# Torsion of a helical rod

• reterty
In summary, the conversation discusses a massless, homogeneous helical spring with infinitesimal wire diameter and length. The spring radius is denoted as R and a curvilinear section of length dl is considered. The second cross-section rotates relative to the first by an angle dφ after twisting deformation, with M representing the twisting torque, G the shear modulus, and J the torsion constant. The second end of the section is shifted along the spiral axis by a distance dz and the resulting equation is M/(GJ)=sinα/(Rcosα). However, this differs from the equation given in the cited article, and the speaker is seeking help in finding the mistake in their derivation.

#### reterty

Let us consider the massless homogeneous helical spring with the infinitesimal wire diameter d and wire length l. We denote the spring radius as R. Now we consider the curvilinear spring section of length dl. We draw radii from the spiral axis to the centers of the end cross-sections of this section. After the twisting deformation the second cross-section rotates relative to the first by angle dφ=Mdl/(GJ), where M is the twisting torque; G is the shear modulus; J is the torsion constant. At this rate second radius rotates relative to the first one by the same angle dφ and second end of the section is shifted along the axis of the spiral by a distance dz=Rdφcosα, where α is the current pitch angle of spring (helix). Then z=Mlcosα/(GJ), where l is the total rod length (we assume that this length remains constant during the torsion process). On the other hand, if the initial pitch angle (before twisting) close to zero, then z=l sinα. As a result, we have: M/(GJ)=sinα/(R cosα). This equation differs from that given in cin literature http://www.manuscriptsystem.com/Journal/articles.aspx?journalid=1108 article"Solving Geometrically Nonlinear Problem on Deformation of a Helical Spring through Variational Methods" (there is M/(GJ)=sinαcosα/R), but I can not find mistake in my derivation. Please help me with this problem

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If you are twisting a helical spring, I believe the stress in the wire is essentially simple bending, not torsion. The wire of a helical spring subjected to compression parallel to its axis is stressed in torsion.

## What is torsion of a helical rod?

Torsion of a helical rod is a type of mechanical deformation that occurs when a helical rod is twisted about its axis. This results in a torsional stress and strain on the rod.

## What factors affect the torsion of a helical rod?

The torsion of a helical rod is affected by several factors, including the material properties of the rod, the diameter and length of the rod, and the magnitude and direction of the applied torque.

## How is torsion calculated for a helical rod?

The torsion of a helical rod can be calculated using the equation T = kθ, where T is the torque applied to the rod, k is the torsion constant, and θ is the angle of twist.

## What are some practical applications of studying torsion of helical rods?

Understanding torsion of helical rods is important in various engineering and scientific fields, such as in the design and analysis of mechanical components, in the study of DNA and protein structures, and in the development of medical devices.

## How can torsion of a helical rod be prevented?

To prevent torsion of a helical rod, proper material selection and design considerations should be taken into account. Additionally, using support structures or increasing the diameter of the rod can help prevent excessive torsion.