Reinforced Concrete Slab Design
Reinforced concrete slabs span either one-way or two-way, depending upon their support conditions.
1) A one-way slab spans between parallel line supports such as walls or beams. At every point the axis of bending is parallel to the supports. One-way slabs are essentially wide beams and are designed following the same principles that apply to any beam.
2) A two-way slab spans in two directions and bends about two the axes. The orientation of the principle axes of bending change throughout the slab. There are many variations of two-way slabs, three of which are shown in Fig. 5.1. Two-way slabs are highly statically indeterminate structures and a detailed prediction of their behavior requires complex analysis. Traditionally two basic methods have been used to design the vast majority of two-way slabs, the Direct Design Procedure and the Equivalent Frame Method. Both of these procedures are detailed in Clause 13 of the CSA A23.3 Standard. More recently, the advent of user friendly finite element analysis (FEA) programs have allowed designers to design slab geometries that fall outside the limitations of the Direct Design and Equivalent Frame analysis procedures.
Figure 1 below depicts the characteristic deflected shape of a two-way slab.
With the availability of slab design program such as PCASLABTM, the use of the Direct Design Method has declined dramatically. More detailed analysis results can be obtain in less time that can be generated from a manual analysis using the Direct Design procedure. As a result the Equivalent Frame method of analysis is the highly preferred method of choice when it comes to designing slabs.
The design of any slab system may be divided into the following steps:
Step 1 - select slab thickness
Step 2 - obtain design moments
Step 3 - choose flexural reinforcement
Step 4 - check shear capacity, and
Step 5 - design beams and/or other elements (if any)
As the slabs in a building will comprise a high percentage of the overall mass of the structure, the selection of slab thickness should be made carefully. The slab thickness will generally be driven by deflection limits and punching shear at the supports. The success or failure of a slab design is almost always judged on the basis of serviceability. The minimum thickness for one-way slabs without the need to compute deflections, is given in Table 9-2 of the A23.3 Standard. Clause 13.2 contains provisions for the minimum thickness of regular two-way slab systems as defined in Clause 2.2.
Slab Design Moments:
The design moments at supports and at mid span are determined from one of a variety of analysis procedures specified in the CSA A23.3 Standard. Once obtained, these moments are designed for using the standard methods of flexural design. In addition to the provision of sufficient reinforced to resist the design moments the designer must detail the slab reinforcement in accordance with the requirements of Clause 13 of the CSA A23.3 Standard. These detailing provision ensure that sufficient reinforcement is placed in the areas of the slab where it can be best utilized to resist the design moments and provide the best deflection and crack control possible to the slab.
The A23.3 Standard specifies a minimum area of slab reinforcement in each direction equal to 0.002 Ag. This ensures sufficient shrinkage crack control in the slab. The capacity of this level of reinforcement in the slab should be evaluated early in the design as it will in many instances be sufficient to resist the factored moments in the slab. Additional concentrated reinforcement will be required in the negative moment region over supports to provide sufficient negative moment resistance in these high stress areas. The CSA A23.3 Standard also requires structural integrity reinforcement in the bottom of the slab directly over supports to ensure that a catastrophic punching shear failure leading to a progressive collapse will be averted.
Shear and Moment Transfer:
One-way slabs are designed for 1-way beam shear only. While two-way slabs are also checked for beam shear although it is rarely critical. Two-way punching shear is usually the critical shear failure mechanism in two-way slabs. Slabs supported by beams are treated as unit strips spanning to the beams. The CSA A23.3 Standard contains prescriptive punching shear design requirements for corner, edge and interior columns. In addition to pure punching shear, additional shear is imparted to the slab at supports through unbalanced moments that develop on either side of the support. These additional shears must be added to the straight punching shear stresses to determine the full two-way shear demand on the slab at the support.
Where shear is determined to be a problem several solutions are employed. In addition to increasing the slab thickness, the designer may use column capitals, drop panels or both. As a somewhat more elaborate measure, slab shear reinforcement may be included where circumstances warrant such a measure.
Design examples are presented to assist in interpreting the provisions of specific clauses of the Standard. It should be pointed out that each example is an incomplete design in that only portions of the slab system are considered. Computations described in other chapters of this Handbook are usually omitted.