Reaction forces and moments for cylinder with two fixed rods

[physicsdumby]

Homework Statement

A cylinder with two rods coming out of it. The ends of the rods are fixed. A force is applied through the center of the top surface of the cylinder. What are the reaction forces and moments at the rod ends?

Here is a diagram of the scenario: http://www.imgur.com/Tsdhmzf.jpg

Homework Equations

The Attempt at a Solution

I don't have exact dimensions and forces because this is a conceptual question. From what I can process, the applied force at the cylinder will cause reaction forces in the Z-direction at both rod ends. The rods will also have reaction bending moments and torsion as well? Summing moments forces and moments about one of the rod ends gave me 3 equations with 4 unknowns. Is this a statically indeterminate problem?

 

[haruspex]

Suppose there were only one rod. Could the system be stable (theoretically)?

 

[physicsdumby]

Suppose there were only one rod. Could the system be stable (theoretically)?

With just one rod, the vertical reaction force at the rod end will be equal (and opposite) to the applied force. The bending moment will be equivalent to the moment arm (distance from center of cylinder to rod end) times the applied force. No torsion in this case.

 

[haruspex]

With just one rod, the vertical reaction force at the rod end will be equal (and opposite) to the applied force. The bending moment will be equivalent to the moment arm (distance from center of cylinder to rod end) times the applied force. No torsion in this case.

Sure, but could it be stable?
If so, the other rod is redundant. This means it is impossible to tell how the load is distributed between them without considering how the rods deform.
A simple assumption would be that the rods behave identically, so symmetry is preserved. For small deformations, there will be no torsion. Greater deformations will involve some complicated geometry.

 

[physicsdumby]

Sure, but could it be stable?
If so, the other rod is redundant. This means it is impossible to tell how the load is distributed between them without considering how the rods deform.
A simple assumption would be that the rods behave identically, so symmetry is preserved. For small deformations, there will be no torsion. Greater deformations will involve some complicated geometry.

With a single rod, I don't see why it would be unstable. There are no lateral forces applied. Unless, of course, I'm overlooking something.

Under the simple assumption and thus acting in symmetry, each rod will have half of the applied force as its reaction force. I don't have a pen and paper right now but I assume setting the reaction bending moments of each rod equal to each other will give me a complete solution..