Alexandi;r and Jackson — Pohigons to Generate Diur/rians, St'c. 25 



keystone aud springing stone are determined witli tlie lioop-tbrusts and 

 factors of safety against crushing. It is an advantage to this segmental 

 pai't of the semicircular arch not to be hampered by rigid backing as 

 it yields elastically as the load moves. Of course, rubble spandrils acting 

 by their weight chiefly may he necessary to check the upward swing of the 

 half-arch wheii the locomotives are on tlie other half-arch only. Note, too, 

 there is another joint of rupture where the slope 6 = 30° ; this is where the 

 noses of the line of stress (or elbows of the basket-handle) touch the upper 

 limit of the middle third. The joint here is inclined to gape at its lovxr end ; 

 the joint of the keystone at its upper end. At the springing the stress is 

 nearly at the centre of the joint, and this springing joint is closer to = 60° 

 than = 45°. These two, P, about 60^ and &i = 30, ottr jxdr of joints of rupture, 

 replace scientifically Eankiue's joint of rupture, which he roughly estimates 

 to be about Q = 45^. 



a7ic =7f7<n. A 



level of RaAZs. 



IJ 





W^ T-T~ zLir'tBy. 



Alexander & Jackson, 



Fio. 3«. 



The horizontal conjugate load is the passive resistance of the heavy square- 

 dressed backing to resist the spreading of the arch even in the slightest 

 degree. The shape of the conjugate load area enables the stability of the 

 arch to be secured economically, and there is great economy in the arch- 

 ring, whose "kernel" just accommodates the line of stress. 



Appj'oximate Solution of the Semicircular Arch. 



On fig. 3a, DE is the surcharge (parallelogram), and EA^B the spandril- 

 area, whose density is much less than that of the arch-ring, due to the voids, 

 and may be taken as the average \ and later on the ring-area is increased by 



