Length change of rod under torsion force

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Discussion Overview

The discussion focuses on the change in length of a cylindrical rod under torsional force, specifically examining the effects of such forces on elongation and deformation. Participants explore theoretical frameworks, numerical methods, and empirical observations related to the topic.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant seeks formulas and data sheets for calculating the change in length of a steel cylinder under torsional force, suggesting Saint-Venant's theory as a starting point.
  • Another participant shares FEM results indicating that the cylinder experiences a slight elongation on average, with a reduction in length at the circumference, and questions the validity of these results.
  • A third participant states that classic linear elasticity theory suggests no elongation occurs under torsional load, implying that the FEM results may indicate negligible elongation.
  • Further discussion includes the consideration of second-order effects, with one participant noting that the shape of the cross-section can influence whether the rod elongates or shortens when twisted.
  • Reference is made to Roark's work, which mentions that a solid circular cylinder tends to lengthen under twist, although the longitudinal deformation and stress may not be significant in practical engineering terms.
  • One participant inquires about the application of torsion and boundary conditions to the rod, seeking clarification on the setup used in the FEM analysis.
  • A participant describes their method of applying torsion force symmetrically across internal boundaries at one end of the rod, with the other end fixed, and all other boundaries remaining free.

Areas of Agreement / Disagreement

Participants express differing views on the elongation of the rod under torsional load, with some asserting that classic theory predicts no elongation while others provide empirical results suggesting otherwise. The discussion remains unresolved regarding the exact nature and significance of the elongation.

Contextual Notes

Participants note limitations in existing theories and seek approximate formulas for elongation, indicating that current understanding may depend on specific conditions and assumptions related to the material and geometry of the rod.

kernel2705
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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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