CHAP. Vm.] CONTINUOUS GIRDERS. 125 



CHAPTER YIII. 



APPLICATION OF THE GRAPHICAL METHOD TO CONTINUOUS 

 GIRDERS GENERAL PRINCIPLES. 



8O. molir's Principle. Thus far, in addition to the general 

 principles of the Graphical method, we have noticed more or 

 less in detail its application to the composition and resolu- 

 tion of forces, and the corresponding determination of the 

 strains in the various pieces of such framed structures as Bridge 

 Girders, Roof Trusses, etc. We have also illustrated the 

 graphical determination of the centre of gravity and moment 

 of inertia of areas, as also of the bending moments and shear- 

 ing forces for simple girders, including several important cases 

 in practical mechanics. (See Art. 41.) Lastly, we have taken up 

 the subject of Bridge girders more in detail, and developed in 

 order the principles to be applied in the solution of any par- 

 ticular case. Although brief, it is hoped that this portion will 

 be found sufficient to illustrate fully the method of procedure 

 to be followed in practice. 



As regards simple girders, the principles referred to are so 

 easy of application that the reader will find no difficulty in 

 diagraming the strains in any structure of the kind, as explained 

 in the " practical applications " of Arts. 8 to 13 ; or he can find 

 the maximum moment at any cross-section for given load- 

 ing according to the last chapter. In the case of .beams or 

 girders continuous over three or more supports, however, we 

 meet with difficulties which for some time were considered in- 

 superable. 



Thus Culmann, in the work which we have so often quoted, 

 says : * " The determination of the reactions at the supports for 

 a continuous beam, which depend upon the deflection, the law 

 of which is given by the theory of the elastic line, is impossi- 

 ble by the graphical method, at least so far as at present de- 

 veloped. The theory rests upon the principle that the radius of 



*Culmauri's Gra/phische Statik, p. 278. 



