MECHANICS 113 



The point where the shear on a beam changes sign, 

 that is, changes from positive to negative, or from nega- 

 tive to positive, is the point around which the maximum 

 bending moment occurs. The point where the shear on a 

 cantilever beam changes sign, that is, the point around which 

 the moment is maximum, is always at the point of support. 

 Sometimes, the shear will change from positive to negative 

 or vice versa two or more times on a beam, and each sec- 

 tion, when the shear is zero, must therefore be investigated 

 to determine around which point the maximum moment 

 occurs. Fig. 16 shows an example of this kind. To solve 

 this example, it is first necessary to find the reactions. The 

 moments of the loads about R lt in foot-pounds, are as follows: 

 500X 2 = 1000 

 800X 5 = 4000 

 300X14 = 4200 

 Total, 9200 



R 2 X 10 =9,200 ft.-lb.; # 2 = 9,200 -MO =920 lb.; and RI 

 = 500 + 800 + 300-920 = 680 lb. 



FIG. 16 



At Rj, the shear is + 680 lb., and at 2 ft. from the left-hand 

 end the shear changes from +680 to 680-500= +180 lb. 

 At 5 ft. from the left-hand end, the shear changes from 

 + 180 to 180-800= -620 lb. This, therefore, is one place 

 where the shear changes sign. Under the reaction R 2 , the 

 shear changes from -620 to 920-620= +300 lb., and this 

 is therefore another point where the shear changes sign. 



There are therefore two places to be investigated for 

 maximum bending moment, one 5 ft. from the left-hand end 

 and the other 10 ft. from the left-hand end. The bending 

 moment about the point 5 ft. from the left-hand end is 



