Torsional Analysis

[cazkoop]

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?

 

[rb1957]

so there's a good structural connection between the girder (a three sided box) and it's cover ?

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

 

[cazkoop]

Thanks rb1957. These equations do work for our live load analysis where the concrete deck is assumed to be rigid and can distribute the live loads. However, in determining the dead load stresses, the deck is considered as wet concrete, only applying load to the open steel section. The section does not have a closed top cover. Is there any information on this situation out there?

 

[rb1957]

i guess then you have an open section, shear flow = T*3/(bt), where b is the developed length of the girder cross-section.

 

[crisb]

ROARK's formulas for stress and strain (chapter 9) is a good starting point for standard open walled sections.

Alternatively try a simple FE analysis... using shell elements?

 

[JStephen]

You'll find that all the torsional design data is for straight members. And all the actual members with considerable torsion turn out to be curved. Which means in many cases, you're on your own to find the stresses and to determine what a reasonable allowable is.

 

[GregLocock]

...so you need to use FEA. Make sure you maximum deflections are very small, otherwise you'll need non linear FEA.

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.

 

[prex]

I understand that you have a curved beam: this case is treated in detail in ch.8 table 19 of my Roark's 5th edition. There are formulae that allow to calculate all the load components in a curved beam loaded normal to the plane of curvature.
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

 

[cazkoop]

We have entered the bridge into STAAD 2004, and it does appear that the torsion is a result of the curvature, even though we do have the ends braced against bending. I am unfamiliar with Roark. What does he have in regards to shear stress in poen sections?

Thanks for the input.

 

[GregLocock]

prex, those equations only hold for elastic beam theory. In this case it is unlikely that plane sections will remain plane, which is a fundamental assumption in beam theory.



Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[JStephen]

"There are formulae that allow to calculate all the load components in a curved beam loaded normal to the plane of curvature."

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.

 

[prex]

GregLocock, the theory of torsion in an (open) beam section does not assume that sections remain plane: the torsional load in each beam section would be treated as for any section under torsion (adding bending and shear of course).
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

 

[feadude]

this thread could be helpful

http://eng-tips.com/viewthread.cfm?qid=95155&page=9

good57morning@netzero.com

 

[JStephen]

prex, suppose you take a straight box section and deflect it vertically. The shear deflection on each side is the same, so stresses are the same. However, if you do this with a curved beam, the deflection will be the same, but the lengths of the inner and outer faces are different, so the shear stresses will not be the same. The same holds true for a curved beam subject to torsional loading or out-of-plane bending. In the general case, you can not use straight beam assumptions for the stress distributions in curved beams.

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.

 

[prex]

cazkoop,
of course for any thin walled open box section the torsional constant is
K=[Σ]s_it_i³/3
where s_i and t_i are the lengths and thicknesses of section segments.
The shear stress in a section segment is
[τ]=t_iM_t/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 C_w, 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

 

[JStephen]

"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"

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).

 

[GregLocock]

"of course for any thin walled open box section the torsional constant is
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.