Art. 114. COMBINATIONS OF BUCKLING AND BENDING. 197 



The moments are a maximum at the ends of the segments, 

 and have opposite signs above and below the points of division. 

 The maximum moment is Pe at the top of the column. The mo- 



/> 



ment at the bottom of the upper segment is Pe 1.61P T- 1= 



i 



O.GLPe. At the top of the second segment the moment is 

 0.61Pe+Pe=+0.39 Pe. At the intermediate points (three 

 stories or more from the top or bottom), the moment is %Pe. 

 This is the resultant of the opposite kinds of bending produced in 

 any particular story by the various loads. 



In high office buildings, each story is usually treated as an 

 independent column or rather as a block for eccentric loads, 

 and the moment is taken equal to Pe. These columns are usually 

 so short that their bending, compared with the eccentricity which 

 may be somewhat indefinite, is negligible. To get an idea of how 

 much this bending is, consider an 8"X W ^-bar column having 

 a length of 14 ft. and carrying a load of 25,000 Ibs. with an ec- 

 centricity of 6 inches. Assuming pivoted ends, equation (50) is 

 applicable provided I is taken as half the length. 



25000 



. 3X29000000/ 

 =(sec 17.09 1)=6 (1.046 1)=0.276 inches. 



If the entire load on the column is eccentric, the bending 

 will, of course, be much greater. 1 



115. Combinations of Buckling and Bending. When a 

 column is subjected to a transverse load in addition to the longi- 

 tudinal load, the bending due to the transverse force has more 

 influence upon the buckling stress than that due to the longitudi- 

 nal force P. The lever arm of P is due to a combination of the 

 action of both loads. In practice, such a column is sometimes 

 treated as a block in which the unit stress in the extreme fibre is 



and is allowed to be as large as the working stress in tension. Of 

 course s should not exceed the working stress given by a column 



1 For stresses in columns due to transverse forces, see Wind Stresses in 

 the Steel Frames of Office Buildings, by W. M. Wilson and G. A. Maney, 

 Engineering Experiment Station, University of Illinois, Bulletin No. 80. 



Stresses in Tall Buildings, by Cyrus A. Melick, Bulletin No. 8, College 

 of Engineering, Ohio State University. 



