Find the load, then size the bolts

In a previous column, David Dearth, a consulting analyst and president of Applied Analysis & Technology, Huntington Beach, Calif. ( [email protected]), discussed four ways to handle fasteners and preloads with FEA in assemblies. This article continues by solving a bolt problem by hand and using an FEA program.

Dearth suggests this problem as an example of using FEA to determine reactions at bolts. "I recommend working through a few sample or warm-up problems with textbook solutions before tackling the real one. This problem simulates a 300-lb load on a bracket and tube. The task is to estimate reactions at the four mounting locations so bolts can be sized for them. This problem contains features of real-life engineering challenges and can be solved with pencil and paper using conventional static analysis — summing the forces of a free body diagram. A second task estimates reactions at the bolt locations using FEA. Then compare results," he says.

Hand calculations rely on equations found in most engineering textbooks with sections on finding reactions in assemblies. "To check your work, the detailed static calculations can be downloaded from machinedesign.com or by requesting a copy from me by e-mail," says Dearth.

Formulating a rigid model, the second task, generates results using an FEA model and compares them to the hand calculations. The rigid model shows the geometry of the loaded tube. "The stick-figure model uses rigid elements," says Dearth. "Solve for the reactions to four decimal places using simple equations that sum static forces and a spreadsheet to minimize roundoff in the arithmetic," he adds. The calculation-table summarizes and comparesresults from manual calculations and FEA outputs for the rigid body. The FEA model was processed using MSC/Nastran.