Background

The BRAB analysis is performed in accordance with the design methodology presented in Criteria for Selection and Design of Residential Slabs-on-Ground prepared for the Federal Housing Administration by the Building Research Advisory Board in 1968 (referred to in this manual at the BRAB Report). The Building Research Advisory Board was a Special Advisory Committee of the Division of Engineering of the National Research Council. We recommend that engineers wanting to design using this method obtain and read the full text of the BRAB Report as it contains additional limitations, design requirements and background information not discussed in this manual. The BRAB Report may be obtained from the National Institute of Standards and Technology or the National Academies Press at http://www.nap.edu.

Design Methodology

Similar to the other three design methods implemented in SlabWorks™, the BRAB method is at it simplest level a method of predicting the maximum moment, shear and deflection occurring in a slab-on-grade. Once these values are established, the actual design of the beams is conventional and will not be unfamiliar to anyone who has performed conventional reinforced concrete beam design.

In the BRAB method, the foundation is designed in the following steps

1. Determine dead and live loads
2. Divide slab into overlapping rectangles (see Figure 1).
3. Calculate imposed shear and moment in slab using BRAB equations.
4. Select trial geometry (beam depth, width, spacing and reinforcement)
5. Check allowable moment and shear against imposed moment and shear.
6. Check actual deflection against allowable deflection.
   

The BRAB report determines moments, shears and deflections in the slab by assuming that the slab is only partially supported by the underlying soils. The soil is assumed to be rigid in the areas of support (inelastic support conditions). Two design conditions are considered, loss of support at the edges (center lift/edge settlement) and loss of support at the interior (edge lift/center settlement):
The amount of slab support provided by the underlying soil is called the support index, C, and is defined as the fraction of the foundation that is supported by the soil. The support index is a function of the climatic rating (CW) and the effective plasticity index of the soil (PIE). The higher the plasticity index, the higher the potential for soil movement and the less support considered in the analysis. The chart for determining the support index as a function of CW and PIE is shown in Appendix 2.

Once the support index is found, moment, shear and deflection are found as shown in Figure 3.

The BRAB report makes certain simplifying assumptions in order to reduce the two load cases to one set of design equations for shear, moment and deflection. Additionally, certain assumptions are made that reduce the uniform load in the long direction relative to the short direction. Once these simplifications and modifications are made, the actual design equations for shear, moment and deflection are shown in Figure 4.

The w in these equations in the effective uniform load (wE). In the short directions, w is equal to wE. In the long direction, the effective load is calculated using the equation in Figure 5.