RANKINE THEORY APPLICABILITY TO SHORT AND LONG COLUMNS

The Rankine theory, also known as the Rankine formula or Rankine's theory of columns, is a widely used method for analyzing the stability and strength of columns. It provides a simplified approach to determine the ultimate load-carrying capacity of columns based on their slenderness ratio. The slenderness ratio is the ratio of the effective length of the column to its least radius of gyration.

Applicability of Rankine Theory:

The Rankine theory is applicable to both short and long columns. However, it is important to note that the assumptions and limitations of the theory differ for each type of column.

1. Short Columns:

Short columns are those in which the slenderness ratio is less than a certain critical value. The Rankine theory is most commonly applied to short columns because their behavior is governed by their material strength rather than their slenderness.

The assumptions for applying the Rankine theory to short columns are as follows:

- The column is subjected to axial compression only.
- The column is homogeneous and isotropic.
- The material of the column behaves elastically up to failure.
- The cross-section of the column remains plane and perpendicular to the axis of the column during deformation.
- The load is applied concentrically to the centroid of the cross-section.

Under these assumptions, the Rankine theory provides a reasonably accurate estimate of the ultimate load-carrying capacity of short columns.

2. Long Columns:

Long columns are those in which the slenderness ratio exceeds the critical value. For long columns, the Rankine theory is not directly applicable as it neglects the influence of buckling.

When a long column is subjected to axial compression, it may undergo buckling, which is a sudden lateral deflection caused by the compressive load. The buckling behavior of long columns is more complex and requires a different approach, such as the Euler's theory or the Perry-Robertson formula.

However, the Rankine theory can still be used to estimate the ultimate load-carrying capacity of long columns by considering the additional effect of buckling through appropriate modification factors. These modification factors are typically obtained from experimental data or more advanced analysis methods.

Conclusion:

In conclusion, the Rankine theory is applicable to both short and long columns. However, it is important to consider the assumptions and limitations of the theory, especially when applying it to long columns where buckling behavior becomes significant.