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Spring stiffness of a helical spring

Once in a while I have to find the stiffness of a spring that I get from the local hardware shop.  I usually use a formula that can be found in some books on mechanics of materials.

But the assumptions bother me a bit because the springs that I used usually underwent large deformations and I wasn't sure whether the numbers I was using were correct or not.  

To check the formula I compared its predicted k to numbers from Abaqus simulations and found reasonably good results for many situations - but not for soft springs.

I've attached a write-up on that that contains a python script to generate the geometry.  Let me know if you find it useful.

PDF icon HelicalSpring.pdf136.54 KB
Plain text icon spring.py_.txt10.76 KB
Plain text icon springDataPlot.m.txt1.73 KB


Frank Richter's picture


Hello Biswajit,

thank you for your posting. Please note the thread

and my reply in it. A while ago I downloaded a "helical wire plugin" from an ABAQUS web server, but the zip file was empty. Maybe your file will do the same job.


------------------------------------------ Ruhr-University Bochum Germany

Thank you for the link Frank.  I've attached the python script to this post for convenience.

-- Biswajit

Amit Acharya's picture


Would wire ropes be a good idealization of soft helical springs? Both you and I know of one application from our u/g days where that stuff is really useful!

In any case, if you think that is relevant, you may want to look up the work of G. A . Costello.

- Amit

Thanks for the pointer to Costello, Amit.  

Computing the deformation of wire ropes, particularly in compression, can get quite messy.  My question would be the opposite of yours, i.e., can we go from  helical spring -> wire rope additively ? Costello says no in most situations.

Soft helical springs bend quite easily but are elastic and stable even for large deformations.  That makes them suitable for many applications.   Wire ropes probably have many advantages over single strand springs over a large range of length scales, as exemplified by hair/wool.  But few natural structures have the coiled shape of a typical hardware-store spring.  I wonder why.

-- Biswajit

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