4. Columns and Struts | EULER’S THEORY OF AXIALLY LOADED ELASTIC LONG COLUMNS

Steel is a very commonly used elastic material for columns and struts. Since steel can take high strength the columns and struts are usually slender. When such members are under axial compression, due to some unavoidable eccentricity, the lateral displacement may take place. Because of such displacement bending moment develops. This bending moment causes additional stresses. This results in the failure of the column at a load much smaller than its crushing load.
This type of failure of columns due to excessive displacement is called buckling failure.
The buckling load depends upon the slenderness ratio of the column, length of the column, and also the end condition.
Leonard Euler (1707-1783), a Swiss Mathematician was the first to derive a theoretical expression for buckling load

[avilobaiahbv]

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[indrakumartak]

Sir, why reactive moment is not considered for the case 'one end fixed and other end free' ?

[raviashbeltorbay]

Good day sir, please a little confuse about how you arrived at equating the last differenial equation to one. why is it that the last finding was not put back into the general equation to be able to equate to one