HOOKS, LINKS, AND SPKINGS 147 



05) p=]S ky*- 



y + p 



Under the assumption of pure bending strain the shear is zero 

 and the normal stresses form a couple. Therefore the algebraic sum 

 of the normal stresses is zero ; that is to say, 



pdF = 0, 

 or, substituting the value of p from equation (95), 



y + p 



Since k and E are constants and not zero, the integral must be zero. 

 Therefore, separating the integral into parts, 



f 



J 



y + p J y 



whence ~ 



(96) d=- J 



+ P 



which gives the distance of the neutral axis below the center of 

 gravity <f the section. 



Now let M denote the external bending moment acting on any 

 given section of area F, dF an infinitesimal area taken anywhere in 

 this section, p the stress acting on it, and y its distance from the 

 gravity azii *','/.. Then 



or, substituting the value of p from equation (95), 

 consequently 



and hence 

 (97) 



