record exists of the first calculations of the strength of structural members or the behavior of structural material, but the profession of a structural engineer only really took shape with the Industrial Revolution and the re-invention of concrete (see History of Concrete). The physical sciences underlying structural engineering began to be understood in the Renaissance and have since developed into computer-based applications pioneered in the 1970s. Timeline 1452–1519 Leonardo da Vinci made many contributions. 1638: Galileo Galilei published the book Two New Sciences in which he examined the failure of simple structures. 1660: Hooke's law by Robert Hooke. 1687: Isaac Newton published Philosophiæ Naturalis Principia Mathematica, which contains his laws of motion. 1750: Euler–Bernoulli beam equation. 1700–1782: Daniel Bernoulli introduced the principle of virtual work. 1707–1783: Leonhard Euler developed the theory of buckling of columns. 1826: Claude-Louis Navier published a treatise on the elastic behaviors of structures. 1873: Carlo Alberto Castigliano presented his dissertation "Intorno ai sistemi elastici", which contains his theorem for computing displacement as the partial derivative of the strain energy. This theorem includes the method of "least work" as a special case. 1874: Otto Mohr formalized the idea of a statically indeterminate structure. 1922: Timoshenko corrects the Euler–Bernoulli beam equation. 1936: Hardy Cross' publication of the moment distribution method, an important innovation in the design of continuous frames. 1941: Alexander Hrennikoff solved the discretization of plane elasticity problems using a lattice framework. 1942: Richard Courant divided a domain into finite subregions. 1956: J. Turner, R. W. Clough, H. C. Martin, and L. J. Topp's paper on the "Stiffness and Deflection of Complex Structures" introduces the name "finite-element method" and is widely recognized as the first comprehensive treatment of the method as it is known today. Structural failure The history of structural engineering contains many collapses and failures. Sometimes this is due to obvious negligence, as in the case of the Pétion-Ville school collapse, in which Rev. Fortin Augustin " constructed the building all by himself, saying he didn't need an engineer as he had good knowledge of construction" following a partial collapse of the three-story schoolhouse that sent neighbors fleeing. The final collapse killed 94 people, mostly children. In other cases structural failures require careful study, and the results of these inquiries have resulted in improved practices and a greater understanding of the science of structural engineering. Some such studies are the result of forensic engineering investigations