Torsional Warping Constant, Cw
Torsional Warping Constant, Cw
(OP)
Can anyone tell me how to calculate the warping constant for a composite plate girder? The formula for the girder itself is from AASHTO C6.9.4.1.3-1. However, how do I account for the transformed slab?






RE: Torsional Warping Constant, Cw
One could make an estimate of this but I suspect that it's the wrong approach for your situation. You're doing a lateral torsional buckling (LTB) check, right? Assuming that to the be the case, you've got a few popular approaches to choose from, in order of decreasing capacity:
1) Convince yourself that the slab provides continuous torsional bracing to the beam and LTB is not possible.
2) Assume that the connection to the slab forces LTB to occur about a point of rotation located at the underside of the slab. This is called restrained axis buckling in the literature and yields a pretty high capacity. It's a fair bit of work to do the first time however.
3) Assume that your slab provides only lateral flange restraint but that LTB will occur about the shear center of the girder. This is your "normal" LTB check between points of lateral restraint.
While I do have some ideas about how to calculate Cw based on a transformed section including your slab, I'll hold off on that until you confirm that you still want to head in that direction.
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.
RE: Torsional Warping Constant, Cw
RE: Torsional Warping Constant, Cw
1) Construct a transformed section (TS) ignoring the presence of the web. Keep your concrete width the real width and perform the transformation using the thickness instead.
2) Vertically locate the shear center of the TS. Do this by finding the combined centroid of the section with one important difference: replace the areas in the calculation with the lateral moments of inertia of each flange.
3) Calculate the lateral moment of inertia of the bottom flange and multiply it by the square of the distance from the flange centroid to the TS shear center. in^6
4) Calculate the lateral moment of inertia of the transformed top flange and multiply it by the square of the distance from the transformed flange centroid to the TS shear center. in^6.
5) Add #3 and #4 to get an estimate of Cw.
Note that this procedure gives no account of any cracking or long term effects in the concrete.
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.
RE: Torsional Warping Constant, Cw
RE: Torsional Warping Constant, Cw
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.
RE: Torsional Warping Constant, Cw
RE: Torsional Warping Constant, Cw
RE: Torsional Warping Constant, Cw
Yeah, that would be... much easier really.
In my opinion Case 1 is not applicable to either the J or the Cw calculation. It should be case two for Cw with the following properties:
1) Transformed Concrete Width = physical concrete width.
2) Transformed Concrete Vertical Centroid Location = vertical location of centroid for physical concrete slab
For Cw, the thing that matters most is the lateral moment of inertia of the transformed slab/flange. And that's all about width as the width is the h in bh^2/12.
While it's surely possible to come up with a transformed section for J, I doubt that it would be worth the trouble. It would be a different transformed section than you're using for Cw. I think that you'd be better off just adding in a bt^3/3 term to your total using the actual concrete dimensions and shear modulus. Moreover, you may want to reconsider using the J value of the concrete at all. If concrete cracks in torsion, it's torsional stiffness drops upwards of ten fold.
We've been talking about Cw but are you trying to come up with one transformed section for use with strong axis bending, weak axis bending, Cw, and J? If so, I'm not sure that's even possible.
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.