Steel deck diaphragm

[dcStrucEng]

(Sorry if this question has been posted previously, but I couldn't find my exact answer after performing a forum search.)

I am designing a one-story steel warehouse-type structure per IBC 2006/AISC 360-05/AISC 341-05/ASCE 7-05. Approximate plans dimensions are 500' x 160' with a height of 40'. The roof is proposed to be steel deck without concrete infill, with a standing seam roof system over. The lateral bracing system are three SCBF (one at each end, and one in middle) in the short direction and one SCBF along one of the end walls in the long direction.

My question is whether I can analyze the roof as a rigid diaphragm assuming that I comply with the appropriate fastener layout pattern, end lap and side lap provisions, and any other rigid diaphragm requirements.

The reason why I want to assume a rigid diaphragm is because I want to be able to distribute the lateral forces and moments to my roof structure (particularly for all the different wind load cases, see figure 6-9 of ASCE 7), which in turn gets distributed to the lateral bracing system.

If I assume a flexible or semi-flexible diaphragm I don't intuitively understand how this distribution of forces and moments occurs, from the roof structure to the lateral bracing system.

Any advice/opinions are more than welcome.

 

[Lion06]

If you assume a flexible diaphragm then you distribute loads to the lateral frames based on trib width rather than stiffness. I actually think that the flexible diaphragm makes the lateral distribution easier, not harder.

That being said, The IBC has criteria to determine if you can assume a rigid diaphragm. It's based on the diaphragm deflection compared to the story drift.

 

[dcStrucEng]

Thanks, StructuralEIT.

Is the "trib width rather than stiffness" distribution of loads for flexible vs. rigid specified in the codes somewhere? I didn't realize this distinction.

Also, regarding the code criteria for diaphragm deflection, it's in section 12.3.1.3 of ASCE 7-05. However, isn't deflection a function of material properties and don't I need to initially assume stiffness vs. flexible in order to calculate whether the maximum diaphragm deflection is greater than 2x the average drift?

 

[steellion]

Assume flexible, which means simple geometric distribution. Since wind load is going to control your design, it makes sense that the load is going to be distributed according to tributary area anyway.

Also, you probably need an expansion joint to split that 500' span in half. 500' is a long way, and you have a plan aspect ratio of more than 3:1. It should be less than 2:1.

 

[Lion06]

I can't say I know if the trib width vs stiffness is in a code, but it's a mechanics issue. Think of a flexible diaphragm as distributing loads similar to a beam. It doesn't rotate and move as a rigid body, therefore it doesn't care what part of the building has the greates stiffness.

It's the difference between a flexible beam on rigid supports and a rigid beam on flexible supports.

 

[frv]

The OP mentioned that there ate 3 frames in the short direction, meaning aspect ratio for the diaphragm is less than 2.

You don't need the EJ for the diaphragm, but it would still be a good idea to include one to accommodate thermal stresses in the long direction

 

[dcStrucEng]

Thanks to everyone so far for your responses. I understand the flexible vs. rigid diaphragm concept much better.

My only remaining issue is how to distribute the torsional moment that is created in Cases 2 & 4 of ASCE 7-05 (figure 6-9). It seems that this moment would need to be resisted by the roof structure and then distributed to the lateral braces. If that's the case, is this analogous to a beam with an applied moment at the midpoint? If so, then the roof member closest to the center of the structure are going to feel large moments in their minor axis as compared to those members towards the perimeter. Is this a fair statement?

 

[DaveAtkins]

For lateral force in the long direction, you will need to assume the diaphragm is rigid, since you only have a braced frame on one of the long sides.

To answer your question on torsion, the Code does not want you to literally apply a moment at a discrete point on the roof. The moment is acting on the entire diaphragm, to account for the fact that wind loads will vary on different parts of the building, causing uneven diaphragm loading.

DaveAtkins

 

[msquared48]

I agree with Dave here that in the long direction the analysis will probably be rigid, but the transverse direction flexible. Do verify that with the code equations too though.

Mike McCann
MMC Engineering
Motto: KISS
Motivation: Don't ask

 

[bigmig]

Dave and Mike,

So what happens when your lateral force is at an angle to your building and is not in line with either the flexible side, or the rigid side? The initial analysis would assume flexible in one direction, rigid in the other.

The flexible analysis would assume distribution per tributary width and wall length (assuming walls instead of frame, since I can picture this better). The rigid would distribute per diaphragm center of rigidity v.s. mass center, the 5% accidential eccentricity, and wall stiffness. The comparison of shear values in any given wall, based on whether flexible or rigid was used could be on either side of the line (conservative or non conservative). You would end up with an overdesign in parts, and an underdesign in others.

Would you run both ways with both methods (flexible in the x and y directions, then rigid in the x and y directions) and take the worst values for each wall?

Thanks in advance.

 

[DaveAtkins]

bigmig,

Good question, and I look forward to Mike's response.

My response? I typically design buildings for each direction separately, and don't concern myself with lateral loads at an angle.

I know, I know, that's not the greatest answer...

DaveAtkins

 

[Lion06]

Dave-
Are you allowed to just neglect some load combinations like that? What about all the torsional wind cases or accidental eccentricities for seismic?

 

[DaveAtkins]

When I design in a seismic zone, I DO account for the accidental eccentricity.

For wind load, unless two perpendicular braced frames or moment frames or shear walls meet at a corner, I think wind in an orthogonal direction will control.

DaveAtkins