CONTINUOUS GIRDER. [_CHAP. XIH. 



CHAPTER XIII. 



ANALYTICAL FORMULA FOE THE SOLUTION OF CONTINOU8 GIRDERS. 



I 



129. Introduction. As we have seen in the preceding 

 chapter, the complete and accurate determination of the strains 

 in the continuous girder, both for uniform and moving loads, is 

 easy, provided we can find the moments and shearing forces at 

 the supports for the various states of loading, and for each apex 

 load. Now this we are able to do with mathematical accuracy, 

 and without much labor. The formulae necessary for the pur- 

 pose, when put into proper shape for use, are neither difficult of 

 application nor more complicated than many which the practi- 

 cal engineer is often called upon to manipulate. Since the 

 publication of Clapeyrorfs paper * in 1857, in which, for the 

 first time, his well-known method was developed, and his cele- 

 brated "theorem of three moments" made known, the subject 

 has engaged the attention of many mathematicians. In 1862 

 WinMer f first developed a general theory, and gave general 

 rules for the determination of the methods of loading causing 

 greatest strains, together with tables for the maximum values 

 of the moments, shearing forces, etc., for various numbers of 

 spans of varying' length. In the same year Bresse \ followed 

 with a similar work. In 1867 Winkler gave a general ana- 

 lytical theory, and, finally, in 1873 Weyrauoh \ has treated the 

 subject with a degree of completeness and thoroughness which 

 leaves but little to be desired. Pie discusses the subject in its 

 most general form, for any number of spans of varying length, 



* Clapeyron Calcul d'une poutre elastique reposant librement sur des ap- 

 puis ine"galement especes. Compte rendus, 1857. 



f Beitrage zur Theorie der continuirlichen Briickentrager Civil Ingenieur, 

 1862. 



$ Brewe Cours mechanique appliqude. Paris, 1862. 



Winkler Die Lehre von der Elasticitat und Festigkeit. Prag. 1867. 



| Weyrauch Allgemeine Theorie und Berechnung der continuirlichen und 

 einfachen Trager. Leipzig, 1873. 



