254 PRACTICAL STRUCTURAL DESIGN 



suggested methods for dealing with this condition are not always 

 correct. 



The effect of an eccentric load is assumed to disappear at each 

 story height. That is, the tension, or additional compression, 

 caused in any story length of column by eccentric loading is 

 assumed to be a maximum at the mid-length of the column on 

 that story and to be zero at the ends. 



With a concentric load the unit compressive stress over the 

 cross-sectional area of the column is 



f W 

 f= A' 



in which / = unit compressive stress in pounds per square inch, 

 W = concentric load in pounds, 

 A = area of cross section in square inches. 

 Let e = eccentricity in inches, 



n = distance from axis of column to extreme fiber in the 



direction of the eccentric load, 

 P = eccentric load = A or A + B. 



The bending moment due to the eccentric load is 



M = Pe, 



and the extreme fiber stress due to the combination of direct and 

 eccentric load is r^ *, 



f = ~A ^> 



in which / = moment of inertia in direction of bending. 



The positive sign (+) is used to obtain the compression and 

 the negative sign (-) is used to obtain the tension. The com- 

 pressive stress cannot exceed the safe allowable stress determined 

 by a column stress reduction formula and the tensile stress is 

 not considered. 



The foregoing is an approximation only, but is satisfactory 

 when the flexural stress due to eccentric loading is not large. 

 The majority of designers use only seventy-five per cent of the 

 moment due to eccentricity and reduce the eccentric load to an 

 equivalent concentric load by the following expression: 



W , _ 0.75 



in which W e = the equivalent eccentric load, 

 r = radius of gyration. 



