Calculating Loads in Two Co-Axial Helical Springs

  • Thread starter Alwightmush
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In summary, the problem involves two helical springs with the same initial length, made from the same wire and with the same number of coils, being compressed by a force of 450 N between two parallel plates. The mean coil diameters of the outer and inner springs are 100 mm and 75 mm respectively. To determine the load in each spring, you can use the formula for the spring constant, where G, d, and n are the same for both springs and the ratios of D are known. Solving simultaneously will give you the load in each spring as 316 N and 134 N. However, finding the correct formula may be a challenge and further assistance may be needed.
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Alwightmush
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Homework Statement


2. Two helical springs of the same initial length are made from the same circular section wire and have the same number of coils. They are assembled co-axially and are compressed between two parallel plates by a force of 450 N. The mean coil diameters of the outer and inner springs are 100 mm and 75 mm respectively. Determine the load in each spring.
(Answer: 316 N, 134 N)

Homework Equations


F = (Τ x Pi x d^3) / (8 x D) ?

3. Own working
I tried using the figures in the above equation to calculate values for the Shear Stress T but wasn't sure how to separate the loads into a part for each spring.

Question as above, answers as well, but I can't figure out how to calculate them as I don't have the correct formula I presume.

Any help would be much appreciated, exam tomorrow looms. :(
 
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  • #2
how about using the formula for the spring constant (the shear stresses will be different in each spring, so you're adding a variable) ie.
k = (G*d^4)/(8*D^3*n)
you know that G,d and n are the same for each and you know the ratios of D.
You should then get to something like:
(0.75^3)F1 + F1 = 450N
and F1 + F2 = 450N
solving simulatneously should get you the answers specified.
 

1. How do I calculate the load in two co-axial helical springs?

The load in two co-axial helical springs can be calculated using the formula F = k(x1 - x2), where F is the load, k is the spring constant, and x1 and x2 are the deflections of the two springs.

2. What is the spring constant and how do I determine it?

The spring constant, denoted by k, is a measure of the stiffness of a spring. It can be determined experimentally by measuring the force required to extend or compress the spring by a certain distance.

3. Can I use the same formula for calculating the load in all types of co-axial helical springs?

Yes, the formula F = k(x1 - x2) is valid for all types of co-axial helical springs, as long as the springs are identical in terms of their dimensions and material.

4. What factors can affect the load in two co-axial helical springs?

The load in two co-axial helical springs can be affected by factors such as the material and dimensions of the springs, the number of active coils, the initial tension in the springs, and the direction and magnitude of the applied load.

5. How do I ensure the accuracy of my calculations for the load in two co-axial helical springs?

To ensure the accuracy of your calculations, it is important to use accurate measurements for the dimensions and material properties of the springs, as well as the applied load. Additionally, it is recommended to double check your calculations and consider any potential factors that may affect the load in the springs.

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