Brick Cladding Deflection Limits 3

[KarlT]

I have a project in Winnipeg, Canada with an exterior load bearing wood wall ranging in height from 20 ft to 30 ft. In addition, there is a partial height exterior brick veneer from the foundation up an elevation of 7'-0" above the foundation.

To ensure the brick doesn't get unacceptable tensile stresses we need to limit the deflections of the structural backing to L/720. Now if the brick ran full height, I would check the mid span deflection and compare to L/720. However, in this case how would I check that the wall deflections are acceptable? I would think that L/720 at mid height of the wall is too restrictive, since the brick only runs between 1/4 and 1/3 of the way up the wall?

 

[DaveAtkins]

I have always felt L/720, or L/600, or even L/480 deflection is too stringent for studs (wood or steel) behind brick veneer. I use L/360 -- testing done at Clemson University in 1981 confirmed that L/360 is adequate stiffness to prevent cracking in the brick veneer. Having said that, the stud should be limited to the same deflection, whether or not the brick runs full height. The brick has to assume the same curvature as the stud behind it.

DaveAtkins

 

[KarlT]

thanks DaveAtkins

Unfortunately by our code I have to meet L/720 deflection limits. I agree that the brick veneer would follow the same curvature as the studs behind them, but the L/720 deflection limits are based on the brick veneer extending the full height of the stud wall, with the maximum deflection at the wall mid-height.

In this case the brick veneer would only tend to lean outwards and the actual deflection of the top of the veneer would be less than that at mid-span. What I'm wondering about is if I calculate the stud/brick deflection at the top of the veneer, what "L" would I compare that deflection to for L/720?

 

[JAE]

KarlT -
When we check deflections of "cantilevers" we double the cantilever length and then take the end-of-cantilever deflection as the D, limiting it to L/360 or L/600, or whatever, where L = 2 x cantilever length.

The reasoning behind this is that if you look at the curvature of a cantilever, and picture a mirrored image of it where the mirror is at the fixed end, you get a shape similar to a simple span member where the imagined supports are at the cantilever ends and the midspan deflection is at the fixed end.

For your wall then, I would take L = 14 feet and use your L/720. By the way, in the US, the predominant requirement is L/600. While DaveAtkins may be correct on the research, many codes still require a brick deflection limit (especially vertical deflection for supporting beams) and I would tend to stay with the more strict requirement.

 

[ishvaaag]

These things opens the interesting debate of how a masonry panel (of variegate kinds) break under deflection and drift. All I have seen are partial portraits of the thing, that one by one should be satisfactory enough, but make a general poor and incomplete portrait of the behaviour.

 

[KarlT]

JAE...that's what I also assume for cantilevers and I have thought to use the same idea in this case. However I was thinking over lunch...

What if one were to make up an excel spreadsheet, & plot the deflection of the wall using the standard deflection equations. Then graph it to scale and draw on the brick wythe. Then draw a straight diagonal line from the top of the brick wall to the bottom and scale off the deflection of the curved brick wall at the mid height of the brick wall relative to the diagonal line. Then ensure this deflection is less than L/720, where L = brick wall height. I am assuming that the bottom of the brick will be pinned and rotate about the foundation. Does this sound reasonable?

To me it seems that the maximum stress in the brick wall would be halfway up the brick height, based on the way the brick wythe follows the curvature of the wall behind it. The point of the L/720 deflection limit is to prevent cracking of the brick at the point of maximum stress.

The reason I am going through all this hassle is that I don't want to end up with a wall that is incredibly thick and expensive to build due to the L/720 restriction on the entire wall height.

 

[AlohaBob]

I had the same question the other day so I again looked at several brick references and code prescriptions. They pretty much don't spell out deflection out of plane. They leave it to the engineer to calculate the deflection of the brick withe and compare it to stress - strain relations and geometric assumptions for crack widths.

When the brick is continuously - uniformlt tied to the backing, the deflection geometries must conform. So you can check and predict a crack width at the bottom of the wall. It becomes a matter of what will you live with.

AISI uses a similar approach in their recomendations for backing of masonry.

 

[JAE]

KarlT -
I guess your method would offer the out-of-plane deflection of the brick wall from its original planar condition. That does make sense.

But I think you also need to remember that the "theoretical" wall that backs up your brick is assumed pinned at the base. This allows the wall to rotate at that point. So the brick would also follow the wall and rotate at the base, which would be your worst case in terms of rotation. The first mortar joint at the base would then be subjected to a high rotation.

In real-world action, the base would perhaps get a lot of stress, perhaps opening up the bottom mortar joint and the first few lower mortar joints would also be bending a bit as the brick is not really a true pin. As the wall proceeds upward, the bending would begin reducing for a while, and then perhaps increas a bit to follow what you stated above, that there is a true plane that the wall originally followed, but now it is bent a bit. I perceive the least bending in the brick as at the top.

The bottom few courses perhaps can bend a bit anyway as it has the most axial load, probably has thru-wall flashing or grout behind it at the bottom, etc.

 

[paullaup]

I would think of it a different way. Imagine that the brick runs the full length of the wall. (lets take your 30ft wall). When your 30ft wall is deflected to L/720, your maximum allowable deflection is at the midspan, and is 0.5". This 0.5" is at 15ft. Now, while the stud is deflected to the maximum, figure out what the 'out of plane' DISTANCE is at 7'-0" from the end. For the 7'-0" wall height of 7'-0", limit the deflection at the top wall to this distance. This allows the brick to deflect, and curve identically to an equivalent brick wall which runs the full height.

