Alexander and Jackson — Polygons to Generate Diagrams^ i'c. 5 



span, together with an upward concentrated load at the centre, and 

 numerically equal to tivice, the base of the generating triangle or to the 

 distance between the wheels of the locomotive considered previously. Fig. 4 

 shows a load downward at the centre added to a uniform load, with the 

 B. M. diagrams separate. If we suppose there are two parabolic segments 

 coincident for the distributed load alone, then the addition of the central 

 load makes them rise up and cross each other, with I) the highest point of 

 the joint locus. Had W been upward, the two segments would have sunk 

 down and receded, with Ai and A^ the highest points of the joint locus, and 

 B a lower point between these, as on fig. 3. Then with the values of the 

 loads already stated, the stress diagrams of figs. 3 and 4 would be identical. 





ROLLINO TRIANGLES GENERATING DIAGRAMS OF THE SO- ROOTS 

 OF MAX. BENDING MOMENTS. 



-^o\V'-9 



J769fi},"K/Kax. 



Fig. 5. 



Fig. 6. 



Direct and Inverse Boiling. 



It will now be readily understood from figs. 5 and 6 the complementary 

 nature of the stress diagrams generated by the direct and inverse rolling of the 

 generating triangle. Two triangles are used in order that the two diagrams 

 generated may have a common span of 36 feet. The triangles have a 

 common base of 10 feet, but have different side values — 13 feet in the one 

 rolling clockwise directly, and 23 feet in the other ; and the span is twice 

 13 plus 10, and twice 23 minus 10. In the tigs. 5 and 6 the triangles are 

 shown turned through a small angle from their first position. 



In fig. 5 the two circular arcs, less than quadrants, meet at D, the 

 highest point of the locus. Its height is ^ (23^ - 5^), the height of the 

 generating triangle. The square of this height is 504 foot-tons, and is the 

 bending moment at the centre due to a uniform load of 72 tons, numerically 



