Live LOad Reduction ( Tributary area and Influence ARea ) 1

[Saedhalteh]

Hello All,
I have read that to determine the "Tributary area" for a Column by Taking the half-area each way, aka "simple tributary area", will always underestimate the reactions to interior columns. and using the unit load approach will give more accurate results for determining the Tributary Area.

Can Someone guide me on this unit load approach(What is it and how we can perform it manually ) , if there is example that explains how we can Find Tributary area for a column using this method, That would be really helpful.

Additionally, I want to check about the Influence area term, Is it the product of (Tributary area ) And ( KLL) "Live Load Element Factor ) ??

 

[KootK]

I have read that to determine the "Tributary area" for a Column by Taking the half-area each way, aka "simple tributary area", will always underestimate the reactions to interior columns.

That is sometimes the case, particularly at the first interior column in from the building perimeter.

Can Someone guide me on this unit load approach(What is it and how we can perform it manually ) , if there is example that explains how we can Find Tributary area for a column using this method, That would be really helpful.

While I've never heard it called the unit load method, I believe that the procedure that you're thinking of is this:

1) Run an FEM model of your slab considering a unit value of your loads, say 1 PSF (the unit load).

2) Use #1 to work out the column reactions for your unit load.

3) For any actual load, estimate your column reactions as [unit load column reaction x actual load / unit load]

I've seen this used to advantage for tall structures with many floors having the same column layout. It's important to be aware of the limitations of the method, however, which include:

4) The results are specific to the particular load configuration being considered and will be affected by pattern loads, point loads etc.

5) The results are only strictly valid for elastic analyses. Once you introduce concrete cracking and other non-linear effects, things will redistribute a bit.

As always, there's no perfect estimate in structural engineering.

 

[KootK]

Additionally, I want to check about the Influence area term, Is it the product of (Tributary area ) And ( KLL) "Live Load Element Factor ) ??

That is correct. I always recommend disregarding K_LL and, rather, thinking of the influence area as "every square foot or area which, when loaded, would add some increment of load to the member being considered". This is dirt simple to apply and will always lead too the correct estimate of influence area.