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.)

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.

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.

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


New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

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.

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.

"the torsional constant for a thin walled tube, and the same tube with a slit in it."

A core from a roll of paper towels and a pair of scissors has made a convincing experiment/demonstration a few times.

When the ice cubes break loose from the plastic ice cube tray the torsional stiffness plummets a bit.

A few months back a big name equipment manufacturer paid us a couple hundred K-bux in part because the concrete "fill" of the three identical steel bases made of channel rails relied on wishful thinking to make a monolithic structure under the motor and coupled equipment. Their 2 attempts to weld on ribs to make a real base were sad, and futile. I got a cool North Face jacket because I was a whiny bee-atch about the design and the project still made some money.

A former employer made a floor mounted vice stand from ~ 5" I-beam. It was hilariously flexible in torsion. I tried to talk them into stitch welding light gage full length plates to the edges of the flanges to make a pair of closed sections, and make it about 20 X stiffer.