Modeling Diaphragm Strength of Roof Sheating

[ToadJones]

I am trying to model the diaphragm stiffness of B-deck roof sheathing on 30" bar joists with insulation and rubber membrane.

I am using STAADPRo.

Any tips?

I can model the bar joists and all the roof members accurately, I am really just after modeling the b-deck itself.

I am not even sure I should be counting on the roof for a diaphragm but this is an existing structure and there is nothing but some bracing in the end walls.

 

[abusementpark]

I've been curious how corrugated metal deck should be idealized in an FE model. Good question.

 

[ToadJones]

abuse-
Any quick and dirty way I can incorporate the roof stiffness as I analyze the columns not using FEM?

The problem I have is determining the lateral support offered by the roof system at the tops of the columns.

 

[JAE]

Besides any built-in methods within your software, I've used two different modeling methods:

1. Equivalent X-brace.

What you do is create a series of multiple X-braces throughout the diaphragm plane. These braces are simply modeled as generic members that only take axial load and are weightless.

The amount of X braces depend on your model size but similar to finite elements, the more the better.

Once you get the braces in place the key here is to set the cross sectional area of all the braces to mimic the behavior/stiffness of the metal deck diaphragm.

First you need to do some hand calculations to find out, for some given lateral diaphragm load, what the deck deflection will be. Vulcraft or other deck manufacturers (or in the US - the SDI manual) will provide stiffness parameters for various decks and fastenings. With the G' value you can calculate the deflection at the midspan of the diaphragm.

Now with that delta deflection, go to your model, apply the same lateral diaphragm force, and vary the area of the X-braces to achieve a similar deflection. Once set, you can now continue modeling the framing and size the members. Once you design the diaphragm, you need to back-check that the fastenings and deck thickness you need for strength is consistent with the X-bracing stiffness - you may need to iterate a bit.

You also need to be very aware of the discreet nature of the individual X-braces and how they might affect the framing members. An end of a brace may indicate to automated features within your software that there is a brace point, etc. and affect design routines. Just set up the braces to only act as braces and not members taking other out-of-plane forces or affecting member sizing routines.

2. Equivalent plate elements

Similar to above except instead of using discreet X-braces you use finite elements that only take in-plane forces. Vary the element thicknesses to get a matching deflection to that determined by hand calculations.

 

[ToadJones]

JAE-
Thanks....I actually already had the model made using plate elements in place of the B-deck.
I will have to do a little digging to find the stiffness information for the b-deck in my Vulcraft books.

 

[Gumpmaster]

One BIG warning on using plate elements. The plate elements will increase the flange area of the beams/joists and will act compositely. This will greatly reduce the loads in the beams, resulting in beams that don't quite fare so hot.

I knew of someone once who did this and the beams were drastically undersized and needed retrofitting after construction.

I think in SAP you can assign a zero axial stiffness but still have a shear stiffness. That would be the way to go, but I would still run some hand checks.

 

[ToadJones]

In STAAD you can make the plate elements "plane stress" elements, they will not take any transverse shear or bending...only in plane stiffness.

 

[DST148]

@ToadJones: typically steel deck design manual and catalog of products provide permissible diaphragm shears and stiffness values based on the roof deck gage, span, sidelap screws, and weld patterns. May be you can get more info from SDI Diaphragm Design Manual.
Ref United Steel Deck, 1999 - B Deck with 5/8" welds to steel and #10 sidelap screws - the stiffness varies from 7 kips/inch to 95 kips/inch for various combinations of gage of deck, span of deck, and weld patterns.

 

[DST148]

@ToadJones: I googled, and this is what I have found -
Ref: Chapter 5 Structural Steel Design by James R. Harris, et. el., which is based on 2000 NEHRP Recommendations. There is an example of a steel framed building with a 1 1/2", Type B, 22 gage metal deck. The analytical model uses plate elements (membrane) with 1 / 10 the stiffness of plane plate of 22 gage steel.

 

[ToadJones]

@DST148:

Thanks for the info.
"...The analytical model uses plate elements (membrane) with 1 / 10 the stiffness of plane plate of 22 gage steel...."

That's much less stiff than I would have anticipated.

So basically I can model 22 gage steel plates and reduce E to match

 

[JAE]

Gumpmaster,

I hear what you are saying, and if ToadJones models the beams and plates in a 3 dimensional sense, then yes, you can get a composite like behavior - when there are nodal connections of the plates along the span of the beam.

But if he is modeling the beams as two-node sticks, and the finite elements are on the same plane, there is no aspect of the stiffness matrix that includes horizontal shear between them - they are essentially dimensionless vertically and on the same plane. Bending in both would not affect the moment coming into the beam as the plates would have zero stiffness in bending.

The only effect would be axial loads the beams would be altered as the plates would be able to take some of any axial loading relative to their stiffnesses and areas.

 

[DST148]

@ToadJones: I googled with a search string "Modeling steel roof diaphragms" . The subject heading is P:\bssc\Guide\....\Chapter05-rev.wpd. There is also an article by modern steel construction.
I have not used STAAD for a long time. I would modify stiffness properties like f11, f22, etc. of membrane elements (assuming the software has the capabilities) rather than the value of E.

 

[ToadJones]

Thanks guys...this is good stuff.

 

[UcfSE]

Effective modulus for diaphragm design

 

[SethGuthrie]

It's a fairly common question for RAM structural System and it's pretty much the same in STAAD.pro, here is a wiki with some information that we put together:

http://communities.bentley.com/Prod...Design__Wiki/ram-ss-semirigid-diaphragms.aspx

 

[Lutfi]

I always modeled roof deck in STAAD using steel plate element and provided the gauge as the thickness of the element. The model will be OK. I used that for years. Use the element numbering properly as STAAD is picky as how you connect elements to nodes.

Regards,
Lutfi

 

[Gumpmaster]

JAE, The problems I've seen have been in long span roofs where some of the beams/joists are supported on roof trusses. The plate acted as additional steel area for the truss top chord, resulting in the top chord being sized way too small, resulting in some not very pleasant consequences.

If you do use plates, I'd advise checking stresses in the plates for the dead load only case to make sure that they're not sucking up any stress.

 

[ToadJones]

Gump-
Most FEM programs have parameters you can assign to the plate to be sure that there is no composite/shell action