THE STRESSES IN A STEEL WATER-TOWER. 121 



The girder rests on the tops of the tower posts, and transmits 

 the load to them. There may be four or more posts or points 

 of support. 



Consider first a girder with four points of support.* Let W 

 be the total load, and let A, B, C, and D be the points of support 

 of the circular girder (Fig. 26). By symmetry the reactions R A9 



W 



R , R c , and R D are equal to each other, hence each is R = . 



Assume the axes of reference X, Y, and Z passing through O, 

 the axis of Z being vertical. Consider the left half of the girder 

 cut away by a plane just to the left of the points of support A 

 and C. The forces required to maintain the equilibrium of 

 the right half equal the stresses in the girder at A and C. The 

 possible forces at A are 



a horizontal force parallel to X=+S X ', 



a horizontal force parallel to Y=+S y ', 



a vertical force parallel to Z = + S z ; 



a couple perpendicular to X, whose moment +M,; 



a couple perpendicular to F, whose moment = +M V ; 



a couple perpendicular to Z, whose moment =+ M z \ 



and at C the possible forces are 



and M z . 



The external forces acting on the portion of the girder considered 



W 

 are , R A , R s , and R c . These external forces have no com- 



ponents parallel to X, hence 



Likewise S y = o. 



* Adapted from "The Bending Moment in a Circular Girder," by G. P. Stark- 

 weather, Engineering News, Nov. 15, 1900. 



