Reaction Loads for Beam with 3 Supports

aero_guy

Hi All,

I have been trying to figure this problem out for a little while, and I would like to seek the input of the bright people on this forum.

I have a vertical gantry design that has 3 linear bearings on each of the two vertical rails as shown in the attached image. The gantry is subjected to lateral load near the end. This system is like a beam with 3 supports, and a cantilever.

My objective is just to get the reaction loads acting on the linear bearings, due to the lateral load.

I modeled the gantry as a rectangular plate, since I am not interested in stressing the actual design. Then I tried 2 different approaches for the constraints:

First Approach: I constrained 6 nodes (representing each linear bearing) in the direction perpendicular to the guide rails. The resulting reaction loads were such that the lower two pairs of bearings reacted the moment, and the upper set did nothing really. See attached liml file with "rigid constraints".

Second Approach: I supported the gantry with spring elements. At lower spring constants, the resulting reactions are such that the upper and lower pairs react the moment, while the middle set does very little. The more stiff I make the springs, the more the solution approaches the rigid constraint results of Approach 1. See attached liml file with "spring supports".

So my question is, which approach seems more logical?

My thoughts are:

- The supports should be pretty rigid, because the gantry design has very stiff side plates.
- I would however expect (or want) the extreme sets of bearings to take the load since they have greater separation, resulting in lower magnitudes.
- If the results for rigid constraints model are more correct, then would it make sense to just remove the middle set of bearings from the design? The reaction forces would be reduced.

Thanks in advance to all that have input.

Victor

Since this is a statically indeterminate support, the elasticity of the parts is important. By using spring constraints, you're substituting the stiffness of the gantry and its rails with those springs. That might be OK if you have a way to find what their stiffness should be, but by the time you've done that, you might as well model the whole thing anyway.

So I think you need a more accurate model of all the parts whose elasticity is relevant, and use rigid constraints or perhaps contact for the bearings.

If you don't want to do all that, then perhaps it's enough to find the worst case, such as all the load being carried by two adjacent bearings?

aero_guy

Victor,

Thank you for your valuable input. I'm glad to have the second opinion.