Curved beam 1

[MotorCity]

Can someone please shed some light on the design procedure for a curved beam. I assume it is slightly different than a traditional design. I don't have a particular problem that I am trying to solve, just something I'm curious about. Thanks.

 

[Drej]

One thing to be aware of is that the neutral axis of a curved beam may not necessarily pass through the centroid of the section. Treatment of curved beams is therefore separate from "straight" beams. See any strength of materials textbook for a full treatment, where you will probably see the analysis of a lifting hook, which is a classical example of the analysis of curved beams.

-- drej --

 

[AlohaBob]

Torsion must be considerred.

The calculations are more rigorous than normal concentric bending or axial loading.

Good design will attempt to minimize torsion effects.

 

[awcsag]

Here are all the references that I have on curve beam design, all out of past AISC Engineering Journals.

Horizontally Curves Steel Girders-Fabricated & Designed
by W.M. Thatcher, July 1967.

Analysis of Curved Girder Bridges by Charles Culver,
Darryl Brogan & David Bednar, January 1970.

Straight-Element Grid Analysis of Horizontal Curved Beam
Systems by Herbert A. Weissman, April 1970.

Approximate Torsional Analysis of Curved Box Girders by
the M/R-Method by David Tung & Richard Fountain, July
1970.

Box Girder Bridge Design-State of the Art by C.P. Heins,
Fourth Quarter 1978.

The Application of Flexural Methods to Torsional
Analysis of Thin-walled Open Sections by Thomas Boothby,
Fourth Quarted 1984.

I've read these papers, but, fortunately, so far, I never had to apply them to a practical problem.

 

[dgidwani]

I've found the easiest way is probably to discretize the beam into sufficient number of straight segments, and run it on the computer. Avoids complicated equations that you don't understand and can't rely on. Make sure you get the support conditions right.

 

[AlohaBob]

Are you referring to a curve in plane or out of plane? I suppose an in - plane curve would be more of an arch.

 

[MotorCity]

My original idea was a beam curved in a horizontal plane. Although, an arch would also be considered a curved beam but in a vertical plane.

 

[dbuzz]

There is a good paper on the subject:
Bradford, M and Pi, Y-L
Design of Steel I-Beams Curved in Plan to AS4100
Australian Journal of Structural Engineering, Vol 3 Nos 1-2 Pages 85-97, 2000

AS4100 is the Australian limit state steel structures code. The bending-torsion interaction equations proposed in the paper incorporate the effects of the included angle, secondary bending about the minor axis and torsion actions for several lateral bracing configurations.

 

[rowe]

All the above responses are correct and appropriate. For a single curved beam, the lifting beam is the best design example. For a system of curved beams (like a curved girder bridge deck), it is usually required to analyze/design the curved girders as a system (i.e. 3-D) because the lateral bracing components are considered as primary structural members. The M-R method mentioned above is very easy to understand and visualize (it's also known as the "V-Load" method - and it's an approximate method that was used for years before curved girder software was economical).

It is commendable that you are interested in the subject. I would suggest that you obtain some of the resources noted above and after some study, ask more specific questions - it helps me to become more knowledgable if I have to do some research or review before I post answers in this forum.

Good Luck Rookie76 (although I've been an engineer for almost 15 years, I still have to review and re-learn many of the basic principles - and I still enjoy it).

 

[patna]

Helical stair is also an example of curved beam. This can be solved by inputting the co-ordinartes and load magnitude in computer program. I use MULTIFRAME 3D program.

My question is: Is the result from the computer program acceptable as regards its output on tosional stresses

Can any of our members of this learned body help me.

 

[AlohaBob]

Use AISC Torsion analysis for steel.

ACI Ch 11.6 for concrete.

I think most programs don't automatically consider torsion. Some have particular switches you must flip before the torsions analysis is done if at all. I use hand calcs to check the computer output. Then refine the computer models.

 

[patna]

Dear AlohaBob:
Subj: Helical Stair

I would rephrase my question this way:

Is the output as regards torsional magnitude as given by computer program good enough for further calculation for stress analysis through hand calculation by AISC/ACI methods?

With best regards, I end here.

 

[AlohaBob]

I'm not familiar with multiframe 3d. A good starting point though would be just to look at the output. The codes provide allowable stress limits and methods to torsionaly stiffen or strengthen elements to increase the torsion capacity.

Does it provide a seperate calculation for torsion stresses?

1,2 Direct shear stresses in flange and web due to principal bending.

3,4 Pure torsion stresses in flange and web.

5 Normal warping stress in flanges.

6 Warping shear stress in flanges.

The stresses vary depending on end restraints along the beam. So location of stresses are fussier than normal loads. The program should have interaction combinations for torsion and shear stress as well as normal torsion stresses combined with principal bending stresses 7,8.

 

[jheidt2543]

rowe,

"(although I've been an engineer for almost 15 years, I still have to review and re-learn many of the basic principles - and I still enjoy it)"

As my high school Latin teacher use to say, "Repetition is the Mother of learning".

 

[AlohaBob]

Torsion is a bear.

I think most engineers think so too.

I have to carefully methodically check and recheck my calculations and understanding of what I'm doing when I work with it.

For steel, I use the the AISC torsion reference examples to check my methodology. Or I would certainly get lost and fail to design for torsion properly. Let me put it this way. I wouldn't attempt torsion analysis without it.

 

[PXC]

I have often had to design curved I-sections for monorail beams, and they are not straight forward.

There is a problem with using beam elements as most if not all beam element formulations include pure torsion only, not warping torsion. Pure torsion dominates for closed sections, warping for open sections.

You can use FEA with plate elements and this will accurately model the longitudinal warping stresses in the flanges. These are in addition to longitudinal stresses from axial and bending, and are very significant.

Deflection can also be critical and this will not be modelled accurately with beam elements.

The modelling of the supports is critical when calculating longitudinal stresses from warping. You should either design supports that are true pins or true rigid supports about the axis being considered, or else accurately model the support to model the correct rotational stiffness.