Section III, 1889. [ 3 ] Trans. Eoy. Soc. Canada. 



I. — Tlie Maximum Shear and Bending Moment produced by a Live Load at different 

 points of Horizontal Girder AB of span 1. By Prof. H. T. Bovey, McGill 



University. 



(Kead May 31, 1889.) 

 At any giveu instant let the load consist of a number of weights 



M'„ W,, W,, M'„, 



concentrated at points distant 



up «o, c.„ a,„ 



respectively, from B. 



Let W,. be the sum of the first r weights. 

 " Tr„ " " n weights. 



The reaction R^ at A is given by the equation 



and the shear Si at any point P between the j-"" and the (r+l)* weights, by the equation 



6\ = i?, — (m)i+!«,+ ?i'„) = iJ, — TF,. 



Let all the weights now move towards A through a distance x, and suppose that the 

 first p weights move off the girder, that q of the weights are transferred from one side of 

 P to the other, and that s new weights advance upon the girder. 



Denote these new weights by 



?«« + !, M'n+2, Wn+,, 



and let their distances from B be 



Û^n+lj ^n+2) 0,n+ai 



respectively. 



Let Wp be the sum of the first p weights. 

 " T " total weight transferred from one side of P to the other. 

 " Bp.l = io,.a^ + w.,.a.,+ -{- w^.a^,. 



" B,j.l=Wr+l-ar+l+U)r+2.ar+2+ +!«r+«-ar+7- 



" IIJ= W„+i.a„+l+W„+2-an+2+ +«'„+,.«„+,. 



