Prismatic bar with noncircular cross section under torsion.

[quantumdude]

I'm looking either for online resources or reference to a good book. I've been trying to help someone with a homework problem in a course entitled, Elements of Mechanical Design which uses Mechanical Design of Machine Elements and Machines by Jack A. Collins. The book sucks.

The system under analysis is a cantilevered bar with square cross section under torsion. The problem is to determine all stresses (shear and normal) at various points around the fixed end (all along the edges). The book explains that the maximum shear stresses will be at the midpoints of each edge, and that there will be zero shear stress at the corners. That's all fine and dandy, but when I go to calculate the other stresses I have no guidance. The book mentions how difficult it is to develop the equations, but it never presents them!

Any ideas?

 

[Bystander]

Should be in Machinery's --- you'll probably have to "reverse engineer" the expressions since there isn't a whole lot of theory presented.

 

[quantumdude]

Should be in Machinery's ---

Is that a book? If so, who's the author?

you'll probably have to "reverse engineer" the expressions since there isn't a whole lot of theory presented.

No problem there, even a heuristic argument would help. The book I mentioned gives nada.

 

[Bystander]

Properly, Machinery's Handbook (A Reference Book for the Mechanical Engineer, Draftsman, Toolmaker and Machinist), Erik Oberg, Franklin D Jones and Holbrook L. Horton, Paul B. Schumbert, Ed., Graham Garratt, William J. Semioli, Karl h. Moltrecht, Asst. Eds., various editions, Industrial Press Inc., or

http://search.yahoo.com/search?p=ma...hoo!+Search&fr=FP-tab-web-t&toggle=1&ei=UTF-8

If you can't find it in the library, run down to the shop --- I ain't never been near no shop without a shop copy plus the staffs' personal copies. Your topic will be hiding in the strength of materials section --- tables and tables of expressions for moduli of this, that, and the other of various x-sections and shapes under this, that, and the other load conditions.

Figured you were familiar with that little green 4 1/2 x 7 x 3 inch thick book --- it just goes by "Machinery's."

 

[FredGarvin]

The book is correct in stating that the theory behind non-circular sections is quite difficult. I remember discussing them in mechanics of materials classes. As far as I know, numerical methods are needed for real results.

From Marks Standard Handbook for ME's:

"When a section is not circular, the unit stress no longer varries directly as the distance from the center. Cross sections become warped and the greatest unit stress usually occurs at a point on the perimeter of the cross section nearest the the axis of twist; thus there is no stress at the corners of square and rectangular sections. The analyses become complex for non-circular sections and the methods for solution of design problems using them most often admit only approximations.

That being said, I would HIGHLY recommend Roark's Formulas for Stress and Strain. I do not have mine in front of me right now, but that is the bible for this type of work.



Machinery's Handbook is really not going to help you on this one I think. If you'd like I can attach a section pertaining to what we are talking, but they do not discuss non-circular sections in torsion. They talk about them in bending, but not in torsion.

 

[Chronos]

Load factors are complicated. Slight changes in load direction can induce huge stresses. In structural loads, a 1x1x1/4 piece of angle iron is hugely stronger than a 3/4 inch round, even though the round has more cross sectional area. Loads transfer across surfaces, not volume.

 

[PerennialII]

The book is correct in stating that the theory behind non-circular sections is quite difficult. I remember discussing them in mechanics of materials classes. As far as I know, numerical methods are needed for real results.

Agree with this, usually it is easier to tackle these sorts of problems by introducing for example a finite element or two, and you can solve in closed form in a very much swiftier and easier way.

 

[badeacodruta]

Hello, I did my PhD Thesis on prismatic bars subjected to torsion using Optical methods.

 

[badeacodruta]

Here you can find the abstract of the thesis.

http://www.utcluj.ro/download/doctorat/Thesis_Abstract_BADEA.pdf

I hope is useful for you!