BEADING-MOMENT AND SHEAR DIAGRAMS 



41 



at its center of gravity G. Therefore, if d denotes the distance of 

 G from the left support, 



wed 



=^ and 



Also, the bending-moment diagrams for the portions AB and CD 

 are the same as though the load were concentrated at 6r, and are 

 therefore the straight lines A'H and D'K, intersecting in the point 

 T vertically beneath G (Fig. 43). 



From B to C there is an additional bending moment due to the 

 uniform load on this portion of the beam. Thus, if LMN is the 

 parabolic moment diagram for a beam of length LN or <?, the ordi- 

 nates to the line HK must be increased by those to the parabola 

 LMN, giving as a complete moment diagram the line A'HJKD'. 



Analytically, if x denotes the distance of any section from the 

 left support, the equations of the three portions A'H, HJK, and 

 KD' of the moment diagram are 



JCut = 



M BC = Rx - 







29. Relation between shear and moment diagrams. Consider a 

 beam bearing any number 

 of concentrated loads -ZJ, \ PI 



P^, -, J;J, at distances c^, i T 

 c? 2 , ., 6? n from one end A 

 (Fig. 44). Then the mo- 

 ment M at any section mn, 

 distant x from the origin 

 A, is 



M 



FIG. 44 



