204 CONTINUOUS GIEDEB [CHAP. XIII. 



and the deplorable fact that the "authorities " do but too often 

 treat the subject with "judicious silence," and that, therefore, 

 there exists in our engineering literature no collection of prac- 

 tical and useful formulae for this important class of bridges, 

 though such formulae are, and have been for years, free to all 

 for the asking, all these facts may serve as apology for the in- 

 troduction of the present chapter, in a work which professedly 

 treats only of Graphical methods. The apologies of those who 

 professedly treat the subject analytically, and have yet omitted 

 such formulae, are not so numerous. 



We propose to give the analytical results necessary for com- 

 plete solution of a girder of uniform cross-section over anv 

 number of level supports, with all spans of different lengths: 

 for uniform load over whole length from end to end of 

 girder, for uniform load over any single span, and for con- 

 centrated load in any single span at any point of that span. 

 These three cases, as we have seen in the preceding chapter, 

 are sufficient for the complete solution of framed Bridge 

 Trusses.* 



Many of these results are here given for the first time, at least 

 in their present shape, in any published treatise, though, as re- 

 marked, some of them in more or less practical form have 

 long been common property for all who may have desired to 

 make use of them. 



The formulae only will be given, in such shape and with 

 such illustrations of their application that, we trust, they will 

 be found free from complexity, and of considerable practical 

 importance. In the Supplement to this chapter a demonstra- 

 tion of the formulae is presented. 



13O. Notation. The notation which we shall adopt is as fol- 

 lows [see Fig. 89, PI. 23] : 



* The formula for concentrated loads are alone all that is really necessary. 

 Their addition gives, as we have seen in our tabulation, Art. 127, the strains 

 for uniform load also. In fact, for strict accuracy, only single isolated loads 

 should be considered, as the results given by the formulae for uniform load are 

 not perfectly accurate. This may be seen from the well-known fact that, for 

 a girder fixed at one end, and supported at the other, the reaction at the free 



5 

 end for a load in the middle is TQ of the load, while if the same load were uni- 



8 6 



formly distributed, the reaction is gths, or ^a of the load. The difference, 



however, for any practical case, where there are a number of panels, is very 

 alight. 



