EXTERNAL FORCES 11 



All formulas and rules for obtaining the effect of loads on beams 

 are derived from the fundamental principle of the lever. It makes 

 no difference whether the beam rests on one, two, or more sup- 

 ports, the principle of the lever, as represented by the cantilever 

 beam in Fig. 1, gives the key for obtaining the desired information. 



All formulas and rules for obtaining the strength of a beam to 

 resist the bending effect are similarly based on the principle of 

 the lever. 



The bending effect is termed a " Bending Moment " and the resist- 

 ing effect, dependent upon the form, size, and material, of the 

 beam, is termed the " Resisting Moment." The bending moment 

 is first found and then a beam having an equal resisting moment 

 is used to carry the load. 



In structural design the moment may be compared to the com- 

 mon denominator in problems involving fractions. There are two 

 quantities which must be reduced to a common measure before 

 operations involving both can be performed. This explains why 

 engineers invariably equate (make equal) the bending moment 

 and resisting moment instead of working by rules derived by other 

 men. Each man who does much designing work derives rules 

 for himself because only by so doing can he be certain of their 

 correctness. When the underlying principle of moments is under- 

 stood no man should have trouble in verifying rules which he may 

 run across in his work or reading. 



Tables are published of resisting moments of standard size 

 beams from which a designer may readily obtain a beam to resist 

 a bending moment^ which is calculated for each case. Spans and 

 also loads to be carried on the spans vary considerably, every 

 building presenting a number of different combinations. All 

 rules and formulas apply to beams which are secured against side- 

 wise bending. 



When the resisting moment is greater than the bending moment 

 there is obtained a factor of safety. 



Let M - moment. This may be either bending or resisting 



moment. 



Mb - bending moment. The subscript is used only when 

 both moments are used in the same expression, and 

 there must be some dMtmganhilig mark. 

 M r - resisting moment, the subscript being used only when 

 the subscript b is. used for the bending moment. 



