This article presents guides to designing flat slabs to EN 1992-1-1-2004 as well as the superseded UK standard BS 8110-1-1997.

Flat slabs are slabs that are directly supported on columns. They can be categorized based on their thickness specifically above supporting columns.

Types of flat slab

Flat Plate: A flat plate is a flat slab of uniform thickness

Slab with drops: Slab with drops are flat slabs that have thicker sections over supporting columns. The thicker section can either be a wider column head called capital, or a thicker slab depth called drop panel.

 

Advantages of flat slab

Flat slab provides numerous advantages over traditional solid slabs as follows:

• Better illumination: Since there is no intermediate beams, there is no obstruction to light so the illumination becomes uniform all through the space
• Reduced building Height: Absence of beam also provides reduced floor-to-floor height which also translates substantially to reduction in over-all building height especially for high-rise building
• Faster Construction: Flat slab offers faster construction as there is simplicity in formwork due to absence of beam.
• Better ventilation: The absence of beams means greater window height as they can extend directly under the slab increasing the volume of air exchange between the building and outside. Air can also circulate freely within the internal space without obstruction from beams.
• Better fire resistance. Absence of sharp edges caused by deep depth of beams below slab makes the slab have better resistance against fire due to lack of points of stress concentration

Methods of Analyzing a Flat Slab

There are several elastic and plastic methods of analyzing flat slabs. Some of them includes:

• Grillage Analysis
• Finite Element Analysis
• Equivalent Frame analysis
• Yield Line method
• Simplified method of moments and shear coefficients

 

All these methods have their merit and demerit in analyzing flat slabs. Eurocode 2 permits whatever tested method catches the fancy of the designer. It limits its recommendation of equivalent frame method and grillage method for flat slabs with regular column layout and irregular column layout respectively to Annex I, outside the main body of the standard.

BS 8110 permits all the analysis method above and also stipulates specific guidance on maximum moments that can be distributed from edge columns for each analysis method. The Simplified method of moments and shear coefficients is peculiar to BS 8110-1-1997 and UK experience due to the application of ultimate moment on all spans with 20% redistribution just as for continuous sold slab or beams. We shall discuss further on equivalent frame method and Simplified approach in the subsequent headings.

Equivalent Frame analysis:

In equivalent frame analysis, the structure is divided into frames consisting of columns and slab strips in both longitudinal and transverse spans of the slab. Each orthogonal span (longitudinal and transverse) is considered separately, and the resulting frame is analyzed like that of a multi span frame or continuous beam using elastic method like moment distribution method. According to CIRIA 110, “A flat slab supported on columns rather than on perimeter beams, can fail as a one-way mechanism just as a single way slab, and it should be reinforced to resist moment from the full load in each orthogonal direction”.

Generally, the width of the slab considered for the equivalent frame is based on the width between centerlines of panels. When the width of adjacent panels common to a line of support are not equal, the width of the larger panel should be taken for both panels.

The stiffness of the slab when considering gravity load is also calculated using the full panel width. However, when lateral loads are being considered then 40% of the value of the width is taken according to EN 1992-1-1-2004 or 50% of the width is taken according to according to BS 8110-1-1997. These reductions are recommended so that the analysis model reflects the increase flexibility of slab and column connection under lateral loads.

Click here to study a worked example where equivalent frame method is used in analyzing a flat slab.

Simplified method of moments and shear coefficients

Provided that the flat-slab structure’s lateral stability is not dependent on slab-column connections, rather than using moment distribution or other rigorous alternatives, the equivalent frame can be analyzed using table 3.12 of BS 8110-1-1997 provided that, according to clause 3.7.2.7 of BS 8110-1-1997, the following conditions are met:

• Design is based on the single load case of all spans loaded with the maximum design ultimate load, (i.e. the conditions of 3.5.2.3 are satisfied. The conditions are listed below).

1. The area of each bay exceeds 30m2.

2. The ratio of the characteristic imposed load to the characteristic dead load does not exceed 1.25.

3. The characteristic imposed load does not exceed 5kN/m2 excluding partitions

• There are at least three rows of panels of approximately equal span in the direction being considered
• Moments at supports taken from Table 3.12 of BS 8110 may be reduced by 0.15Fhc; and
• The limitation of 3.7.2.6 of BS 8110-1-1997 need not be checked. Allowance has been made to the coefficients of Table 3.12 for 20 % redistribution in accordance with 3.5.2.3.

Click here to study a worked example on analysis of flat slab using simplified moment coefficients 

Moment transferable to end and corner columns

Design moments will be transferred between the slab and corner column or edge column by strip of slab narrower than that associated with the internal column. This necessitates that the moment capacity of narrow slab width adjacent to edge/corner columns is thoroughly scrutinized.

Annex I:1.2 (5) and Annex I:1.2 “Unless there are perimeter beams, which are adequately designed for torsion, moments transferred to edge or corner columns should be limited to the moment of resistance of a rectangular section equal to 0.17b_ed²fck”. The span (positive) moment should be adjusted according to this reduction to maintain equilibrium.

