Effective Stiffness Modifiers > 1.0 1

[Trenno]

I was reading a paper recently and it highlighted something I'd not given much thought to previously.

The paper discusses the idea that effective stiffness modifiers, i.e. the scaling of the gross moment of inertia of concrete elements within FEA, can potentially be greater than 1.0 when the reinforcement present within the section is known and the concrete is working at stresses less than rupture.

What are others thoughts on this?

This would obviously influence modal, acceleration and deflection performance of structures that lie essentially within the elastic realm (e.g. not seismically driven structures).

 

[rowingengineer]

It is common for columns and walls to be modelled this way in fea programs, so I am comfortable with the idea.

http://www.nceng.com.au/

"Programming today is a race between software engineers striving to build bigger and better idiot-proof programs, and the Universe trying to produce bigger and better idiots. So far, the Universe is winning."

 

[RPMG]

It is not common. First order and second order elastic analyses are common, for which inertia must be less than Ig. Designing with inertia greater than one would have to be designed per an inelastic second order analysis, which per the premise, is possible because it behaves elastically. Other than stating it isn't common, I have no opinion and didn't read the paper.

 

[davab]

Never heard of this before. I don't think is the industry practice. Stiffness modifiers specified in ACI 318 reduces it. Are you saying that the paper / research states that reinforcements actually do not reduce the stiffness of beam, column, slab, wall, etc.?

 

[Settingsun]

How much higher than 1.0 did it get? More than the uncertainty in E?

Did the analysis account for shrinkage restraint and other effects lowering the cracking stress?

 

[JoshPlumSE]

Theoretically, this is certainly possible. Especially with service loading on PT concrete elements. For service level deflection limits, I'm more than happy having a little extra safety factor by restricting the stiffness modifier to a max of 1.0. For service level vibration that could be a different issue. Though I don't think it comes up much.

Now, if we're talking about ultimate level loading and failure, which is the load levels at which most of our analysis is done, then I don't think it matters at all.

 

[r13]

I think "common" was meant the general practice of reducing moment of inertia to account for cracked section. I practiced it, but never embraced it, always ended up envelope the cases that were modeled in both ways (full and reduced inertia). It will be interesting to read the paper though. Was it published? By whom?

 

[Trenno]

As implied in the original post, I'm talking SLS not ULS here. A transformed uncracked section.

When we start talking ULS, it's more about trying to accurately model the post-cracking behaviour. I could see it affecting link beam shear/moment distributions, amongst other things. Obviously this starts going down the non-linear path, which crude effective stiffness multipliers may not cut it.

 

[r13]

If I am not misunderstanding, the transformed area concept is a very old practice in designing reinforced concrete flexural members. The steel area is replaced with an equivalent concrete rectangular block (a line has same thickness and centroid as the rebar). The resulting moment of inertia will be larger than the original computed using concrete dimensions (b & h) only.

 

[IDS]

As noted by others, the effect of the reinforcement in an uncracked section would normally be much less than creep and shrinkage effects, and I think it is standard practice to ignore it. I don't do multi-story building work, so I can't comment on whether the ACI provisions for stiffness modification are over-conservative in that application, but in the areas where I do work the ACI values for stiffness just after cracking are often very unconservative (i.e. much too stiff).

Also it's not just seismic design where non-linear behaviour becomes important. Reinforced concrete is highly non-linear after cracking, which occurs well below service loads in most structures. My practice is to ignore the stiffening effect of reinforcement in uncracked sections, and if deflections are critical, do a non-linear analysis using the Eurocode 2 method for effective stiffness (or equivalent), and allow for the effects of creep and shrinkage and differential temperature.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[rowingengineer]

"The consequences of overestimating or underestimating the actual stiffness's of structural members depend on the type of structural system and the response parameter of interest" in your case, underestimating the column stiffness in a flat slab can cause problems with punching shear, however over estimating you column stiffness in a moment frame will lead to larger than expected deflections and cracking.

In the paper referenced in the original post by trenno is for shear wall and columns normally elements that are under high compression in the building with very high two ratios 4percent, compared to beam type elements with Les than 1. I personally like 0.7 as my starting stiffness but I can see in a building core that is heavily loaded that you may go over 1 to ensure your period is selected conservative. I believe upper and lower bonds must be considered in fea if the part under consideration would be affect buy the assumption.

http://www.nceng.com.au/

"Programming today is a race between software engineers striving to build bigger and better idiot-proof programs, and the Universe trying to produce bigger and better idiots. So far, the Universe is winning."

 

[rowingengineer]

As to my common comment, there are a number of fea programs that do this stiffness analysis and after working it out end up with Ig above one for similar situations as described in the paper. You need to remember that we are referring to a paper and a specific limited situation in the paper.

http://www.nceng.com.au/

"Programming today is a race between software engineers striving to build bigger and better idiot-proof programs, and the Universe trying to produce bigger and better idiots. So far, the Universe is winning."