# A close coiled helical spring with torque acting about longitudinal axis

Consider a close coiled helical spring which is acted upon by a torque about its longitudinal axis as shown. I'm interested in knowing the effect of this torque on the spring wire.

Here's my take: I made an imaginary cut via a plane (shown in red) to expose the cross section of the wire as below.

The upper part of the spring (unshaded) has to remain in equilibrium, hence the torque from the support (ceiling) about the longitudinal axis has to be balanced by another torque developed about the longitudinal axis. This would happen if on the cross section internal resistive forces are developed in such a way that they cancel out producing no net force but producing a net moment about the point A. This moment of the internal resistive forces developed on the c/s about A, will balance the torque T from the upper end and bring the upper part of the spring in equilibrium.

In effect of the arguments above, the spring wire should experience bending. I do know that the correct answer to this question is bending, but is my reasoning correct?

• Well, having screwed helicoils into holes, if you turn the spring in the direction of the coil it will reduce its diameter and if you turn opposite it will expand and lock into the hole... Dec 16, 2021 at 20:47

The longitudinal torque causes a pure moment in the spring the same way as you show, except the neutral axis is not at the center of the coil it is near the vertical diagonal of the section. it is closer to the inside. See the figure.

The moment will be the same along the length of the coil all the way to the top, then it will affect a torque on the top vertical stub, which has to be canceled by the support at the ceiling.

This moment on the coil will tend to unwind it or wind it depending on the direction of the torque. If the torque is in the same direction as the coil it will wind the coil tighter and make it shorter. Otherwise, it unwinds the coil and makes it wider and longer.

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• Will the neutral axis be like this (in green)? - drive.google.com/file/d/1lyPSWyLEpYuiaGrC1-pNf1JGluNkcOZ3/… Dec 17, 2021 at 8:32
• @HarshitRajput, if you mean the green line yes. but don't forget the stress distribution is not linear, is like the lower diagram on my answer. its linear for a square section. Dec 17, 2021 at 12:17
• Got you. Thanks Dec 17, 2021 at 12:48