Stiffness Equation for Spring Dimensions: How is it Derived?

  • Thread starter ajd-brown
  • Start date
  • Tags
    Derivation
In summary, the equation attached is for the stiffness of a spring in terms of its dimensions, specifically the shear constant, wire diameter, coil average diameter, and number of active coils. The conversation involves someone asking for help in deriving this equation for a university project. Several resources are suggested, including a mechanics of materials text and a post on deriving the shear modulus from the spring constant. The person expresses their enthusiasm for learning and gratitude for the helpful response.
  • #1
ajd-brown
30
0
Equation attached.

For those who can't see the image here it is in text form, k=(Gd^4)/(8D^3 n )

It is the equation for the stiffness of a spring in terms of its dimensions:

G - shear constant
d - wire diameter
D - coil average diameter
n - number of active coils (total coils -2 as the top and bottom coils are not considered active)

I would like to know how to derive this equation as it is a big chunk of my project,

I am doing this as part of a university project, and your derivation will be duly noted/referenced.

Thanks in advance!

Anthony
 

Attachments

  • spring constant.png
    spring constant.png
    561 bytes · Views: 691
Physics news on Phys.org
  • #2
Since you are at university, why can you not look this up for yourself in a mechanics of materials text in the library?

For instance page 82 - 83 of

Singer

Strength of Materials

or

Hearn

Mechanics of Materials p299 to 301
 
  • #3
I'll do that now, thank you for the book!
 
  • #5
yeah! i found that post very helpful for understanding the concept, jheez, i love this stuff, i wish i could have the time in the day to learn it all, along with everything else i want to do :( anyway! thank you very much! best first post ever i think!
 

1. How was this equation derived?

The equation was derived through a logical and systematic process of applying mathematical principles and theories to solve a specific problem or to describe a phenomenon.

2. What are the assumptions made in the derivation of this equation?

The assumptions made in the derivation of an equation depend on the specific problem being solved. However, they are usually based on simplifying assumptions and approximations in order to make the problem more manageable.

3. Are there alternative ways to derive this equation?

Yes, there can be multiple ways to derive an equation depending on the approach and assumptions used. Some equations may have been derived through experimental data, while others may have been derived through theoretical modeling.

4. Can this equation be applied to other situations or cases?

It depends on the validity and limitations of the assumptions made in the derivation of the equation. If the assumptions hold true for a different situation, then the equation can be applied. However, if the assumptions do not hold, the equation may need to be modified or a new one derived.

5. How can I understand the steps of the derivation process?

The best way to understand the derivation process is to have a strong foundation in the relevant mathematical principles and theories. It also helps to have a clear understanding of the problem being solved and the assumptions being made. Consulting with experts or studying similar derivations can also aid in understanding the steps.

Similar threads

Replies
1
Views
7K
  • Mechanical Engineering
Replies
1
Views
563
  • General Engineering
Replies
15
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
939
Replies
3
Views
641
Replies
2
Views
3K
Replies
6
Views
954
  • Introductory Physics Homework Help
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
881
Back
Top