360 NOTE TO CHAP. I. [APPENDIX. 



diagonal at this point The shear is always in such cases the 

 reaction at the end minus the weights between that end and 

 the apex in question. 



The flanges are easily obtained by moments, as above. 



The following points need attention, however. First, if 

 there are two or more systems of diagonals, as represented in 

 PI. 2, Fig. VII., by the full and dotted diagonals (omitting the 

 upright lines), we must find the strains for each system sepa- 

 rately, and then add them together. Thus, if the strains found 

 in ac and ce. etc., for one system, are 50 and 60 tons, and 

 those in df and fg, for the other, are 40 and 70 tons, we have, 

 when the two systems are combined, dc = a c + df= 50 -f- 40 

 = 90, cf df + c e = 40 + 60 = 100, fe = c e +fg = 

 60 + 70 = 130, and so on. This holds true, of course, whether 

 the strains are obtained by calculation or diagram. Thus, for 

 a lattice girder, we calculate or diagram each system by itself, 

 and then the strain in any flange, when the two are combined, 

 is equal to the sum of the strains on that flange-due to each 

 system of triangulation which includes it. 



There is another point to be observed in connection with 

 the system known as the Howe or Pratt Truss. Inserting the 

 dotted verticals into our Fig., we have this system of square pan- 

 elling. Let us suppose that the diagonals take tension only, 

 and the verticals compression only. 



Now for a weight at apex 9 of 10 tons, we have a right re- 

 action of 1 ton, which, running through the system, causes strain 

 in the diagonal of yP 4 . For the flange D, then, our point of mo- 

 ments is at/", and if the height of truss is equal to panel length, 



1 x 50 

 viz., 10 feet, we have the strain in D = - = 5 tons, for 



P 9 . In the same way for P 8 , we have for D 10 tons ; for P 7 , 15 

 tons ; for P 6 , 20 tons ; for P 5 , 25 tons. For P 4 , on the other 

 hand, we have a left reaction of 4 tons, which causes strain in 

 diagonal e 7c, and for this weight and all succeeding weights 

 our point of moments for D is then at e. We have then P 4 



- = 24 tons ; for P 8 , 18 tons ; for P 2 , 12 tons ; and for 



P!, 6 tons. 



For all these weights, then, acting together, we have 135 tons 

 strain in D. 



