HOMOGENEOUS BEAMS 129 



HOMOGENEOUS BEAMS 



PROPERTIES OF SECTIONS 



MOMENT OF INERTIA 



The strength and the stiffness of a beam depend on vari- 

 ous factors. For instance, the load that a beam can bear 

 depends on the material of the beam, on the manner in which 

 the load is applied, and on the length and cross-section of 

 the beam. As to the area of the cross-section, the strength 

 does not depend on that area itself, because, as every-day 

 experience shows, a plank used as a beam will sustain a 

 greater load when placed edgewise than when placed on its 

 broad side, although it has the same area in both cases. 

 The strength of a beam depends on the manner in which 

 the area is distributed or disposed with respect to the neutral 

 axis of the cross-section. The effect of the cross-section 

 is measured by a quantity that depends on such disposition 

 or distribution of area, and is called the moment of inertia 

 of the cross-section with respect to the neutral axis. The 

 moment of inertia of a plane figure has really nothing to do 

 with the property of matter known as inertia, and as here 

 used it is simply the name for a certain constant depending 

 on the shape of the cross-section of a beam. It is not a 

 moment as the word is generally understood, and it might 

 have been called anything so far as the structural engineer 

 is concerned, but it has received its name from some relations 

 in higher mathematics where it is derived. This quantity 

 must be considered simply as a constant that has been found 

 suitable for use in certain formulas for the design of beams, 

 which will be explained later. 



The following table, entitled Elements of Usual Sections, 

 contains, in the column marked 7, the moments of inertia 

 of the shapes of beam sections commonly used in practice. 

 The axis in each case passes through the center of gravity, 

 and is designated neutral axis in the table for reasons that 

 will be explained later. The square may be regarded as a 



