Diaphragm deflection's impact on unreinforced masonry 4

[WARose]

The situation: A portion of a existing floor acting as a diaphragm is supported (vertically only) by 8' tall cantilever, unreinforced masonry columns. The lateral force resisting system is masonry shear walls.

The Problem/Question: My calculations indicate the diaphragm deflection (as well as other displacements) would create more displacement and moment in the columns than is allowed. (This is for wind loading by the way. Seismic is nothing where this is.) Ergo, my question is: what does that mean for the columns? That they will be destroyed and not be able to transfer vertical load during (and after) such a event? I've never been too clear about this on unreinforced masonry.

Notes: As stated, this is for wind loading only. Also, please don't make any alteration suggestions. For right now, I just want to get those questions answered.

Thanks.

 

[Ron]

Good application for carbon fiber wrap.

 

[bones206]

This is actually happening to my parent's chimney in slow motion. Large differential settlement causing roof and upper story wood floor to push the chimney over. Looks eerily similar to KootK's sketch...

Intuitively though, it does seem hard to imagine your typical wind load having such a dramatic effect on a masonry column.

 

[KootK]

This is actually happening to my parent's chimney in slow motion. Large differential settlement causing roof and upper story wood floor to push the chimney over. Looks eerily similar to KootK's sketch...

The thing that really concerns me about the mechanism shown in my sketch is whether or not you preserve shear capacity at the crack when it forms. If the thing stays put then, sure, it probably just rocks back into place when the load is gone. If it ratchets over, however, that would get ugly. How is your parents' chimney doing in that respect? I guess they're dealing with monotonic load which is a bit different.

 

[bones206]

I think theoretically if the resultant is still within the kern, it should be stable, right? But I don't think that is a code-compliant argument if the allowable stresses are exceeded. More of a beyond design-basis mechanism that we would be trying to avoid.

In the case of my parents' chimney, pretty sure the wood structure is providing all the stability at this point. The chimney is just leaning on it. Slightly terrifying.

 

[hardbutmild]

Are you certain that the wall and the diaphragm will deform together?

I think that KootK's mechanism is conservative.
Let's assume that the wall can rotate at the top. Wouldn't that mean that the load would enter the wall at the right corner? See the bottom left part of my picture. This would make the mechanism more stable. Also, if the deformation shape is as KootK proposed, then looking at top right of my drawing (i named it b)) you can see that it all just shifts laterally. I don't honestly see that changing much (or am I wrong?), because the wall can still span between the perpendicular walls like an arch. If the deformed shape is a straight line, nothing's changed in that direction really.
The problems start to arise when diaphragm starts locally deforming (like in my picture a)) because then, like in my bottom right picture that arch becomes more shallow close to the top of the wall.

Maybe I'm wrong, but like some of you said before, masonry cracks almost instantly. If cracking meant failure, there would be 0 existing URM buildings.

 

[r13]

A simple stability check on case (a) above can tell the fate of the wall.

 

[WARose]

Are you certain that the wall and the diaphragm will deform together?

It's not a wall: it's a column. And yes, I am certain that there will be deformations due to the diaphragm's deformation.

Maybe I'm wrong, but like some of you said before, masonry cracks almost instantly. If cracking meant failure, there would be 0 existing URM buildings.

I don't think it's a question of cracking....it's a question of: if the allowable tensile stress is exceeded.....what happens? Destroyed?

This would make the mechanism more stable. Also, if the deformation shape is as KootK proposed, then looking at top right of my drawing (i named it b)) you can see that it all just shifts laterally. I don't honestly see that changing much (or am I wrong?), because the wall can still span between the perpendicular walls like an arch. If the deformed shape is a straight line, nothing's changed in that direction really.

Yes, I can see a argument for inside-the-kern (as several have made). Just not sure of it.

 

[r13]

This is how I see the simply supported masonry column.

 

[hardbutmild]

It's not a wall: it's a column.

Sorry, I somehow missed this. In that case no two way action is possible.

I don't think it's a question of cracking....it's a question of: if the allowable tensile stress is exceeded.....what happens? Destroyed?

