COLUMNS AND STRUCTURES 



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in trusses are apt to contain considerable excess material because 

 they are usually composed of angles, but the excess material is 

 often of considerable advantage when wind is considered. The 

 consideration of holes in tension members leads to an excess of 

 material, and the effect of the radius of gyration is similar in com- 

 pression members. 



Eccentric Loads on Columns 



The column formulas heretofore considered are based on a 

 load acting vertically and applied at the upper end of the vertical 

 axis of the column. This is termed concentric loading. The only 

 tendency to bend is that caused 

 by the fibers being too strong 

 to crush or tear until after 

 considerable side bending 



takes place. 



An eccentric load is one ap- 

 plied at some distance off the , 



e ., , , Fig. 165 Eccentric Loads on Columns 



center of the column and act- 

 ing vertically. This is illustrated in Fig. 165. At (a) two loads 

 are shown carried on opposite sides of the column. Each reaction 

 is assumed to act vertically at the middle of the bracket on which 

 the beam rests. From the reaction of A to the axis of the column 

 the distance is x and from the reaction of B to the axis of the 

 column the distance is y. The center of gravity of the two loads 

 is found by the principle of moments, and the distance of the 

 center of gravity from the axis of the column is e, the eccentri- 

 city of the loads. 



(Ax) + (By) 

 A + B 



This eccentricity is always on the side of the heavier load. 



At (6) the eccentricity is the distance from the center of the 

 bracket support to the center line (axis) of the column. In both 

 cases the load is the total eccentric load, which, multiplied by 

 the eccentricity, causes a bending moment in the column. This 

 bending moment increases the compression on the side of the 

 column on which the eccentricity exists and causes tension on the 

 far side. Sometimes this tension may be great enough to over- 

 come the compression caused by the direct load, in which case 

 the column will fail. All columns are loaded eccentrically and 



