Length change of rod under torsion force

AI Thread Summary
The discussion centers on calculating the change in length of a steel cylinder under torsional force, specifically with a fixed end and a torque of 450 Nm. While classical linear elasticity theory suggests that elongation under torsion is zero, the user’s FEM analysis indicates a negligible elongation, with the cylinder's circumference experiencing a slight shortening. The conversation highlights the complexity of torsional effects, noting that a circular cross-section can lead to elongation, albeit minimal. Participants reference Roark's work and Poynting's experiments, which support the idea of longitudinal strain in twisted circular cylinders. The need for an approximate formula to quantify this elongation remains a key point of inquiry.
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Hi I want to calculate the change in length of a cylinder under torsional force. (e. g. material = steel, initial length 1500 mm, diameter 25 mm, one end fixed, other end 450 Nm).

Can anyone point me to the proper formulae (Saint-Venant??) or data sheets.

Thanks
 
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I calculated the problem with FEM. The result was the zylinder gets (in average) longer by a fraction of a micrometer, at the circumference (approx. outer 10%) it gets shorter by about 10 % of the maximum elongation. The elongation profile of the cross section looks like an inverse parabola.
Do you agree with this result?
Is there an approximation formula for this problem (elongation as a function of zylinder length, radius, torque, elastic modulus)?
Regards
 
In classic linear elasticity theory, the elongation of a cylinder under torsional load is zero. Your FEM results suggest that the actual elongation, if nonzero, is negligible.
 
Hi yes I know that according to Saint-Venant it is zero. But if you include 2nd order effects it isn't zero. From what I read depending on the shape of the cross section of the rod the rod can become shorter or longer when twisted. I also read that if the cross section is a circle (if the rod is a cylinder) it will elongate. But I cannot find a formula which would allow me to calculate the elongation - if only approximately - in numbers.
I am sure some mechanical engineering handbook will contain something about this problem.
Regards
 
Roark says that:
Chapter 10: Torsion said:
In addition to these deformations and stresses, there is some longitudinal strain and stress. A solid circular cylinder wants to lengthen under twist, as shown experimentally by Poynting. In any event, for elastic loading of metallic circular bars, neither longitudinal deformation nor stress is likely to be large enough to have engineering significance.
Poynting, J.H.: Proc. R. Soc. Lond., Ser. A,vol 32, 1909; and vol 36, 1912

He gives a semi-way to get longitudinal stress in a narrow rectangle, but the term vanishes for a circular cross section.
 
How are you applying the torsion and fixed boundary conditions to the rod?
 
Hi Minger thanks for that nice quote, I am now quite confident that the result is true.

@Mech Engineer:
I applied the torsion force averaged to (6) symmetrically spread out internal boundaries of about 1 cm^2 each at one end of the rod, the other end of the rod is fixed (i.e. circular boundary area fixed), all other boundaries are free.
Regards
 
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