Definition of Slenderness Ratio:
The slenderness ratio of a column is the ratio of its effective length (l) to its least radius of gyration (r). It is a measure of how slender or stocky a column is.

Importance of Slenderness Ratio:
The slenderness ratio is an important factor in the design of columns because it determines the column's ability to resist buckling. Buckling is a failure mode in which the column bends or buckles out of its straight shape under compressive loads.

Short Column:
A short column is one that fails primarily due to crushing of the material rather than buckling. In other words, the failure of a short column is governed by its compressive strength rather than its slenderness ratio.

IS 456 Guidelines:
According to IS 456:2000, the code of practice for plain and reinforced concrete, the slenderness ratio for a short column should not exceed 12.

Reasoning:
The specific value of 12 is chosen based on the assumption that a column with a slenderness ratio less than 12 can be considered short and will predominantly fail due to crushing rather than buckling. This assumption is based on empirical evidence and experience from past structures.

Limitations:
It is important to note that the slenderness ratio is not the only factor to consider in column design. Other factors such as the material strength, column dimensions, and load conditions also play a significant role. Additionally, the slenderness ratio limit of 12 is applicable for normal conditions and may vary for special cases or specific design requirements.

Conclusion:
In conclusion, according to IS 456:2000, the slenderness ratio for a short column should not exceed 12. This limit is based on the assumption that columns with a slenderness ratio less than 12 will predominantly fail due to crushing rather than buckling. However, it is important to consider other factors and design requirements in column design.