A book that covers the topic of Stiffness of thin-walled rectangular tubes under torsion loadings

[silvamat]

Hello All,

I would like to know if someone can give me a good reference of a book that covers the topic of torsion of thin-walled rectangular tubes from a stiffness perspective". I have a book with the theory for non-circular hollow-sections, but that's not really much.


Thanks,
Miguel Silva,MSc.

 

[GregLocock]

I don't have them to hand but I suspect one of Timoshenkos books is a good bet.

Be very careful, if you can check with FEA as well.

Cheers

Greg Locock


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[JStephen]

Check in Roark's Formulas for Stress and Strain, and look up the references listed there.

 

[Sparweb]

Bruhn has a couple of chapters on this. Sorry, it's a terribly old book, and I doubt it will impress you, Miguel. But the aero engineers swear by it, and they are definitely concerned with thin-walled sections, of every shape, and equally concerned with their deflections, too. "Analysis and Design of Flight Vehicle Structures" by E.F. Bruhn, 1973, Jacobs Publishing.
Chapters A6 (Torsion) and A15 (Shear-flow in Closed Thin-walled sections).
Twist (radians per inch length of the member) is proportional to the torque divided by Shear Modulus and a constant. The constant is a shape factor determined by the cross-section.
Sometimes the shear stress can be estimated (if the section is simple enough) with just the enclosed area and the wall thickness.
Depending on the size and wall-thickness ratio, you may be concerned with wall buckling, and Bruhn has that, too.




STF

 

[GregLocock]

"The constant is a shape factor determined by the cross-section." Indeed, and that is the trick. Methods that have been used in the automotiv industry that I know of:

[ol 1]
[li]enclosed area to mid section *wall thickness (shear flow assumption)[/li]
[li]membrane analogy[/li]
[li]thin plates in bending (doesn't work)[/li]
[li]FEA[/li]
[li]serious maths[/li]
[li]inscribed circle[/li]
[/ol]

If you start from a thin walled rectangular box, with equal thickness sides, then that has been well analysed. However, as you introduce asymmetries, variable wall thickness, and re-entrant shapes then the task gets harder. The inscribed circle method has a long history as a back of envelope method, for complex shapes like rockers and A pillars, and tends to be conservative but I think it has little to recommend it theoretically.



Cheers

Greg Locock


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[silvamat]

Hi all,

Thanks for all the replies,

"Depending on the size and wall-thickness ratio, you may be concerned with wall buckling, and Bruhn has that, too."

Sparweb, can you point the chapters where wall buckling is analyzed for torsion and for bending, if there is??

thanks,
Miguel Silva

 

[Sparweb]

"The middle".
The subject of buckling in every imaginable condition pervades most of the book.


STF