APPENDIX.] 



NOTE TO CHAP. I. 



355 



special attention to the points to be observed in the tabulation 

 of the strains. There is, indeed, no more satisfactory, complete 

 and rapid method for the solution of bridge girders generally 

 than that afforded by the graphic method. 



As an example, let us take the Bow-string Girder given by 

 Stoney,]). 131. Span, 80 ft., divided into 8 panels; rise of 

 bow, 10 ft. Load, 10 tons at each lower apex. 



We construct the two strain diagrams * given in Fig. V., 

 PI. 2, viz., one for the load P 7 at the first apex, and one for the 

 load at the last apex, P,. Referring, if necessary, to Art. 12, 

 Chap. I., the reader can easily follow out these diagrams. "We 

 then scale off the strains, and obtain, for the strains in the 

 diagonals 



Now from the strains thus obtained for these two weights 

 we can easily obtain all the others. 



Thus, as the end reactions are inversely as the distances of 

 the weight from the ends, the reaction at the left end due to 

 P a will be twice that due to P!. For P 8 three times that due 

 to P,. The strains will therefore be twice and three times 

 those due to P 15 until we arrive at the weights P, and P a re- 

 spectively. So also for P 6 the reaction at the right is twice 

 that due to P T , and the strains are therefore double up to the 

 weight P 6 . To the right, then, of P 8 the strains are twice 

 those due to P 7 , and to the left of P 6 they are six times those 

 due to Pj. Take, for instance, P 5 . _The right reaction is -fths 

 of the apex load, and the right reaction of P 7 is ^th of that 

 load. For P 5 , then, the strains in all pieces to the right of that 

 weight are 3 times those due to P 7 . Again, the left reaction 

 is for P 5 fths the apex load. But the left reaction for P : 

 is |th the same load. The strains then in all the pieces to the 

 left of P 5 are 5 times those due to P t . So for any other load. 

 We can therefore form at once the following table : 



* Strain diagrams in Fig. V. , and also in Fig. VL , are, for obvious reasons, 

 drawn to different scales. 



