Calculating "J" in RISA

[Trackfiend]

I'm trying to figure out how RISA is using the "J" value for concrete properties. When comparing my hand calculations to RISA's results for a concrete 20" x 16" beam, the J's don't add up.

From my mechanical of material's text, the formula for J (polar moment of inertia) for a rectangular section is simply adding up the Ix and Iy. When I do this by hand, my calculation is coming out to be 17493.3 in4. RISA is calculating J to be 13544.1 in4.

By RISA's definition, J is the "cross section torsional stiffness". Is RISA using J differently than I am? If so, what is the equation that RISA is using to get to its results?

 

[swearingen]

This is another of those J confusions - in the US at least, J is used for both the polar moment of inertia and the torsional constant. Further confusing the issue is the fact that the polar moment of inertia and the torsional constant are IDENTICAL for a circular or circular tube cross section. However, the two constants are used for different calcs and vary for any other shape, including rectangles.

The rough calc I use gives 13804 in^4 for the torsional constant and I agree that the polar moment of inertia is indeed what you calculated.

Remember, however, that when designing for concrete, once the beam has cracked, torsion is resisted mostly by the steel near the surface of the beam. The contribution of the core of the beam is neglected and the section becomes a thin-walled tube. This may explain some of the difference between my number and RISA's, but I would have expected the difference to be more than that.


If you "heard" it on the internet, it's guilty until proven innocent. - DCS

http://www.eng-tips.com/supportus.cfm

 

[Trackfiend]

The formula I found for torsional constant, J, is J=B*a*b^3 where:

B = a/b constant (in this case 0.1633)
a = length of the long side
b = length of the short side

The answer I'm getting, 13,377 in^4, is closer to what RISA is getting.

Is this the correct formula for a solid, rectangular section?

 

[swearingen]

Yep - that's the one I used, just with a linearly interpolated beta from the table I have, which explains the difference between RISA, you and me.


If you "heard" it on the internet, it's guilty until proven innocent. - DCS

http://www.eng-tips.com/supportus.cfm

 

[JoshPlumSE]

The J value calculation in RISA actually gets more complicated than we would typically do by hand. In RISA this value is, of course, the TORSIONAL CONSTANT.

The most accurate formula for the torsional constant of a rectangular cross section that I have found is actually:

J = a*b^3 / 3 * ( 1- 0.63*b/a + 0.052*b^5/a^5)

Where a is the longer dimension and b is the shorter dimension of the rectangle.

However, I believe the concrete codes ignore that 3rd term (the one that starts with 0.052). Therfore, that is what RISA does as well.

The primary reference for this is "Formulas for Stress, Strain and Structural Matrices" by Walter Pilkey.

I hope that clears things up.

 

[Trackfiend]

Thanks. It does seem that RISA is ignoring the last part of that equation.

For this particular project, torsion isn't a concern, but I still like to be able to cross check the numbers by hand calculations that RISA is giving me. Assuming the pretty little black box is correct can be a slippery slope....