Alexander — Maximum Bending-moments on Short Girders. 35 



uniform load. To see how tliis may be done let us compare the modification 

 of the bending-moment diagram in tig. 5 to allow for change of span with 

 that for the addition of a uniform load. 



(1.) Gliangc of Span. — The ordinates of the polygon ^CZ'^i^.S, the unit of 

 length and the unit of bending-moment are all altered inversely as the span, 

 while the unit of load is unaltered. 



A SHORTER, HEAVIER IDEAL LOCOMOTIVE, EQUIVALENT TO 



A REAL LOCOMOTIVE 



(2.) AddifAon of Uniforrii Load. — The ordinates of the polygon ACDEFB, 

 the unit of load, and the ujiit of bending-moment are all altered iuversely as 

 the sum of the rolling load and half the uniform load, while the imit of length 

 is unaltered. 



The effect on the/orm of the diagram in fig. 5 of an increase of span from, 

 say, 42 to 56 feet, would then be the same as that due to the addition of a 

 uniform load of 2 x (56 - 42) or 28 tons ; i.e. to a load of two-thirds of a ton per 



