Tributary Areas of Structural Elements

Introduction

The design of structural elements requires an appraisal of the actions (static and dynamic forces) to which supporting are subjected to, loads transferred from floor slabs to beams and columns. In order to estimate these loads one of the methods available to the designer is the Tributary Area Method (TAM).

The tributary area is a loaded area that contributes to the load on the member supporting that area. For example, the load supported by the middle joist in figure 1 is the area from the centre of the first two joist to the centre of the next two joist. This distance is known as the tributary width.

Tributary Areas in Columns

The area surrounding the column bounded by the centerline of the panel is the tributary area on which the loads are supported by the columns at the center of the area as shown in figure 2. The shaded area represents the tributary area of the columns column.

To obtain the load transferred to the middle column from the floor the tributary area is simply multiplied by the floor design load 

Axial Load on Column = Design Load x Tributary Area

When the tributary area method is used in estimating the loads on columns, the position and areas of the beams are ignored and an allowance made for the self-weight and additional loads on the beam when summing-up loads on the column

Tributary Areas in Beams

The tributary areas of beams in one-way system is the same as the joist shown in figure one. However, the tributary areas of beams in two-way systems do not have obvious tributary width instead the load distribution is modelled using the yield line approach i.e. using a 45-degree tributary boundary that is halfway between the supporting elements, in this case edge beams. Figure 3 illustrates tributary areas in two-way systems.

To obtain the load transferred to each beam the tributary areas is multiplied with the floor design loads

Load on Beam = Design Load x Tributary Area

Analyzing beams with triangular or trapezoidal loads is rather complex and therefore the load can be conservatively taken as uniformly distributed using the following formulas

Beams in the longer direction

Beams in the shorter direction

Limitations of Tributary Area Method (TAM)

Indeed, the tributary area method is a very simple and fast method of estimating forces on structural elements if the tributary areas can be identified. It is often not necessary to compute the progression of load transfer through the load path. However, the tributary area method however has some limitation.

Tributary Area Method (TAM) is a simple and fast method of estimating loads on structural elements but is less accurate and result obtained could be Incorrect

Irregular column layout: If the layout of grids or columns is irregular it becomes very difficult to identify the tributary areas of structural elements, as a result, the use of TAM becomes difficult to apply.

Stiffness of adjacent supporting member varies significantly: In reality load distribution is based on stiffnesses of structural elements, stiffer elements attract more loads than less stiff elements.

Hence, when the above listed conditions exist TAM is not applicable instead a more sophisticated method such as the Finite element analysis (FEA) should be utilized.