 

[ERV]

Reading all the posts, no one has mentioned horizontal deflection of the wall. It has been my experience that horizontal deflection can be more of a problem than vertical deflection. For instance, if your wall is 30 ft tall and 60 ft wide, with L/720, horizontal deflection would be 1".

Just something to consider.

 

[JAE]

ERV - the whole post is about horizontal deflection.

 

[ERV]

JAE,

Maybe I'm missing something here. I am under the assumption that deflection of the studs (30 ft) is vertical deflection. I'm referring to the top plate deflecting in or out, over the length of the wall (longtitudinal deflection?), stiffness being controlled by the diaphragm (unrestrained). Should overall deflection of the wall include a combination of the deflecion of the studs and top of wall?

If the bottom of the wall is pinned or fixed (attached to foundation) and the top of wall unrestrained (bending controlled by diaphragm), the brick is pinned at base and unrestrained at top, what is the total deflection at the midspan of the wall and top of brick (7' height)? If the wall was 60' long (for example) the maximum deflection at 7' high and center point of the wall would be 11/16" with criteria L/720. At L/360 this would be 1 3/8". That is out of plumb in only 7'.

If I'm wrong please correct. I did not calculate exact, only rough estimate.

 

[JAE]

ERV - re-read KarlT's original post - he has a 20 ft. to 30 ft. high wall and has brick running up to 7 feet (vs. the full height of the wall).

His original question dealt with the deflection limits for the brick based on the back-up wall. These are all HORIZONTAL deflections (in-out movement of the wall and thus perpendicular to the wall).

There is nothing in this thread yet that I read as speaking of vertical deflections. But you do have to consider both vertical and horizontal deflections in your calcs. Vertical - in that the underlying supporting structure must not bend downward (not in KarlT's post) - or horizontal deflection of the backup wall.

 

[ERV]

JAE,

My error sorry.

What I meant was lateral displacement of the wall due to deflection of the vertical and horizontal wall elements caused by out of plane forces (in or out). All considered L/720 is not that stringent, which is the point I was trying to make. In my haste and not proof reading my post, I miss stated what I was getting at. You are absolutely correct.

 

[connect2]

A very complicated interaction. The assumption that the FULL wind load is transfered thru the masonry, then thru the masonry tie and ultimately to the structural back up, in this case wood studs, is jump in modelling thats for sure. EI ?, go figure. Model a unit length of wall?, model a stud spacing?, pinned,pinned? and yes what about diaphragm deflection along the length of the wall, and vertically up its height as a result? and what wind load do we apply to the wall system, and what wind load do we apply to the frame to model this system? we'll be back on this one, but as a foot note most of the failures we have seen in masonry walls, structural issues of gravity and lateral loading aside, relate to poor detailing of control joints, expansion joints and the miss matching of materials within the system, ie thermal loads.

 

[haynewp]

JAE, I have been trying to derive your method of doubling the cantilever to get the allowable deflection.

I have a cantilever of 10.5'. I want to keep about L/600 well, that is the equivalent of L/600 if it was a simple span condition.

I see what you are saying by trying to make the cantilever curve limited to look the same as an equivalent simple span curve, but I am having trouble arriving at it by using the slope formulas.

The formula for simple span slope is:

slope=wss*(L^3)/24EI

For cantilvers:

slope=wc*(L^3)/6EI

where 'wss'=simple span uniform load
'wc'=cantilver span uniform load
E=3605ksi
I=1000 in^4

Just by equating the slope formulas, the same slope for a cantilever would occur at 'wss'x0.25 of a simple span. That's with all other variable being equal, and thinking that the slope itself would be the cause of brick failure.

However my actual cantilever deflection would come out to be L/250? Which is basically saying that the brick won't crack until a cantilever's deflection is equal to L/250.
Does that seem right?

Where for the simple span, for the same length, could take 4 times the load before it cracks, yet it's deflection would only be L/600 at cracking?

 

[JAE]

I agree they are not a perfect match - In fact, I believe that the deflection slope for a cantilever is 1/2 that of the full beam (don't forget that your L's are different...for your two formulae - if L is for the full simple span, then instead of L in your cantilever formula, it should be L/2. This gets you a slope of wL^3/48EI for the cantilever slope (where L = 2 x cantilever length) and wL^3/24EI for the simple span.

But while the slopes are off by 1/2, the full deflection is off by a factor of about 1.64 (the simple span deflection being larger).

It's just that the general curvature is about the same. But you're right, you could probably go 1/1.64 = 0.61 times the simple span length instead of 0.5 x L for the cantilever comparison.

 

[haynewp]

I think I am trying to look at the slope only as the determining factor instead of the overall curvature. Is that wrong?

1)I got the load that would cause a corresponding deflection=L/600 in a simple span beam. Then I took this load and found the max slope which would form in the simple span beam.

2)I took that slope (and the same L) and solved for the load using the cantilever slope formula to find the CANTILEVER load which would bring about that cracking slope for the same length of beam.

I am saying that the slope is what is causing the cracking, even if you use the same length of beams in each case, once that slope is realized the brick cracks.

 

[haynewp]

Well, slope and of course moment that causes the crack.

And that factor of 1/4 is in both the slope and moment formulas, wl^2/2 and wl^2/8.

It's just the deflection that will be different in each case when the same moment is produced. In the cantilever the deflection=L/250, and in the simple span the deflection=L/600.

What do you think?

 

[JAE]

I think that the curvature is what is sort of looked at in the L/600 - and they have set upon the L/600 number based on knowledge, experience, etc, based on a simple span condition. For a cantilever, I guess just trying to find a good "mimic" to the simple span is the way to go - I would guess that there is nothing absolute in the 600 number - more an order of magnitude issue so you have some leeway in relating the cantilever behavior to the simple span behavior.