1C4 



COLUMNS IN TOWERS. 



Art. 114. 



the axes of the columns. With square ends, they would move 

 toward the load when the lower story of the column is bent so 

 as to be convex toward the loaded side, decreasing the eccen- 

 tricity; in the opposite case the eccentricity would be increased 

 as the column bends. The effect of y on the moment is neglected. 



H'Pf 

 P 



Fixed at B 



I J_ 



f 



I 



(OJ 



V 



I 



JU 



CF 



(cj 



<~-",'ffPf 



ft 



I 

 \P 



4^ 



fp 

 65/ 



i p f 



, i 

 !^ 



^P 



^/ 



Fig. 144. 



The eases of the one story column, (a) and (?>), Fig. 144, 

 are given for the sake of completeness. The other cases show that 

 the influence of the eccentric load decreases very rapidly in the 

 stories above or below it, and may be neglected in the third or 

 fourth story from the load. In case (/), for example, the maxi- 

 mum moment in the lower story is j^Pe at C. The maximum 

 moment in any case occurs at the top of the column when the 

 load is at the top, and is Pe. 



The horizontal reactions are gotten by applying the differen- 

 tial equation of the elastic line to each segment. In case (c), for 

 example, there are seven quantities to determine three reactions 



