Talk:Torsion (mechanics)

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can anybody tell me what "torsional stiffness of 12MNm/rad" really means?

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It means that in order to twist it one radian (angle measurment) you need to apply a torque of 12MNm (millions of newton-meters).

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I consider the wikipedia article useful for its links to related articles despite the article content being brief. Wikionary does not serve this purpose. Rtdrury 02:13, 5 December 2005 (UTC)

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Can someone knowledgeable on the subject confirm that the first formula is correct in using I (moment of inertia) instead of J (polar moment of inertia)? Moment of inertia is dependent of density, and it seems unreasonable that density should enter into this formula (density should not affect stress) --Avl 20:01, 30 July 2006 (UTC)

You are correct that density has no direct effect on stress, the polar moment of inertia used in this case is that of the cross-sectional area, not the mass. The equations given for calculating the stress and the polar moment of inertia in the text are completely correct. 74.60.57.253 (talk) 01:45, 1 August 2009 (UTC)

Also, when I think about it, isn't the sentence "a solid material (e.g. Steel)" highly suspect? Do these formulas not work on Styrofoam? Later in the same text, there seems to be a confusion of object shape and material. "tube" is not a material - a tube can be made of different materials, including steel.--Avl 20:21, 30 July 2006 (UTC)

I think a more appropriate description for the valid shapes would be bars of circular cross-section (either solid or hollow). As for materials the only limitations are that they are linearly elastic and obey Hook's Law. 74.60.57.253 (talk) 01:45, 1 August 2009 (UTC)

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I don't think this artical is factually correct. I have been given notes in which the exact same problem as the article discribes ( a hollow shaft). In my notes the polar moment of inertia is calculates as being over 32 rather than over 2. I don't think my professer of over 20 years experence is likly to have got this wrong and so it makes me wonder whether it is this article. This also appears to be supported by the article on polar momment of inertia which has a formula using 32 rather than 2.

You will find the rather crucial detail is that your prof, and whoever wrote the page, pays attention to details. Your prof used D, this page uses r. You may remember from school that D=2r hence D^4=16*r^4 hence D^4=32/2*r^4 Greglocock 02:15, 29 April 2007 (UTC)

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Two questions about how the article presents using the polar moment of inertia (J):

J is the torsional constant for the section . It is identical to the polar moment of inertia for a round shaft or concentric tube only.

Is J not equivalent to the polar moment of inertia for non-round cross sections? Other basic cross-sections will have their own analytical equation to determine this quantity, but wouldn't the appropriate polar moment of inertia be correct in the case of a square cross-section?

No, J is not generally equal to the polar moment of inertia. eg for a square section see http://www.civl.port.ac.uk/britishsteel/media/SP%20and%20MC/Notes%20to%20section%20property%20tables.html

Alternatively, a very simple example is a thin wall section tube. That has a given J and polar moment of inertia. Now slit the tube along its length. It has the same polar moment of inertia, but J will be ~1% of the original tube. Greglocock 06:43, 9 September 2007 (UTC)

For other shapes J must be determined by other means. For solid shafts the membrane analogy is useful, and for thin walled tubes of arbitrary shape the shear flow approximation is fairly good, if the section is not re-entrant. For thick walled tubes of arbitrary shape there is no simple solution, FEA may be the best method.

Is FEA the proper tool to determine J for arbitrary cross-sections?

Yes Greglocock 02:56, 8 September 2007 (UTC)

FEA could be used to determine stresses and deformations, but I think this statement should read "For other arbitrary shapes, J may be determined through numerical means." Jim Lipsey 17:53, 7 September 2007 (UTC)

OK, but FEA is the normal method these days for complex sections. Greglocock 02:56, 8 September 2007 (UTC)

Shear stress formula modification

Would you agree to change the main formula for shear stress from ${\displaystyle \tau _{\varphi _{z}}={Tr \over J_{\text{T}}}}$ to it as a function of radius of the cross section of the shaft like: ${\displaystyle \tau (r)_{\varphi _{z}}={T\cdot r \over J_{\text{T}}}}$. Because it can be confusing to just write it as: "the shear stress at a point." 93.136.172.101 (talk) 19:10, 18 August 2024 (UTC)

and than maybe add

${\displaystyle \tau (r)_{\varphi _{z}}={T \over J_{\text{T}}}}{\frac {d}{2}}={\frac {T}{W_{p}}}$