equilibrium and Compatibility torsion 3

[perfectaccess]

Hi Community


Actually I do understand the differences between them,but I still have specific doubt long time ago and I need to clarify it.

equilibrium torsion is like beam carrying cantilever ,if you release the torsion of the beam the cantilever will be unstable

But if I am modeling and I ignore compatibility torsion for example for two span beam(in reinforced concrete,I will reach a state that beam is not stable in torsion.
I do know that there is threshold limit for the distribution of torsion in code,but In general practice many engineers take the modifier for the compatibility torsion to 0.1 from the actual value, So I think hey ignore torsion, but could the beam fail in torsion under this case?and could the beam become unstable in torsion(here i am speaking about compatibility torsion)


Thanks

 

[perfectaccess]

any comment please

 

[KootK]

When looking at compatibility torsion, you've got a rotational force that needs to go somewhere. And it has two choices:

1) Torsion in the beam.
2) Flexure in something attached to the beam.

As long as one of those load paths is competent, the system is rotationally stable.

Are you worried about real world physical instability or modelling software mathematical instability?

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.

 

[perfectaccess]

Thank you

I am worried about real world situation according to this assumption Kootk!!!

Assuming torsion is 0.1 form actual value,will lead to situation that the beam is totally unstable in torsion,but again the slab and the column supporting it will have flexure stiffness that will prevent that(sort of that maybe,that why people may ignore compatibility torsion)?

 

[KootK]

People don't ignore comparability torsion. They find another home for it in the form of added bending in an adjoining flexural members. The rotational action just gets designed into other members as flexure instead of the beam as torsion.

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.

 

[perfectaccess]

Kootk

So You are saying that the torsion in beam become positive moment in slabs, but the deformation in the beams exist ,since the increased moment in the slab is due torsion.
my point that I may have miss-understanding in it ,is that beam will under go torsion that it may affect stability,regardless if the moment increases in the slab(I am concerned with the beam).

 

[KootK]

Try this:

1) Instability is continuing movement in the absence of additional load.
2) The beam's torsional movement will be limited to the flexural rotation of the adjacent slab.
3) Since the beam's rotation is restrained, it is torsionally stable.



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.

 

[hokie66]

Take the case of a cast in place concrete floor system, with beams at the edge, and slabs framing into those edge beams. The slab and beam are cast monolithically, so the reinforced slab will provide rotational constraint to the beam if reinforced accordingly. There is torsion in the beam, but we call it compatibility torsion, and the beam itself is only required to have nominal torsional resistance, which is provided by continuous top and bottom bars and by prescribed closed stirrups.

Now take the case of a precast beam, with a precast slab or steel members supported on the side of the beam and not intentionally designed so that the secondary members prevent rotation of the beam. In that case, the beam itself must provide its own resistance to twisting, and thus must be designed for equilibrium torsion, also known as stability torsion.

 

[Agent666]

perfectaccess you can design any supporting beam in the arrangement being discussed to carry the torsion that would result from achieving a state of equilibrium. For example model the beams with fixed ends at the supports. There will be some torsion in the supporting beams and moment in the supported beam, with negative moment at the ends of the supported beam and positive moment within the central region of the supported beam.

However its generally more economical and practical to allow these equilibrium torsions to redistribute and be carried as a moment in the beam/slab, provided there is a load path for the torsion to redistribute to a moment the system is stable (i.e. sufficient positive moment capacity to support the simply supported beam moment). Usually there is also a provision in codes that the longitudinal reinforcement at the support needs to be fully developed into the supporting beam to provide a load path for this redistribution. There is usually other limitations like the spacing of stirrups and the distribution of longitudinal reinforcement around the beam perimeter not being greater than a certain critical spacing (this may force you to also have bars on the sides of the beam as well as top and bottom)

In reality some degree of torsion will still be carried in the supporting beam, and there will be a negative moment at the end of the supported beam (dependant on the real level of cracking that occurs in the beam which drives the level of torsion really being redistributed to a beam moment). In this scenario you can reinforce the supporting beam to the compatibility torsion provisions. This generally either means reinforcing to a minimum torsion capacity (to control any cracking), not to 10% of the actual equilibrium torsion as you eluded. Refer to your code of choice for the provisions relating to compatibility and equilibrium torsion. The point is there is a load path for this to occur if it does/wants to occur, so the system remains stable. In essence turning from a continuous beam to more of a simply supported beam. If you are familiar with the concept of moment redistribution in a moment frame, the concept is the same, but instead of the redistributed actions being moment to moment, its torsion to moment.

