Rigid Diaphragm - Wall Stiffness - Multistory Application

[Nulukkizdin]

All,

I'm putting together a spreadsheet right now to analyze a multi-story wood building that takes advantage of the "open front structure" provisions of the 2015 SDPWS. We meet all requirements to allow us to idealize our diaphragm as rigid, so we're headed that direction. Basically I'm inputting my diaphragm geometry and wall geometry, and using the spreadsheet to distribute my applied load to the various walls based on stiffness. As of now, I'm treating my stiffness term as 4(h/L)^3+3(h/L) and getting results that match up almost exactly with outputs from RAM SS and RAM Elements. At some point I'll update to include more accurate SW deflection components based on NDS, but that will be for later.

My question at the moment is how best to deal with the rigidity effects that come as a result of multiple stories of shear walls. Idealizing the walls as continuous along their height (the way they'd be treated in an FEM layout) gives them continuity of deflection along their height that changes their rigidity in the rigid diaphragm example. As such, whereas Wall #1 sees 5k in a single story rigid diaphragm analysis (both in spreadsheet and FEM), it will not attract 10k in a two-story FEM model with the same load applied at both stories. The spreadsheet approach treats these as discreet floors and thus simply will double the load.

I assume there to be some sort of modifier of rigidity as multiple levels are encountered in your building. Does anyone have any insight into the best way to quantify these multi-story effects of shearwalls as they pertain to rigid diaphragm force distribution?

Thanks!

 

[KootK]

It sounds as though your algorithm is not properly accounting for flexural effects such as chord and hold down elongation. Adopting the SDPWS four term equation might rectify that.

 

[phamENG]

To my knowledge, the prevailing practice is to not consider the shear walls as full height of the building. Start at the top floor and distribute your roof diaphragm forces to the supporting shear walls. Then, apply the reactions from the bottom of those walls directly to the wall below along with the shears from this level. Because the shear wall deflection equation for wood is non-linear, as KootK posted, the stiffness of the walls will vary based on these applied loads from above in combinations with the loads of the current floor.

When I say the walls aren't considered full height, I only mean for distribution through the shear wall. You may have continuous hold downs, etc, and those will obviously need to be analyzed for the full height and elongation values of the continuous rods at each level would further vary the stiffness based with level as you're suggesting.

 

[DCBII]

I recently ran into this issue on a highly irregular multistory structure and had the same questions. I finally made the following assumptions (for better or worse) that greatly simplified the problem:

1. Once a lateral force enters a lateral force resisting system (LFRS) it stays there all the way down to the bottom of the LFRS. It doesn't migrate back out of the LFRS and into another diaphragm at another level. This seemed reasonable because:

a. Generally (though not always) the longer the load path, the more flexible it is. Straight down is the shortest load path, and therefore likely (though not always) the stiffest for a load already in the LFRS.​

b. If loads can migrate out of a LFRS the rigid diaphragm analysis for each floor must consider the stiffness of the other diaphragms and their LFRS's. You'd have to model the entire thing together, or iterate until equilibrium is satisfied everywhere. Very few people were modeling everything together or iterating before FEA software became commonplace, but they were designing these types of buildings all the time.​

2. The height of the the LFRS used to calculate its stiffness should be the total height up to the applied story force, not the inter-story height. My rationale for this was:

a. Because of assumption #1, the the lower diaphragms do not provide restraint to the LFRS. If they did, load would be migrating out of the LFRS.​

b. A LFRS is really only as stiff as the other LFRS's it's tied to.​

c. My PCA handbook (7th edition) uses this approach on one of its multistory examples.​

d. Even if this assumption is wrong, load redistribution can occur if the LFRS's are ductile. Providing a load path that is continuous and analytically consistent is the most important thing. Admittedly, load redistribution may be a stretch for R <= 3 systems, but hopefully there's some redundancy as well to cover this.​

e. Because shear wall deflection is a function of (h/L)[sup]3[/sup], using the inter-story height greatly increases and overestimates the stiffness of the shear wall. Imagine a 2 story building that's symmetric except for a soft 1st story on one side. Would the 2nd story split its diaphragm shear evenly between the two sides? If so, the load would have to exit the LFRS at the 1st story, and then travel across the 1st story diaphragm to the adjacent LFRS's. I would think this uneven load distribution would occur directly at the 2nd story, instead of first working its way down through the 2nd story LFRS to redistribute via the 1st story diaphragm (see 1a and 2a).​