Wind loads on buildings with non-orthogonal walls

[pyseng]

I am struggling to decide on the most appropriate way to apply wind loads to a structure that has a significant skewed portion and am curious as to how others might approach it. I have attached a prototype of a floor layout to demonstrate my situation. The structure isn't large enough to require an expansion joint - although, I presume one option may be to put one in to split up the structures, but that seems like a bit of an expense for the sole purpose of making the analysis easier.

The approach I'm leaning towards:
I am leaning toward this approach. Project the skewed walls onto the N/S and E/W axis to get a total wall length that includes the situations that the wind will "hit" the building twice (in N/S direction). Apply the resulting force at the geometry center of the "bounding box" of the floor. Apply torsional load cases with eccentricities based on the bounding box lengths and widths.

Reasons for indecision
- In an ideal world where I got paid a lot more, I could imagine running some crazy analytics on this situation. Essentially, you would need to come up with a function for pressure vs wall skew angle and then, for each wind direction (1 deg increments?), go around the structure and find forces for each wall and sum them up. I think most would agree that this is overkill? Not to mention, ill-defined (sidewall pressures... torsional load... yuck).

- What are my "principle axes" that I have to apply wind load to (according to ASCE 7). Theoretically, I could do some more analytics to find a principle axis, but that seems excessive.

- Is my suggested approach the only real, practical approach? I struggle sometimes to understand what the "cutoff is". How long does the skewed portion have to be to become the primary orthogonal portion?

 

[sdz]

In an ideal world you might do a wind tunnel test or computational fluid dynamics (CFD) to determine loads. As it is you probably need to use engineering judgement and your wind code to determine reasonable approximations.

If you have wind from the east the U shape could give higher than normal pressures on the windward walls. But the wind load will still act normal to the wall as a reasonable approximation. You should be able to get close enough for design purposes. I would think that at worst you would look at 8 directions but I think you could reduce it to wind from NE, E, S, W, NW.

One question is what happens when you are combining moment frames at non-orthogonal angles? My approach, for shear walls, was to assume a uniform displacement at eaves level, say 10mm. Count only the displacement in the plane of the frame, so frames at zero degrees have 10mm in plane displacement, those at 90 deg have 0 in plane displacement, and those at 45 deg have 10xCos(45)=7.1mm in plane displacement, causing a resisting force F. The resisting force is then resolved back to the direction of the load so walls at 45 deg produce FxCos(45) resistance. Assuming resistance proportional to displacement then the frame at 45 deg has kx10xCos(45)xCos(45) resistance, or 50% capacity. (I hope that makes sense)

However if you are using a structural analysis model the effect of having frames at 45 deg should come out in the analysis if it is correctly modeled.

 

[Tomfh]

If you model the walls in FEM using the actual orientations then apply 8 wind direction load cases that should cover it. Certainly no need for 1 degree increments.

 

[Lomarandil]

I'm generally not a fan of Tekla Structural Designer, but it apparently does wind load generation in 12 or 16 increments of rotation around the structure to envelope the worst cases. From the demo I saw, seemed like it was based on some part of the British standards about prevailing wind directions?

Might be worth looking into if that's in your company's catalog of resources.

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just call me Lo.