Solve Prob. 4–79, using beam elements. Use a one-half model with symmetry. At the plane of symmetry, constrain translation and rotation.

Data from 4-79

A steel piston ring has a mean diameter of 70 mm, a radial height h = 4.5 mm, and a thickness b = 3 mm. The ring is assembled using an expansion tool that separates the split ends a distance δ by applying a force F as shown. Use Castigliano’s theorem and determine the force F needed to expand the split ends a distance δ = 1 mm.

h = 4.5 mm F