If doing this redistribution results in a unstable system, for example the classic scenario of a beam cantilevering off the side of another beam, where if you ignored the need to carry the torsion the cantilver wouldn't be stable. Then you require the torsion to be resisted from an equilibrium point of view so your reinforcement must be provided to the equilibrium torsion requirements (which are generally more onerous in terms of the reinforcement required dependent on the magnitude of the torsion of course).

 

[Agent666]

Read this if still in doubt

http://www.structurepoint.org/publication/pdf/pdh-Torsion-Concrete-Design.pdf

 

[perfectaccess]

Fabulous Answers ..Thanks guys.

I just want to wide the discussion more and put my hand on the critical point
1.I do agree that slab flexural will prevent torsion of the beams in monotonically reinforced concrete(but how much is allowed to accept is depending on the code),code is important
2.ACI 318 code allowed for portion of comparability torsion to be distributed

So as I designer I am comparing general practice with code requirements,to understand what I am doing
Thus My office is Ignoring torsion by multiplying it with 0.1,and not strict to the code threshold after distribution.Logically as you said guys 0.1 will be definitely less than threshold of code after distribution,
but on the other hand code is strict with the threshold.

Thus I had discussion with one of senior engineers in the office and he is saying that code =practice,but I didn't receive proper answer

To me as structural engineer,I conclude that beams will not fail in torsion due to slab support,and the code threshold is an conservative solution but not need to be followed if proper judgment has been made(I am speaking about compatibility torsion only)

A final Comment

I contact CSi ,the people responsible for creating Safe Program,which a wide used program to design slabs,and I asked them many questions ,one of them was ,what is the torsion modifiers in the program
I have been told that torsion modifiers is 0,1 for beams,to allow for maximum positive moment in slabs, and again this will support the practice .

Thank you guys,your answer really opened my mind further.

 

[Agent666]

You don't just design for a torsion of 10% of the equilibrium torsion as I noted previously. You need to provide the minimum reinforcement for torsion (area of longitudinal reinforcement and stirrups) if the code says so.

Usually codes treat it as follows:-

For equilibrium torsion:-
Design for the greater of the minimum torsional reinforcement requirement or for the actual torsion ignoring any reduction to torsional stiffness
Usually this means you are designing for the actual torsion requirement

For compatibility torsion:-
Design for the lesser of the minimum torsional reinforcement requirement or for the actual torsion ignoring any reduction to torsional stiffness
Usually this means you are designing for the minimum torsion reinforcement requirement

Depending on what code you are using it might be slightly different, but the few codes I've dealt with have the above 2 cases in one form or another. Hopefully you appreciate the difference in the two design approaches.

 

[perfectaccess]

For compatibility torsion:-
Design for the lesser of the minimum torsional reinforcement requirement or for the actual torsion ignoring any reduction to torsional stiffness
Usually this means you are designing for the minimum torsion reinforcement requirement

I cant find such statement in ACI318-11?

Can you refer to it ,if your are using this code please?

 

[Agent666]

It's hidden in clause 11.5.2 in ACI318-08 (presumably the same in 2011 version) if you read between the lines.

It doesn't state it particularly clearly though compared to my national code. But if you follow the logic presented it results in something similar to my statement.

 

[perfectaccess]

Thank you

Agent666

Just curious ,which code you are following?

 

[Agent666]

Nzs3101, the New Zealand concrete code. It's based loosely on ACI318, so shares a lot of the same philosophies.

 

[chekre]

My interpretation to section 11.5.2.2. Of aci 11 is that even though redistribution of moment can occur, there is a certain amount of torional moment which u should reinforce ur section to handle it.
Therefore assigning 0.1 modifiers to beams carrying torsion will not prevent the fact that they should be reinforced to handle a reduced moment.[pre][/pre]

 

[KootK]

Some things are best expressed in computer code (see below). When firms do the 10% business, usually they are skipping straight to the bolded section of code below. And the 10% modifier is usually applied to the gross torsional stiffness of the member (GJ). That's in the right ballpark as, after a concrete member cracks torsionally, it's torsional stiffness drops dramatically. I've seen estimates in the 5-15% range depending on who's research you're looking at. This modification is not about getting the right torsion in the beam as, as Agent666 has mentioned, that's not what we design the beam for anyhow. The modification is about getting the right forces in the rest of the structure once torsional cracking and redistribution is accounted for.

Similar to Agent666, I believe that the intent of the minimum compatibility torsion reinforcement is to ensure that the member can undergo the rotations required to redistribute its torsion without excessive cracking and brittle failure.

IF T < T_cracked THEN

do nothing, beam possesses required torsional capacity w/o reinf​

ELSE

IF compatibility_torsion = TRUE THEN

(design for applied torsion) OR (provide compatibility torsion reinf)​

ELSE

design for applied torsion​

END IF​

END IF

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.