Alexandek — Maximum Bending -moments on Short Girders. 23 



c'mnb' to be the end of a pack of cards stacked vertically into a rectangle, and 

 having the right parabolic segment painted upon it, each vertical hatchment 

 being on the edge of a card. The pack is then to be distorted and packed 

 into the parallelogram cmnh, and lifted up till A coincides with Aq, and Di 

 coincides with di. We shall then have the arc of the oblique parabolic 

 segment GAsdi) coinciding at every point with the arc of the segment BA„C. 

 Also £ will be above at a height A^o= 189 foot-tons, audi*' will be above i^j 

 at a height Didi = 117 foot- tons. Hence UF is an oblique base whose horizontal 

 range is OFi = 12 feet, the extent of the fourth field, and the vertical ordinates 

 from that oblique base measured up to the segment BA(,C give the maximum 

 bending-moments at each point of the fourth field individually as Wi 

 comes over it. The maximum of these maxima is given by /S^i«i = Si^4=261 

 foot- tons. 



SA = Sa =26jp tons. 



If each of the five right parabolic segments on fig. 2 be distorted and lifted 

 up in a like manner, we then have, on fig. 5, only one parabolic right segment 

 of the height 441 foot- tons standing on the span as a base, and a polygon 

 ACDEFB standing on the same base, and on the same side of it, having its four 

 apexes on the lines dividing the five fields from each other. The heights of 

 these apexes are 



C B E F 



85 145 189 117 foot-tons, 



being the same as the depths of the junctions of the arcs -Di, !>%, D^, and Bi 

 below the dotted parabola on fig. 2. 



B.I. A. PROC, VOL. XXX., SECT. A. [4] 



