Art. 71. 



LOCATION OF THE 1NKUTRAL AXIS. 



99 



sometimes an important consideration as in the case of floor 

 beams carrying plaster. 



A similar calculation usually fully determines tin- si/<; of 

 a beam to carry a given load, except in certain cases, of long or 

 very short beams (76). 



If t\ and v. 2 are not equal, the section moduli for tension 

 and compression are not equal. If the working stresses in tension 

 and compression are the same, that one governs whose extreme 

 fiber is the farther from the neutral axis, and this is the one given 

 in the handbooks for unsymmetrical sections. The other one 

 may be easily calculated from the moment of inertia which is 

 also given for various axes. How to calculate the moment ol 

 inertia for any section about any axis is explained in Art. 72. 



71. Location of the Neutral Axis. The neutral axis is 

 located by the requirement that the total tension on a cross sec- 

 tion must equal the total compression, or that the algebraic 

 sum of the normal stresses must be zero, that is, 



/+Wl 

 sdA == 0, 

 -V 3 



= 0, which from equation (9) becomes 

 This can be true only when 



/+vi 

 vdA = 0. 

 -V 2 



/'+wi 

 vdA 

 V2 



(13) 



This is the algebraic sum of the moments of the areas about 

 the neutral axis, and requires that the moment of the area abovt; 

 the neutral axis shall balance the moment of the area below it; in 

 other words, the neutral axis must pass through the center of 

 gravity of the cross section. 



Unless otherwise particularly specified, the moment of in- 

 ertia of a cross section is referred to an axis through its center of 

 gravity. 



The location of the center of gravity of the sections of rolled 

 shapes is given in the handbooks. For other areas the engineer- 

 ing pocket-books, or any book on theoretical mechanics may be 

 consulted. 1 The location of the neutral axis, or center of grav- 

 ity, is determined below for a few cases. 



The center of gravity of an area is simply the point about 

 which it would balance if it had weight which was uniformly 



!See Goodman's Mechanics Applied to Engineering, chapter HI, 

 and "Cambria" 



