Torsional Analysis
Torsional Analysis
(OP)
I am analyzing a curved open box girder that is subjected to torsional effects. The section is composite with the concrete deck, so I am assuming it is a closed section under live load stresses. To determine the dead load stresses, I need to assume that the deck does not have any stiffness which results in analyzing the girder as an open section. I have found some complicated equations for shear stress in AISC's Torsional Analysis handbook. Is there any other guidance out there for determining the shear stress in open sections such as this?





RE: Torsional Analysis
the in-plane shear flow, q, for a closed section is T/(2*[A], where [A] is the enclosed area. and the shear stress is q/t (t=the local thickness).
the in-plane shear flow develops out-of-plane warping, so the load that the attachments between the cover and the girder have to react is q*l (l is the distance between attachments)
good luck
RE: Torsional Analysis
RE: Torsional Analysis
RE: Torsional Analysis
Alternatively try a simple FE analysis... using shell elements?
RE: Torsional Analysis
RE: Torsional Analysis
Alternatively build a physical model out of card and hot glue, and have a good long think. You might end up putting bulkheads or tension members inside the section.
The torsion of open curved sections is very interesting.
Cheers
Greg Locock
Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.
RE: Torsional Analysis
If your torsion comes from the curvature, also consider that there is not necessarily torsion in such a beam: this is true for example if both ends of the beam are clamped against bending.
prex
http://www.xcalcs.com
Online tools for structural design
RE: Torsional Analysis
Thanks for the input.
RE: Torsional Analysis
Cheers
Greg Locock
Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.
RE: Torsional Analysis
The problem is, what do you do with it after you calculate all the loads (or rather internal forces). You calculate the torsion in the member, but there aren't any provisions in Roark for finding torsional stress in a CURVED member. You find bending moments and stresses, but AISC ASD doesn't give provision for allowable stresses in these curved beams. And the problems go on.
By the way, those curved beam equations are a mess, if you've never used them before.
In many cases, you also can select free body diagrams and use symmetry to find internal forces. But you still have the problems above.
RE: Torsional Analysis
JStephen, I agree that those equations are quite complex, and of course as cazkoop seems to have a FEA model already calculated, there is no reason to go with them. However, once the stresses in each section are known, be it by means of FEA or Roark, then they would be treated just like for a straight beam, assuming of course that the radius of curvature of beam axis is much higher than beam height.
The stresses due to torsion, if using Roark, are calculated just as for any open section: Roark has formulae for this, and, if I recall correctly, the case of a C section is included. And the allowable will be as for any other shear stress (not considering local buckling, that will need a separate treatment and local stiffeners).
Your problem, cazkoop, might be the deflections: if you really have torsion (and I would double check this), as the stiffness in torsion of an open section is very low, you could get unacceptable distortions that would be frozen by the concrete deck.
I'm not at office now: when I'm back, I'll try to post a few relevant equations for you.
prex
http://www.xcalcs.com
Online tools for structural design
RE: Torsional Analysis
http:
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RE: Torsional Analysis
There are some other effects that are not obvious at first as well. You can get bending moments from torsional loading and vice versa. What appears to be "balanced" uniform loading over a curved beam will actually give a net outward-rolling moment.
If this is a highway bridge, the curvature may be sufficiently large to just ignore stress variations due to curvature. Or, for that matter, to ignore the curvature altogether. But that won't work as a general approach to the problem.
RE: Torsional Analysis
of course for any thin walled open box section the torsional constant is
K=Σsiti3/3
where si and ti are the lengths and thicknesses of section segments.
The shear stress in a section segment is
τ=tiMt/K
But all this is basic stuff and you were likely not looking for that.
The next step is to calculate torsional deflections for a beam with torsional and warping end restraints. This requires the determination of the warping constant Cw, that Roark has for a C section (also with inwards or outwards projecting lips), and the use of formulae, that are also in Roark, that account for the combination of end restraints that may have or not a torsional restraint and/or a warping restraint.
However I'm afraid that those formulae are too complex to be reported here, you should get a copy of Roark if that is what you need.
Concerning the moment distributions in a curved beam, Roark's formulae are also too complex to be copied here.
However I can confirm to you that if a curved beam has both ends slope-guided (the term Roark uses for clamped against bending) and not roll-guided (the term for restrained against torsion), the beam will develop no torsional moments, and you should be able to see this in your STAAD calculation.
Of course if you have some degree of torsional restraint, some torsion will occur, but I think that you can safely assume zero torsional restraint, even if this is not exactly what you do.
prex
http://www.xcalcs.com
Online tools for structural design
RE: Torsional Analysis
I don't think this is correct- analysis of circular rings with simple supports shows that there ARE torsional moments developed. With equally spaced supports, they disappear at the supports (unless the supports are off-centered from the beam) and disappear at the midpoints of the span (due to symmetry, as with shear).
RE: Torsional Analysis
K=?siti3/3"
Not usefully. There are many assumptions in that equation, which are not valid in typical thin walled structures, such as car bodies.
Cheers
Greg Locock
Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.