Combining Steel Moment Frame & CMU Shear Walls 2

[SteveGregory]

I have a one story Seismic Design Category D building with a steel beam/metal deck roof. I assume this is a flexible diaphram. The building is almost rectangular, but it has a couple of jogs in one corner.

For loads perpendicular to the long dimension wall, there are CMU shear/bearing walls on each end and one near the middle of the building. I will load these shear walls with the tributary widths for the wind and seismic loads.

For the loads perpendicular to the short dimension walls, there is a long CMU shear wall on one side. The other side is adjacent to an existing building that I don't want to make a structural attachment. So, we have a steel moment frame about 15' away from the existing bldg. The short dimension of the building is about 48' wide.

1. How should I go about distributing the wind and seismic loads between the moment frame and the shear walls?

2. Should 1/2 of weight of the CMU partition walls (4" to 8") contribute to the seismic load at the roof level?

 

[Lion06]

1.
If your diaphragm is flexible, then distribute the lateral forces by trib area. If it is a rigid diaphragm then distribute lateral forces by stiffness. You should be doing the same thing in the long direction. Don't just use trib area if it is a rigid diaphragm.

2.
Yes

 

[msquared48]

As a corollary to #2 above, only if these walls are attached to the roof diaphragm, which they usually are.

Regarding #1, due to the 15' cantiltver of the roof diaphragm, that implies that the diaphragm forces perpendicular to the short face direction need to be analyzed as a rigid diaphragm to make it work. Otherwise you have a pinned connection over the mnoment frame and that will not work. I would look at the reactions to a uniformly loaded cantilevered beam - AISC beam diagram #24 - for starters, and play with the results from there.

Mike McCann
McCann Engineering

 

[SteveGregory]

Everyone thanks for your input. Mike using your suggestion gives me 50% more load on the moment frame than the long shear wall. Intuitively, it seems to me that the shear wall would take more of the load since it is more rigid.

The other alternative would be to take all of the shear on the 3 exterior walls of the addition and leave out the moment connections. The open side is against the existing building. However, the diaphram is metal roof deck and should be considered flexible.

 

[msquared48]

The open sided scenario is possible, but will result in much more lateral deflection. Use the frame to limit that.

You could run the solution as I described with the frame, then, considering the deflections, determine the relative rigidities of the frame and CMU walls, and re-analyze using a rigid diaphragm analysis. This should lower the force to the frame. The allowable deflection or story drift will control the size of the frame anyway, not bending stress.

Mike McCann
McCann Engineering

 

[SteveGregory]

Mike,
I revised my simple beam analysis and the frame load is about 2.5 times the shear wall load. Oops!

What is the simplest way to evaluate and compare the rigidity of the 2 different systems?

 

[Lion06]

build a model of the moment frame in RISA or RAM Advanse (or just do it by hand) and put a 1 kip load at the top and calc the drift. Do the same thing for the shearwall. Then just compare the drifts and hat ratio will equal your ratio for rigidities.

 

[msquared48]

The simplest way is 1/deflection of each component, and adjusting the member sizes of the frame until they work per code requirements. This is an iterative process.

Had too do this for a multi-story hospital expansion in Anchorage years ago with steel moment frames and concrete shear walls. Method worked well. No earthquakes there yet! (post 1965)

Mike McCann
McCann Engineering

 

[SteveGregory]

We use STAAD Pro to model our structures. How do you recommend modeling a shear wall? Should I apply a factor like 0.5 to the modulus of elasticity of CMU to account for cracking?

 

[Lion06]

You can do it for a shearwall by hand. It is a simple cantilever beam, just use the beam charts in AISC. Also,
maybe you could use the 0.5 factor for getting the max load going to the moment frame, but I would not use any factor to find the load going to the shearwall.
This will be a little conservative, but will give you a good envelope. After all, those EI coefficients are just approximations and it is very difficult to predict how it will actually behave. Also, I don't know how different masonry is from concrete, but 0.5 sounds reasonable.

 

[SteveGregory]

The 0.5 factor was a wild guess to reduce the stiffness of the masonry (Em) to account for a cracked section. It had nothing to do with the load distribution.

I have 2 walls (offset by 8'-10") parallel to the moment frame. One is 31' long and one is 75'-8" long. The walls are 17'-4" tall from the footing to the top.

 

[Lion06]

but it does have something to do with load distributiion if you have a rigid diaphragm. EI are in the deflection equation and go into figuring out your relative rigidities.

 

[DaveAtkins]

I doubt the rigidity of the shear wall will be reduced 50% under lateral load--this is not like a concrete beam cracking.

If you have Amrhein's masonry textbook, there are tables for the rigidity of CMU shear walls, based on height and length.

But when all is said and done, I would just put all the lateral load into the shear wall. I doubt any moment frame will even be close to the stiffness of these long shear walls. Yes, I know that a steel deck is supposed to be considered a flexible diaphragm. But engineering judgment seems to indicate it will behave like a rigid diaphragm in this situation.

DaveAtkins

 

[miecz]

Since you don't know of the roof diaphragm is "rigid". I think you need to analyze it both ways, and design each element for the worst case. For the rigid analysis, I would assume the wall cracks in flexure, but not in shear. To account for cracking, it depends on how STAAD handles the shear stiffness, E[sub]v[/sub]. If E[sub]v[/sub] is independent of E[sub]m[/sub], then reduce E[sub]m [/sub]by 50%, but not E[sub]v[/sub]. If E[sub]v[/sub] depends on E[sub]m[/sub], reduce E[sub]m[/sub] in STAAD by [Δ][sub]u[/sub]/[Δ][sub]c[/sub], where [Δ][sub]u[/sub]=h[³]/12E[sub]m[/sub]I+1.2h/E[sub]v[/sub]A, and [Δ][sub]c[/sub]=h[³]/12(0.5*E[sub]m[/sub])I+1.2h/E[sub]v[/sub]A.

 

[Grizzman]

I believe steel deck with a span to depth ratio of <= 2:1 are considered rigid.

 

[apetr26542]

If you can make a 3D model as suggested in Risa Or advance, you could change the properties of the wall rather easily, E'm that is. I think you will find when a moment frame shares load with a shear wall, don't expect much contibution from the moment frame.

I would also expect such a lopside center of rigidity that the perpendicular shear walls would be needed to handle the torsion on the building (if modeling as a rigid diaphragm)