124 TOWERS AND TANKS FOR WATER-WORK'S. 



The unknown forces are those required at P to maintain 

 equilibrium and equal the stresses in the girder at P. The pos- 

 sible forces at P 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 m , 



a couple perpendicular to X' whose moment =M f x \ 



a couple perpendicular to Y' whose moment = M' y \ 



a couple perpendicular to Z' whose moment = M' Z . 



By summation of components, 



Wa 







_^_W_Wa = W^i^_a\ 



~ 4 8 27T 2 \4 ff/ 



is a maximum when a=o; then 



when a = , 

 4 



that is, the point of zero shear is midway between supports. 



Since the only horizontal forces acting are couples in verti- 

 cal planes, 



