In-Plane Curved Reinforced Concrete Girder Design and Analysis

[memphiseng]

Looking at adding equipment loads to a 40+ year old design made up of continuous reinforced concrete girders atop rc columns. The girders I'm looking at now are at an 84' radius cl, spanning 22' c/c across the columns. Girder is 12" wide and 24" deep. Hope this will help anyone picture the condition in question.

The girders are braced continuously at the top by a 4" roof slab integrated into the member on the inside of the curvature, and at the bottom by precast roof slab T-beams attached on 36" o.c.

Currently I've split the curve into 10 straight "members" and modeled 2 girder sections across 3 supports in RISA 3D. The reactions, bending, and shear all seem reasonable and are reflective of a preliminary rough approximation calculation of the beam idealized as straight.

The issue is that I'm getting the error that the threshold torsion is exceeded. I've attempted to approximate this with the model by bracing at 36" c/c, but because of the curve it is not possible to brace the sections exactly perpendicular. Should this be the case per the bracing conditions outlined, as torsion in the beam is resisted by other members?

First for me dealing with curved beams, and I've been struggling to find information on this topic thus far that's related to reinforced concrete rather than steel. The existing condition is already close to capacity in terms of shear at the column faces and so there's apprehension towards introducing additional loads without a more thorough understanding of this situation and based off of an approximated RISA model.

Any directions towards relevant resources are welcome.

 

[ash060]

There is no picture attached.

I have experienced this before in RISA, and the problem is that the torsional stiffness is very conservative. Since they use GJ the stiffness is extremely large and concrete beam will suck alot of torsional moment that will most likely get redistributed at the onset of cracking (if statics allows).

If the threshold torsion is exceeded, than there is cracking and the moments are going to redistribute. In RISA I would create a special section that had a reduced "J" to help with this issue, otherwise the design is ridiculous.

Also, the radius is pretty large, have you checked the results if the members were modeled straight with no curve, you might get close to the same results in which case I would check as a straight beam.

 

[WARose]

What are your boundary conditions? You've talked about a 4" slab and a T-Beam to restrain it. I don't know how the T-beam is attached.....but in the case of the slab, even if it is fully integrated with the girder....it's not going to provide that much rotational restraint. If there is something on the boundary that restrains both the slab and the T laterally.....you might be in business.

You say "threshold torsion is exceeded". What does that mean? Are you referring to the limit for compatibility torque in ACI [318] code? Or the torsional capacity of the girder?

By the way, make sure (for a curved girder) you have it meshed well. I've typically kept the element sizes real small for a curved one (typically 1-2 feet or less).

 

[WARose]

[blue](ash060)[/blue]

I have experienced this before in RISA, and the problem is that the torsional stiffness is very conservative. Since they use GJ the stiffness is extremely large and concrete beam will suck alot of torsional moment that will most likely get redistributed at the onset of cracking (if statics allows).

ash is correct.....typically after cracking we are talking about 6-20% of the uncracked rotational stiffness. (See ACI's 'Analysis of Structural Systems for Torsion' SP-35., p. 397.)

 

[Lomarandil]

Sidebar, but you can brace the sections in the perpendicular direction. Rather than directly creating boundary conditions, use a short dummy member to a fixed boundary. You can orient the dummy member any way you want, then use member releases to create the correct boundary condition response.

You could even use this to model the rotational stiffness of the 4" slab -- if that has any value, per WARose's comments. (e.g. if it's supported near (but not at) the curved girder.)

----
The name is a long story -- just call me Lo.

 

[memphiseng]

Also, the radius is pretty large, have you checked the results if the members were modeled straight with no curve, you might get close to the same results in which case I would check as a straight beam.

The difference between the curved model and a straight girder model is significantly different - 2x Shear and 5x Bending Moment on the curved model compared to the straight girder. Makes me more skeptical that there isn't an issue with the curved model, at the midpoint the CL of the curved beam is 0'-8" from the straight line between supports - doesn't seem like it should be making such a dramatic difference. Everything else on the model is identical.

You say "threshold torsion is exceeded". What does that mean? Are you referring to the limit for compatibility torque in ACI [318] code? Or the torsional capacity of the girder?

By the way, make sure (for a curved girder) you have it meshed well. I've typically kept the element sizes real small for a curved one (typically 1-2 feet or less).

Both are being exceeded, technically. It's triggering the warning to design for torsion because it exceeds the ACI provision (1/4)Tcr. It also exceeds the torsional capacity of the girder by 3%, with all transverse steel considered in torsion rather than shared between torsion and shear.

I've broken the beam into 1' sections just to check, and there are no real differences. Original model had larger sections around the curve, due to RISA rejecting it as a 'deep beam' with the shorter sections.

Attaching sketched plan and section view if it will help clarify the situation.


I'd feel a lot better if I could just do it by hand at this point, but I've had a hard time tracking down concise guidance on calculating the shear, bending moment, and torsional moment in a curved beam.



EDIT: Curved model had incorrect end conditions at the columns. With this corrected the results make far more sense, and falls in a much more comfortable range of the capacity. Apologies everyone.

I'd still like to find more concise guidance on the hand-calc however, if anyone has a good text or guide in mind. The little that I've found have been more researched focused papers.

 

[WARose]

The difference between the curved model and a straight girder model is significantly different - 2x Shear and 5x Bending Moment on the curved model compared to the straight girder.

EDIT: Curved model had incorrect end conditions at the columns. With this corrected the results make far more sense, and falls in a much more comfortable range of the capacity. Apologies everyone.

Yeah, I was beginning to say: I'm used to seeing a increase in bending moments from curvature....but not that much.

Don't forget to check your longitudinal steel for the torque. That can take away from your flexural capacity.

I'd still like to find more concise guidance on the hand-calc however, if anyone has a good text or guide in mind. The little that I've found have been more researched focused papers.

For RC horizontal girders? Good luck. (I've looked myself.) The best you can find is typically some AASHTO stuff (or old AISC articles)....and most of that deals with steel. The reference I mentioned before (i.e. ACI's SP-35: 'Analysis of Structural Systems for Torsion') is about the best I've seen for concrete torsion.