Shear Center of Solid Section 2

[cal91]

In the NCEES Practice Exam I was reviewing this problem, where the torsion due to the reaction is asked for. The solution calculated the eccentricity with respect to the center of gravity.

I would've thought that the eccentricity would be with respect to the shear center...

For solid sections, is the shear center the center of gravity? If not, how do you calculate it?

All of the resources I have (text books, internet) only provide information for thin wall sections, not solid sections for calculating shear centers. Does anyone know of a source for solid sections?

Thanks

 

[Agent666]

The shear center and centroid only coincide when there is symmetry about an axis. So for your shape they do not coincide.

As for how to calculate it, I actually don't know.

But intuitively if the beam stirrups resist the torsion (ignoring the support ledge) then I would be taking the eccentricity as 2" plus 16/2" (to the centre of the beam).

 

[rb1957]

i'd start with "what is the distribution of shear stress across a solid section ?" ... soap bubble analogy ? sand-pile (plastic stresses) ? for direct shear, for torque ??

then the shear section is defined as the location such that a load applied here does not cause the section to twist. so the idea is the off-set between the loading point and this position is creating torque on the section.

another day in paradise, or is paradise one day closer ?

 

[cal91]

Thanks for the replies.

Right, I understand the concept. I was hoping to find a source about how to determine the exact location for the shear center for solid shapes.

This problem made me realize that I've never encountered shear center / torsion problems for solid shapes before, only thin wall shapes. And I guess circular bars.

 

[hokie66]

My old Mechanics of Materials textbook (Popov, 1963) states that "The exact location of the shear centre for unsymmetrical cross-sections of thick material is difficult to obtain and is known in only a few cases." Not sure which cases it is known for, but two rectangles together would seem a useful one. In 50 years, maybe someone has found a better way.

 

[KootK]

Yeah, I've been down this rabbit hole before. And didn't get too far...

Link
Link

And this stuff wouldn't even cover any of the plethora of non-linearity involved in concrete structures. In practice, it's Agent666's method for me.

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.

 

[JAE]

Your section may be too thick for this but does this help?

Derivation of Shear Center Q for "L" shaped section (from Roark's)

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[haynewp]

See page 312 here. There was discussion for a similar shape in my Gere and Timshenko book when I looked at the office today but didn't have a chance to post it. You should be able to apply this to the shape you have after separating it into 2 parts. And this looks like it is the same way as posted above from Roark (the inertia draws the shear in each part which is then balanced to find the shear center).

http://ocw.mit.edu/courses/civil-an...-control-spring-2004/readings/connor_ch11.pdf

 

[Guest262653]

The easiest way to approach this is using numerical methods. Take a look at CTICM's software for the calculation of section properties:

PropSection

 

[mike20793]

These are all great references but it doesn't address the original problem that this was a practice problem on the NCEES practice exam, so it needs to be done in under 6 minutes. I'm with Agent666's method but apparently it would have been incorrect. Does the solution go through calculating the centroid, or do they just assume you have a reference that gives you a quick way to calculate it? Is there any additional information given in the problem?

 

[haynewp]

You can't find inertias and sum forces in less than 6 minutes?

 

[mike20793]

I was getting at the quick reference to solve this problem. I doubt the average engineer sitting for the PE is going to have a reference to calculate the shear center of an L beam.

 

[cal91]

Thanks everyone, as Mike said, great references.

Mike, yeah the solution took the eccentricity to be with respect to the centroid. Doing it the solutions way is easy enough, but it's incorrect!

So that's what made me ask about methods to find the shear center.

I think that I've indirectly got my answer, that it's much more rigorous then just finding the centroid or other section properties.

If I see a question like this on the actual PE I will just assume centroid = shear center.

 

[cal91]

And also, JAE and haynewp I believe those methods assume that the shear stress is constant across the thickness of each wall segment, which is only accurate for thin wall structures :/

No worries though, it seems that there's just no quick way to go about it by hand!

 

[jayrod12]

I also would argue given the proportions of that L-beam, that the shear-centre is so close to the centroid that the final answer would remain unchanged regardless of the method chosen.

I actually like that they require you to make a reasonable judgement call like that.

 

[JAE]

cal91 - that's why I mentioned that your section might be too thick.

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[rb1957]

how do you argue with examiners ? write it in your answer ?

Are they after a practical answer, like we'd use in the business (torsion on that large a section would be pretty small ?) or the "truth" ?

another day in paradise, or is paradise one day closer ?

 

[cal91]

If anyone was curious, using avscorreia's program...

Actual Shear Center
(16.15, 13.59)

compare with shear center = centroid
(14.29, 16.29)
SRSS error = 3.27

thin wall approximation
(15.5, 16.71)
SRSS error= 3.19

Looks like neither are a great approximation for thick objects, but neither are horrible either.

 

[rb1957]

wonder how it calculates that ?

another day in paradise, or is paradise one day closer ?

 

[cal91]

I believe it makes a finite element mesh of triangular elements, then numerically solves for the properties.