Summary: This paper presents the analysis of frequency expressions corresponding to an arbitrarily restrained uniform single-span Euler--Bernoulli beam. Simple formulas are derived that allow one to express the frequency equation of a beam with more complex boundary conditions in terms of frequency expressions corresponding to beams with simpler boundary conditions. In this way a method is developed that enables one to build up the frequency equation of a restrained beam from the simplest frequency expressions corresponding to classical boundary conditions, such as clamped, pinned, free and guided. The proposed method has the advantage that by using it one avoids the necessity of rather tedious evaluations of frequency determinants.