Load Distribution Theory

[bearjew]

Hi all,

When modeling uniformly applied gravity loads to a structure, engineers often distribute them based upon tributary area. However, I have been thinking, whats the theory behind this? Wouldn't a steel deck behave as a flexural member and distribute load to supporting members via beam theory, thus loading interior supports more than the end supports?

Similarly, wouldn't a rigid diaphragm such as concrete on metal deck distribute its load to to supporting members based on the relative stiffness of each supporting member, loading stiffer girders more than joists or beams?

What argument is there for semi-rigid diaphragms such as plywood sheathing or steel plate?

I have other examples that I am curious about, but I will let the conversation start with the above.

 

[MotorCity]

In theory, you are correct that load would be distributed according to the member and support stiffness as well as the interior or exterior support condition. Here is what I can offer. For the case of a slab or deck supported on beam elements, the beams are usually the same size (or very close), so they have the same stiffness. Think typical floor beams spaced at say 5' on center, each beam is not a different size. Secondly, considering a multi span condition will produce smaller moments compared to assuming a single span simply supported condition. Therefore, its conservative to assume a simple span which is consistent with distributing loads on the basis of tributary area.

 

[EngineeringEric]

Does it matter to be that accurate in design? When we are developing our floor system in your analysis we cannot know the stiffness of everything... so we assume they are nearly equal = trib area loading.

When we are done if we went back and iterated the loading for different sized members that say have a deflection of 0.5" vs 0.6" (when based on trib area) which are spaced 25 ft apart; would it really matter? i am guessing infinitely rigid floor would make them both 0.55" a semi-rigid may be more like 0.52" and 0.58"... but how accurate is that semi-rigid analysis? And again, did it matter to be that accurate? Then what happens when my beam has a 1/32" thicker flange due to mil tolerance and my Ixx just increased by 7 in^4...

What I am trying to say, probably very poorly, the extra degree of accuracy is not actually more accurate and requires a large amount of additional analysis. It isn't worth it 99% of the time for new design for what I do.

 

[bearjew]

In theory, you are correct that load would be distributed according to the member and support stiffness as well as the interior or exterior support condition. Here is what I can offer. For the case of a slab or deck supported on beam elements, the beams are usually the same size (or very close), so they have the same stiffness. Think typical floor beams spaced at say 5' on center, each beam is not a different size. Secondly, considering a multi span condition will produce smaller moments compared to assuming a single span simply supported condition. Therefore, its conservative to assume a simple span which is consistent with distributing loads on the basis of tributary area.

For a rigid diaphragm, I would agree that a typical floor has mostly the same size joists/beams, so equal stiffness and the tributary area method holds water. I'm curious the argument for when girders come into play or weird framing such as if you have a lot of floor openings.

For a flexible diaphragm, considering a simple span condition is conservative for diaphragm design only. Unless I am thinking about this the wrong way, it would be unconservative to design the supporting members using the simple span condition.

To be clear, I design based on tributary area. In my experience, everyone does. However I was thinking about all of this last night and couldn't come up with any good answers to my questions and thought I'd enlist the brain trust here to satisfy my curiosity.

 

[bearjew]

Does it matter to be that accurate in design? When we are developing our floor system in your analysis we cannot know the stiffness of everything... so we assume they are nearly equal = trib area loading.

When we are done if we went back and iterated the loading for different sized members that say have a deflection of 0.5" vs 0.6" (when based on trib area) which are spaced 25 ft apart; would it really matter? i am guessing infinitely rigid floor would make them both 0.55" a semi-rigid may be more like 0.52" and 0.58"... but how accurate is that semi-rigid analysis? And again, did it matter to be that accurate? Then what happens when my beam has a 1/32" thicker flange due to mil tolerance and my Ixx just increased by 7 in^4...

What I am trying to say, probably very poorly, the extra degree of accuracy is not actually more accurate and requires a large amount of additional analysis. It isn't worth it 99% of the time for new design for what I do.

This is a fair argument, and I agree. If this is the only answer I receive, I accept it just fine. I just know that there are a lot of people here who understand structural analysis much more so than myself.

I did some searching on this forum for this question before posting, and some discussion was brought up about steel deck behaving more like the simple span condition because its shear deformation is much greater than its flexural deformation. But it did not provide much closure. Why is this the case? This is the type of discussion I am looking for.

 

[EngineeringEric]

Ahh so more of a theoretical than the "I am an engineer on a budget". And I am in the same boat, others here are better at structural derivations than I!

 

[klaus.]

that's why structural engineers study a long time.....

a long time ago there was a time without computers....so engineers used simple methods do do the work by hand




best regards
Klaus

 

[rb1957]

I think it's good to question basic assumptions, rather than "this is the way we've always done it".

However, you can work through the different cases yourself, to gain a better understanding of what "rigid" and "flexible" mean, to appreciate when the beams are doing the work and when the floor is.

I suspect that you can always use tributary area [1], and the section supporting this is the deck and the beam. When the beams are large they dominate the I and are doing the work; when the deck is large it dominates I (and is reinforced on the tension side). Possibly the question may become does the deck work as a membrane (and develop in-plane tension) ?

[1] with uniform beams; non-uniform beams is a different matter.

another day in paradise, or is paradise one day closer ?