166 METHODS OF LOADING [CHAP. XI. 



If the beam be continuous for three spans only, B G and C H 



innst be made equal to (18 *t 16 **>*+ ( 2 -# + ?), where 



32 3 1 \ 7 2 ' 



I* = . Further, the value given to B D for the inner span 



1O8. Aletbod by Resolution of Forces Draw Spans. 



The most usual cases of continuous girders which occur in prac- 

 tice are draw or pivot spans, which when shut must be consid- 

 ered as continuous girders of two spans. The graphical method 

 becomes for such cases short and easy of application. In the 

 case of framed structures of this character, it may, however, be 

 more satisfactory to first find the maximum shearing forces 

 (Art. 104), and then follow the reactions thus obtained through 

 the structure from end to end by the method of Arts. 8-13. 

 As a check upon the accuracy of the work, we may apply the 

 " method of sections " referred to in Art. 14-. In either case 

 we must, of course, start from an end support where only two 

 pieces intersect and the moment is zero. 



Still again, we may find the reactions by calculation, and 

 then apply the method of Arts. 8-13. In the case of two spans 

 onl} 7 , the formulae for the reactions are sufficiently simple, and 

 the ready and accurate determination of the strains offers, there- 

 fore, no difficulty. 



We shall give here, therefore, the analytical formulae requi- 

 site for our purpose, referring the reader to treatises upon the 

 subject for their demonstration.* 



Formulae for Reactions. Continuous Girder of two un- 

 equal Spans, I and n I. 1st. Concentrated weight P, in first 

 epan I, distant a from left end support. Reaction at left end 

 support : 



Reaction at middle support : 



* Bre-vse La Flexion et la Resistance, and Cours de Mecanique Applique. 

 Weyrauch Tkeorieder Trdger. CoUignon Theorie Elementaire des Poutret 

 Drrites, etc. Also Supplement to Chap. XIII. 



