Torsion Constant (J) for Concrete Inverted Tee Section

[astructurale]

Anyone know the hand calculation for the torsion constant (J or sometimes shown as Jt) of an inverted tee section of concrete? My college mechanics of material book only gives examples for thin wall tubes and pipes. I'd rather know how to do it by hand instead of letting a computer tell me the answer if anyone knows how.

 

[StephenA]

This site looks as if it will give you the answer

http://ocw.mit.edu/NR/rdonlyres/Civ...231E-407B-8073-A64CCB089D06/0/connor_ch11.pdf

 

[astructurale]

Thanks for trying to help. Wow that is ALL theory! I know some people can digest that stuff, but I'd need a decade to absorb all that. I never even saw the word "torsion constant" in the text. And why is it that all I can find is on thin walled sections? What do most people do for concrete cross sections, particularly the inverted tee type?

FYI - All I am trying to determine is the rotation of an IT beam due to an eccentric point load plus eccentric uniform loading.

I've got the formulas for the rotation, but I cannot determine what the torsional constant is that is used in determining the rotation.

I've posted a similar question before. And I plan on providing some restraint for the rotation to resolve any rotation issues, but I want to know how this beam is behaving without restraint at the application of the eccentric point load.

Any help is appreciated.

 

[WillisV]

Though written for steel sections the following reference might be of some use:

http://www.cisc-icca.ca/files/technical/techdocs/updates/torsionprop.pdf

 

[UcfSE]

The torsion constant "J" for a "T" section is found by adding the the torsion constant for the component elements of the section. You have a width of section, b, and a thickness, t. Your torsion constant is then J = alpha*b*t² where alpha is a constant that depends on the b/t ratio. For thin-walled sections, alpha is approximately 1/3 (equal to 1/3 at b/t = infinity). You calculate alpha*b*t² for each part of the section, the flange and the web in the case of a "T" section, and then add those together to find "J" for the whole section. For thick-walled members like we usually see in concrete, the alpha = 1/3 is not accurate. Check out an Advanced Mechanics of Materials book. Boresi and Schmidt have a good text. You'll find this information in section 6.6 of Boresi.

 

[astructurale]

Thanks for the help. I just learned of a short cut to just use a conservative rectangular section neglecting the reinforcing to get my torsional constant, which ends up being an easy calc. Since my beam does not rotate harldy at all (totally negligible) under that assumption I should be fine not knowing the finite value of it.

 

[graybeach]

UcfSE - I think the "t" needs to be cubed. One of the best references for torsional properties is "Design of Welded Structures" by Omar Blodgett. It used to be available from Lincoln Electric Company for very cheap.

 

[UcfSE]

graybeach, you are right!

Sorry for the typo. "t" should be cubed, "J" has unit of length⁴