SECTION VIII 



COLUMNS AND STRUTS 



51. Nature of compressive stress. When a prismatic piece of 

 length equal to several times its breadth is subjected to axial com- 

 pression, it is called a column, or strut, the word column being 

 used to designate a compression member placed vertically and bear- 

 ing a static load, all other compression members being called struts. 



If the axis of a column or strut is not perfectly straight, or if the 

 load is not applied exactly at the centers of gravity of its ends, a 

 bending moment is produced which tends to make the column deflect 

 sideways, or " buckle." The same is true if the material is not per- 

 fectly homogeneous, causing certain parts to yield more than others. 

 Such lateral deflection increases the bending moment and conse- 

 quently increases the tendency to buckle. A compression member is 

 therefore in a different condition of equilibrium from one subjected 

 to tension, for in the latter any deviation of the axis from a straight 

 line tends to be diminished by the stress instead of increased. 



The oldest theory of columns is due to Euler, and his formula is 

 still the standard for comparison. Euler's theory, however, is based 

 upon the assumptions that the column is perfectly straight, the 

 material perfectly homogeneous, and the load exactly centered at 

 the ends assumptions which are never exactly realized. For 

 practical purposes, therefore, it has been found necessary to modify 

 Euler's formula in such a way as to bring it into accord with the 

 results of actual experiments, as explained in the following articles. 



52. Euler's theory of long columns. Consider a long column sub- 

 jected to axial loading, and assume that the column is perfectly 

 straight and homogeneous and that the load is applied exactly at 

 the centers of gravity of its ends. Assume also that the ends of the 

 column are free to turn about their centers of gravity, as would be 

 the case, for example, in a column with round or pivoted ends. 



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