Spring and its shear, torsion, tensile stresses...

[fog37]

TL;DR Summary

Spring and its shear, torsion, tensile stresses...

Hello Forum,

After watching a video on how some insects can achieve amazing accelerations (hundreds of gs) by using their bodies like springs (instead of just using muscle generated forces to propel themselves), I started thinking about springs again and wanted to check some concepts and intuition with you.

Let's consider a simple linear spring of larger diameter $D$ and smaller wire diameter $d$. By pulling the string's end, we apply a longitudinal tensile force ##F# which elongates the string (see figure below).
As a simplistic reminder, stress=force, strain=deformation, torsion stress is about changing the cross-sections mutual's angles, shear stress is about shifting the cross-sections of a beam/wire/member parallel to each other.

The figure below shows the spring being pulled and completely untwisted (which means that it means that it originally was in a twisted state). And to untwist something, a torsional stress must be applied!

View attachment 336565

This also means that the longitudinal force $F$ elongates the spring by causing the wire to (un)twist, i.e. there is a torsional stress that does that. The torsional stress, implicitly, causes a shear stress which is is internal to the wire and not directly visible (we can have shear without torsion). In very raw terms, the force $F$ gets "translated" into twist and shear stresses.

Is my understanding correct?

How is a spring made? A spring is created by first turning the wire into a coiled shape and freezing it into that shape (prestressing process) so that is permanently stays in that shape (same ideas a prestressed concrete). What is the benefit of a spring? Obviously, springs compress/stretch linearly storing and releasing potential energy...We would not be able to do that with a simple straight piece of wire not into the shape of spring. The clever shaping of a wire and freezing it into that stressed condition (like when we cure an epoxy by analogy) allows us to use the fact that is can be reversed in shape (compressed/decompressed) to store energy.

Thank YOU!

 

[jrmichler]

A coil spring can be made by winding wire on a mandrel. The wire is bent far enough that it plastically deforms, and then stays bent, although with some springback. The spring in the photo below was made that way:

This particular spring was my first attempt at making a replacement spring for a mechanical seal in a trash pump. High speed production spring making machines use a slightly different method, but the results are the same. Straight wire is bent into the spring shape. Small springs are bent cold, while very large springs may be made by hot bending and heat treating.

The primary stress state from using a helical spring in its elastic range is torsion. The best source to learn about spring design and stresses is the SMI Handbook of Spring Design: https://smihq.org/store/viewproduct.aspx?id=8525988. This book is 100 pages of spring goodness, and is highly readable. Strongly recommended.

And it you REALLY want to understand stresses and energy storage in springs, the book is Mechanical Springs by A.M. Wahl: https://smihq.org/store/viewproduct.aspx?id=8088306. This book is not available from Amazon.