Art. 115 COMBINATIONS OP BUCKLING AND BENDING. 



203 



If the longitudinal forces are eccentric, the moment is in- 

 creased or decreased; the eccentricity is added to or subtracted 

 from the maximum deflection as given in the above equations. 



The column load is often made eccentric in order to neutra- 

 lize the maximum bending moment due to the transverse load. 

 Thus in the case of Fig. 146, it would only be necessary to move 

 the forces P downward so that 



Pe=l WL 



the column then being treated s if it carried a concentric load P. 

 On account of the moment Pe being constant throughout the 

 whole length of the column, and the moment from the uniform 

 load decreasing toward the ends, the column would bend in two 

 segments, and a small excess of Pe over % WL would cause the 

 column to go over into single flexure the weakest condition. It 

 would be better to make the moment zero at about i/^L from the 

 ends so that the column would have two points of contra-flexure 

 and be bent into three segments, but the end conditions are us- 

 ually too uncertain to make this assumption safe. 



If the ends are partly fixed, as they always are in practice, 

 it may be impossible to counterbalance the center moment, be- 

 cause it may not be practical to have an eccentricity large enough 

 to turn the ends sufficiently; besides, as the center moment de- 

 creases, the end moments increase. It might be a question of 

 equalizing the end and center moments (see equations (74) and 

 (75) ), but the uncertainty of the end conditions would render 

 the problem indeterminate. 1 



1 See article by Prof. J. E. Boyd, in Eng. News, Vol. 57, page 404. 



