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Distribution of loads, flexible vs rigid diaphragms

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Naggud

Structural
Jan 31, 2013
42
Hi guys,

I am a recently graduate, I'm looking at a building (prelim. seismic assessment).

We are not assessing the rigidity of the diaphragms. In general we are assuming a timber floor/roof is a perfectly flexibly diaphragm and a concrete diaphragm is assumed to be completely rigid (relatively short spans - commercial buildings).

The seismic load is distributed based on trib area for a flexible diaphragm and based on the relative stiffness of the vertical elements for a rigid diaphragm.

If I have a simple timber building, square on plan. If I have 3 vertical support systems in one direction - on the west wall I have post and beam construction (assumed no lateral stiffness), a timber stud wall in the middle of the building the length of the building north south and a partial timber stud wall on the east wall.

In my analysis of this I originally attributed the lateral loads based on tributary area. i.e. 1/3 to the post and beam, 2/3 to the central wall and 1/3 to the shorter stud wall.

On this basis the post and beam wall would fail (negligible later stiffness), lets assume the middle wall is adequate and the shorter east wall fails.

I have been speaking to some of our more senior guys about this in the past while. They have been saying to me that the post and beam wall will not fail - that the load would be transferred back into larger middle wall.

When I find that the short east wall fails based on the tributary load he says to leave that wall as having failed (I think this is inconsistent).

I would appreciate your views. To emphasis, this is a very preliminary assessment, we are not going into very much detail, I just find the approach inconsistent.

Thank you.



 
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Your instincts are correct. What your boss is describing would require the diaphragm to act as a rigid diaphragm to transmit forces based on stiffness of the lateral elements. If you are taking the post wall to failure, then the deck diaphragm is a cantilever from the post wall to the center wall. Unless you are talking about a small plan, I can't believe that the wood floor would have adequate stiffness to act in this manner.
 
Thanks steellion, that was my take on it too. Appreciate your reply.
 
"They have been saying to me that the post and beam wall will not fail - that the load would be transferred back into larger middle wall."

This is only true of the doaphragm is stong enough to do the transferring, and if the cantilevered diaphragm meets the current limitations of the IBC. Otherwise, no.

Mike McCann
MMC Engineering
 
Well, there are not really any "flexible" diaphragms such that they can't cantilever - in truth all diaphragms are partially rigid, right?
 
You need a rigid diaphragm for the loads to redistribute. You may be able to consider even a wood diaphragm as rigid though if you can put the numbers behind it.
 
Thanks guys, that was my understanding too.

I take it then that if you do assume a diaphragm to be perfectly flexible (never is) it cannot cantilever.

We are making that assumption at this early stage of this study. We are attempting to assess a lot of buildings on a high level to gain an order of magnitude cost to move forward to more detailed engineering. Because of this we are therefor assuming that some walls are failing when in reality they will be okay provided the diaphragm is able to redistribute the load to the stiffer vertical lateral force resisting system.

I guess for our purposes from a costing point of view what we are doing is accurate enough to get order of magnitude cost.

Back to the technical side, I just felt our methodology was inconsistent and it is, sometimes we are assuming that the diaphragm is perfectly flexible and sometimes when it suits we are not.

Thanks for clarifying.

 
If a diaphragm cannot cantilever, it cannot span either which would suggest to me that it is not a diaphragm. If the building is square in plan view, why can't the central wall carry 100% of the lateral force if need be? If torsion is present, the end walls may come into play as well.

BA
 
The key to designing a "flexible" diaphragm for a cantilever is to consider a couple of things in your design:

1. Design should bracket the theoretical high and low possibilities depending on relative stiffnesses of the diaphragm vs. braces. Assume fully flexible and find the max. brace loads from that perspective and then assume a rigid diaphragm and get brace loads from that. The answer is somewhere in between and you would know that your brace designs are covered either way.

2. With a non-concrete (ie. assumed flexible) diaphragm, watch out for the lack of stiffness in the diaphragm and its potential effects on lateral sway. With large horizontal deflections at the end of your cantilever, or anywhere for that matter, you can have very high second order PDelta effects on your building which also add to the X-brace/shearwall loads. Nailing down the actual, or maximum, deflections in your cantilever is difficult - especially for ill-defined wood diaphragms.

 
I have been speaking to some of our more senior guys about this in the past while. They have been saying to me that the post and beam wall will not fail - that the load would be transferred back into larger middle wall.

If you take that approach, then you are using a cantilevered wood diaphragm. Cantilevered wood diaphragms aren't allowed to extend more than 25' or 2/3 the diaphragm depth, whichever is smaller. Check to see if you violate that.

When I find that the short east wall fails based on the tributary load he says to leave that wall as having failed (I think this is inconsistent).

What do you mean "leave that wall as having failed"? That's obviously not cool for final design.

 
Hi amusement park.

At this point we are just assessing existing buildings. It is a performance based design with a methodology approved in our region, it is a high level assessment based on the likelihood of the element exceeding a specifie drift limit. If it exceeds that we recommend further work be done on the element/structure depending on the specific situation. That I'd what I meant by a wall failing.

Thanks for the info. could you point me to where you got this information?

Thanks
 
It could also depend upon the stiffness of the walls. While unconventional, if the walls were flexible in comparison to the diaphragm, the function would not be a simple SE I exam problem.

A professor told me (repeatedly) to do as JAE suggests. He said to take it both ways and use the higher values for each wall. My experience tells me that this approach would cover the real world problems, and change orders during construction (like changing the floor system.)
 
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