THE STRESSES IK A STEEL WATER-TOWER. 13! 



case a continuous curved girder in the horizontal plane may be 

 used (Fig. 31). 



The stresses in this horizontal girder can be determined by 

 treating it as an arch without hinges. Assume the girder to 

 be cut in two equal parts by the plane mm. Then the half-girder 



FIG. 31. 

 ABD will form a semicircular arch, sustaining a load of H 



TT 



pounds at the crown and a thrust of - - pounds at each abut- 

 ment. At each abutment there is also a couple whose moment 

 must be determined in order to find the stresses in the girder. 

 The bending moment at the abutment and the resulting bend- 

 ing moments at the other points in the arch may be determined 

 by the methods usually employed in the analysis of the elastic 

 arch. Graphical analyses of the stresses in horizontal curved 

 girders having four, six, eight, and twelve loaded points, or points 

 of support, give coefficients varying not more than three per cent, 

 from those given in the table of Stresses in Ring at Top of 

 Posts (page 130). Strict mathematical analysis would probably 

 give identical results. In any case, the variation is so small 



