Computations by Means of Drawings

Abstract

The second half of the 19th century saw a very quick diffusion of graphical statics. Lectures on graphical statics were given in Switzerland (Zurich); in Germany (Berlin, Munich, Darmstadt, Dresden); in the Baltic regions (Riga); in the Austrian-Hungarian empire (Vienna, Prague, Gratz, Brunn); in the United States; in Denmark. The author that mainly developed its techniques was the German scholar Carl Culmann, who placed graphical statics besides the newborn projective geometry. Culmann's approach was enthusiastically followed in Italy, where, first in Milan at the Higher technical institute, then, after 1870, in many Schools of application for engineers, among which those of Padua, Naples, Turin, Bologna, Palermo, Rome, and, eventually, also in the universities of Pisa and Pavia, courses of graphical statics were activated. The Italian scholar who collected Culmann's inheritance, and extended it, was Luigi Cremona. Graphical StaticsIn the second half of the 19th century there was a very quick diffusion of the techniques of graphical calculation to solve engineering problems, above all the determination of the forces in the trusses frequently used for industrial buildings and for bridge construction. The term used to denote these techniques was graphical statics.Classes on graphical statics were held in all Europe (Zurich, Berlin, Darmstadt, Munich, Dresden, Riga, Vienna, Prague, Gratz, Brunn) and in the United States. In Italy there were classes in Milan (at the Higher technical institute) and, after 1870, in many Schools of application for engineers, among which those of Padua, Naples, Turin, Bologna, Palermo, Rome, and also in the universities of Pisa and Pavia.The meaning of the locution 'graphical statics' is rather nuanced, and has undergone changes in time. At the beginning of the 1800s, and in our time, the term simply indicated a part of geometrical statics, that is of statics developed by geometrical means. We may say that geometrical statics, properly stated, deals with the geometrical deduction of the laws of statics, while graphical statics deals with the geometrical procedures that let the problems of statics of engineering practice be solved by graphical means. Among these practical problems, besides the structural verification of trusses, there were those of geometry of masses (centers of gravity, moments of inertia, principal axes, and so on), of verification of beam cross-sections undergoing eccentric tension and of retaining walls, of metrics in ground movements, and so on. In the second half of the 19th century, after Culmann's fundamental monograph in 1866 [28], 1 the term 'graphical statics' was used in a restricted sense, to indicate a discipline unifying graphical calculus and projective geometry, or geometry of position, as it was then called.Geometrical statics may go back to Stevin [76], but a fundamental role was played by Pierre Varignon, who, in the Nouvelle mécanique ou statique [81], besides using in an extensive way the rule of parallelogram, taught us how to construct bo...