Creating a spring using only beams

[Kristopher Horn]

Attached is my ANSYS model of a spring made using cantilever beams. In playing around with with different dimensions, I noticed that the longer I made the connecting section (dirty green section) the less of a total deflection there was. Could someone explain to me why this is?

The overall goal is to be able to make this spring deflect a certain distance, but I am having a really tough time getting my math to equal my ANSYS analysis.

 

[mfb]

Where do you apply forces, which deflection do you measure?
A longer green section (to the right in the right picture?) increases the stability of this part a bit. There is a deformation which let's the green section look a bit like "U" (outer sides of U are connected to the blue area) that is part of the spring.

 

[Kristopher Horn]

Where do you apply forces, which deflection do you measure?
A longer green section (to the right in the right picture?) increases the stability of this part a bit. There is a deformation which let's the green section look a bit like "U" (outer sides of U are connected to the blue area) that is part of the spring.

The force is applied directly on the end of the middle beam ( the red section ) and the defelction is highest at the red section, but what is confusing me is that, in looking the the side view at the longest beam there looks to be a force being applied that pulls the beam down, just like a normal cantilever beam, but there also appears to be a force applied somewhere at the end that is trying to pull the beam up.

So is this why it is increasing the stability of the part?

 

[SteamKing]

The force is applied directly on the end of the middle beam ( the red section ) and the defelction is highest at the red section, but what is confusing me is that, in looking the the side view at the longest beam there looks to be a force being applied that pulls the beam down, just like a normal cantilever beam, but there also appears to be a force applied somewhere at the end that is trying to pull the beam up.

When the force is applied to the red part, that central cantilever is pushed down in response. However, there is a reaction moment which is produced by this same force which acts on the cross-piece. It is the reaction moment, I believe, which is tending to curl the cross-piece in a CCW direction when viewed from the side, making it appear that the side beams are pulling up.

 

[Kristopher Horn]

When the force is applied to the red part, that central cantilever is pushed down in response. However, there is a reaction moment which is produced by this same force which acts on the cross-piece. It is the reaction moment, I believe, which is tending to curl the cross-piece in a CCW direction when viewed from the side, making it appear that the side beams are pulling up.

Ok, that's what I was thinking as well, now how would i represent that in a FBD. Would their be a distributed load on the end of the long beam because the cross piece is rectangular and wider than it is thicker, or would it be that there is just a point force on the very end of the long beam. This is for the force due to the torque.

I tried to assume that it was just a point force, because that makes the most sense to me but I couldn't seem to make the beam bend like it is in the side view. The only other explanation I can come up with is that it should be a distributed load.

 

[SteamKing]

Ok, that's what I was thinking as well, now how would i represent that in a FBD. Would their be a distributed load on the end of the long beam because the cross piece is rectangular and wider than it is thicker, or would it be that there is just a point force on the very end of the long beam. This is for the force due to the torque.

Because of the size of the cross piece relative to the side beams, I think the reaction moment from the load applied to the center beam is not producing much deflection in the center piece itself, but instead the apparent counterclockwise rotation results from the slender side beams curling up where they are attached to the cross piece. The cross piece, by virtue of its size, is much stiffer than the center beam or the two side beams.

As to producing a FBD of this situation, this should not be too complicated depending on what you take to be included in the FBD. The center beam and its applied load can be replaced by a force and moment acting at the connection with the cross piece. In turn, this force and moment can be split and applied to the connections with the cross-piece and each side beam.

I tried to assume that it was just a point force, because that makes the most sense to me but I couldn't seem to make the beam bend like it is in the side view. The only other explanation I can come up with is that it should be a distributed load.

The type of load applied to the center beam is irrelevant w.r.t. the reaction moment on the cross piece. A moment is going to be produced for a point load or a distributed load.