. Before deciding what concentrated loads to include as inputs, designers should ensure there are no adjacent loads that could also affect a given area of slab.

References

1. BS EN 1994-1-1:2005, Eurocode 4 – Design of composite steel and concrete structures – Part 1-1: General rules and rules for buildings, BSI, 2005.
2. AD450 Resistance of composite slabs to concentrated loads, SCI
3. AD477 Transverse bending of composite slabs subjected to point loads, SCI
4. https://steel-sci.com/sci-tedds-modules-for-specialist-steel-design.html
5. P359 Composite design of steel framed buildings, SCI, 2011