- The Bernoulli-Euler and Timoshenko beam theories are reformulated using a modified couple stress theory and through-thickness power-law variation of a two-constituent material [functionally graded material (FGM)]. The model contains a material length scale parameter that can capture the size effect in a FGM. The equations are then used to develop algebraic relationships for the deflections, slopes, stress resultants of the Timoshenko beam theory (TBT) for microstructure-dependent FGM beams in terms of the same quantities of the conventional Bernoulli-Euler beam theory (BET). The relationships allow determination of the solutions of the TBT for microstructure-dependent FGM beams whenever solutions based on the BET are available. Examples of the use of the relationships are presented using straight beams with simply supported and clamped boundary conditions. 2012 Springer-Verlag.