Tributary area

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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)

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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.

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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.

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 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.

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Table 8 - Tributary areas and loads for columns supporting a concrete slab

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The table indicates that the central column bears more than twice the load of a corner

column, and one and one-half 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.

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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.

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Now let's see how structural members are combined to build complex residential, public,

commercial, and industrial buildings.

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 Page 124 - Building stability - Tributary area