Series or Parallel Springs? | Homework Help

[zorostang]

Homework Statement

All springs are the same. There's a horizontal Bar. 1 spring is attached to the top of the bar on the left most side. Then a distance "a" from that is a 2nd spring attached to the bottom of the bar. Then the same distance "a" from that is a 3rd spring attached to the top of the bar. A force P is applied down a distance "a" from the 3rd spring. Is this a series or parallel system?

Homework Equations

The Attempt at a Solution

Even though all springs are attached to the bar, won't their displacements be different because they are different distances from P? And so the springs are in series. is this correct? Thanks for any help.

 

[tiny-tim]

Welcome to PF!

All springs are the same. There's a horizontal Bar. 1 spring is attached to the top of the bar on the left most side. Then a distance "a" from that is a 2nd spring attached to the bottom of the bar. Then the same distance "a" from that is a 3rd spring attached to the top of the bar. A force P is applied down a distance "a" from the 3rd spring. Is this a series or parallel system?
…
Even though all springs are attached to the bar, won't their displacements be different because they are different distances from P? And so the springs are in series. is this correct? Thanks for any help.

Hi zorostang! Welcome to PF!

Well, the 1st and 3rd springs look parallel to me …

if this was an electric circuit, you'd say they were parallel, wouldn't you.

 

[Rake-MC]

Yes, springs 1 and 3 are in parallel, however if you give them a single equivalent spring constant and call them spring A. Then spring A and spring 2 are in series.

 

[zorostang]

Ok thanks! I used that to help me solve the part b of the homework problem, which was to find the vertical displacement of the point where the force P was acting. But now I've stumbled onto one more problem. Maybe I should repost the entire problem, but I'll just do it briefly here first.

Springs 1 and 3 are hinge supported on the rigid bar and are hinge supported to an upper wall a distance L from the bar. Spring 2 has a fixed connection at the bar and is hinge supported on a lower wall a distance L from the bar.

I want to find the forces in the springs. I am given the force P and the distance L. I've also solved for the spring constant k. I believe what I have here is a statically indeterminate structure so I need to find an equation of compatibility. So my solution is to find the displacements at the points where the springs are connected.

The question is, How will the bar rotate? Will it stay fixed at spring 1, rotate about spring 2 or 3, or could it rotate about its center?

Or is it even going to rotate, could it just go straight down? I'm assuming no to that because the problem said to ignore horizontal displacement, but how am I supposed to know for sure?

 

[Rake-MC]

Well if there is rotation, it's going to screw up a colossal amount of assumption we've made.
Are they linear springs ie f = -kx
We need more information. If all you know is f = -kx, then you can't solve it with rotation.

 

[tiny-tim]

Springs 1 and 3 are hinge supported on the rigid bar and are hinge supported to an upper wall a distance L from the bar. Spring 2 has a fixed connection at the bar and is hinge supported on a lower wall a distance L from the bar.

Hi zorostang!

I'm confused …

is this like a window with no glass in …

so that the bar is where the glass would be, with two springs attached to the top of the window-frame, and one to the bottom of the window-frame …

and what do you mean by hinge supported?

can the bar rotate only vertically (staying in the window), or can it rotate horizontally also?

 

[zorostang]

Yeah sorry, I guess this is a little confusing. The Springs are actually flexible bars. And I've been given their modulus of elasticity. Here's an image of the problem.

So I solved part b by taking the the parallel spring equivalent of of the first and 3rd springs and then the series equivalent of that and the bottom spring. I did P/(k equivalent) = displacement of d = .045in.

I hope my question makes more sense now that you see the picture. I think there is some small rotation but it's effects are negligible when finding spring equivalence? But I do need to know how to relate the displacements of each point with each other to get a 3rd equation. Right now I have 3 unknowns and 2 equations (Sum of the Moments and sum of the forces).