THE STRESSES IN A STEEL WATER-TOWER. 129 



When struts between diagonally opposite posts are used 

 to resist this thrust the compression in each strut equals H . 

 (Fig. 29.) 



If struts are not used, the radial forces may be resisted by 

 the bottom flange of the circular girder. Since the width of 

 the girder flange is small compared with the radius of the girder, 

 the solution of the stresses in a circular hoop may be applied. 



When a pair of radial forces H act on a hoop, as at A and C 

 (Fig. 30), the stresses at any point / resulting therefrom are:* 



Bending moment, M' =Hrl -). 



"TT 



Shear, S' = cos a'. 



rr 



Compression, C' = sin a'. 



A second pair of forces H acting at B and D produce stresses 

 at /: 



S" = cos a''; 



C" = sin a". 



2 



Then the stresses at / resulting from both pairs of forces are 

 the algebraic sums of the partial stresses, The general equa- 

 tions for these stresses when the forces are in equal pairs are 



* Transactions Association of Civil Engineers, Cornell University, 1896. 



