Non-Linear FEA for Concrete Slab Design

[hannis]

Hi,

The use of Non-linear FEA for the design of concrete building structures would appear to be more common. My experience is very much in the use of Linear FEA models and in this respect when dealing with reinforced concrete appears a safer approach. I would be grateful for any opinions by others on this subject since my Non-Linear understanding is more limited. But as I understand it the use of Newton family (modified Newton-Raphson etc) methods appear to be limited since modelling the strain softening of concrete after yielding, the stiffness matrix becomes unstable and convergence difficult to obtain resulting in an increase in iterations. But I could be wrong in my understanding!

Regards

Hannis

 

[EdR]

Just for my own understanding......

Why would anyone attempt to use the strain softening properties of concrete in the "design" of a structure unless it was a research project or other specialized structure....particularly for a "building" structure.....

This is the kind of false attempt at doing it cheaper that gets people killed when a structure fails due to unanticipated loads, defects, etc.....

Just my opinion....

Ed.R.

 

[btrueblood]

Not clear to me either why you would want to examine post-"yield" concrete behavior, as said yielding actually means the concrete has cracked and failed. Unless you are doing simulations for crash barriers or weapons bunkers?

 

[hannis]

My apologies if I was not clear, this has come about from a review of a non-linear design of concrete floor slabs within a multi-storey building. Basically the concept of non-linear design of concrete makes me concerned and as you correctly point out the slab has cracked and is yielding. Non-linear design of steel makes more sense since it will behave perfectly plastically and hence is more predictable. Concrete once it is cracked, is not predictable.

Hannis

 

[EdR]

Again I don't agree...Even cracked concrete behavior is predictable so long as you don't get too picky about wanting results within a few percent...i.e. you are looking for gross structural behavior and approximate collapse loads, etc....I have done many analyses like this when evaluating blast loading and gotten "good" results that show the overall structural behavior...even using small strain/displacement codes.....

My point is that for building structures you should not be considering anything in the post yield range (and indeed for some actual lesser values which includes a factor of safety) and if the slab is cracked and yielding you need a thicker slab, more reinforcing, or something else that is real...not a more sophisticated analysis procedure...

Ed.R.

 

[jhardy1]

EdR,

Yes, you generally want to ensure that in service, the structure is remaining well within the nominally elastic range, but ...

There are valid reasons why you might want to simulate the actual non-linear collapse behaviour of concrete slabs and the like. In limit state design methods, the approach is basically to apply a factor of safety to the design loads (typically about 1.5), apply a material capacity reduction factor to the characteristic strength of materials (typically about 0.8), and then the proof of the structure is given by:

(Load Factor x Design Load) less than or equal to (Material Reduction Factor x Characteristic Failure Load)

In such Strength Limit State methods, you actually want to know about the real failure mode and failure load to determine the strength limit state. Elastic analysis methods will not always give a good prediction of failure load for redundant concrete structures, such as irregular 2-way slabs etc. In many cases, though, elastic analysis will be all that is required.

A key point to remember in limit state design methods is that you must also consider the Serviceability Limit State, which si typically about deflection, vibration, cracking etc at the Service Load level. In many cases, the serviceability limit state will govern. There are numerous instances of poor design where people have forgotten about the serviceability requirements. The structure may be shown to have an ample factor of safety on collapse, but performs poorly in service due to excessive deflection or cracking.

(Note that I am not advocating that ALL concrete slabs warrant a full non-linear analysis - just pointing out that SOMETIMES it can be appropriate.)

Hope this helps!

 

[EdR]

Julian:

I never said anything about using only elastic analysis to make predictions or to determine strength limit states and/or limit design values .... I only said the resulting design should not result in stresses, etc. being in the non-linear range, particularly for "building structures" that are presumably used by people.........

Ed.R.

 

[ThomasH]

Interesting discussion.

Just remember one thing. Reinforced concrete cracks, otherwise you wouldn't need the reinforcement. That's stating it a bit brutal but I think the argument holds.

A few thoughts:

Serviceability limit state very often governs the design (as previously stated). For this state the forces can often be computed with linear elastic methods.

Ultimate limit state can also often be analysed with linear elastic methods. You don't get the exact "truth" but due to limit load criteria you usually get a "safe" solution. Equilibrium is safisfied.

For accidents such as explosions etc. Might require nonlinear analysis but not neccesarily. I won't go into that here.

Typically I would not use a nonlinear analysis for a "normal" DESIGN. The savings in reinforcement etc would probably not justify the more complex and timeconsuming analysis.

When to use it then?

Lets say that you have an existing structure and want to increase the load. And the cost for a more sofisticated analysis is probably much lower than demolishing and rebuilding a stronger structure based on a simpler model. This is an approach that I know have been used in some cases.

So nonlinear analysis in design might not be justified but for analysis it can be.

As for the numerics, Newton-Raphson, strain softening etc. They can be handled.

Like I said, just a few thoughts.

Thomas

 

[hannis]

All,

Many thanks for your valued responses and I would agree with the general sentiment that non-linear analysis is perhaps best suited to either accidental loading, blast loading or to the validation of an existing structure for an increase in floor loading. There are situations when one does need to know the full plastic capability of a structure before failure and not for the normal design of a building structure where generally serviceability requirements limit. As designers we are being asked to make structures more economic, thinner,longer and pushing materials further, hence the perceived need to have more powerful tools for analysis. This brings into the question the software houses pushing their wares and allowing us to believe that they have the next best thing. But as this limited thread has shown up perhaps it is a need to far and we should think as engineers and ask the right questions before we believe what we are told.

Many thanks

Hannis