A slab is a structural member whose depth is considerably smaller than the lateral dimensions. They provide useful surfaces for supporting loads, and may be supported on beams, columns, walls, or masonry. When a slab is supported on two opposite sides, they are referred to as one-way slabs because the load is transferred from the slab to the beam in the perpendicular direction.
However, if a slab is supported by beams on the four sides, and the ratio of length to width is greater than 2, majority of the load is transferred to the short direction to the supporting beams, and one-way action is obtained in effect, even though supports are provided on all sides. The structural action of one-way slabs may be visualized in terms of the deflected surface. This can be approximated as a cylindrical surface, and curvatures and bending moments are parallel to the short side Lx. The slab is normally analysed a beam of a unit strip, with the bending moment, shear forces, and reinforcement determined per unit strip.
In many design circumstances, rectangular slabs have dimensions where the ratio of the longer side to the shorter side is less than 2 (and are also supported in such a way that two-way action results). When loaded, such slabs bend into a dished surface rather than a cylindrical one. This means that at any point the slab is curved in both principal directions, and since bending moments are proportional to curvatures, moments also exist in both directions.
|Typical Two Way Deflection in A Flat Slab|
To resist these moments, the slab must be reinforced in both directions, by at least two layers of bars perpendicular, respectively, to two pairs of edges. The slab must be designed to take a proportionate share of the load in each direction.
Why Short Span?
When civil engineering students enter a structural design classroom for the first time, they are told that the shorter span is more critical in the design of slabs. This is usually source of wonder for first timers because by mere instincts, the longer span should be more critical. This article shows very simple proofs why the short span is more critical in slabs.
(1) Deflection of centre-strip approach
This offers an extremely simplified concept that shows that the load transmitted to the shorter span is greater than the load transmitted to the longer span.
Let us consider the two way action of the slab shown below;
The force parallel to the short span (Px) = 2 × 8.6825m2 × 1 kN/m2 = 17.365 kN
The force parallel to the long span (Py) = 2 × 6.316m2 × 1 kN/m2 = 12.632 kN
Total load on slab = (5 × 6)m2 × 1 kN/m2 = 30 kN
Therefore, you can see why the shorter span is more heavily loaded based on the yield line pattern.
(3) Finite Element Analysis
When we carry out finite element analysis on slabs, the result offers an insight;
Let us check out the slab investigated above using finite element analysis results from Staad Pro.