This article addresses some basic design issues that are typically encountered in the preliminary design stage of a nonprestressed concrete flat-plate floor system. The information presented is based on the American Concrete Institute’s Building Code Requirements for Structural Concrete (ACI 318-05) and Commentary (ACI 318R-05). Section numbers referenced herein are from that document.

Preliminary slab thickness
Serviceability, strength, and fire resistance must be considered when determining an initial slab thickness for any concrete floor system. Section 9.5.3 contains serviceability provisions for nonprestressed, two-way construction. According to Table 9.5(c), the minimum thickness of slabs without interior beams and without drop panels is l_n/30 for slabs with Grade 60 reinforcement, where l_n is the longest clear span (measured face-to-face of supports) in the system. In no case shall the slab thickness be taken less than 5 inches. It has been demonstrated for many years that slabs conforming to the limits in Table 9.5(c) have performed adequately under normal conditions.

Two-way or punching shear plays a key role in determining the thickness of a flat plate. In order to satisfy shear-strength requirements, the slab thickness must usually be greater than that required for serviceability, especially for flat plates with longer spans and/or larger superimposed loads. The shear stresses developed at perimeter columns are particularly critical, since these columns are subjected to relatively large, unbalanced moments.

For members without shear reinforcement, Section 11.12.6.2 requires that the maximum shear stress v_u, due to the combination of direct shear force V_u and unbalanced moment M_u, be less than or equal to the design shear strength Φv_n:

.

In this equation, Φ = strength reduction factor = 0.75 for shear; b_o = perimeter of the critical section for shear defined in Section 11.12.1.2; d = distance from extreme compression fiber to centroid of longitudinal tension reinforcement; and, V_c = nominal shear strength provided by the concrete, which is defined in Section 11.12.2.1 as:

V_c = smallest of

where β = ratio of the long side to the short side of the column; f ’_c = specified compressive strength of the concrete; and α _s = 40 for critical sections with four sides, 30 for critical sections with three sides, and 20 for critical sections with two sides.

Section 11.12.6.2 permits the shear stress resulting from moment transfer by eccentricity of shear to vary linearly about the centroid of the critical section. Thus, the maximum factored shear stress v_u is determined by



where A_c = area of the concrete section resisting shear transfer; gamma _v = factor used to determine the unbalanced moment transferred by eccentricity of shear =



where b₁ = dimension of critical section measured in the direction of analysis; b₂ = dimension of critical section measured in the direction perpendicular to b₁; c_AB, c_CD = distance from the centroid to the faces of the critical section in the direction of analysis; and J_c = property of the critical section analogous to the polar moment of inertia. Equations for the section properties b₁, b₂, c_AB, c_CD, A_c, and J_c of interior, edge, and corner columns can be found in numerous references.

The following strength equation must be satisfied at any column:



Figure 1, which is based on the two-way shear strength requirements of ACI 318-05, can be used to determine a preliminary slab thickness h for a flat plate assuming the following: square-edge column of size c₁ bending perpendicular to the slab edge (three-sided critical section with α _s = 30); column supports a tributary area A; square bays; gravity load moment transferred between the slab and edge column in accordance with Section 13.6.3.6; and 4,000 psi normal weight concrete.

Fig. 1


The total factored load q_u must include an estimate for the weight of the slab. The ratio d /c₁  can be determined from Figure 1 as a function of q_u and the area ratio A/c₁². A preliminary h can be obtained by adding 1.25 inches to d. Figure 1 should help decrease the number of iterations that is needed to establish a viable slab thickness based on shear strength. It can also be used to check the accuracy of computer output.

The slab thickness required for strength and serviceability is usually more than sufficient to satisfy fire-resistance requirements. Provisions of the governing building code must be checked to ensure that the specified slab thickness provides the necessary fire resistance.

Shear reinforcement
When shear-strength requirements are not satisfied, slab thickness and/or column sizes can be increased. When these options are not viable, the slab can be thickened locally around the columns. In such cases, overall cost is greater than that of a flat plate, since it takes more time and material to form the additional concrete.

Providing shear reinforcement can supplement the shear strength of concrete. Provisions for shear reinforcement consisting of bars or wires or single- and multiple-leg stirrups are given in Section 11.12.3. Another type of shear reinforcement is shearheads, which are typically structural steel sections that are cast in the concrete at the slab-column joints (Section 11.12.4). Due to high labor and material costs, this type of shear reinforcement is rarely used any longer.

A type of shear reinforcement that has become increasingly more popular in recent years is shear studs, which consist of vertical rods that are mechanically anchored by heads on one end of the rod and a base rail at the other end. Rails are shared by more than one stud and are nailed to the formwork around the columns. The dimensions of the shear studs are such that they can develop their full-yield strength in tension. Design provisions and other pertinent information can be found in the ACI document Shear Reinforcement for Slabs (ACI 421.1R-99) or in literature from proprietary manufacturers. Design requirements for shear studs will likely be included in an upcoming edition of ACI 318.

It is important to determine as early as possible whether shear reinforcement is required or not, since it has an impact on slab thickness, column size, overall cost, and design time.

Slab openings
Slab openings for mechanical, electrical, or plumbing equipment are almost invariably situated in close proximity to columns. In addition to a possible influence on flexural strength, these openings have a direct impact on shear strength when they are located anywhere within a column strip or within a distance of 10h from a column (Section 11.12.5). Figure R11.12.5 illustrates the portion of the critical shear perimeter that is considered ineffective due to an opening. For slabs with shear reinforcement, the ineffective portion of the perimeter is one-half of that for slabs without shear reinforcement.

For columns without significant unbalanced moment (for example, interior columns subjected primarily to direct shear V_u), the area A_c is affected by slab openings. Since A_c decreases when openings are present, the shear stress v_u increases. When columns are subjected to both direct shear V_u and unbalanced moment M_u, the quantities A_c, gamma_v, c_AB, c_CD, and J_v are all affected by openings. In lieu of computing reduced-section properties of the critical section (which can be quite cumbersome), it would be conservative to regard any side of the critical section that is affected by openings as a free edge.

Establishing the layout of slab openings early on is advantageous for many reasons. It is best to locate openings as far as possible from edge and corner columns in order to utilize the maximum shear strength that is available at these locations.

Conclusion
In structures utilizing flat-plate floor systems, the likelihood of encountering costly design issues throughout the life of the project is significantly reduced when, during the early stages of design, the minimum slab thickness is established considering strength, serviceability, and fire-resistance requirements and when the location of slab openings is coordinated with other members of the design team.