542 



STRUCTURAL MECHANICS. 



CHAP. XVI. 



55. MAXIMUM SHEARS AMD MOMEHTS in SIMPLE. BEAMS FOR MOVIHG COHCEMTRATE.D LOADS. 



Criterion For Maximum Shear. 



The maximum shear due to moving concentrated loads will occur at one support when one 

 oFthe loads isat that supportand will equal the total reaction. The load qivinq the maximum 

 must be determined by trial. 



Criterion For Maximum Moment. 



The maximum moment due to moving concentrated loads will occur under one of the 

 loads when that load is as far From one end as the center of gravity of all the loads on the 

 beam is from the other enc/. The load giving the greatest maximum must be Found by trial. 



For beams Fixed at one orbothends and carry ing one load, see 49and54, In this chapter. 



a.OftELOAD. 



X 



Max.Shear, X=0; V=P; at/?,. 

 Max.Moment, X=^i M=+PL; at P. 



b. Two EQUAL L OADS. 







2 



Max.%ear,X=0; V=P+P 1 -^- ; atR, 



7 t i'* 



/Fa is greater than 0.5862 t one load gives max. /lasiha. 



c. THREE EQUAL LOADS, EQUALLY SPACED. 



a 3 



d. FOUR EQUAL LOADS } EQUALLY SPACED. 







; atR, 



Max.Shear, X--a; 



Max-Moment, /^l; 

 IFais greater than O.MOljtwo loads givemax.tlaslnb. 



Max.5hear. 



y=4P 



Max.Momenk,X*l(l-L); 



atR. 

 $S*tZ> 



I Fa is greater than 0.26B2, three loads give max. Mas in c, 



e. Two UHEQUAL LOADS. 



a I 



F. Two EQUAL Lo ADS AfioOriE SMALLER LOAD. 



a b , 



. 

 



\2 3 



, X=0; 





rlaxthear, X=a; V* 



Max.moment may occur For one load as in a. 



Sia*. moment may occur For two egual loads asinb. 



