THE STRESSES IN A STEEL WATER-TOWER. 119 



It is this that makes the hemisphere the most desirable form of 

 bottom. 



It will be noted that the value of V is independent of the 

 shape of the bottom. 



The above analysis assumes that the joint is theoretically 

 perfect, that is, that the lines of action of H, V, and T inter- 

 sect in a common point. In the case of both the conical and the 

 segmental bottoms the plates have to be flanged so as to become 

 tangent to the cylinder. Thus the element of the cone and the 

 element of the cylinder must be connected by a curve, likewise 

 the meridian element of the segment and the element of the 

 cylinder (Fig. 25). This connecting curve may be part of a sphere 



FIG. 25. 



or part of an ellipsoid of revolution. In the former case r 3 equals 

 r, and in the latter case r 3 is less (or greater) than r. 



The stresses in this connecting part of the bottom are com- 

 plex. An analysis of them is given by Professor Talbot,* from 



which it seems that when the ratio of - = 2, H = o and there is 



r 3 



no resulting tension or compression on the joint-ring; when 



<2 there is tension; and when >2 there is compression. 

 r a r s 



* See "Stresses in Tank Bottoms," by Professor Arthur N. Talbot, The Tech- 

 nograph, No. 16, page 139. 



