PHYSICS, CHEMISTRY AND ENGINEERING 173 



3. The point of contra-flexure of each girder is at its mid- 

 length. 



4. The direct stress in a column is directly proportional 

 to the distance from the column to the neutral axis of the 

 bent. 



ASSUMPTIONS IN METHOD II 



1. A bent of a frame acts as a series of portals. 



2. The point of contra-flexure of each column is at mid- 

 height of the story. 



3. The shear is the same on all columns of a story. 



4. Each pair of adjacent columns of a bent acts as a 

 portal, and each interior column is a member of two adjacent 

 portals. The direct stress in an interior column, when the 

 column is considered as a member of the portal on one side, 

 is of opposite sign from the direct stress in the same column 

 when considered as a member of the portal on the opposite 

 side and the resultant direct stress is equal to zero. 



ASSUMPTIONS IN METHOD III 



1. A bent of frame acts as a continuous portal. 



2. The point of contra-flexure of each column is at mid- 

 height of the story. 



3. The direct stress in a column is directly proportional 

 to the distance from the column to the neutral axis of a bent. 



4. The shear is the same on all columns of a story. 



Professor Albert Smith, in a paper before the Western So- 

 ciety of Engineers, describes a method which he has used in 

 his classes in Structural Engineering at Purdue University. 

 This method is here designated as Method IV : 



ASSUMPTIONS IN METHOD IV 



1. The point of contra-flexure of each column is at mid- 

 height of the story. 



2. The point of contra-flexure of each girder is at its mid- 

 length. 



