358 NOTE TO CHAP. I. [APPENDIX. 



cable to any structure where the reactions are inversely as the 

 distances from the end. The strains due to the first and last 

 weights are all that we need in order to thoroughly solve any 

 case of the kind. It is advisable, however, to construct a 

 third diagram for an intermediate weight, in order to serve as 

 a check upon the others.* 



9. Method of Calculation by moments. We may illus- 

 trate here the method of calculation by moments referred to in 

 Art. 14, Chap. I., a little more fully. Thus in the example 

 above, Fig. "V., suppose we wish the strains due to P x . Reac- 

 tion at left end is evidently th of 10 tons = 1.25 tons. Con- 

 ceive the lower flange Y a cut. Rotation would evidently take 

 place about apex a, and we have, therefore, strain in Y a x its 

 lever arm from apex a = 1.25 x 5. The depth of truss, or 

 lever arm of If a, from apex a, is 2.58 feet. Hence we have 



1.25 x 5 . . __ ' 



rr - = strain in Y a = 2.42 tons, 

 z.oo 



This strain is evidently, by reason of the direction in which 

 the two portions of the truss would rotate about a, tension. In 

 like manner, for upper flange X &, if we know the lever arm of 

 this flange from the opposite apex, we can easily find the strain ; 

 for the diagram shows that Xb,bc and Y c are in equilibrium 

 with the reaction, and hence, if we take the point of moments 

 at the intersection of the two pieces b c and Y c, the moments 

 of these pieces are zero, arid we have remaining only the mo- 

 ment of the strain in X 5 balanced by the moment of the reac- 

 tion. 



Again, if X 5 and Ye are thus found, and if these two strains, 

 together with the reaction, are in equilibrium with the diago- 

 nal b c, we can find the strain in this diagonal by taking the 

 apex d as a centre of moments. The moment of Y c then is 



* It may also be well to notice here that the practice of deducing in the 

 tabulation the dead load from the live load strains is not strictly accurate, aa 

 the live load acts at the lower apices only [or at the upper apices only, if the 

 bridge is under grade] , while the dead load is distributed along both flanges, 

 and acts at both upper and lower apices. 



In every case, however, the greater portion of the dead load, say, for in- 

 stance, *ds of the whole, owing to the track, platform, cross-girders, etc., 

 acts at the same apices as the live load itself ; and the error is in any case 

 very slight, and practically of no account. 



