Equivalent Truss Method for Wood Diaphragms

[D.E.N.]

Has anyone on here used (or heard of) the "Equivalent Truss Method" for diaphragm design? I believe the idea was originally proposed (or popularized) by J.M Scarry in New Zealand specifically for designing irregular shaped semi-rigid concrete diaphragms. I've attached one of his papers for reference. Essentially, the Truss Method is similar to strut and tie theory with some simplifications. It is really helpful for determining force concentrations at reentrant corners and openings in irregular shaped diaphragms, where the traditional "girder/beam analogy" for diaphragm design does not apply. It is an alternative to pure FEM diaphragm design, which IMO spits out hard to process stress contours at best.

I successfully used this "truss method" to design an irregular shaped concrete diaphragm on a 5-over-2 podium structure and locate chord steel at internal stress concentrations. On the same building I am now trying to design the even more irregular shaped wood diaphragms which all have to be modeled as semi-rigid, since there are a lot of cantilevered diaphragm areas (very few exterior shear walls). I found another paper building on the "original truss method" for concrete by Daniel Moroder (also from New Zealand) that outlines a "truss method" for wood diaphragms. Attached here for reference as well. Conceptually, the procedure in the paper makes sense to me, but what I am getting hung up on is the that some of the units for the "truss elements" don't exactly work out (specifically the cross sectional area of the diagonal element and the equivalent E & G values). They even address this in the paper, but I don't think they provide enough explanation of why that is ok or how to fix it.

I have not seen this method referenced or mentioned outside of the few resources I found from New Zealand and it does not seem to have much "support" from the engineering community or maybe just not enough exposure outside of NZ. To get to the point, I am a structural engineer in the US trying to adapt the truss method for use with my irregular semi-rigid wood diaphragms and need all the experts on here to weigh in on whether they think this is a good idea or not. Let me know if you think it makes sense conceptually and if so, what are your thoughts on the weird units for A, E, and G on page 164 of the wood paper?

I have built a model in RISA 3D (a 2D model though) that has a 2'x2' bay spacing for all of the truss elements. I have modeled all of the floor trusses, joists, and top plates in there respective locations to represent the chords, collectors, and drag struts for the diaphragm. The remainder of the truss elements are comprised of the floor sheathing transverse to the floor trusses and the diagonal floor sheathing elements as described in the paper. I am hoping to run the model and identify areas where the transverse truss elements need to be replaced with something more substantial like blocking and simpson straps. I have the shearwalls all modelled in as spring supports to more "accurately" represent the global stiffness of the building for force distribution purposes. I am mostly hung up on what values to use for the transverse and diagonal truss elements (cross sectional area and equivalent modulus of elasticity is all I really need I think).

Project info:
- 5-over-2 podium building
- stick framed wood over concrete
- 3/4" advantech floor sheathing for diaphragms
- wood floor trusses @ 24" oc for most of the floor framing, 2x10 joists for the corridor framing
- SDC = B, wind loads control all directions
- building loosely represents an "L" shape and is about 268'x213'

Screenshots:
- Truss elements in RISA 3D (little springs represent shearwall "supports")

Resources:
- Concrete Truss Method: [URL unfurl="true"]https://res.cloudinary.com/engineering-com/image/upload/v1663704562/tips/Floor_diaphragms_and_a_truss_method_for_their_analysis_txjp0w.pdf[/url]

- Wood Truss Method: [URL unfurl="true"]https://res.cloudinary.com/engineering-com/image/upload/v1663704577/tips/Moroder_Daniel_Final_PhD_Thesis_gz8ect.pdf[/url]

 

[dold]

Do you not have access to Risa Floor? Are all of these nodes connected with members or are those all plate elements? If members, why not use plate elements with the properties of the plywood sheathing. Risa floor allows you to simply define a semi-rigid diaphragm and Risa3d will automatically mesh the diaphragm for you. You can also draw walls which will exhibit the "correct" behavior and stiffness. Furthermore, you can model the entire building.

Your method seems entirely too complex. For your chord forces you should be able to find those pretty easily by just finding the forces in the walls and backing out a total load on that portion of the diaphragm. Ditto for collectors.

Or is this more of a 'theoretical study'?

 

[phamENG]

That method makes sense if A) you don't have a computer (and you're doing a much smaller building) or B) you have a computer but can only perform a stiffness matrix analysis with no plate elements.

It could also be a worthwhile method for validating a design using RISAFloor, though I'd drastically reduce the number of nodes/members in the validation model.

 

[D.E.N.]

dold - I do have RISA Floor, but I have a hard time translating the plate stress results into forces in collectors, drags, etc. The truss method seems to give me the axial forces for those elements directly. The model I currently have (the one in the screenshot) consists of members only, no plates. I welcome any advice on how to best use the semi-rigid diaphragm plate results that RISA provides to determine force demands in collectors and such.

I wouldn't say this is a 'theoretical study', I am trying to use this to do a real diaphragm design. I am able to make this model using plate elements instead, but I chose the truss method since it made more sense to me conceptually. The truss method takes into consideration the stiffness of the chords, collectors, and drag struts, in addition to the equivalent stiffness of the sheathing including nail slip so I thought it would be more 'realistic' in that sense.

Doing a semi-rigid diaphragm in RISA with plate elements assumes that the diaphragm is an isotropic material, which makes more sense when you are doing a concrete diaphragm. But in reality a wood diaphragm is an assembly that should consider nail slip and stiffness of the framing members too IMO. For example, the 'gen_Plywood' material in RISA is set as isotropic with E=1800 ksi and G=38 ksi. Does that include a 'nail slip allowance'? Honestly curious on this.

phamENG - There are definitely A LOT of nodes and members in my truss model. I set the bay spacing at 2' to represent the spacing of the trusses and help make the shape of the truss match the actual shape of the building more closely (+/- 1' essentially).


If you guys think that doing a plate model in RISA makes more sense, do you have any tips on interpreting the plate results? I am assuming that the plate stress contours are what you would use to determine force in collectors and drags at reentrant corners?

Also, any thoughts on the weird units for Aef and Eef from the truss method?

Thanks

 

[XR250]

Does a building of this size require an expansion joint? If so, do you have that modelled?

 

[D.E.N.]

XR250 - I do not think that it requires an expansion joint. Do you have a specific reference in mind that I should check out for this?