CHAP. XI.] CAUSING MAXIMUM STRAINS. 161 



Of course, the same circumstances can hold good for third 

 and fourth spans as for first and second, except that positive 

 shears on one side of centre support are the corresponding 

 negative shears upon the other, and vice versa. 



Following carefully the above with the aid of the Fig., the 

 reader cannot fail to grasp the method. An independent con- 

 Btruction for a similar case will make both principles and de- 

 tails familiar. Once thoroughly understood, the method is 

 rapid, accurate, simple, and of general application. 



1O5. Determination of tbe Maximum moments. In 

 like manner, it is easy, according to the general construction 

 given in Art. 97, and referring to Arts. 98 and 99, to determine 

 the maximum moments. In Fig. 72, PL 20, we have the same 

 example as before, concerning which we have but little addi- 

 tional to remark. Fig. 64, Art. 100, shows that the end tan- 

 gents give the moments within the unloaded portion of the 

 girder. These tangents are constructed precisely as before in 

 the several spans, except it will be noticed that in the first, 

 span we have made use of the construction given in Art. 97, 

 Fig. 61. Thus the point F' is determined so that K F' = 



/A 2 

 KF (j-j , and thus the moments are measured directly at the 



end vertical. Also upon the left support vertical we have laid 

 off the distances between the cross-lines in the second span 



(7 \2 

 T) ' 



The only thing new in the PI. is Fig. c, which, as we have 

 seen in Art. 103, Fig. 70, gives the points at which the positive 

 moment is a maximum for each position of load. The positive 

 moments can then be taken directly off upon the verticals 

 through these points, and are limited by the horizontal through 

 the supports and the tangents, as above. 



Thus, at second support the vertical distance to a, for first 

 span, gives the moment at the support. Lay it off in Fig. a 

 from the support line. For a load over span, we see at once 

 the point for which the positive moment is a maximum from 

 Fig. c. Follow up the vertical through this point. The dis- 

 tance on this vertical in Fig. J, between the support line and 

 tangent 5 J 1? gives the moment to be laid off in Fig. a upon 

 this vertical. So, for load over ^ span, we have next vertical 



and tangent cc^ and so on. "We thus obtain the curve for 

 11 



