Multi Story Live load reduction

[mla163]

Help me prove an old engineer wrong...

It sounds like an easy question: IBC live load reduction is Lo * [0.25 + 15/sqrt(Ai)].

At the bottom story of a multi story building, is the reduced live load calculated using the influence areas of all floors summed up? = Lo * [0.25 + 15/sqrt(sigma Ai)]

or

Is the reduced live load at the bottom story the sum of the reduced live loads from each individual floor? = sigma [ Lo (0.25 + 15/sqrt(Ai)]

 

[JAE]

The LL reduction for a column is based on the influence area which is the sum of ALL the areas above. The equation, for that column, should be based on the areas, not the individual reduced live loads from each column above.

In other words, the LL for any particular element in a structure should be reduced using its OWN total area.

The LL reduction for an element is not a sum of other reduced live loads from other elements, but rather a uniquely reduced live load for that element alone.

 

[archeng59]

there is also a limit on the reduction:

0.40LL for members supporting more than one floor, where LL is the live load per table 1607.1. see the nomenclature in section 1607.9.1 of the IBC.

in my opinion, the total live load reduction cannot be less than the 0.4LL for the first floor column.

 

[JAE]

Yes, I'd agree with the limit shown.