THE STRESSES IN A STEEL WATER-TOWER. 125 



The moment at P about the axis of X' is a torsional moment, 



27T 



Wr/i i \ . Wr f Wr f 



= ( --- Ism a -- (a sin a)+ -5-11 cos a) 



2 \4 7T / 27T V 



- Wr Wra 



=-^-(i + sma cos a) -- . 



O 27T 



M' x = o when a = o and when = -, i.e., there is no torsional 



4 



moment at the point of support nor midway between supports. 

 To determine the place of maximum value of M' xt 



Wr Wr 



-- = o. 



da b x 27T 



4 

 cos a+ sin a = = 1.2732, 



a = 19 1 2 / or 70 48', 

 and the maximum values are . ^ , 



M' x = o.oo^Wr when a = 19 12' = 0.3351 radians, 

 and M^=+o.ooS3>Wr when 05 = 70 48' = 1.2356 radians. 



The moment at P about the axis of Y' is the bending moment 

 in the girder at P. It is 



W/y _ W _ 



Ml = M v cosa --- QG+-^AS 



27t O 



Wr/i i\ War W 



= - ( - -- ) cos a ---- (i cos a) + -5-7 sin a 



2 \4 7T/ 271 CT 8 