BS 8110-1-1997 (3.7.4.2 & 3.7.4.3) also limits the moment transferrable to edge or corner columns to 0.15b_ed²fcu

Additionally, BS 8110 states that the maximum moments transferable to the column should not be less than 50% of the design moment obtained when equivalent frame method is used or should not be less than 70% of the design moment obtained when finite analysis or grillage analysis is used. This measure is to put an overall upper limit on moment transferred to the edge/corner columns even before redistribution of moment from edge/corner columns. Should the moment transferred to edge/corner columns prior to redistribution of moments from edge/corner column exceed the permissible limit then the structural arrangement should be change by incorporating any of the following adjustment.

1. Introduce an edge beam
2. Reduce the span of the slab
3. Increase the thickness of the slab
4. Reduce the slab loading
5. Increase the concrete strength
6. Introduce a shorter cantilever in the edge slab and decrease the out-of-balance moment by increasing be

It should also be noted that this moment over edge column in a flat slab is not distributed into column and middle strip like other internal span and support moments, rather it should be concentrated within effective width be (Check the definition of be below under the section “reinforcement detailing requirement for flat slabs”.

As recommended in clause 3.7.4.4 of BS 8110-1-1997, the free end of the column strip, except if it is subjected to a local moment-inducing loading at its free end beyond the column, should be provided with minimum area of reinforcement extending at least 0.15l or an anchorage length, whichever is the greater, into the span.

Lateral distribution of moment across Flat slab width

Sequel to analysis, interior panels (excluding edge and corner columns) should be divided into column strips and middle strips, then the design moments (span and support moments) obtained from analysis should be distributed between the column and middle strips in the proportions given in the table I.1 and table 3.8 of EN 1992-1-1-2004 and BS 8110-1-1997 respective. The table I.1 of Eurocode is reproduced below

The division of the strip width should be based on the shorter length of the panel. Wherever there are drops, the column strip width takes the width of the drop. However, where the smaller dimension of the drop is less than one-third of the smaller length of the panel then the drop should be ignored and the panel divided as though the drop is not present. Although, the ignored drop in moment distribution can still be taken into account when assessing the resistance of the slab to punching shear.

 

flat Slab Section Design

The column and middle strips should be designed to withstand the design moments obtained after obtaining the moments in the column and middle strips, the design exercise proceeds like that of a typical solid slab.

• Flexural Design

 The slab should be designed against bending moment. The steps in designing against bending moment are enumerated below

1. Calculate the effective depth (d):

The effective depth should be calculated after a specific size of reinforcement has been assumed for design and a nominal cover chosen in accordance with the requirement for durability. The effective depth is calculated using the equation: d = h – c – dia/2

2.Check whether the section is singly or doubly reinforced:

We check whether K (M/bd²fck) is less than K’ (0.168). Slabs are always design as singly reinforced except in very special cases

3.Calculate the lever arm: Use Z = $
Z\,\,=\,\,d\left( 0.5+\sqrt{\text{0.25}-\,\,\frac{K}{1.134}} \right)
$

4. Calculate the area of steel required: use  $A_{st\,\,=\,\,\frac{M_{Ed}}{0.87f_{ck}Z}}
$

       Punching Shear Design

The slab also has to be design for punching in regions around columns when necessary. Punching shear occurs in flat slab due to direct support of the slab on columns. This creates a tendency of the columns to punch through the slab. Click here to study a well detailed article on the design of punching shear to Eurocode 2

       Deflection Check

The basic span-effective depth ratio is used for deflection check as in the case of solid slabs; however, the span should be based on the longer span of the flat slab and not the shorter span. For flat slabs where the greater span exceeds 8.5 m, and which support partitions liable to be damaged by excessive deflections, the basic-ratio values given by Expression (7.16) should be multiplied by 8.5/effective span.

Click here to study a worked example on the design of flat slab to Eurocode 2

Reinforcement Detailing of Flat Slab

• Arrangement of reinforcement in flat slab should result in concentration of reinforcement over columns than spans as this reflects the behavior of flat slab under service load.
• At least two bottom bars in each orthogonal direction should pass through all internal columns for robustness
• The placement of reinforcement over internal columns to resist negative moment requires special details and both standards acknowledge this:                                                                                                                                  Clause 3.7.3.1 of BS 8110 stipulates two-thirds of the amount of reinforcement required to resist the negative design moment in the column strip should be placed in a width equal to half that of the column strip and central with the column.                                                                                                                                                             On the other hand, clause 9.4.1 (2) of Eurocode 2 stipulates that half of the total area of reinforcement required to resist negative moment over internal columns should be placed in a width equal to the sum of 0,125 times the panel width on either side of the column.
• Slab reinforcement for edge and corner columns should be concentrated within width be (width be is defined in the figure below)

 

 

 References

EN 1992-1-1:2004 (Eurocode 2): Design of concrete structures – Part 1-1: General rules and rules for buildings

BS 8110-1-1997: Structural use of concrete — Part 1: Code of practice for design and construction

Design of reinforced concrete flat slab to BS 8110 (CIRIA, Report 110)