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Out-of-plane loading on historic masonry

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milkshakelake

milkshakelake

Structural
Jul 15, 2013
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I have an existing brick wall. I'm adding 3 stories above it, seismically isolated. I put a deflection clip to restrain the out-of-plane bending. A regulator said that my new 3 story addition will bring the old masonry wall along for the ride and put forces on it.

I did a calculation for the bending moment in the brick, and it's overstressed by 80%. Is there something I'm missing here? And is there a better way to do this or think about it?

This is a summary of calculation. I didn't post the whole long thing since I'm not paying y'all enough, but I can if needed.
1. Max seismic displacement is 0.32" at the story where I restrain the 10' tall wall.
2. I calculated the stiffness of the brick wall. This involves f'[sub]m[/sub]=600psi and E=420ksi lower bound values from from ASCE 41-17 (thanks Celt83). Considering 10' cantilever and K=3EI/L^3, K=1260lb/in for a 1' section of wall.
3. Using Hooke's law of F=Kx where K=1260lb/in and x=0.32", F=403lb applied at top of wall.
4. This part is iffy, but...since seismic displacement is at strength level, I use 0.7F=282lb to get it to ASD level.
5. Applying the force at the top of the wall: M=10'x282lb x 12=33,869lb-in.
6. Design check using tension stress f[sub]t[/sub]=M/S=33,869/288 - axial compressive load of masonry=109 psi. This is 80% higher than the allowable lower bound stress of 60psi per ASCE 41-17.
7. *@$&#@^! Life sucks.

This is a sketch of the situation:
Screenshot_2023-10-08_170521_p9c7di.png


These are the details I use to restrain the top of the brick wall:
Screenshot_2023-10-08_170725_pbetu2.png

Screenshot_2023-10-08_170835_d1xk8l.png


Real life:
2023-07-28_12-13-29_5_laifhs.jpg
 
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It could potentially collapse and hurt people, I guess. I'm not sure how far I can get by saying that some cracking is okay, unless there's a way to do that.

Edit: Also, it could potentially crack on both sides, since seismic forces can reverse direction. That means that it has almost zero capacity at that point.
 
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Yeah...cracking in reinforced masonry is fine, but in URM a crack sends flexural tension capacity (and, therefore, flexural capacity) down to about zero. Shear capacity through the cracked bed joint is also questionable.

I think you're penalizing yourself too much with the assumption of zero displacement at the second floor level. I'd work out the maximum seismic displacement at that floor and then determine the angle of the entire wall.

OR, actually use seismic isolation and don't lock the addition into that wall.

 
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The problem with non-zero displacement at the lower floor is that it should be added, not subtracted. The seismic response and periods for the existing and new structure are different, and you can have something akin to pounding.

I'm not sure how I can not lock the addition. If I don't, the wall becomes fully cantilevered. Per empirical design in ACI 530, you can't have a cantilevered height of more than 4 x thickness, which places a limit of 4'. The wall is 10'. And also, the wind load might not work since the moment will be about 2 times as much, if I remember my formulas correctly.

Though you did give me an idea. Maybe I can use 20' instead of 10' for calculating the cantilever stiffness of the wall, which will make it absolutely work. The ratio will be 20% instead of 180% since cantilever stiffness is a cubed function. It's a bit tricky because the 2nd floor does have a diaphragm, so it's technically not 20'. But then again, the stiffness contribution of the front/rear walls will be almost zero, because brick isn't good as a shear wall when it's interrupted by windows. I'll have to ponder this.
 
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I think you would want to tie the brick to every diaphragm if possible. I’d rather have 10’ wall sections oscillating in an earthquake than 20’ sections. Maybe you could reinforce the brick with FRCM or some other fiber reinforcing system. Or maybe post tensioning could be added to keep the wall in compression top to bottom.
 
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@bones206 I don't think owner wants to spend money to reinforce that brick. Trying to see if I can make it work somehow with calculations.

@SWComposites It's a local practice. An altered building has far less taxes than a new building, so people will do anything to keep part of the building. It leads to some weird situations, like a high rise with an old 2 story at the bottom. Then you have the extreme, which is buildings that kept a single 10' long wall so it qualifies as a major alteration instead of new building, though the building department has cracked down on that lately.

@XR250 Agreed. I've argued that point, but the building department here is maybe too strict at times.

I think I'll just add vertical expansion joints at the out-of-plane restraint and call it a day. I'll see where that gets me.
 
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Will there be stud walls on the interior of the brick? You could tie the brick to the stud backup wall to help take the out of plane loads.
 
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