THE STRESSES IN A STEEL WATER-TOWER, 



123 



To determine the stresses at any point between supports, 

 consider the arc AP, A being a point of support and P an inter- 

 mediate point at which the stresses are required. Assume the 

 axes of X', Y', Z' through P. Let a be the angle AOP expressed 

 in circular measure, then the load on A P is 



Wa 



271 ' 



The centre of gravity of the load is at G. 

 The geometric relations of the figure 

 are (Fig. 27) 



FIG. 27. 



OG = 



2 rsm 

 2 



a 



. a a 



2T Sin COS 



2 2 r sin a 



a 



r sin a r 

 QP = r- -^-(a-sina); 



2f sin 2 



2 r 



OG= = (i cos a): 



a cr 



AS = r sin a; 



SP = r(i cos a). 



W 



The known forces acting on AP are the vertical shear S 2 = 



8 



on the left of A, the reaction R Ay the couple at A whose moment 



. _ . Wr/i i \ Wa 



is M y = ( I. and the load . 



2 \4 n/' 2?r 



