Euler presents Young's modulus for linear elasticity. With this in hand, he derives the forumla M = EI/r for the bending moment acting on a beam. (Based on Clifford Truesdell's An idiot's fugitive essays on science: methods, criticisms, training, circumstances.)
Original Source Citation
Opera Postuma, Volume 2, pp. 129-131.
Opera Omnia Citation
Series 2, Volume 11, pp.378-383.