HOMOGENEOUS BEAMS 145 



ened when the beam is bent; that is, SS"=S / S". A line 

 drawn through this fiber SS" when the beam is straight is 

 called the neutral line, and the horizontal plane in which this 

 line lies is known as the neutral surface of the beam. The 

 neutral line corresponds to the center line ab, Fig. 3, on 

 which the center of moments x was taken. 



The line SiS 2 , which passes through any beam section, as 

 abed, Fig. 4, at the neutral line, perpendicular to the direc- 

 tion in which the beam bends, is called the neutral axis. 

 It is shown in works on mechanics that the neutral axis 

 always passes through the center of gravity of the cross-section 

 of a beam made of uniform material. 



Thus, in a beam, it is evident that the neutral axis of any 

 section is a horizontal line at which the fibers composing 

 the beam are neither stretched nor compressed. The axis 

 is horizontal because it is at right angles to the direction of 

 the load, which, in structural problems, usually acts down- 

 wards. It so happens that in a beam made of one material, 

 this line will pass through the center of gravity of the sec- 

 tion. It is for this reason that the neutral axis has been 

 spoken of as a line through the center of gravity of a section. 

 It happens, however, that in many beams made of two 

 materials, as, for example, concrete and steel, the neutral 

 axis that is, the horizontal line along which the particles 

 of the beam are neither stretched nor compressed does not 

 pass through the center of gravity of the section. 



SECTION MODULUS 



The modulus of a section of a beam is equal to the moment 

 of inertia of the section about its neutral axis divided by 

 the distance from the outermost fiber in that section to the 

 neutral axis. This fiber may be either above or below the 

 neutral axis, and it is immaterial whether the beam is a 

 simple beam, a cantilever, or any other kind of beam. If 

 the moment of inertia of a section about its neutral axis is 

 represented by /, the distance from the neutral axis to the 

 outermost fiber by c, and the section modulus by S, then 