Isn't cracking a consequence of stress reaching tensile strength? I wouldn't say that reaching tensile stress at one point leads to failure, I'd check it like a footing, assume tension can not be resisted and the resultant of an axial force and bending moment defines the position of the compression stress resultant. Then you can get a compression area and use a friction model to check for shear.

 

[KootK]

Questions for WArose:

1) How tall are the piers?

2) What's your max diaphragm drift?

3) Is the drift perpendicular to the 12" dim or the 16" dim?

4) Is this the second floor of a building with a roof above? Upper story height?

5) Perimeter walls delivering wind to the diaphragm are URM as well?

 

[WARose]

1) How tall are the piers?

Like I said in the OP: 8'.

2) What's your max diaphragm drift?

I hate to commit to a number....because every method I am trying gives a different one. (As you will recall, this is a odd diaphragm.) But the peak I am getting so far is 0.75".

3) Is the drift perpendicular to the 12" dim or the 16" dim?

There are components of both. But the real issue appears (for the piers/columns) when most of the displacement is perpendicular to the 12" dim. (I.e. it produces (thankfully) the moment on the strong axis of the pier.) Most is in that direction.

4) Is this the second floor of a building with a roof above? Upper story height?

The bottom of the piers/columns is the ground. The top of the piers support a roof. The roof consists of rafters (and nailers, tin and so forth) nailed to a ridge beam. The ridge beam is at about 7' above the top of the piers.

5) Perimeter walls delivering wind to the diaphragm are URM as well?

Yep.

 

[KootK]

Like I said in the OP: 8'.

You'll forgive me if I don't hang on your every word.

Yep [those are URM bearing walls KootK, thanks for asking].

In real life, I'm sure that the walls are just flag poling up from their foundations and delivering very little load to the diaphragm. Have fun proving that of course.

 

[WARose]

In real life, I'm sure that the walls are just flag poling up from their foundations and delivering very little load to the diaphragm. Have fun proving that of course.

In some cases I have no doubt of that.

It's actually a pretty sturdy building by my numbers (except for the subject of this thread).

 

[KootK]

Even if the walls didn't flag pole, I bet you'd still get that kind of action from the wall segments shown in yellow below just by virtue of their two way spanning capability near the corners.

 

[KootK]

As we know from the other thread, these deck board diaphragms suck because they act like a bunch of crappy vierendeel frames. Buuuut, if you toss in some tin sheathing as tension only diaphragm capacity, you're back to something a lot more rigid.

 

[structSU10]

late to the party here, but just stumbled on guidance from the diaphragm design manual version 3, limiting masonry deflection to H^2*f/0.01*Ew*tw where H is height, f is allowable compressive stress, E modulus, and t is depth of masonry. It points to two references where this may come from:

Nelson, A.H., "Shear Diaphragms of Light Gage Steel" Journal of the Structural Division, ASCE, Nov. 1960

Yu, Wei-Wen, Cold-Formed Steel Design, John Wiley & Sons, New York, 1985

 

[KootK]

Thanks for bringing this to our attention structSU10. I swear, rarely does a month pass where I don't discover yet another way in which I've been doing my job incorrectly all this time.

 

[WARose]

Thanks structSU10. Embarrassingly enough, I have this reference. (I.e. the 3rd ed. of Cold-Formed Steel Design; it's on p. 540.)

Only thing about it is: the number it spits out is way less than the allowable seismic drift (as per the IBC).....so I don't know what to think of that.

In any case, thanks again.


[red]EDIT:[/red] By the way, the units to use in the formula described above is:

h=[ft] (unsupported height of wall)
t=[in] (thickness of wall)
E=[psi] modulus of Elasticity of wall material
f=[psi] allowable compressive stress of wall matierial

total allowable deflection of diaphragm= h²f/0.01Et

 

[r13]

You have those choices 1) stiffen the building frame to reduce the drift, 2) reinforce or increase wall thickness to allow for more deflection, and 3) do nothing - the wall maybe damaged, but the building stays as it was. Also, what analysis method was used to get the drift, LRFD/ASD, what is the allowable stress f then?