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# Direct Analisys Method (DM): Stiffnes in hybrid structures (concrete + steel)

## Direct Analisys Method (DM): Stiffnes in hybrid structures (concrete + steel)

(OP)
Dear Sirs,

I Have a question about Stability Design with Direct Analisys Method (DM).

In steel structures, when I use the Direct Analisys Method (from AISC) I need apply a adjustment to stiffness = 0.8.

Do I need to do any adaptation in DM when designing hybrid structures (for example: concrete core + steel moment frame in the same building)?

What is the stiffness of concrete elements in a hybrid structure? What is the adjustment to stiffness in concrete elements from hybrid structure? And what about composite column (concrete + steel)?

### RE: Direct Analisys Method (DM): Stiffnes in hybrid structures (concrete + steel)

Thought that the Direct Analysis Method (DM) is used for steel structure stability analysis. Concrete component normally provide lateral resistance and stability for hybrid structure. The strength and stability of concrete component should be investigated per ACI 318

### RE: Direct Analisys Method (DM): Stiffnes in hybrid structures (concrete + steel)

Excellent question. Per Chapter C of the AISC code, the answer is yes.... Section C2.3 of the 2010 specification makes no distinction between steel and other members. It merely says that the analysis of the structure used to determine required strength shall use reduced stiffnesses.

If you reduce only the steel members and not the concrete, then the concrete will absorb more of the applied forces, resulting in an non-conservative design for the steel members.

To me, however, this is a more complex issue. Since concrete cracks, the behavior of concrete is fairly non-linear. AISC would suggest a 20% reduction in the concrete stiffness. But, I would argue that you may want to use a larger value based on the expected level of concrete cracking at ultimate loads. Something like 0.35 for beams, and 0.7 for columns. I'd have to pull up ACI to see what the recommendations for shear walls are. But, I would think something like 0.7 as well.

### RE: Direct Analisys Method (DM): Stiffnes in hybrid structures (concrete + steel)

(OP)
In Section 3.2 of AISC Design Guide 28, “The DM can be used to design all types of building frames, including moment frames, braced frames, combined systems of braced and moment frames, and other hybrid and combined systems such as shear walls and moment frames.”

As in Section 5.2-9 of the Design Guide 28, “Enveloping Frame Stiffness in Mixed Frame Systems (I call hybrid structures). When steel moment or braced framing is combined with concrete or masonry shear walls or composite columns or walls used in lateral frame resistance, consideration should be given to cracking of the concrete and masonry elements under different degrees of lateral loading. It is wise to assume various degrees of stiffness for these elements to check the sensitivity of the story shear participation of the steel elements and to design them for the worst effects from various degrees of stiffness. Guidance for stiffness of concrete elements can be found in the ACI 318-08 building code (ACI, 2008).”

As in Table 6.6.3.1.1(a) of ACI 318-14:

Do I need to use the ACI Moments of inertia and apply a adjustment to stiffness? what adjustment to stiffness?

### RE: Direct Analisys Method (DM): Stiffnes in hybrid structures (concrete + steel)

There is specific section in ACI318 talking about the concrete structure second order analysis and stability. Does the section in ACI 318 more suitable for the stability design than that in the AISC360

### RE: Direct Analisys Method (DM): Stiffnes in hybrid structures (concrete + steel)

(OP)
Jiang, my question is about Mixed Frame Systems, combined systems (steel + concrete) in the same building. Not a building only in concrete. And, I want use the Direct Analisys Method (DM).

### RE: Direct Analisys Method (DM): Stiffnes in hybrid structures (concrete + steel)

I don't know that you're going to see an authoritative reference on this. But, what you posted about the AISC design guide is pretty close. Especially when combined with that ACI table.... It seems to me like you did a pretty good job answering your own question!

Ultimately, this will be a question of engineering judgement. Estimating the proper concrete stiffness to use in an elastic analysis is always a matter of judgment. Even more so, when you throw in Direct Analysis Method.

Some might even suggest increasing the reduction from that ACI table by an additional 20%. Or, analyzing it both ways. One for the concrete design (where the concrete elements are not reduced by as much) and one for the steel design (where the concrete members are reduced more).

### RE: Direct Analisys Method (DM): Stiffnes in hybrid structures (concrete + steel)

(OP)
Thanks JoshPlum, but can I use the moment of inertia fron table 6.6.3.1.1.(a) with adjustment to stiffness = 0.8 (columns = 0.8x0.7xIg and for beams = 0.8x0.35xIg)?

Or only the the moment of inertia fron table 6.6.3.1.1.(a)(columns = 0.7xIg and for beams = 0.35xIg)?

Or with another coefficient?

### RE: Direct Analisys Method (DM): Stiffnes in hybrid structures (concrete + steel)

Well, let's think about what the goal is for each of the various stiffness adjustments.

For the 0.8 Direct Analysis Method reduction, the point is to approximate the "inelastic buckling" of the steel structure by artificially increasing the P-Delta effect. This doesn't reflect a real change to the stiffness of the structure.

The ACI stiffness factors are there to represent the cracking of the structure. Since concrete is not an elastic material, this is also an approximation. However, it does represent a real reduction in the stiffness of the structure.

Now, if the combined structure uses a the DA Method to reduce steel stiffness and the ACI method to reduce concrete, then the steel members are slightly less stiff than they would be (if this were an elastic analysis).... which means the concrete members will be designed for slightly higher forces. Conservative for concrete, but un-conservative for the steel.

Now, if the combined structure uses the DA method to reduce steel stiffness and the ACI method + an extra 20% stiffness reduction, then the concrete is softer than it would be (if this were a pure elastic analysis per ACI). Therefore, the concrete members will have slightly lower forces. Conservative for the Steel, but un-conservative for the concrete.

In reality I think either method is probably okay. The estimate of concrete stiffness is very rough and probably not that accurate. But, if you want to be guaranteed to always be conservative then I would run it both ways.

### RE: Direct Analisys Method (DM): Stiffnes in hybrid structures (concrete + steel)

My understanding is that the lateral stiffness of concrete components is much larger than that of the steel members. Assuming that the lateral load is taken by the concrete components which is transferred by the diaphragm. Then check the concrete components stability per the ACI318 code.

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