MECHANICS 97 



one of the other vertexes, as fd, and bisect this line as at g. 

 Connect g and b and lay off one-third of its length from g 

 at the point h. This point is the center of gravity of the 

 figure. 



The distance of the center of gravity of the surface of a half 

 circle from the center is equal to the radius multiplied by 

 .424. 



Neutral Axis. The neutral axis of a flat or plane figure 

 may be considered as any line passing through the center of 

 gravity. This definition of neutral axis is correct for use in 

 the mechanics of ordinary materials. However, in speaking 

 of the neutral axis of reinforced-concrete beams, something 

 else is meant. This will be explained later. The location 

 of the horizontal neutral axis, that is, a horizontal line 

 through the center of gravity of a plane figure, is of great 

 importance in engineering. Of course, if the center of 

 gravity is located, the horizontal neutral axis can be located 

 easily; but, as a rule, the horizontal neutral axis is located 

 without first locating the center of gravity. 



Locating the Neutral Axis by Means of the Principle of 

 Moments. A convenient method of locating the neutral 

 axis is based on the principle that the moment of any plane 

 figure, with respect to any given line as an axis or origin of 

 moments, is equal to the product of its area by the perpen- 

 dicular distance from the center of gravity of the figure to the 

 given axis. 



Let M represent the moment ; A , the area of the figure or 

 section; and c the perpendicular distance from center of gravity 

 of figure to given axis. Then, ., 



M = AXc andc = 



If necessary, the figure may be subdivided; then th& 

 moment of the figure is equal to the sum of the moments ol 

 its separate parts with respect to the same axis. Designa- 

 ting the areas of the subdivisions by the letters a, a', a", etc. 

 and their moments by nt, m', m", etc., then the preceding 

 formula becomes 



m + m' + m", etc. 



a + a' + a", etc. 



