30 BENDING. 



So that the total force upon this strip is 

 f y .b.Sy=y.f.b.Sy. 



This can be written, with a somewhat different mean- 

 ing, as 



- - -T?_ 



r 



urea 



Fig. 13. 



or, instead of saying the total force on the strip is the 

 reduced stress f y multiplied by the whole area b . S y, we may 

 say it is the maximum stress, f, multiplied by a reduced 



-^ . b . 8 y V which comes to the same thing. To 



obtain this reduced area graphically, it is only necessary to 

 draw straight lines from A and B to the middle point of 

 the neutral axis and they intercept a b in c and d, and the 

 required area is the one shown darkened. If the process 

 be extended to the whole area, a triangle similar to that one 

 shown on the lower half of the beam, is obtained. 



This figure, which in this case is a triangle, is called 

 the "modulus figure," for one side of the beam, and it is 

 such that a constant stress / acting upon it would have 

 precisely the same effect as a variable stress acting upon 

 the rectangular section C F G D. The resultant of this 

 constant stress acting upon the various parts of the area 

 passes through the centre of gravity of the modulus figure, 



