Macaulay's method
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Macaulay's method (the double integration method) is a technique used in structural analysis to determine the deflection of Euler-Bernoulli beams. Use of Macaulay's technique is very convenient for cases of discontinuous and/or discrete loading. Typically partial uniformly distributed loads (u.d.l.) and uniformly varying loads (u.v.l.) over the span and a number of concentrated loads are conveniently handled using this technique.
The first English language description of the method was by Macaulay.[1] The actual approach appears to have been developed by Clebsch in 1862.[2] Macaulay's method has been generalized for Euler-Bernoulli beams with axial compression,[3] to Timoshenko beams,[4] to elastic foundations,[5] and to problems in which the bending and shear stiffness changes discontinuously in a beam.[6]