Tributary area 
. 
The
proportion of the floor or roof load bearing down on an individual support
beam or 
column
is estimated by dividing the total loaded surface into tributary areas
corresponding 
to each
particular support member. The following model shows how the
tributary areas of 
a
reinforced concrete slab are allocated to each of its supporting columns.
The boundary 
of a support's tributary
area is demarcated as half the distance to any adjacent supports. 
. 



Fig. 208  Tributary areas 
of columns supporting 
a concrete slab 

each square is 2' x 2' 

(training aid model) 


. 
The four
corner columns and their corresponding tributary areas are colored yellow.
The 
four
perimeter columns and their areas are red. And the central column
and area is blue. 
. 
Let's
say the slab is 14 feet by 14 feet for a total area of 196 square feet.
It has a dead load 
weight
of 286 lbs./sq. ft. and is designed to carry a live load of 90 lbs./sq.
ft. The following 
table
calculates the total maximum anticipated load for each column position. 
. 
Column 
Tributary area 
Live load 
Dead load 
Total load 
All columns 
corner 
4x4 = 16 
16x90 = 1440 
16x286 = 4576 
6016 lbs. 
24064 lbs. 
perimeter 
4x6 = 24 
24x90 = 2160 
24x286 = 6864 
9024 lbs. 
36096 lbs. 
center 
6x6 = 36 
36x90 = 3240 
36x286 = 10296 
13536 lbs. 
13536 lbs. 

Total 
73696 lbs. 

. 
Table
8  Tributary areas and loads for columns supporting a concrete slab 
. 
The
table indicates that the central column bears more than twice the load of
a corner 
column,
and one and onehalf times the load of a perimeter column, at the maximum 
design
load. This is a very simplified presentation of the tributary area
concept, which can 
get much
more complex depending on the framing plan of the building. 
. 
If you
were designing this structure you would need to combine this load data
with other 
information on the maximum allowable deflection, critical buckling load,
maximum tensile 
and
compressive stress, maximum bending moment, safety factor, etc. in order
to select 
the
appropriate material and dimensions for its members.

. 
Now
let's see how structural members are combined to build complex
residential, public, 
commercial, and industrial buildings. 
. 
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to Knowhere 

Page 124
 Building stability  Tributary area 

