Distribution of shear forces in four story building 1

[calculor]

I am a recent graduate that has been given the task to design a four story timber frame building. The building consists of two wings that are at an angle of 140 deg. It has an elevator shaft that extends from the underground parking garage to the fourth floor.It also has a fire separation wall that also extends from the first floor to the fourth floor. The fire wall is approximately 5 feet from the edge of the elevator shaft. the length of each wing is approximately 219 feet. Wind load always governs in this part of the country (eastern Canada), wind load is 30psf.How do you locate the centre of resistance (CR) for this shape building? Should I project the lengths of each wing vertically and consider the building as a rectangular building or should I consider each wing to be an individual building and locate the CR for each wing? If the shaft and fire wall do not provide enough shear resistance I will have to use some of the timber walls. I assume I would have to calculate the stiffness of each element (concrete, masonary wall, and wooden wall), k=EI=EtL^3/12 and distribute the load according to the stiffness of each element.Any help would certainly be appreciated. P.S. I know, I know, this is way too long.

 

[ishvaaag]

Well, seems an inordinarily long building for my standards of structures without joints. In any case truly and for such lengths and significant wind load I from the start would add additional shear resistant elements, since for your somewhat L-shaped building differential torsion will become a reality and you will be subjecting your shearwall and core to significant forces, in more than causing cantilever-like diaphragm action at floor levels.

Respect how to attribute the loads it depends from the framing you adopt. If somewhat irregular I would likely go for a 3D complete FEM model with some simplified assumptions of the connections, which would discover what elements work harder and give forces for design.

 

[JAE]

For wood construction - and your situation - a few comments:

1. Over 400 feet in building length is a good candidate for a building expansion joint. Near the elevator, or near the fire wall would be a good place to start. This will separate your building into two distinct "buildings" which can then be analyzed separately.

2. With wood construction, you most likely do not have a rigid diaphragm but a flexible diaphragm, which would not necessitate a determination of a center of rigidity. Essentially, with a flexible floor diaphragm, you can distribute your lateral wind forces by tributary area/width between shearwalls.

3. Four story wood construction is usually prohibited in the US but I know that Canada tends to use wood more often and may have different code limitations.

 

[Taro]

"Four story wood construction is usually prohibited in the US"

In my neck of the woods (Seattle, USA) FIVE-story wood buildings are the norm. I'm not saying it's a great idea, but it is done regularly.

UBC 2308 limits wood stud wall systems to 3 stories unless an analysis is performed to account for shrinkage effects. I don't think this is commonly enforced in my area though.

Another requirement that seems to be mostly ignored around here is UBC Table 7-B, Footnote 18 - "The design stress of studs shall be reduced to 78 percent of allowable F'c with the maximum not greater than 78 percent of the calculated stress with studs having a slenderness ratio le/d of 33". I don't think most of these 5-story buildings would pencil out if this requirement was enforced. Like a lot of fire protection issues, it is commonly overlooked because it is a structural requirement that is hidden in a non-structural section of the code.

 

[JAE]

Taro you are absolutely right....I should have qualified "prohibited" with the analysis that you stated.

 

[calculor]

I agree, with wood construction the diaphragm could be considered relatively flexible. However would this also be true if the subfloor was overlain with 1.5" of concrete. I know for composite deck this would be considered a rigid diaphragm.

 

[ishvaaag]

Calculor, concrete on wood is not a great idea, since it may crack for the overally allowed deflections for wood and then its shear strength be highly compromised. Of course in a final mechanism of resistance interlock and a suitable orthogonal mesh may still deliver "enough" final strength even for such deteriorated situation, but in general I think is not a good idea. It is better to always implement clear load paths, you need not to forfeit any available diaphragm strength, but you need to determine reasonable values for it. Somewhere -maybe some ICBO qualification- I think to have seen estimates for shear strength of panels made of parallel wood members of rectangular section.

 

[JAE]

calculor - are you really using concrete?? or gypsum underlayment such as Gypcrete? Either way, the concrete is probably placed between the stud walls such that there is little continuity and no true way to verify the bond to the wood. ishvaaag is correct that placing concrete on wood isn't the most desireable.

 

[calculor]

JAE and Ishvaaag
In eastern Canada using a concrete overlay on plywood subfloor is extremely common, virtually all multi story timber framed buildings use this type of floor system. I agree I don't see how any composite action could take place. I'm not sure of the logic in using the overlay, however the client has had several buildings designed using the overlay and has no complaints, go figure.

 

[BuddyShowalter]

Another requirement that seems to be mostly ignored around here is UBC Table 7-B, Footnote 18 - "The design stress of studs shall be reduced to 78 percent of allowable F'c with the maximum not greater than 78 percent of the calculated stress with studs having a slenderness ratio le/d of 33".

See

http://www.awc.org/Publications/dca/dca3/index.html

for one and two hour assemblies tested to 100% design load to resolve this issue.