Surface-Loading on the Flexure of Beams. 



491 



Distance («) of given 

 points on normal from 

 top of beam, in millim. 



Load ((3) on roller (weight of 

 shot) x 50 in lb. 



/3/«. 





1. 



2. 



Mean. 





1-15 



40 



39 



39-5 



34-34 



3-2 



114 



105 



1095 



34-22 



4-2 



145 



149 



147 



35-00 



5-2 



182 



180 



181 



34-80 



6-2 



218 





218 



35-16 



If the shear at 4*2 millim. with 147 lb. be taken as unity, 

 the shear at 5*2 millim. with this same load will be ^-f j-, since 

 the same shear is produced at 5*2 millim. with 181 lb. as is 

 produced at 4*2 millim. with 147 lb. Hence if the curve of 

 loading is an hyperbola, we should have 



4-2x1 = 



147 

 181 



x 5*2 or /3/a a constant. 



From the third column given above the values of /3/a will 

 be seen to be nearly equal in each case ; the value of 6 has 

 here been neglected ; if we put # = 0'04 millim., the values of 

 Blot, become 



34-6 33-8 34-7 34*5 34-9. 



Proposition II. 

 Things being arranged as in Proposition I., it is required to 



Fig. 2. 



determine the locus of points of equal intensity of shear, and 



