Summing Shear Wall Lines 1

[medeek]

To be honest it seems like everytime I open the AWC SDPWS-2008 I find another tidbit I seemed to have overlooked or plain out missed.

My latest gem is section 4.3.3.4 (Summing Shear Wall Lines)

It reads: The nominal shear capacity for shear walls in a line, utilizing shear walls sheathed with the same materials and construction, shall be permitted to be combined if the induced shear load is distributed so as to provide the same deflection, d_sw, in each shear wall.

Typically when I look at a segmented shearwall with multiple panels/segments with similar construction I assume that all segments have the same unit shear which is the method I took from D. Breyer's book "Design of Wood Structures". Section 4.3.3.4 appears to run contrary to this method. Am I interpreting this incorrectly?


A confused student is a good student.
Nathaniel P. Wilkerson, PE

http://www.medeek.com

 

[Lion06]

The way I read that provision is consistent with your approach and the Breyer text. If you have 3 segments - 9', 7', and 4' for a total of 20' - and you have a total shear force on that line of 6000 pounds, you would design each segment for a unit shear of 300 plf. One takes 2700 lb, one take 2100 lb, and one take 1200 lb for a total of 6000 lb.

You're combining the nominal shear capacitors of 2700, 2100, and 1200 to get your 6000, and you also have a single unit shear.

 

[KootK]

X2. Just like Lion06 explained it.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[Once20036]

I don't have experience with wood, but I read it differently.
If you have a cantilever with a unit load at the top, and a second cantilever with twice the load at the top, they will not deflect the same amount - the first cantilever will deflect more. Deflection is related to the depth^4, so the second wall is 16x stiffer.

Taking this to the shear wall analogy - the 9' shear wall will attract more than its "fair share" of load, because it is a stiffer wall.

 

[medeek]

I analyze my shearwalls just like Lion06 explained it but my fear is that Sec. 4.3.3.4 may actually be describing a method (non-linear) as Once20036 suggests.

A confused student is a good student.
Nathaniel P. Wilkerson, PE

http://www.medeek.com

 

[KootK]

The provision doesn't actually specify the distribution of forces to the wall segments. It only requires that displacement at the tops of the wall segments be uniform. And, in my opinion, the top plates acting as stiff axially loaded drag struts satisfy that requirement.

Whether the distribution of shear to the segments considers shear flexibility (me, Lion, Breyer), bending flexibility (Once 20036), or both seems to be left to the discretion of the designer.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[RWW0002]

If the walls are of similar length and are at the same height I think the equal unit shear would be a reasonable assumption, and one made my many engineers. Where I sometimes find myself distributing based on stiffness (which I think is the intent of the code provision referenced) is for gable walls where the wall segment length and height may vary greatly. I find this approach leads to much more reasonable holdowns for tall walls, as the shorter longer walls (i.e. stiffer walls) draw more of the load. It also helps for walls where the unit shear resistance must be reduced based on aspect ratio.

By the way, shear wall deflection is not a product of wall length^4 as Once suggests - see SDPWS 4.3.2 for deflection estimates. Using the example given by Lion (assuming the same plate height and shear distributed for equal deflection), I get 3.6k resisted at 9' wall, 2.7k @ 7' wall and 1.5k at 4' wall yielding a variation in unit shear of less than 10%. If the walls heights varied, this would not be the case.

 

[RWW0002]

Edit: I have fat fingers. The post above should read "I get 2.8k resisted at 9' wall, 2.1k @ 7' wall and 1.1k at 4' wall yielding a variation in unit shear of less than 10%."

 

[Lion06]

Once - RWW points out the difference between wood shearwalls and other elements. Additionally, walls are often (not always, obviously) not what I would call a Bernoulli beam element because shear deformations play much more of a role. In that case the stiffness is a function of length. The answer is somewhere between the two, which is where the shearwall deflection equation comes in.

