Plastic Neutral Axis in Composite Beam 1

[Perception]

Hello everyone,

I have a question about locating the plastic neutral axis in a composite beam. In a steel design book it is stated that the plastic neutral axis will be located in the slab if:

a < ts where a is the depth of the compression block, and ts is the thickness of the slab.

Wouldn't the plastic neutral axis be located in the slab if c < ts where c = a/beta1? In reinforced concrete the plastic neutral axis was also located a distance c down from the top of the beam.

Thanks

 

[Teguci]

I think this is a problem with crossing terms. "a" when used for elastic stress in concrete, is the height of an idealized rectangular compression zone in concrete located above the neutral axis (distance "c" from the extreme compression flange). The reality is that this elastic compression zone in concrete is parabolic (?) and extends all the way down to the neutral axis at a distance "c" from the extreme compression flange. As a comparison, the elastic zone in steel would be triangular with an idealized rectangular height of a = c/2.

When looking at "a" for plastic stress in concrete, the plastic compression zone runs right to the Plastic Neutral Axis and the term "c," as it refers to the neutral axis, does not apply.

 

[KootK]

Wouldn't the plastic neutral axis be located in the slab if c < ts where c = a/beta1? In reinforced concrete the plastic neutral axis was also located a distance c down from the top of the beam.

This had never occurred to me before but I definitely see where you're coming from with this. I don't have a definitive answer but I have a theory.

The mechanism of horizontal shear transfer to the compression block is different in a composite beam than it is in a regular concrete section (obviously). In the former, it's discrete studs rather than continuous shear transfer which will tend to deliver the horizontal shear more concentrically to the compression block in my opinion.

As such, I speculate that the compression block in a composite beam more closely resembles a member loaded in concentric axial compression than a true flexural compression block. In support of this idea, I submit that, in my country's concrete standard, the permitted composite beam compression block stress is 0.85 x phi_c x f'c which exactly matches the stress allowed for unconfined, uniformly compressed bearing zones.

In conclusion, I speculate that we're treating the compression blocks in composite beams as simple, unformly compressed compression blocks rather than true flexural compression blocks. And our assumptions regarding the location of the PNA (a versus c) stem from that.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[Perception]

KootK,

I could see how that might be the case. If that is the case, I wonder how appropriate it is to superimpose concepts from concentric axial compression and bending in this fashion. I don't see a section where the steel code AISC explicitly states that if a < ts the plastic neutral axis is in the slab. My guess is the book I am looking at neglected the difference between a and c since the compression block will be small.

 

[KootK]

If that is the case, I wonder how appropriate it is to superimpose concepts from concentric axial compression and bending in this fashion.

I wouldn't sweat this. Testing has been performed to confirm the appropriateness of our modern composite design method. Even in a regular concrete beam, Bernoulli theory of plane sections remaining plane isn't strictly applicable at any given cross section. It's only applicable if one averages effects over a few flexural cracks. And I'd have to think that composite beam design would drift even further from Bernoulli theory. This thread of mine from a while back delved pretty deeply into the consequences of accomplishing horizontal shear connection with uniformly spaced studs that would allow some slip between beam and slab and not match VQ/I style demand: Link

I don't see a section where the steel code AISC explicitly states that if a < ts the plastic neutral axis is in the slab. My guess is the book I am looking at neglected the difference between a and c since the compression block will be small.

Out of curiosity, I consulted one of my own composite design references: Link. It contains a sentence that reads:

The depth of the concrete cmpression stress block "a" is equal to or less than the slab thickness

So "a" could extend all the way to the underside of the slab. To me, this suggests one of two things:

1) a=c for the stress block pattern assumed. This would be consistent with the theory that I presented above.
2) a/c is assumed close enough to unity that the difference is negligible (your suggestion above).

I really feel that you've honed in on something interesting here. I've taken composite design courses, read numerous composite design books, and designed hundreds of composite beams. In all that, it had never once occurred to me that composite beam design procedures might be based on a compression zone stress pattern different from that which we use for concrete beam design. In consulting a few of the references that I keep at home, I've yet to find an instance of an author highlighting that feature of composite design.

Hopefully we can rope a few more forum members into the conversation to get this resolved.



I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[mike20793]

Some wording from my steel design textbook by McCormac:

The concrete slab compression stresses vary somewhat from the PNA out to the top of the slab. For convenience in calculations, however, they are assumed to be uniform, with a value of 0.85f'c over an area of depth a and width be, determined as described in Section 16.4. (This distribution is selected to provide a stress block having the same total compression C and the same center of gravity for the total force as we have in the actual slab.)

 

[KootK]

Interesting. My Salmon and Johnson text simply describes the compression zone as a Whitney stress block which would suggest business as usual (a, c, parabola).

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.