Shear Center of Solid Section
Shear Center of Solid Section
(OP)
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
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






RE: Shear Center of Solid Section
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).
RE: Shear Center of Solid Section
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 ?
RE: Shear Center of Solid Section
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.
RE: Shear Center of Solid Section
RE: Shear Center of Solid Section
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.
RE: Shear Center of Solid Section
Derivation of Shear Center Q for "L" shaped section (from Roark's)
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RE: Shear Center of Solid Section
http://ocw.mit.edu/courses/civil-and-environmental...
RE: Shear Center of Solid Section
PropSection
RE: Shear Center of Solid Section
RE: Shear Center of Solid Section
RE: Shear Center of Solid Section
RE: Shear Center of Solid Section
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.
RE: Shear Center of Solid Section
No worries though, it seems that there's just no quick way to go about it by hand!
RE: Shear Center of Solid Section
I actually like that they require you to make a reasonable judgement call like that.
RE: Shear Center of Solid Section
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RE: Shear Center of Solid Section
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 ?
RE: Shear Center of Solid Section
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.
RE: Shear Center of Solid Section
another day in paradise, or is paradise one day closer ?
RE: Shear Center of Solid Section
RE: Shear Center of Solid Section
another day in paradise, or is paradise one day closer ?
RE: Shear Center of Solid Section
Unless you're amazingly quick at finite element by hand.
RE: Shear Center of Solid Section
if you state "assume shear center = centroid", are they going to respond "-50% for simplistic assumption" ?
question to you guys who work in this field ... is this a "good" question ? is this something you see at work ?
another day in paradise, or is paradise one day closer ?
RE: Shear Center of Solid Section
It would be better if it stated the coordinates of the shear center as well as the coordinates of the centroid, and then had a wrong answer that you would arrive at had you taken the eccentricity with respect to the centroid.
The question asks for the ultimate torsion produced by the load. The answers are (k-ft)
A) 18.7
B) 20.7
C) 28.6
D) 34.5
using centroid, you get the "correct" answer of 28.6 k.
Using the actual shear center, you see that the "correct" answer is unconservative as the exact answer should be 35.1 k.
Not only that, but if you did the exact method somehow, you would choose D) and get that problem wrong.
This is a frustration I've dealt with in school - poorly written tests question. Many times you need to think, "okay what assumptions did the test writer make that they didn't state? What were they thinking when they wrote this"
I'm actually an excellent test taker, but some of that is because I've learned how to deal with situations like these, which doesn't have much (if any) real world application.
RE: Shear Center of Solid Section
I don't have near the experience that others on this forum have, and they might know it won't make a difference in the design and ignore the eccentricity all together.
RE: Shear Center of Solid Section
It can be quite frustrating trying properly calibrate your level of detail to match that of the examination questions.
I remember an exam question that was a moment loaded shear wall with boundary columns on each end. The columns sat on big concentric pad footings and there was an itty bitty strip footing under the wall connecting the columns. They wanted the max bearing pressure under the footings. I thought to myself "don't over think this, do what you'd do in practice". So figured out the compression chord reaction and divided it by the footing area to get a uniform bearing pressure on that end.
Years later, I saw the same question show up in a practice exam a that a colleague was working through. As it turns out, I got it wrong. The right answer was to treat the two pad footings and the strip footing as a composite section for the purpose of determining the max stress. Just like how you'd figure f_b for a wide flange in flexure. Go. Figure.
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.
RE: Shear Center of Solid Section
http://www.pci.org/uploadedFiles/Siteroot/Publicat...
RE: Shear Center of Solid Section
Maybe in 1984 this was the best method for a quick approximation of the shear center? I don't know. I wasn't born yet :)
Unfortunately, this method does disagree with the section property calculator provided by avscorria, so one of the is wrong.
RE: Shear Center of Solid Section
One of the practice problems in the same NCEES book asks for the moment capacity of a W10x22 Steel beam spanning 20 feet braced at ends and 10 foot mark. There is a point load at the 12 foot mark.
Answers are (k-ft)
A) 68
B) 76
C) 84
D) 97
Looking at plastic yielding, answer is 97. Looking at LTB, and conservatively taking Cb = 1, the answer is 76. Solving for Cb= 1.43 justifies using the full plastic moment capacity. Answer is 97.
If you went the extra mile you got the answer wrong. B) is the "correct" answer.
RE: Shear Center of Solid Section
RE: Shear Center of Solid Section
Otherwise you can still use Table 3-10 and multiply the value by Cb, then take the minimum between that and the plastic moment.
This is what frustrates me about many multiple choice test problems. It's not just about what you know, but also about you "calibrating your level of detail to match that of the examination questions" as KootK stated.
If you unfortunately GUESS the wrong level of detail, then you get the problem wrong. Obviously free response is better at eliminating this.
Side note, my teacher introduced Table 3-10 to us as the haystack. The member you are looking for is the needle.
RE: Shear Center of Solid Section
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.
RE: Shear Center of Solid Section
concrete slab spanning (6) 9'-0" bays. Maximum negative moment according to ACI 318 alternate to frame analysis?
Do you use wl^2/10 for negative moment at exterior face of first interior support, or wl^2/12 for ALL supports?
I got it wrong by being conservative and using wl^2/10. (only wl^2/12 required since slab span < 10')
It's a hard life for an engineer...
RE: Shear Center of Solid Section
RE: Shear Center of Solid Section
And my intent for throwing out the 1984 date was not to insult your source, but to offer an explanation why they used that method. I doubt section property calculators existed in 1984. Then again who knows.
RE: Shear Center of Solid Section