non-symmetric beam theory 1

[AXNRXN]

Howdy Y'all,

I'm wondering if basic beam theory still applies to x-sections that are not-symmetric across their centerlines. Say, like a c-channel on its side or a right angle bracket. It seems to me that if the load is not going through the centroid of the x-section it will induce a twisting moment in the beam. Is this torsion generally factored in for these types of beams? If so, is it simply calculated by the distance of the applied load to the centroid of the section for the T*r/J shear stress?

Thanks for spreading the knowledge,
---> Karl

 

[GregLocock]

Sounds about right to me. The eccentric load correction is pretty straightforward, apart from working J out. (grins). The structural forum is a good place to ask.

Cheers

Greg Locock

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[GregLocock]

Oh just one nasty. The appropriate centre for non eccentric loading may not be the centroid, from memory.

Cheers

Greg Locock

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[GregLocock]

In fact it almost definitely isn't. Consider my favourite non symmetric section, a tube with one side slit open. The centroid is in the middle, but the slit side cannot support shear, you'd have to be over towards the closed side.

Cheers

Greg Locock

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[AXNRXN]

Thats kind of what I fear. I see in my mechanics of materials book some section on "shear flow" and "shear centers" which bring up the exact x-section you describe. It calculates shear from the load plus the torsion on the beam. This increase in shear seems to act at the neutral axis, but it doesn't say if the max bending stress is affected at all.

 

[Ussuri]

For there to be no torsion the load should be above the shear centre. The shear centre will coincide with the centriod for some sections, but not others (such as angles and channels). Actually, for a channel the shear centre is outwith the section.

 

[rb1957]

it won't change the bending stresses, only add a (torsional) shear stress component ... the problem you'll have is ther isn't much out there on torsional shear stresses for open sections, all i'll seesn is the common expression for the maximum stress, and just about nothing on the distribution ... i think this is because the section distorts significantly.

 

[Ussuri]

You could try:

http://www.aisc.org/store/p-1585-design-guide-9-torsional-analysis-of-structural-steel-members.aspx

 

[Denial]

There is a further potential complication with the "simple" bending of non-symmetric beams, and it applies even when the transverse loading is applied through the beam's shear centre. Unless the load direction is parallel to one of the cross-section's principal axes, the bending direction will not be parallel to the load direction.

 

[swearingen]

An example of what Denial is referring to is an angle, oriented with one leg horizontal and the other vertical, loaded vertically. The shear center is not at the centroid, and when it deflects, it will not deflect straight down; it will deflect both vertically and horizontally, even if the load stays vertical and is through the shear center.


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[kslee1000]

Swearingen:

Excellent explanation.

 

[AXNRXN]

Thanks for all the help. I appreciate it.

However, my main concern is the theoretical maximum stress in the beam. Do you approach this in the same manner as a symmetric beam? The literature I am looking at deals with the shear stresses at the neutral axis and the torsion induced by the load. But, I believe the main design criteria is still governed by Stress = MC/I, with the highest stresses the farthest away from the centroid.

Any thoughts on this point?

Thanks for the additional help,
---> Karl

 

[swearingen]

For cases where plane stresses remain plain, yes, the MC/I will cover the vertical bending stress. You must, however, also include out-of-plane bending stresses as well as stresses induced by the torsion caused by non-shear center loading (not non-centroid loading), which is where this thread started.


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