Definition of Slenderness Ratio:
Slenderness ratio is defined as the ratio of effective length of any structural member to its radius of gyration of its cross section. Generally slenderness ratio is used in civil engineering design for columns, walls,piers etc. This parameter is dimesionless because radius of gyration and effective length both have the same units.
Radius of Gyration:
Radius of gyration is defined as the rooted ratio of moment of inertia and cross sectional area of the structural or any other member.
Thus Radius of gyration =(I/A)^0.5
where, I= moment of Inertia
A=Cross sectional area
Application of Slenderness Ratio:
Slenderness ratio is very important in determining the compressive load carrying capacity of the structural member. Generally the lower the slenderness ratio is the greater compressive load a column or pier can take. A column having low value of this ratio can resist more buckling than others and therefore it can resist more compressive stress.