# Boundary condition at supported end of a rod

I have one end of a rod held in a hole of a 'rigid' part with no clearance, while the other end is loaded with a force. I have shown 3 simple reaction-force models in the picture.

If my intent is to get accurate stresses near point 'A' using FEA, which reaction model is adequate? I would also like to know how other engineers model such problems.

flickr.com/photos/193257915@N03/51252829861/

• If you really want "accurate" stresses, you need to model the "rigid" part, figure out the exact tolerances and interference fits in the "no clearance" joint, and then do a nonlinear analysis including contact and friction forces and probably local plastic deformation as well. But doing all that is rather pointless, because the answer will be very sensitive to the assumption you make, and have no real-world significance - unless you are trying to prove that a bad design will actually "sort of work without breaking," instead of fixing the design problem. Jun 17 at 19:21

None of the three would occur if the material of the element holding the rod is "rigid", or is much stiffer than the rod. For such cases, my assessment is as shown below.

For the case that the rod is much stiffer than the element holding it, the stress distribution is based on the flexibility of the rod.

You can verify the result using a model with spring support.

Example of rock sucket pile subjects to lateral load:

• If the OP is doing a FE analysis, there is no need to try to invent a "spring support" model. Just model the "rigid" block with its real shape and material properties. (But read my other comment as well...) Jun 17 at 19:24
• @alephzero Depends on the type of program available to him. The OP will have difficulty in modeling the clamped support with a general purpose FEM program without using the compression-only springs to represent the support elements. If his program is capable of analyzing solid elements and contact pressure, then, yes, there is no need for the model with springs.
– r13
Jun 17 at 20:51

First, I'd like to point out that your question seems a bit off - IMHO.

In most FEA packages you'd set the boundary conditions (ie. how the nodes are allowed to translate/rotate and the forces) and then solve for the displacement/internal reactions. What I'm trying to say, is that your question would make sense, if you were trying to build a new solver for a specific type of problem.

That aside, the way you specified the problem, there is no one-correct answer here. For example, the following reaction model would be more appropriate if there were a slight clearance and the rod had infinite stiffness (i.e. it would rotate not bend):

The following reaction model would be more appropriate if you had the rod inside a wall that was not rigid (i.e. if the wall was allowed to deform).

The third option (at least IMHO) is the most unrealistic (I can't really think of a case where it would be really appropriate).

The devil is in the detail. It depends on the relative stiffness of the rod versus that of the support.

If Young's modulus of elasticity of the rod is just a bit smaller than the support the rod moment will deform the support as it also deforms by the reaction of the support.

If the support material is much stiffer than the rod it will cause a concentration of stress both on the rod and the hole near the surface of the wall and some crushing of the rod and a small ring around this entry point on the wall will tilt out on top and in on the bottom to accommodate the rotation of the rod.

Try and imagine sticking a rubber pencil into a tight hole in hard playdough and bending it.

If the support material is stiff enough you could add a nominal say D/4 to the length of the rod L and consider the connection's moment fix end moment with D being the diameter of the rod.

If the support is very much stiffer than the rod the rod will deform and by deforming exert all manners of stresses to the wall. eg, it could create radial stresses on the support while crushing on its longitudinal axis attempting to become fatter and shorter in the hole.