Being based on beam elements, I expect Caesar is not the best program for this application, but it is the tool I have available.

Here's the scenario - I am trying to make a recommendation for some field routed tubing that is going to have to be flexible enough for a large displacement between the end points. Using the tubing vendor's minimum bend radius recommendation, I am trying to figure out how many coils of tubing will be required to absorb the deflection. I have made a model that essentially looks like a spring coil with a continuous series of bends with offsets that give a 2" pitch between coils. I have model each end with a 2.1 SIF as I know there will be socket weld fittings near the tubing connections that will likely be the limiting factors on stress.

At one end of the coil there is a full anchor and at the other end I have input a lateral displacement that is parallel to a line runing down the middle of the "spring".

So, essentially, all of the piping (tubing, actually) is perpendicular to the line of displacement and should participate in providing flexibility.

Now, when I model two complete coils, the stresses are pretty low. However, if I model a straight section tangentially out from the end of the last coil, the stresses start going up at the end of the straight portion (where the SIF is applied). The really nasty part is that the longer I make it, the higher the stress goes.

What I can see from the displacements is that, as the straight section gets longer, the displacement shifts from the coil to the straight leg. That much makes perfect sense. What doesn't make sense is that the shift seems to be putting so much displacement into the straight section that it overstresses the end point.

So, what I'm having trouble resolving is, how/why is this happening? And, am I really getting any kind of valid information trying to run a model like this in a program like Caesar?

You can calcuate your "coil spring" stiffness. I found the equations at www.eFunda.com. If needed, you can adjust your CAESAR II model by defining your own K-factor for each "bend".

I can see how the longer straight run can increase the bending moment but only up to the point where the beam becomes more flexible than the coil. With a stiff beam, the longer, effective "moment arm" will drive the moment higher. But as it gets longer, eventually the flexibility willl take over and the moment will drop.

Will your stress drop if you make your straight run even longer?

I found that, up to about four feet from the tangent point to the end of the straight run, the stress at the anchor would continue to increase. Longer than that, and the stress comes back down.

I remember a few years back wondering about the moment arm vs. flexibility question from increasing a cantilever, but keeping a constant deflection at the end. I found that the increased flexibility due to the longer length reduced the force more than the longer length increased the moment arm and, as such, the moments ended up decreasing.

I believe the maximum bending moment in the beam is equal to one half the imposed deflection times the length of the beam times the fraction (Kcoil times Kbeam)/(Kcoil plus Kbeam). Kbeam varies by 1/length cubed. For stiff beams (in relation to the coil stiffness) the length in the numerator controls. As the beam gets longer, the cubed term kicks in and the denominator takes over. The point where this change occurs depends on the stiffness of the coil.