BENDING. 



27 



The relation between stress, strain, and bending moment 

 for a beam of uniform rectangular section is shown in the 

 following way : 



FIG. 12. 



Let it be assumed that the beam is of uniform material, 

 whose modulus of elasticity in tension is equal to that in 

 compression. Let the maximum stresses in the metal in 

 tension and compression be f t and f c respectively. The 

 section of the beam is shown on Fig. 1 2 as A B C D. The depth 

 of the beam is d, and its breadth b. Consider a strip of 

 this section at a distance y from, and parallel to, the neutral 

 axis X Y. Let this strip have a width 8 y, and let the stress 

 at this distance from the neutral axis be f y . 



The total stress on the strip will be 



fy .Sy.b, 



and its moment about the neutral axis 



fy 8 y b y- 



But this stress f y is proportional to its distance from X Y, 

 that is 



2 2 



So that the moment of the stress on the strip may be 

 written 



