PREFACE TO FIRST EDITION. Til 



which bids fair to obtain widespread recognition, in direc- 

 tions in which it has hitherto been supposed of little service. 

 This often, indeed, by the aid of analytical results, we have 

 been enabled to do, and not, as we conceive, without a degree 

 of success. The formulae used are always simple and of ready 

 application, and this union of analytical results and graphical 

 processes the practical engineer will, we think, find of value. 

 Thus, in the braced arch (Chap. XI Y.) and continuous girder 

 (Chap. XII.) new constructions will be found, and both these 

 important and difficult cases may thus be solved with an ease, 

 completeness and accuracy far superior to that of the pure 

 graphical method itself. Those acquainted with the analytical 

 investigation of the " braced arch" as contained in Copt. Sods' 

 Report to the III. and St. Louis Bridge Co., May, 1868 (App.), 

 will not, we feel sure, be slow to recognize the advantages of 

 the present method. The subject in its present state is thus 

 fairly brought within the reach of the practical Engineer and 

 Constructor. 



To simple girders, contrary to usually received opinions, by 

 the means of apex loads, the above method applies directly, and 

 without the aid of analytical results a fact which has been too 

 generally passed over without sufficient notice by writers upon 

 the subject. 



We have devoted considerable space to the subject of the 

 continuous girder, but not, we feel sure, more than its impor- 

 tance demands. The subject deserves more attention at the 

 hands of the practical engineer and constructor than it has 

 hitherto received. That the present indifference Tipon the sub- 

 ject is due chiefly to lack of information can hardly be doubted, 

 when the opinion is current, and is even endorsed by those who 

 are considered as authorities, that the complete solution of the 

 problem is " probably impossible by reason of its complexity," 

 and " too complex for mathematical investigation." * Opin- 

 ions like these are best met by the complete solutions of par- 

 ticular examples, and in Chapter XII. will be found the com- 

 plete calculation and tabulation of the strains in every piece 

 due to every apex load, for the central span of seven continu- 

 ous successive spans, and, as far as any inherent difficulties are 

 concerned, we might as well have taken 50 or 100 spans. 



Graphical Method for the Analysis of Bridge Trusses. Greene. 



