EXTERNAL FORCES 23 



The method given for obtaining the bending moment at any 

 section is used for any number of loads, three loads being used in 

 the examples for the sake of clearness. The computations being 

 illustrative the reactions have been given to fractions of a pound 

 and the moments have been given to fractions of foot pounds. 

 In actual work, it is generally considered that the nearest unit 

 is sufficiently exact. 



Rule for Obtaining the Bending Moment; at any Section 

 of a Beam 



Multiply one end reaction by the length from it to the section. 

 From the moment thus obtained subtract the sum of the moments 

 of the loads lying between the section and the chosen reaction, using 

 as moment arms the length in each case from the center of gravity 

 of the load to the section. The 

 portion of the beam included 

 between the section and the re- 

 action is to be counted as a load. 



A floor is merely a shallow Fig. 16 Concentrated Load at Any 

 beam, usually with a width of Point on Beam on Two Supports 

 , r, i_ as Shown 



12 inches. 



A beam is a secondary girder and the load is usually uniformly 

 distributed. 



A girder is uniformly loaded when it carries the floor slab 

 directly without the floor load going first to beams. When the 

 floor rests on beams the reactions at the ends of the beams are 

 concentrated loads going to the girders. 



A girder is generally carried on walls or columns and beams are 

 generally carried on girders. A rafter is a girder and purlins are 

 beams, or joists. 



For a load concentrated at any point, referring to Fig. 16, 



M - - p-> for load only. 

 Li 



The derivation of the formula is as follows: 



RI j > and R\ P R*, 

 Li 



Then M - ftfc, . . - ^* 

 L 



