center of rigidity outside the building footprint

[SLTA]

An architect just submitted a floorplan with shearwall layouts such that the center of rigidity is outside the footprint of the building. Clearly that won't work, but what would actually happen in a lateral event? I am hoping someone can provide me with a straightforward explanation I could pass on to the architect.

 

[NKT]

Can you post a sketch of the shearwall layout?

 

[dougantholz]

If the building is regular, I would say you have made an error in your COR calcs. If the building is odd shaped, like a C shape or L shape, its not unusual to have the COR and COM be outside the building footprint. I would say in general you have a torsional issue...to say the least.

 

[msquared48]

Soundlike the old problem of where do you load the channel so that there is no torsion - outside the limits of the channel...

Mike McCann
MMC Engineering

 

[RareBugTX]

It is possible to have that situation. While I have not seen your plan ( would be nice to see a sketch ) I think that such an eccentricity will cause significant moment due to torsion either by seismic or wind forces which makes sense by comparison to a perfectly, or almost perfectly symmetrical common building floor layouts where your eccentricities are in the order of a few feet.

 

[haynewp]

The way the center of rigidity is normally calculated for a shear wall building is not equal to the shear center. I think you have mixed the two terms.

 

[sandman21]

He is making an analogy, not telling the person how to compute the COR. The COR being outside does not change how you analysis the building.

 

[haynewp]

I was addressing the original poster. Can you explain "The COR being outside does not change how you analysis the building"?

 

[SLTA]

I've attached a sketch of the building. I'm definitely asking about the center of rigidity, not the shear center.

My response to the architect was to change the shear wall locations such that the COR was back inside the building, but I'd still be interested in exactly what reactionary problems this would create, in actual response to a lateral event.

 

[haynewp]

I think something may be wrong. I can tell you are using Enercalc. I tried putting in a C shape into Enercalc and it gives the COR at edge of the building at the center of the single wall that is parallel with the shear, which is where it should be. (We are not calculating the shear center so the COR is not outside the building for a C shape.)

But when I twist the 2 perpendicular walls of the C shape to 45 degrees, the COR moves outside of the building like in your diagram. I do not follow how they are getting this.

 

[haynewp]

I guess for now I say that I disagree. I don't see how the COR can be outside the building when using the traditional method of finding the location of the COR. If you look in the PCI handbook, there is an example of a C shaped shearwall building and the COR is along the single wall that is parallel to the force, as I said above. Maybe the program is displaying the shear center instead of the center of rigidity when you skew the walls, I don't know. I am confused right now as to what is going on.

The polar moment of inertia is usually calculated after finding the COR when doing it by hand, and this takes into account any twisting affect on the shear walls.

 

[RareBugTX]

After reviewing the plan I do not see how the COR is outside the footprint either. I thought the computation of both COG and COR were done by hand and not by those fancy computer programs. I personally do not trust them at all. Their results have to resemble my hand calculations to say the least.

My 2 cents.

 

[dougantholz]

The center of rigidity CANNOT be north of the northern-most shear wall. There is an error somewhere. Go back and review your analysis again.

 

[haynewp]

It looks like it is not calculating the same COR as we are thinking of. More like the shear center I believe...You might just want to check the whole thing by hand.

The help file says the following:

Distance to Center of Rigidity

This is the calculated distance from the datum (0,0) point to the center of translational rigidity of the system of walls.

The center of rigidity is calculated by:

· Forming a stiffness matrix for each wall. This matrix models each wall's stiffness about its length and thickness axis.
· Solve each matrix for wall rigidities
· Solve simultaneous equations for X and Y locations of center of rigidity.

 

[csd72]

I cannot see how the COR can be correct where you have show.

For example, if there was only 1 shear wall at the top of the page (say the horizontal 60%E wall) then the centre of rigidity would be at the centerline of the wall.

Not if you add additional walls below this then this must by definition shift the center of rigidity down the page.

 

[slickdeals]

Center of rigidity is the point at which the load is applied to produce no rotation.

 

[ssweetland]

It is possible to get the center of rigidity outside of the building envelope. To simplify the situation, ignore the walls that have 1% rigidities and simply turn the building 45 degrees, notice how the building starts to look like a L shape. The COR for an L shape would be at the origin of the shape, in this case the L is truncated at the origin, hence the COR is outside of the envelope.

This building presents two different lateral situations, as is, it looks like a 3 sided box, turn it 45 degrees and it is closer to an L shape, but not quite because of the vector rigidities. Again, I probably would like to see different rigidities on the walls so that it looks less like a L shape in the one direct, but if given no chose, it still could be analyzed. I would recommend doing two sets of lateral checks though, one as is and one with the structure rotated 45 degrees. Then run the analysis as you would normally, apply direct shear to the COR, apply moment to the COR, with the summation of the two giving the total shear. If this was purely an L shape, it would be unstable, no moment arm to resist, but given the vector rigidity of the 45 degree walls, there would be small moment arms to produce moment resistance. In all likelyhood, you will have a torsional irregularity, which may or may not be acceptable, depending on code issues.

Again, I'm not a huge fan of this, not even a fan of three sided box layouts given there lack of redundancy, so this really comes down to engineering judgement.

 

[SLTA]

thanks, everyone. we resolved this by creating a shearwall at the middle 1% E location, which then brought the COR back inside the building. we've decided to treat the outside COR as a symptom of an unbalanced building instead of as the problem itself.

ssweetland, I agree about the unbalanced issues. that's my daily struggle with the architects - either windows everywhere or a house still standing after a hurricane (and more importantly, meeting code)!