Follow up on Torsional Constant J

[Ussuri]

There was a previous thread (thread679-137188) which discussed the calculation of the torsional constant J.

The response indicated it was the summation of 0.333bt^3 for the section.

I have a 400mm deep 200mm wide all 12.5mm plate 'U' shaped section which is subjected to torsion (unfortunately it cannot be avoided) so I need to calculate J.

I used the approach given in the thread, which is how it is explained in Blodgetts Design of Welded Structures. But I get a value of J=5.28x10^8 mm^4. The tabulated value for a closed box section 2.34x10^8 mm^4 so my calculation is obviously wrong as there is no way my open section is better than an equivalent box.

It seems to me that the value of J calculated using the Blodgett approach is dependent on whether you look at the major or minor axis, thus giving two values. Which to me doesn't feel correct as for an applied torsion the major and minor axis is irrelevant because of the polar second moment of area.

Any comments, what am I missing here?

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[GregLocock]

Calculation of torsional constants is fairly non intuitive, for open re-entrant sections made of plates.

I haven't got a value for U channel, but for an I section that is roughly equivalent I get 672e3, which does not seem unreasonable. Typically J for open channels is ~1% of that for similar box sections.

However, using Polyakov's spreadsheet off the internet I get a touch less than 3e8, which is frankly unbelievable.



Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[WillisV]

For a channel the correct way to calculate J, as with all open plate sections, is a summation of (1/3)bt^3 for each linear piece of the section. So for your shape which I believe I am interpreting to have two 400mmx12.5mm sides and one 200mmx12.5mm side the J value would be 1/3*2*400mm*12.5mm^3 + 1/3*200mm*12.5mm^3 = 651,042mm.

 

[Ussuri]

That would be where I was going wrong then.

I was looking at 'b' and 't' in a global sense. So for the 400mm side sections b=12.5mm and t=400mm. When I should have been using t=12.5mm regardless of orientation.

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