Tributary Area

What is Tributary Area in Columns?

Tributary area refers to the area around the column bound by a panel centreline. The tributary method is used to calculate static loads and forces transferred from floor slabs onto columns.

Designers often use the tributary area of columns to transfer loads from slabs into columns or calculate reactions of beams framing into columns. This method is used more often than the latter.

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Tributary area in Column

As shown in Fig. 1. The column supports the dead load equal to the dead weight per unit area multiplied by the tributary.

Figure. Fig. If the spans between columns is nearly equal, then the loads on the corner column will be quarter and half of those on the center and edge columns, respectively.

The floor beam position is not considered when the tributary area has been used. However, it is taken into account for the allowance for their weight.

Designers can calculate live loads using the tributary area. This is because the design codes stipulate that the percentage of live loads transmitted from a column to a column is an inverted function of the designated tributary regions. That is, the live load reduction decreases as the tributary reaches greater heights. Designers favor load transfer in columns because it is easier. ASCE7 standard provides details on how to reduce live loads.

How to calculate Tributary Areas

It can be difficult to calculate the exact area of tributary, as we need to first understand the flow of forces through the slab. A wider river can transport more water. A stiffer column can "transport" more forces.

The slab may also be stiffened in different directions, which can make the flow irregular. One-way slabs that are supported by infill beams can be designed to transfer loads in one direction. Learn more about the differences in one-way and 2-way slabs.

For simplicity's sake, let us assume that the floor and columns below it are isotropic. Then, it boils down to a geometric problem. Which column is closest to each point on the slab? This problem can be solved by identifying each column's neighbor and dividing the distance in half using a centerline. The area to the left of the centerline on each column's side will be its tributary.

This involves finding the middle point between each pair and drawing a perpendicular lines. Once all the perpendicular lines have been drawn, the bounding polygon will define the column's tributary.

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Exemple

Let's look at a simple structure to illustrate how tributary area can be calculated. This article will show you how to build a more complex structure. The following structure is available:

The slab is rectangular in shape, and the columns are arranged parallel to the slab edges. The structural grid is composed of four grid lines in one direction and three grid lines the other. A column is located at every intersection of grid lines.

Column D-1

Let's begin with the column at intersection D-1. These are the steps, as shown in the previous section:

In each direction, identify the column that is adjacent

D-1 is located adjacent to gridline C, and gridline 1.

Take the distance

The distance between D-1, C-1, and D-2 is 16 meters.

Divide distance by 2.

Half the distance between D-1 & C-1 is 16/2=8 m, and half the distance between D-1 & D-2 is 8/2=4 m.

At this point, draw a perpendicular.

Once the midpoints are identified, you can begin to draw perpendicular lines.

Having followed the above steps, you will end up with these two lines in red.

You can see that the lines are drawn in one point. This point is the corner of the tributary polyline. Column D-1 is at a corner and has no neighbors. The outer border of the slab defines the three corners of rectangle D-1.

We can calculate the area of the bounding polygon by multiplying its side lengths. This allows us to easily calculate the area of column D-1's tributary area: 8m x4m = 32m2.

Column C-2

Let's now do the same thing for the interior column B-2. Begin by identifying neighboring gridlines. The gridlines that are associated with C-2 have neighbors on both sides.

Gridline C's left neighbor is B.

Gridline C's right neighbor is D.

Gridline 2's left neighbor is 1

Gridline 2's right neighbor is gridline 3.

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