52 



STRENGTH OF MATERIALS 



D 



The bending moment diagram is therefore a parabola. For a 



W = , which is its maximum value. The bending mmm-nt and 



8 

 shear diagrams are therefore as represented in Fig. ; 



() Beambearing 



uniform load over 

 part of tlit span. 



Let the load ex- 

 tend over a distance 



\-d H Iff, c and be of amount 



w per unit of 1 

 Tlu-n tin- total load 

 is we. The react ions 

 of tin- MipiHirts are 

 the same as though 

 the load was con- 

 t<-.l at its cen- 

 ter of gravit 

 Therefore, if 

 notes the distance 

 of G from tli 

 support, 



FIG. 39 



wed 

 ~T 



'~ 



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

 the same as though the load was concentrated at G, and are there- 

 fore the straight lines A'H and ZXA", intersecting in the IKMI 

 vertically beneath G (Fig. 39). 



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

 uniform load on this portion of the beam. Thus, if /. .i/.v > the para- 

 bolic moment diagram for a beam of length LN or c, tin- ordinates 

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

 giving as a complete moment diagram the line A ll.lh />'. 



