Transfer of Moment to Columns in Two-Way Slabs

[rjmorton42]

I have designed a number of two-way slabs using the Direct Design Method, but I am now designing for the first time a two-way slab using a Finite Elements programs (RAM Concept). The building has a parking garage in basement, the two-way slab at the first floor, then 3 stories of light wood frame construction above. At the garage level I have a number of concrete shear walls as the lateral system, so I feel that the two-way slab is sufficiently braced against drifting.

The DD method requires that interior columns be designed for an unbalanced moment (ACI 318-02 Eq. 13-4) in combination with their axial load. My question is, are there any ACI requirements a for designing the interior columns supporting two-way slabs for a minimum unbalanced live-load moment (or any other moments) if the slab was designed by an FE method and it is braced against lateral drift, eliminating the need to consider second-order effects?

Thanks!

 

[JAE]

Yes, the ACI code specifies that alternate bay loading is required for structural analysis of continuous systems. The unbalanced moment on the columns are due to both lateral wind/seismic forces (drift) and due to alternate live load patterns which induce moments in the supporting columns and walls.

For both of these - second order effects must also be considererd.

 

[rjmorton42]

JAE, thank you for the input. To follow up, I understand that both alternate-bay live loading and the forces induced by lateral (wind & seismic) loads must be considered in the design of continuous systems. In this case, they are considered in the design of the two-way slab.

Clearly, and for obvious reasons, ACI 318-02 Section 10.3.7 requires that the axial load in compression elements be considered in only combination with the maximum moments that accompany it. What am unclear about is how to go about determining what these maximum moments are.

Consider these two assumptions:

First, say the supporting elements of the slab (the columns and bearing walls) are modeled and detailed as pin connections. By modeling and detailing them as such, they should not be required to attract any moments, nor would they secondarily attract any moments.

Second, say the slab is braced against lateral movement (which it will be by the employment of several long, unperforated concrete shear walls as the lateral system). Given this second assumption, there should not be any second-order gravity or story-drift effects induced into the columns.

Provided both of these assumptions to be the correct, how do I go about determining what the maximum moments required for consideration by ACI 318-02 10.3.7 are?

Thanks!

 

[JedClampett]

A couple of choices:
You could apply the minimum design moment from 10.12.3.2.
You could apply the moment from 13.6.9.2.
I'd pick the larger, which is probably the one from Chapter 13.

 

[JAE]

With concrete properly detailed, you can't really just say that a column is pinned, model it as such, and then cast it with integral rebar which ties it into the slab. It WILL attract moment and you should assume it does. Same goes for a wall, although a walls out of plane bending stiffness may be less.

Where there is any stiffness at all, forces will follow it (Hooke's Law). Your modeling should always attempt to mimic reality and the realty is is that there will be slab to column tie-in re: moments.

Your shearwalls will probably inhibit all sway moments to very small numbers and so your assumption that wind/seismic moments in your columns are small, but alternate bay live loading will create those moments in the columns and I wouldn't ignore them.

 

[rjmorton42]

JAE -

Thanks for the additional input. I certainly agree with what you say about Hooke's law. I didn't know it if was accepted practice to compare my situation of the two-way slab to the accepted practice for the design of the footing of a steel column modeled with a pinned base...for in that situation accepted practice is to design the footing with a concentric column reaction, even though the standard four-bolt connection will transfer any second-order column moments from the column to the footing.

The way I see my situation with the two-way slab, I think of two procedures to follow to determine the moment from the unbalanced live load:

First, I could re-model the slab with fixed column heads and apply a "skip" live loading pattern to the slab.

Alternately, as JedClampett suggests, I could simply apply the unbalanced live load equation for the Direct Design method in ACI 318-02 Section 13.6.9.2. However, my interpretation of ACI is that this equation is ONLY intended for use with the DD method.

I think it would be inappropriate to apply the minimum design moment from Section 10.12.3.2 as this is intended only for the development of the column moment magnifier if the column is slender.

Does anyone have any thoughts on which may be more appropriate, or perhaps know of another accepted procedure?

Thanks!

 

[JAE]

rimorton42,

The "normal" ACI method to use here would be the Equivalent Frame method (since you state that you aren't using the Direct Design method). ACI suggests that you fix the far ends of the columns and then perform a first order analysis using the appropriate slab properties and column properties provided in chapters 10 and 13.

This gives you the gravity based moments in your columns that you can then use in design.

I have to admit, I've done hundreds of continuous concrete beam/joist designs assuming the supporting wall/girder/column is pinned and then added some more steel in those "zero moment" areas where the moments would occur despite my model. This works with single beam runs, but can get a little risky when you are working with columns. Even with my simplified...i.e pinned...beam runs, I still was then confronted with the need to get some sort of moment into the columns and that always led me back to modeling the frame correctly in the first place.

 

[ron9876]

Two questions--ACI-02 13.7.6.2 states that when using the equivalent frame method,the live load does not excced 3/4 of dead load and live load is variable it is acceptable to assume full live load on all spans instead of pattern loading (such as a condo). Does anyone see a problem with this approach? Also is there a spreadsheet or program that will do punching shear calcs for the variety of conditions that you encounter in these types of projects.

 

[ron9876]

Sorry my last post was intended to be a new post and not a response. As stated above you have to either model the actual condition or you can use either the equivalent frame method or the direct design method if they apply to your condition. When using the FEM approach it is particularly important to correctly model your condition.

Using either the min moments or the direct design method to determine moments is mixing apples and oranges.