Three Ways to Model a Bolted Joint

Structural Analysis Learning Series #6

"Which bolt model is correct?" The answer: "All of them and none of them!"

Bolted connections may well be the joint type you come across most often in machine design. So it is quite natural for an engineer new to FEA to ask this question. And to tell the truth, the answer is not always the same — because, as I mentioned in my earlier posts, your analysis model can be detailed or simplified depending on what you are examining.

To show this, I modeled the same joint in Abaqus with three different methods:

• M1 — Solid Bolt: bolt meshed as a solid body, contact defined between all mating surfaces, preload applied directly to the shank.
• M2 — MPC – Beam – MPC: bolt replaced by a beam element, connected to the hole surfaces through kinematic couplings, preload applied on the beam.
• M3 — Tie Constraint: no bolt body, no contact — the two plates are tied over the washer footprint, no preload.

First question: should I represent the preload?

The three models already separate here.

In the solid bolt model, a clear compression cone spreads into the plates. In the beam model, the preload is transferred through the couplings. In the tie model, nothing shows up — because no preload was applied. And this is not a modeling error. A tie constraint bonds the parts together, that is all.

If your problem involves clamping force, joint separation, slip or bolt fatigue, the decision is already made at this step.

Second question: how do global stiffness and dynamic behavior change?

Modal analysis of the first two bending modes showed roughly a 3–4% difference in the natural frequencies (Mode 1: 129–133 Hz, Mode 2: 710–739 Hz). In terms of global dynamic behavior, all three models essentially answer the same question. The simplest one is often enough.

If the natural frequencies and mode shapes of a system matter to you, and you are not looking at structural strength, stress concentrations or fatigue life, you can tie the bolted connections and move on. In fact, in Abaqus CAE you can do this quickly with the fastener command, by defining only the bolt locations and the radius of influence.

Third question: in a static analysis, how do local nonlinear effects influence the global behavior?

In this step I applied a high torsional moment to the models, so that we could see the contact separation between the plates and the effect of plastic deformation in the material.

The moment–rotation curves sit almost on top of each other — same initial stiffness, same plateau. Global stiffness hardly depends on how the bolt is built. We had already seen this in the modal analysis results.

But the local stress distribution is a completely different story. In the solid bolt model there are clear concentrations under the bolt head and around the holes. In the beam model the couplings stiffen the hole edge, so the field is smoothed. In the tie model there is neither a hole nor a bolt head — so there is no local peak to show.

Here is what we understand from this: matching global curves are not proof that the local model is correct.

So which one?

Use case	Recommended method
Global stiffness or a modal study	A tie constraint may be more than enough
Bolt forces in large assemblies with many connections	Beam and couplings
Bolt fatigue, separation, contact pressure, local stress	Solid bolt

A good model does not give you every detail of the geometry. It gives you every detail you need to read.

Before deciding how to model a bolt, decide what you are going to read from the result. The method follows the question — not the other way around.

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The full benchmark deck, including the preload, modal, and static comparison plots, is available as a PDF: Three Ways to Model a Bolted Joint.