APPENDIX.] THE CONTINUOUS GIRDEK. 379 



We have then, in the first case, a saving of 8 per cent., in the 

 second, 10, and in the third, 18 per cent, over a simple girder. 

 Quite a notable saving, although the spans are very short, and 

 although, in the first two cases (the spans being end spans), we do 

 not obtain the full advantages of continuity. If, then, instead 

 of three simple girders of the above dimensions, we should con- 

 struct the girder continuous over the piers, we should save in 

 strain, and hence in material, 10 per cent, in each end span, and 

 18 per cent., or nearly twice as much, in the centre span. 



The advantage of continuity is rendered still more apparent 

 by taking a longer span. Thus for a girder of 200 ft., height 

 20 ft. 10 panels, and double system of triangulation, similar to 

 Fig. YII. for a live load of 20 tons per panel, and dead load 

 of 10 tons we have the following results : 



One span. Two spans. Five spans. 



centre. 



Bracing 1398.6 1428.2 1596.2 



Lower Chord.. 2400. 1793.2 1395.7 



Upper Chord.. 2550. 1981.6 1622.6 



Total 6348.6 5203.0 4614.5 



Per cent, saving 18 per cent. 27 per cent. 



That is, we have a saving of 18 per cent, instead of only 8 

 per cent., as before, for two spans, and of 27 per cent, for the 

 centre span of five spans. For three spans, then, of this length 

 we should save 18 per cent, on the end, and at least 20 per cent. 

 on the centre span. 



If we suppose the same girder as above fastened, or fixed 

 horizontally at the ends, we shall have the case of a middle span 

 in a very great number, and may expect to find the greatest 

 saving possible for this length. 



The formulae of Chapter XIII., as also the simple graphical 

 method for this case, given in Chapter XII., Art. 114 [Fig. 80], 

 enable us to solve this case ftasily. The reader will find, on mak- 

 ing the calculation, the following strains : 



Strain in tons. 



Diagonals 1279.2 



Upper Chord 940.2 



Lower Chord 965.4 



Total * 3184.8 



Per cent, saving 49.8 



