Alexander — Maximum B ending-moments on Short Girders. 39 



moments* represent the maximum bending-moments at the junctions of the 

 fields (i.e. in positions corresponding to the points D^, B^, D^, Di in fig. 2) 

 are four other tubular arbors also turning on pins attached to the brass back 

 plate, carrying crank-arms of lengths equal to those on the arbors below, and 

 compelled to rotate in a manner exactly similar to the lower arbors by 

 vertical links between the ends of the upper and lower crank-arms. 



Attached to these upper arbors, and in front of the face-plate, are other 

 four light aluminium hands or pointers. The six pointers are set on the 

 arbors at right angles to the direction of the corresponding sHding-rod and 

 sleeve, or as it is evident that the directions of these sliding-rods are per- 

 pendicular to the directions of the threads on the left of the model (for the 

 figure below made up of rods and sleeves is simply the force-polygon rotated 

 through a right angle counter-clockwise), it follows that the aluminium 

 pointers move so as to keep parallel with the threads forming the polar rays 

 of the force-polygon. Hence the pointers move exactly as the links of the 

 link-polygon in fig. 1. Wlren the locomotive changes its position, the inter- 

 sections of the pointers keep vertically under the corresponding wheels of the 

 locomotive, any instantaneous position of the pointers outlines the bending- 

 moment diagram for the corresponding position of the locomotive, and the loci 

 of the intersections of the pointers form the diagram of maximum bending- 

 moments. 



A sheet of drawing-paper is glued to the face-plate of the model, and on 

 it these loci are drawn. 



The two extreme (blackened) pointers represent the end links of the 

 bending-moment diagram ; their intersection lies vertically under the 0. G-. 

 of the locomotive, and in its motion traces out the parabola which is the 

 diagram of maximum bending-moments for the transit of a single concentrated 

 load equal to the weight of the locomotive. 



The model exhibits very clearly the character and shape of the diagram 

 of bending-moments for any particular position of the load, the manner in 

 which the bending-moment at any point varies as the locomotive moves along 

 the girder, the generation and character of the diagram of maximum bending- 

 moments, the position of the locomotive which gives the maximum bending- 

 moment under any wheel, the position of the locomotive which gives the 

 greatest possible bending-moment, the character and extent of the fields into 

 which the span may be divided so that when each wheel is over any point in 

 its own particular field, a greater bending-moment is produced there than can 

 be produced by any other position of the locomotive. 



• 40 foot-tons to an inch (since the force scale is 4 tons to an inch, and the polar distance 

 10 feet). 



R.I.A. PROC, VOL. XXX., SECT, A. [6] 



