A complex spring's structural analysis

[EN1986]

TL;DR

Hello, I am trying to figure out what is the force in each spring in the structure after the external force is exerted in its specific location (not in the edges).
I would like to know how can I solve this problem methodically - starting with understanding which springs are serially connected or in parallel given the external force location. Pay attention that we have 4 springs in the left branch and one spring in the right branch.

Hello, I am trying to figure out what is the force in each spring in the structure after the external force is exerted in its specific location (not in the edges).
I would like to know how can I solve this problem methodically - starting with understanding which springs are serially connected or in parallel given the external force location. Pay attention that we have 4 springs in the left branch and one spring in the right branch.

 

[anuttarasammyak]

For my interest what Pet stands for and what role does it play ？

 

[Lnewqban]

Welcome!
I am afraid that would need to provide much more information about this problem.
Is the horizontal distance between the points of application of the forces and the bolt irrelevant?
Are springs a-b-c-d and Kb under similar load?
Are springs a and d under any compression load?

 

[EN1986]

For my interest what Pet stands for and what role does it play ？

This is taken from the article attached below, and it means the external load that a bolted joint is subjected to. This load tries to separate the bolted members.
Link: https://www.google.com/url?sa=t&sou...wQFnoECA8QAQ&usg=AOvVaw1F5L5XXZEp7rwUlHr0Z9OJ

Welcome!
I am afraid that would need to provide much more information about this problem.
Is the horizontal distance between the points of application of the forces and the bolt irrelevant?
Are springs a-b-c-d and Kb under similar load?
Are springs a and d under any compression load?

I think the horizontal distance doesn't matter.
I think Springs a-b-c-d and kb aren't equally loaded, and this is basically the asked question - how to solve this problem and what are the correct assumptions.
Springs a,b,c,d are initially (before Pet is exerted) in a compression state and kb is initially in an extension state.

 

[jrmichler]

The paper linked in Post #4 is a good discussion of bolted joints for a person with a background in the subject. It's not so good to learn about bolted joints. Search terms theory of bolted joints found this good hit: https://www.boltscience.com/pages/basics1.htm. The Wikipedia article at https://en.wikipedia.org/wiki/Bolted_joint is a good overview, but not as good an introduction as the boltscience article. There are many other good hits, but I suggest seriously studying the boltscience article before looking at them.

 

[EN1986]

Ok, thanks.
But still, the simplified problem of springs and external force should be a general problem of mechanics. Does anyone know how to solve it?

 

[tech99]

I think my own method here is to work with an electrical analogy. (Of course, it is only my familiarity with electricity which makes me do that, because the equations are equivalent). An analogue of compliance is capacitance. So you can draw a network of six capacitors having values equal to the compliances. As far as I can see, a b c and d are equal, provided there is sufficient pre-tension to avoid separation. In this network, b and c are in series and form one arm. Kb in series with a and d form another arm. You can re-draw your network to make it easier to see this configuration of two arms. Then these two arms are in parallel. So you can work out the total capacitance and that gives you the total compliance. To find capacitances in parallel they are simply added; to find capacitances in series, they behave like parallel resistors, so 1/Ct = 1/C1 +1/C2 +1/C3 etc. I have refrained from working out the total answer. Once you know the total compliance, the extension under the force Pet can be found.
I assume that bending moments are not involved, so in practice the forces must be applied very close to and symmetrically around the bolt.

 

[EN1986]

I think my own method here is to work with an electrical analogy. (Of course, it is only my familiarity with electricity which makes me do that, because the equations are equivalent). An analogue of compliance is capacitance. So you can draw a network of six capacitors having values equal to the compliances. As far as I can see, a b c and d are equal, provided there is sufficient pre-tension to avoid separation. In this network, b and c are in series and form one arm. Kb in series with a and d form another arm. You can re-draw your network to make it easier to see this configuration of two arms. Then these two arms are in parallel. So you can work out the total capacitance and that gives you the total compliance. To find capacitances in parallel they are simply added; to find capacitances in series, they behave like parallel resistors, so 1/Ct = 1/C1 +1/C2 +1/C3 etc. I have refrained from working out the total answer. Once you know the total compliance, the extension under the force Pet can be found.
I assume that bending moments are not involved, so in practice the forces must be applied very close to and symmetrically around the bolt.

Thanks!