COLUMNS AND STRUCTURES 249 



for concentric loading. However, there are cases when the use 

 of the larger radius of gyration may be permitted. If a column 

 is built into a wall of first-class masonry so that it cannot bend 

 in the weaker direction the larger radius of gyration may be 

 used. A casing of a few inches of concrete is not enough to satisfy 

 the requirement that the column be stayed in the weaker direc- 

 tion. The supported length of a column is the length used in 

 the formulas. If a column is supported in the weaker direction 

 by adequate bracing the supported length is the distance between 

 the attached ends of the stays, and the column may be designed 

 with the smaller radius of gyration combined with the shorter 

 lengths, or it may be designed with the larger radius of gyration 

 combined with the greater length. When possible the weaker 

 dimension of the column should be turned in the direction of 

 the closer supports. Even when the least radius of gyration is 

 chosen the column should be so placed in the structure that the 

 heavier loads come on the longer axis. 



The effect of eccentric loading is taken care of by increasing 

 the size of the column. The tendency of the column to bend is 

 determined by the slenderness of the section and it can bend 

 sideways to the load, this being the reason for using the least 

 radius of gyration regardless of the direction from which the load 

 may come to the column. In the column tables in the steel hand- 

 books the total load is generally given, together with a state- 

 ment as to which radius of gyration is used in computing the 

 strength of the column. The tables are computed by one of the 

 several formulas plotted in Fig. 162. 



In assuming column sections the formulas given do not take 

 into account the various methods for attaching the principal 

 parts together. From the result of experiments it is believed safe 

 to use the allowable fiber stress by formula for columns with 

 solid web plates, as for example plate and angle columns. For 

 laced columns use about seventy-five per cent and for columns 

 fastened by batten plates use about fifty per cent of the fiber 

 stress given by formula. 



Fig. 163 appeared in Engineering News, in 1913 in an article 

 by O. von Voigtlander on Approximate Radii of Gyration. The 

 use of the table saves a great deal of labor on the part of the 

 designer when he can know in advance the outside dimensions 

 of his columns or struts. It is not necessary to know this accu- 



