STRESSES IN ELEVATED TANKS ON TOWERS. 367 



Stresses on Radial Joints. Conical Bottoms. In a conical bottom the stress per sq. in. 

 Ti" will be from (a) Fig. I, 



Il'-i-si- 6 

 W CSC 9 



2r,-T-l2/ 

 Now 



W = 62.5* -TTi 1 , 



and 



= 2.6h-ri-cscO/t (15) 



Stresses on Circumferential Joints. Conical Bottoms. In (a) Fig. i pass two horizontal 

 planes through the cone so that the intercept along the cone will be a unit in length. The tapered 

 ring cut away has a pressure of p' Ib. per lineal inch. This pressure p' may be resolved into a 

 pressure along the element of the cone, p\ = p' cot 9, and a Horizontal pressure, p* = p' esc 6. 

 The stress in circumferential joint will be 



Ti" = I2pt-ri/t = i2p'-ri-caceft 

 = 12 X o.434A-ri-csc0// 

 = 5.2/1 TI- csc 0/* (16) 



which is twice the stresses in the radial joints. 



Stresses in Circumferential Joints. Spherical Bottoms. The radial unit stress in a hemi- 

 spherical bottom is given by equation (12). Now in a segment of a spherical shell the curvature 

 is the same in all directions, and the unit stress on a circumferential joint will be the same as on 

 a radial joint, and 



TV = 7Y = 2.6* T,// (17) 



Connection Between Side and Bottom Plates. With a conical bottom the inclined pull per 

 lineal inch at the bottom of the circular tank will be from (15) 



TV" = 2.6* T csc 0. (18) 



The compressive stress in the horizontal ring will be due to the horizontal components of the 

 inclined stresses and will be 



P' = Ti" cos 6-r X 12 



= 3i.2*-r*-cot (19) 



There are no inclined or compressive stresses in a hemispherical bottom unless the circular 

 shell and the hemispherical bottom are joined by an elliptical segment. If the radius of the 

 circular tank divided by the radius of the segment = 2, there will be no secondary stresses (see 

 "Stresses in Tank Bottoms," by Professor A. N. Talbot, The Technograph No. 16, p. 139). 



Stresses in a Circular Girder. The circular girder supports the weight of the tank, the 

 contents of the tank, and its own weight. The load is uniformly distributed along the girder. 

 The girder rests on or is supported by four or more columns, and transmits its load to them. 

 Let W = total load on girder in Ib. ; 

 r = radius of girder in in.; 

 n = number of posts; 



a = 2ir/n = angle at center subtended by radii through two consecutive posts; 

 ' = angle subtended at center by any arc; 



M = direct bending moment in the girder at any point in in.-lb. ; 

 T = torsional bending moment in girder at any point in in.-lb.; 

 5 = shear in girder at any point in Ib. ; 

 Pa = Pb, etc., = reactions of columns in Ib. 



