GRAPHICAL STATICS. 



VL 



GRAPHICAL STATICS. 



The few text-books upon graphical statics and the more numerous works 

 upon its applications, afford us no definition, and can afford none, because 

 neither the method nor scope of this new study are anywhere sufficiently 

 indicated. 



If, following Culmann, we speak of it in contradistinction to the appli- 

 cations of a pure graphical statics, we may define it somewhat as follows : 

 Graphical Statics comprises the theory of those geometrical constructions which 

 qccur in the graphical solution of statical engineering problems ; it treats 

 further of the general relations deducible from such constructions. This 

 limitation, so far as it does not follow from the preceding, we shall seek 

 in the course of these remarks still further to establish. 



Graphical representations of analytically obtained results have, as has 

 been already noticed, long been used in engineering practice. They served 

 also the purposes noticed in the preceding chapter. Often also certain 

 values, whose analytical determination is somewhat complicated, have 

 been sought by graphical constructions. Examples of this may be found 

 in many text-books upon the theory of structures, and we notice only, as 

 one of the most notable of recent date, the construction of lever arms and 

 limits of loading in A. Ritter^s "Theorie und Berechnung eiserner Dach 

 und Briickenconstructioneu " (Hannover, 1862). Poncelet applied analy- 

 sis in general to practical investigations, but sought in several complicated 

 cases to elucidate the deductions of formulae by geometrical constructions, 

 and to deduce graphical solutions from analytical relations. This pro- 

 cedure found considerable acceptance, and the investigations of Poncelet 

 were afterwards resumed upon more general assumptions by Saint Guil- 

 hem (Memoir e sur la poussee des terres avec on sans surcharge, Ann. des 

 ponts et chauss., 1858, sem. 1, p. 319). 



The first, however, to give pure geometrical determinations of stability 

 in structures was Cousinery. He gave a number of examples as applica- 

 tions of his graphical calculus, but his ideas appear to have found in 

 France little acceptance. On the other hand, the graphical construction of 

 the curve of pressure in the arch by Mery (Memoire sur Vequilibre des voutes 

 en ~befrceau ann. d. ponts et chauss., 1840, sem. 1, p. 50) was extensively 

 used, and has since been extended by Durand-Glaye to iron arches also 

 (Ann. d. pants et chauss., 1867, sem. 1, p. 63, and 1868, sem. 1, p. 109). 

 Special prominence was given to graphical investigations of stability by 

 Culmann's " Graphische Statik " (first part, Zurich, 1864, entire work, 

 1866 ; second edition, 1st part, 1875.) 



This work of Culmann must be considered as original in all those parts 

 relating to structures. Poncelet and Cousinery, beyond the general idea, 

 furnished only unessential contributions. Culmann recognized the fruit- 



