200 JOHN C. KOCH 



the section, and this relation is expressed by the following for- 



s 

 nulla ~ 1 = M, in which the symbols indicate the following 

 c 



units : 



s, pounds per square inch; 



c, inches; 



M, bending moment in inch-pounds at section; 



I, biquadratic inches ( = inches'*) . 



40. By the use of this formula the maximum fiber stress may 

 be found in any section of a beam, the cross section of which is 

 bounded by straight or curved lines forming regular geometrical 

 figures, provided the bending moment due to the external forces 

 can be computed by the laws of equilibrium. 



By a graphical method to be described later the principles 

 just discussed may be applied without using the calculus for the 

 determination of the moment of inertia. 



41. The section modulus of any cross section of a beam is the 

 measure of strength of the resisting moment and is equal to the 

 moment of inertia divided by the distance from the neutral 

 surface to the outermost fiber in the cross section. 



Section modulus = — 

 c 



42. Summary. Summarizing this discussion of the moment 

 of inertia, the power of any elastic body to resist the action of 

 forces which produce compression or bending stresses depends 

 upon the following factors: 



1. The physical properties of the material. 



2. The shape of the cross section of the body. 



3. The area of the cross section of the body. 



4. The magnitude and direction of the external loads. 



5. The manner in which the load is transmitted through the 

 body. 



6. The manner in which the body is supported. 



Theory of column action 



43. Factors affecting strength. The essential principles in the 

 mechanics of columns are of importance in this study and will 



