MECHANICS 111 



sidering the portion of the beam to the left of the joint, this 

 portion moves clockwise, and the moment that moves it is 

 therefore posjtive. The magnitude of the moment tending 

 to move the left-hand part of the beam is Ril Wli, since 

 the load W acts in the opposite direction to RI. 



It will thus be seen that no matter in what part of the 

 beam the joint a is placed, the beam will collapse. There- 

 fore, it is evident that in any beam carrying loads, these 

 loads and the reactions exert a moment at any transverse 

 section that tends to bend the beam. It is only on account 

 of its own strength that a beam does not break. A beam is 

 therefore designed to withstand the bending moment of the 

 forces acting on it, and for this reason the engineer must at 

 all times be able to find this moment. With a simple beam 

 the bending moment (considering, as usual, the part to the 

 left of the section) is always positive, while with cantilever 

 beams it is negative. 



FIG. 15 



As an illustration, the bending moment around various 

 sections of the beam shown in Fig. 15 will be considered. 

 It is of course first necessary to find the reactions, so that 

 the moments may be calculated. To find RS, take moments 

 about RI. The positive moments, in foot-pounds, are 



1,200X3= 3600 



(800X9) X10* = 7560.0 



2,000X18= 36000 



Total, 115200 



The span is 24 ft. Therefore, R 2 = 115,200-5-24 = 4,800 Ib. 

 The sum of the loads is 1,200 + (800X9) +2 000 = 10.400 Ib. 

 Therefore, RI = 10,400 - 4,800 = 5,600 Ib 



The bending moment at any section of the beam may now 

 be found. For example, find the bending moment around 