RWW - Did you just set your deflections equal and play with the deflection for each until you got a total force of 6000#? Those results seem very reasonable to me for the assumptions made. Two walls are different - one by 8% and one by 4%. The 8% is on the conservative side and the 4% is on the unconservative side. I never take my designs that close that I'll lose sleep over 4%.

 

[woodman88]

So with 2.8k/9'=311plf and 1.1k/4'=275plf I better look more closely at how I am doing shearwalls. I always assume that a shearwall half the length of the longest shearwall would resist only half the plf.

Garth Dreger PE - AZ Phoenix area
As EOR's we should take the responsibility to design our structures to support the components we allow in our design per that industry standards.

 

[RWW0002]

Lion - I have a spreadsheet I created a while back that distributes load based on relative rigidity - similar to how you would distribute to masonry shear piers.

As pointed out, the results are not worth losing sleep about for when the wall height is the same. For the same example with varying plate heights (say 10' at the 9' wall, 12' at the 7' wall and 16' at the 4' wall) the results would be much different (3.3k at the 9' 2.0k @ 7' and 0.7k @4') This results in about a 20% underdesign of the 9' wall and a 70% overdesign of the 4' wall. As you can see it can be very helpful to take advantage of this, as the 4' wall segment shear resistance will be knocked due to aspect ratio, and the holdowns can be reduced significantly.

Also, @Koot, I think you statement about the wall deflection being uniform due to the plates is exactly why we have this provision. The deflection is going to be the same at the end of the day, therefore load is going to be distributed such that the deflections are equal (i.e based on relative rigidity). This is similar to load distribution theories for shear walls of other materials like concrete and masonry.

 

[manstrom]

*Shear* deflection is proportional to length. It is safe to say that an 8' segment and a 12' segment take the same plf loading if they are in a row.

But, a 2' segment in front of a 20' segment will not take the same load since the slender element is more susceptible to bending deflection as opposed to shear deflection.

*Also note that total shear wall deflection includes shear deflection, nail slip and bending deflection. This makes it very difficult to figure out wall deflections and therefore shear distribution. It is actually harder than concrete or masonry shear wall design since there is another element to calculate and depends on more variables. I have found that shear deflection contributes the majority of deflection for walls with a reasonable aspect ratio (code min or better). It's an interesting exercise to compare the calcs.

Also note that gyp is about 3 times less stiff than OSB (based on G from SDPWS). This needs to be taken into account in load distribution calcs. Of course gyp is about 3 times less strong. So a 10' OSB wall will take about 3 times the load as a 10' gyp wall in the same row.

If you do the calcs and make some simplifications, it comes down to basically this - the wall takes what it can take as long as the aspect ratios are code minimum. If you increase the sheathing, it "attracts" more load. Of course, if you get in to the details that gets more complicated.



When I am working on a problem, I never think about beauty but when I have finished, if the solution is not beautiful, I know it is wrong.

-R. Buckminster Fuller

 

[mike20793]

I believe the 2015 SDPWS has an added deflection compatibility requirement between the shear walls.

 

[mike20793]

To elaborate on my post above, here is the 2015 SDPWS section:

4.3.3.4.1 Shear distribution to individual shear walls in a shear wall line shall provide the same calculated deflection in each shear wall.

There's a couple exceptions based on the shear wall aspect ratios.

 

[medeek]

I guess I should have looked at the 2015 for more clarification. The full text is:

4.3.3.4.1 Shear distribution to individual shear
walls in a shear wall line shall provide the same calculated
deflection, d_sw, in each shear wall.
Exceptions:

1. Where nominal shear capacities of all
wood structural panel shear walls with aspect
ratios (h/b_s) greater than 2:1 are multiplied by
2b_s/h for design, shear distribution to individual
full-height wall segments shall be permitted
to be taken as proportional to the shear
capacities of individual full height wall segments
used in design. Where multiplied by
2b_s/h, the nominal shear capacities need not
be reduced by the adjustment in 4.3.4.2.

