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According to BS8810 : A column is classified as short if Lex/h AND ley/b are :
-less than 15 for BRACED column .
-less than 10 for an UNBRACED column .
*About failures modes : Short columns usually fail by crushing ,but a slender column is liable to fail by buckling .
SHORT COLUMNS ACCORDING TO THEORY IS DEFINED BY SLENDERNESS RATIO(L/R) IF SLENDERNESS RATIO IS LESS THAN12 IT IS SHORT AND IF IT IS GREATER THAN12 IT IS LONG COLUMN.LONG COLUMN IS ALSO SUBJECTED TO BUCKLIN THUS ADDITIONAL REINFORCEMENT CONSIDERING TRAVERSE SHEAR SHOULD ALSO BE CONSIDERED,DESPITE THIS WE HVE TO CONSIDER THE SUPPORT CONDITIONS WHILE DESIGNING
Totally Agree with Usman Guni