126 TOWERS AND TANKS FOR WAl^ER-WORKS. 



Wr . . . Wr 



8 



When a o, 



= -5 (sin a -f cos a) 



O 27T 



which is the bending moment in the girder over the point of 

 support. 



When a. = , 



4 



My = 1 I.4I42 ~ ) = + O.Ol762j'Fr, 



which is the bending moment in the girder midway between 

 supports. 



Between the values of a = o and a = there must be a value 



4 



of a that will make 



Wr Wr 



ML = -5- (sin a + cos a) = o, 



O 27T 



from which 



sin a+ cos a = 1.2732, 

 and =* 19 1 2' or 70 48'. 



A comparison of the values obtained for M' x and My shows 

 the following important results 



1. The points of maximum torsion moment are points of 

 zero bending moment. 



2. The points of maximum bending moment are points of 

 zero torsion moment. 



Considering now girders having a number of points of sup- 

 port other than four, we can make analyses similar to the fore- 

 going. Their results for several cases, including the results 



