APPENDIX.] NOTE TO CHAP. I. 361 



But for all the weights acting together, it is evident that 

 only all the braces sloping each way from the centre are 

 strained. Hence e k is not strained, and our point of moments 

 is for D always at/! Thus for total load we have strain in 



45 x 50 - 10 x 40 - 10 x 80 - 10 x 20 - 10 x 10 



JO = 125 tons, 



whereas we found by addition of the several weights 135 tons. 



There is thus an ambiguity in this class of bracing as to the 

 way in which the strains may go. Two symmetrical weights, 

 as 9 and 1, may either go left and right directly to the abut- 

 ments or a portion of each go towards the centre. The inter- 

 mediate diagonals may be either all strained or not strained at 

 all. The strains may go partly in one way or partly in the 

 other. We should then not rely on our summation of the sepa- 

 rate weights, but always check them by calculation or diagram 

 for the total load also, and take the greatest strain. Practi- 

 cally, for long spans, it is very rare that the difference is of any 

 importance. 



In diagraming by our method such a system of bracing as 

 the above, we should consider but one series of braces, viz., 

 those strained by the uniform load alone. Thus, for our Fig. 

 and loads on the lower apices, we should take only the diago- 

 nals parallel to fh on the left of centre, and f P 4 on the right. 

 If, on the other hand, the verticals are ties and the diagonals 

 struts, we should retain only those parallel to c Jc on the left, 

 and those parallel to k e on the right of centre. The others 

 are to be omitted. Then, the tabulation being formed, if in 

 any diagonal a strain may occur of reverse character to that 

 which it is intended to resist, a counterbraoe must be inserted 

 in this panel to take this reverse strain. 



As in our examples we have taken always a triangular system 

 of bracing, it is important that the reader clearly understand 

 the method to be pursued in other forms. For the rectangular 

 system of bracing generally, the point where for uniform load 

 the shear is zero is the point from which the braces must slope 

 both ways. The other diagonals, or the counterbraces, are then 

 omitted in both calculation and diagram, and replaced from the 

 tabulation when necessary to replace a strain of the reverse 

 character to that which the braces are intended to sustain. 



Attention to the above points will enable us to both calc&late 



