Question

Define slenderness ratio of a column.

Answer 1

In architecture, slenderness ratio is the quotient between the width of the building and its height.
The slenderness ratio is the ratio of the unsupported length of a column and the radius of gyration of its cross sectional area. The sides of the cross sectional area must be in the same units as the length of the column. So, the slenderness ratio is unitless.
  So, mathematically, it is defined as
  
where, L is the effective length and k is the radius of gyration, which is defined by
  
where, A is the area of cross section of the column, and I is the 2nd moment of area of cross section.