36 STRENGTH OF MATERIALS 



/Pc 

 1} 'ft 

 */ 



and therefore 



But the distance of the center of gravity of the section from the axis 

 of Z (or neutral axis) is given by 



. 



dF 



Therefore, since CydF= 0, y must be zero, and consequently the 



neutral axis passes through the center of gravity of the section. 



43. Moment of inertia. For equilibrium, the moment of the IKT- 

 mal stresses acting on any cross section must equal the moment !' 

 the external forces at this section. Therefore, if M denotes tin- 

 moment of the external forces, or external bending moment, as it is 

 called, 



C 



or, from (16), 



-w r 



= M. 



The integral / ifdF depends only on the form of the cross section. 



and is called the moment of inertia of the cross section with respect to 

 the neutral axis. 



Let the moment of inertia be denoted by /. Then 



=/"'", 



and, consequently, 

 (17) 



This formula gives the intensity >f tlu> normal stress p at the distance 

 # from the neutral axis, due to an external bending moment M. If 



