CHAP. VH.] SIMPLE GIRDERS. 93 



76. In Arts. 46 to 50 the above principles have been already 

 deduced so far as relates to the moments alone, and. a reference 

 to Art. 49 will show their application to the investigation of the 

 effect of a 'system of loads moving over the girder. We pass 

 on, therefore, to 



CONTINUOUSLY DISTRIBUTED LOADING. 



Suppose the load p per unit of length laid off as ordinate. 

 The area thus obtained we call the load area. PL 13, Fig. 

 46 (I). 



The equilibrium polygon becomes here a curve, for which 

 the same law holds good. If we draw tangents to the curve at 

 the points D' and E' corresponding to D and E, intersecting in 

 C', then the resultant of the load upon D E passes vertically 

 through C', or C' is vertically under the centre of gravity of the 

 area D D" E" E. 



If we consider the load area divided into a number of parts, 

 the resultant for each will pass through the intersection of the 

 tangents at the points vertically under the lines of division. 

 Since these tangents are parallel to the lines in the force poly- 

 gon corresponding to these lines of division, they form the 

 equilibrium polygon for the concentrated loads, or resultants of 

 the portions into which the load area is divided. 



Hence : if we divide the load area into portions, and replace 

 each by a single force, the sides of the corresponding polygon 

 are tangent to the equilibrium curve at the points correspond- 

 ing to the lines of division. (Art. 42.) 



77. Total Uniform Load. In this case the reactions at the 



supports are V t = V 2 = -= p I. Hence, for any cross-section dis- 

 tant x from the left support, the shearing force is 

 S = V 1 - J p= ^p(l-Zx). 



For x= -xl; S = Q. Sis greatest for x = and for x = l\ 



that is, maximum S = + p I, and S = -~ p I. 

 The moment at any cross-section is 



M = V so + -yp a? = -^p x (I so). 



M will be greatest for x = -~ I, and 



