Bolts are one of the most common ways to connect parts together. They have a high strength capacity and they are great to use when disassembly is necessary. It is important to correctly model these when performing FEA, but the modeling approach can vary quite a bit. In this blog, we’ll examine four different levels of modeling bolted connections in FEA and evaluate each.
A Quick Background
When bolts are tightened, the tightening torque is converted to tension in the bolts, which causes a clamping force in the joint. This is known as bolt preload. Preloaded joints carry shear loads through frictional contact rather than through the bolt itself. However, if enough tension is introduced into the bolted connection to overcome the preload, the bolt will then take all loads in the connection, including shear and bending. Other issues that can occur without preload include fatigue and loosening.
The second concept we’ll go over quickly is the bolt prying effect. Prying occurs as additional tension in the bolt due to bending in the connected parts. This can have a large effect on the bolt forces, but it can’t be properly modeled in FEA unless using contact.
To evaluate each modeling approach, we’ll use a simple example of a through-bolted joint. The +Z and -Z ends of the bottom plate are constrained, and the top of the T section is pulled with a force of 5,000 N in X, 6,000 N in Y, and 7,000 N in Z. Each section will show the modeling approach, but we’ll compare the results altogether at the end of this blog to get a proper comparison.
Level 1 – Tie
The first approach to bolted connections is to simply ignore the bolt holes and tie the parts together. This will work well for linear analyses in non-critical areas and is by far the most time-efficient approach. However, you will not be able to extract bolt forces or apply preloads this way. The only way to do any bolt calculations with this method would be to use section forces and do a hand calculation for the bolts.
Level 2 – Rigid Connector
The second approach to bolted connections is to use a rigid connector element, such as a beam connector in Abaqus [learn more about connector elements in this blog here!]. The bolt holes are attached to the ends of the rigid connector via a kinematic coupling (RBE2). Distributing couplings can be used here as well, but in models with hundreds of bolts this can get very computationally expensive. This approach is also quite time efficient and does allow bolt forces to be pulled directly from the analysis. One downside to this approach, however, is that preload is not accounted for here. This method also does not capture the prying effect that would typically occur in a bolted connection since each element is rigid and there is no contact; however, it does allow surfaces to separate, unlike the tie.
Level 3 – Preloaded Virtual Bolt
The third approach to bolted connections is to use a virtual bolt. Like level 2, a connector element is connected to bolt holes via kinematic couplings. However, instead of a beam connector, a translator is used. The translator is given axial stiffness based on a beam cross section definition using the material and diameter of the bolt. Preload is applied via a connector load along the axial direction of the translator. Using this approach requires the use of contact to properly hold the connection together. A preload step is used to apply the preload before adding additional loading. For our example, a preload of 56,270 N was applied to each bolt. Note that the nut and bolthead shown below is just visual – they are simulated using the coupling shown underneath.
Level 4 – Preloaded Solid Bolt
The final approach is to use solid bolts. With this approach, physical bolts and nuts are added to the model and the preload is applied to the bolt shank via a pre-tension section. General contact is included between all parts. This approach is by far the most computationally expensive, but it is also the only one that can show local bolt stresses since the bolts are physically modeled.
Comparing the Results
Stress Results:
As you can see here, away from the bolted connection, the stresses in the assembly are similar. The approach with the tie does not show any stress in the bolted areas that are present in the other three approaches. The rigid, virtual bolt, and solid bolt all show localized stresses in the bolt holes.
Displacement Results:
Displacements are pretty similar (<3% difference) between levels 2-4. All of these three approaches allow for separation in the middle where there are no bolts.
Bolt Forces:
Here we can see the bolt forces in all directions for each level. For level 1, sectional forces were pulled from the assembly and converted to bolt forces (see calculation below). For levels 2 and 3, connector forces were pulled. For level 4, section forces were pulled on the solid bolt shank. In levels 1 and 2, the bolts aren’t preloaded and take all the applied forces, leading to very conservative shear forces compared to levels 3 and 4, which include preload.
Final Thoughts
There are a lot of ways to model bolted connections in our FEA analyses, with varying levels of accuracy and efficiency. Of the four approaches covered in this blog, ties and rigid elements work well in non-critical areas and help save run time, but virtual and solid bolts offer much better accuracy.
As always, reach out to our expert engineering team for help with your own analysis today!
