Length change of rod under torsion force

In summary, the cylinder gets longer by a small fraction of a micrometer at the circumference (approx. outer 10%). The elongation profile of the cross section looks like an inverse parabola. Roark thinks that this negligible elongation is not of significance.
  • #1
kernel2705
4
0
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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  • #2
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
 
  • #3
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.
 
  • #4
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
 
  • #5
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.
 
  • #6
How are you applying the torsion and fixed boundary conditions to the rod?
 
  • #7
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
 
Last edited:

Related to Length change of rod under torsion force

1. How does torsion force affect the length of a rod?

Torsion force causes a rod to twist, which results in a change in its length. This change is known as the length change of a rod under torsion force.

2. What factors can affect the length change of a rod under torsion force?

The length change of a rod under torsion force can be affected by various factors such as the type of material the rod is made of, the magnitude of the torsion force applied, and the length and diameter of the rod.

3. Is there a formula to calculate the length change of a rod under torsion force?

Yes, the formula for calculating the length change of a rod under torsion force is: ΔL = TL/GJ, where ΔL is the change in length, T is the torsion force applied, L is the length of the rod, G is the shear modulus of the material, and J is the polar moment of inertia of the rod.

4. How does the shape of a rod affect its length change under torsion force?

The shape of a rod can affect its length change under torsion force as it determines the distribution of stress and strain within the rod. A circular rod, for example, will experience a different length change compared to a rectangular rod under the same torsion force.

5. Can the length change of a rod under torsion force be reversed?

Yes, the length change of a rod under torsion force is reversible. This means that when the torsion force is removed, the rod will return to its original length. However, repeated torsion forces can cause permanent deformation in the rod, leading to a permanent change in its length.

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