Tributary Area Calculations and Live Load Reductions

[medeek]

I have a continuous beam with two equal spans. Consequently the bearing load is considerably more at the center post than the two end posts. I'm wanting to calculate the tributary area for this post. If the total beam length is 2L am I correct in saying that the trib. length for this post would be 5L/4? Then K_LLA_T = 5L/4 x W x 4 = 5L x W

A confused student is a good student.
Nathaniel P. Wilkerson, PE

http://www.medeek.com

 

[hokie66]

I think that is stretching it a bit. I have always just used the area of the half span for the purpose of live load reduction.

 

[KootK]

The answer should be 4LW. The code definitions of KLLxAt are clumsy. The best way to think of it is as follows: every square foot of floor that, if loaded, would add load to your column, contributes a square foot to KLLxAt.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[medeek]

I agree with both of you if this were two simply supported beams connecting the three posts, the center post load would then be twice the load of either of the end posts however with a continuous span my center post load is 3.33 of the end post loads so in reality its tributary area must be logically larger than a center post with two simply supported spans.

A confused student is a good student.
Nathaniel P. Wilkerson, PE

http://www.medeek.com

 

[hokie66]

I know what you are saying, but I just don't do it that way. I don't really think of it in KootK's way either, as load anywhere along the span adds load to your column. Of course, the live load is what it is on the continuous span, but the reduction factor is what we are talking about, and I would rather be a bit conservative in that respect.

 

[medeek]

Perhaps this picture will help illustrate what I am trying to describe:

A confused student is a good student.
Nathaniel P. Wilkerson, PE

http://www.medeek.com

 

[KootK]

Remember, this is a probability thing. And the probability of full load with continuous spans is no higher than it is with two simple spans. The parameter of interest is not "tributary area". Rather, it is "influence area" which is as I described it above.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[medeek]

So calculate the tributary area as if all beams were simply supported. I get the probability angle on this.

However, with the actual load to the center post, calculate that based on the mechanics of the situation? In the case where the joists and beam are continuous the center post will see considerably more load than if everything was simply supported.

A confused student is a good student.
Nathaniel P. Wilkerson, PE

http://www.medeek.com

 

[BAretired]

If you are designing the column for a Live Load of 1.25wL², you should be entitled to a live load reduction factor based on the area 1.25L². Like hokie66, I might not do it that way but I believe it could be justified in court when defending your design.

BA

 

[medeek]

56.3% more load.

A confused student is a good student.
Nathaniel P. Wilkerson, PE

http://www.medeek.com

 

[KootK]

I believe that the same probability argument applies in both directions
Medeek.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[hokie66]

I should probably not have participated in this discussion, as "KllxAt" is not in my vocabulary, and neither is "influence area" in this sense. We obviously do it differently in Australia.

 

[BAretired]

It won't be as much as 56.3% more load because the central beams deflect. Each continuous joist settles a variable amount at the central beam and very little at the stud wall, so the negative moment of each joist is somewhat less than wL²/8 due to support settlement. If the central column is deemed to carry 56.3% more load, its design is conservative so a live load reduction factor based on the larger tributary area seems reasonable.

I'm not convinced that making the glulam members continuous is a good idea but that is a separate issue.

BA