MATERIALS AND THE STRENGTH OF MATERIALS 



47 



ported at both ends the bending moment is one-half the 

 weight one-half times the length. 



The maximum bending moment for the cantilever 

 beam of Fig. 28 is at the point where it is supported. If 

 the beam be of a uniform cross section, it will rupture at 

 this point before it will at any other. The bending 



FIG. 28 A CANTILEVER BEAM 



moment in the beam at hand grows less as the distance 

 from the weight becomes less. As the bending moment 

 becomes less, less material is needed to resist it, and 

 hence a beam may be designed of such a section as to 

 be of equal strength at all points, or it is what is called 

 a beam of uniform strength. 



Much material may be saved by placing it where most 

 needed. The location as well as the value of the maxi- 

 mum bending moment depends upon the way the beam is 

 loaded. 



80. Modulus of rupture (M.R.). It is seldom that a 

 material has a tensile strength equal to its strength to 



