Torsional Resistance (Blodgett)

Question

Torsional Resistance (Blodgett)

marcleblanc12 (Mechanical)

(OP)

2 Dec 19 18:20

I just recently bought "Design of Weldments" and "Design of Welded Structures" by Omer Blodgett and I noticed in his chapters on Torsional Loading he talks about using "Torsional Resistance" rather than polar moment of inertia to calculate torsional stress and deflection. (Chapter 3.6 in "Weldments" or Chapter 2.10 in "Welded Structures")

This is great information but I'm quite surprised as to how much of a discrepancy there is in beams and channels between polar moment of inertia and torsional resistance. If Mr. Blodgett is right (I would imagine he is), then polar moment of inertia J = Ix + Iy is completely irrelevant for beams and channels.

I'm just somewhat shocked that I've never heard of the "Torsional Resistance" method in Blodgett.

I also find it odd that it's presented as an alternate method, when in actual fact when it comes to open members like beams and channels they are totally night and day.

Can anyone shed some light on this?

WARose (Structural) · Answer 1 · 2019-12-02 18:42:27

As Roark puts it (in 'Roark's Formulas for Stress and Strain', 6th ed.): "For a circular section K is the polar moment of inertia J....for other sections K is less than J and may be only a very small fraction of J."

So yes, for open sections, the "K" value becomes very important. (The "K" value being equivalent to Blodgett's "R" value.)

I personally haven't used Blodgett's method for torsional member design. I've typically used AISC's Design Guide 9. (Not that there is anything wrong with anything by Blodgett.....I just find DG 9 more straight forward.)

canwesteng (Structural) · Answer 2 · 2019-12-02 21:49:47

What source says J = I.x+I.y? That doesn't even come close to sniffing an accurate answer. For an open section, J is best estimated as the sum of J of the components. Polar moment of inertia will never give good results for open sections, because warping stresses dominate the response.

Hokie93 (Structural) · Answer 3 · 2019-12-03 18:26:26

The "R" factor in Blodgett is equivalent to the torsional constant ("J") in AISC. The polar moment of inertia being equal to I_x + I_y is covered in most Mechanics of Materials textbooks. It can also be seen in AISC 360-16 Eq. (E4-2) where the denominator of the (1/I_x + I_y) term is the polar moment of inertia. AISC does not refer to it as I_p or 'polar moment of inertia' since it is not tabulated in the Manual for rolled shapes.

GregLocock (Automotive) · Answer 4 · 2019-12-03 21:41:48

If you've ever got an idle moment work out the torsional constant for a thin walled tube, and the same tube with a slit in it.

Cheers

Greg Locock

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canwesteng (Structural) · Answer 5 · 2019-12-04 15:14:19

My mistake, I was thinking torsional constant (same mistake as OP which is probably what led me down this path). Although I'm not sure what use the polar moment of inertia has with respect to open shapes.

marcleblanc12 (Mechanical) · Answer 6 · 2019-12-05 11:20:17

Thanks for the input. I've found the reference to this in Roark (I never knew it was in there). I've also gotten my hands on AISC Design Guide 9 which covers this subject in greater depth than Blodgett.

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