2. Where nominal shear capacities of all
structural fiberboard shear walls with aspect
ratios (h/b_s) greater than 1:1 are multiplied by
0.1 + 0.9b_s/h for design, shear distribution to
individual full-height wall segments shall be
permitted to be taken as proportional to the
shear capacities of individual full height wall
segments used in design. Where multiplied
by 0.1 + 0.9b_s/h, the nominal shear capacities
need not be reduced by the adjustment in
4.3.4.2.

A confused student is a good student.
Nathaniel P. Wilkerson, PE

http://www.medeek.com

 

[manstrom]

I haven't wrapped my head around the new SDPWS requirements yet.

Is this more strict, or just an elaboration on what we have been doing?

When I am working on a problem, I never think about beauty but when I have finished, if the solution is not beautiful, I know it is wrong.

-R. Buckminster Fuller

 

[medeek]

Here is a portion of Section 4.3.4:

4.3.4.1 The size and shape of shear walls shall be
limited to the aspect ratios in Table 4.3.4.

4.3.4.2 For wood structural panel shear walls with
aspect ratios (h/bs) greater than 2:1, the nominal shear
capacity shall be multiplied by the Aspect Ratio Factor
(WSP) = 1.25 - 0.125h/b_s. For structural fiberboard
shear walls with aspect ratios (h/bs) greater than 1:1,
the nominal shear capacity shall be multiplied by the
Aspect Ratio Factor (fiberboard) = 1.09 - 0.09 h/b_s.

4.3.4.3 Aspect Ratio of Perforated Shear Wall
Segments: The aspect ratio limitations of Table 4.3.4
shall apply to perforated shear wall segments within a
perforated shear wall as illustrated in Figure 4C. Portions
of walls with aspect ratios exceeding 3.5:1 shall
not be considered in the sum of shear wall segments.
In the design of perforated shear walls, the length of
each perforated shear wall segment with an aspect ratio
greater than 2:1 shall be multiplied by 2bs/h for the
purposes of determining Li and ΣL_i. The provisions of
Section 4.3.4.2 and the exceptions to Section 4.3.3.4.1
shall not apply to perforated shear wall segments.

A confused student is a good student.
Nathaniel P. Wilkerson, PE

http://www.medeek.com

 

[medeek]

Okay, 2015 SDPWS has me thoroughly confused.

In table 4.3.4 of the 2012 SDPWS if your shearwall ratio was between 2:1 to 3.5:1 for seismic then you took a reduction of 2b_s/h.

Now it appears that according to section 4.3.4.2 the reduction factor is 1.25 - 0.125h/b_s, and this applies for both seismic and wind.

Then according to the next section 4.3.4.3 perforated shear walls are reduced with the factor 2b_s/h and they are exempt from section 4.3.4.2 and exception 4.3.3.4.1.

Which then begs the question: When would exception 1 of section 4.3.3.4.1 apply?



A confused student is a good student.
Nathaniel P. Wilkerson, PE

http://www.medeek.com

 

[medeek]

I've searched the document (2015 SDPWS) thoroughly and the 2bs/h reduction factor is only used in section 4.3.4.3 (Aspect Ratio of Perforated Shear Wall Segments). I think I am then correct in saying that Exception 1 of 4.3.3.4.1 is pointless and will never apply unless you were to somehow engineer a shearwall using the 2012 and 2015 provisions simultaneously.

A confused student is a good student.
Nathaniel P. Wilkerson, PE

http://www.medeek.com

 

[wannabeSE]

I don't think it is very hard to calculate the capacity of a line of walls based on there rigidity.
1. Assume the hold down elongation is proportional to the load.
2. Calculate the deflection of the longest segment when it is loaded to capacity.
3. Calculate the unit shear in the balance of the walls based on this deflection using NDS eq 4.3-1 (it just takes a little algebraic manipulation to use the formula to find the unit shear based on deflection).