According to IS 456 ∶ 2000, what is the maximum slenderness ratio for an unbraced column?

Explanation:

By Clause 25.3 of IS 456-2000

• The unsupported length between end restraints shall not exceed 60 times the least lateral dimension of a column.
• If, in any given plane, one end of a column is unrestrained, its unsupported length, it shall not exceed \(\frac{100b^2}{D}\)

where
b = width-of that cross-section, and
D = depth of the cross-section measured in the plane under consideration.

Additional Information

• Slenderness ratio is defined as the ration of effective length and radius of gyration. \(S = \frac {L_e}{k}\)
• Effective length is defined as the distance between two adjacent points of zero bending moment or contra- flexure.
• The moment of inertia of a body about an axis can be represented using the radius of gyration. 
• Radius of gyration can be defined as the imaginary distance from the centroid at which the area of cross section is imagined to be focused at a point in order to obtain the same moment of inertia.
• The formula of moment inertia in terms of the radius of gyration is given as follows:  \(I=m \times k^2\)
• When the column is supported throughout its length, then the effective length of column will be zero so the slenderness ration will also become zero.