They can complicate analysis because even small assemblies can have bolts, screws, rivets, and weld joints, some with preloads. Still, there are ways to consider fastener reactions, says David Dearth, analyst and president of **Applied Analysis & Technology**, Huntington Beach, Calif. (appliedAT@aol.com). "Clients occasionally ask to see everything, including bolt threads," says Dearth. "In most cases it's excessive to explicitly incorporate bolts and other attachments into FEA models. So the questions should be: What's the best way to treat bolts and attachments? There are several.

You could **neglect ****the ****bolts. **"The physical strength of a bolted connection is determined by clamping and frictional forces developed by installation preload torque," he says. Joint connections lose strength when external loadingexceeds these initial clamping forces. The most common approach to treating bolted assemblies in FEA models assumes the attachment system provides sufficient assembly preload to ensure intimate contact of all components for the anticipated loading. With this assumption as the controlling feature, analysts can model entire assemblies as though each component is essentially 100% in physical contact with adjacent parts. The strength of the bolted interface is then estimated using conventional techniques.

**Simplify the reactions. **"When a problem calls for estimating bolt loads, one typically assumes the bolts are acting as discrete reaction points without preload," he says. "One technique for hand calculations assumes each bolt as a series of rigid links. The calculated reactions at these "bolt" locations are compared to the required installation preloads to compute margins of safety for the connection. In these cases, bolt stiffness and initial preload are not included in the analysis results.

FEA techniques are useful for estimating reactions in these applications when many bolts are used and solutions by conventional techniques are statically indeterminate. Bolt reactions in local bolt-coordinate systems can also be determined. It's easy to properly size bolts knowing the axial and shear reactions in the local bolt-coordinate system.

**Discrete attachments with preload. **A few cases may require modeling bolted connections where numerous threaded fasteners, rivets, or spot welds are used to form the joint or when it's required to apply preloads to assemblies so initial compressive stresses can be included in the results. Bolt preload enhances the joint strength.

"For these applications the stiffness or spring rate of each attachment might influence overall deflections of the full assembly. Each component would then be modeled with small gaps between mating surfaces. Attachment connections are idealized as short beams with rigid elements simulating the preload region. The attachment stiffness, *S *(lb/in.), can be represented with:

*S *= *AE/L, *

where *A *= bolt effective area, *E *= Young's modulus, and *L *= effective bolt length.

There are several ways to simulate attachment preload. One method applies actual forces to FEA models at bolt locations. A more elegant approach simulates bolt preload using equivalent, "dummy", thermal loading dT. The thermal load simulates a contracting bolt length which produces a load that would be compared to the preload required in the specs, or to a value from a text such as *Machinery's **Handbook. ***Explicit ****modeling **is the most complex method of modeling threaded connections because it includes everything. "Each interface surface is idealized using nonlinear, contact, and compression elements with sliding friction," says Dearth. "And the bolts are explicitly modeled with preload using the dummy thermal contraction. This is time consuming. Besides, in FEA models, loads tend to take the shortest path and react entirely at a single node point, often the first thread. But I've found that averaging results from the first three threads usually compares favorably with conventional bolt-stress equations."

**MORE ON BOLTS**

A further discussion on simulating bolted joints with a sample problem will appear in the February 3, 2005 issue.