The experimental formula related to the middle pillars, which is the root formula, is useful only on tall columns.

Rankine-Gordan formula and its applicability
The Rankine-Gordan formula is a widely used equation in structural engineering that accounts for both direct stress and buckling stress. It is used to determine the maximum safe load-carrying capacity of columns under compressive loads. The formula takes into consideration the length and other geometric properties of the column, as well as the material's mechanical properties.

Applicability to Intermediate columns (Option D)
The Rankine-Gordan formula is applicable to intermediate columns. Intermediate columns are those whose length lies between the extremes of very long and short columns. These columns are neither slender nor stocky, and their behavior under compressive loads is influenced by both direct stress and buckling stress.

Direct stress and its significance
Direct stress is the stress caused by the axial load acting on the column. It is calculated by dividing the axial load by the cross-sectional area of the column. Direct stress is significant because it directly affects the strength and stability of the column. If the direct stress exceeds the material's yield strength, it can lead to permanent deformation or failure of the column.

Buckling stress and its significance
Buckling stress is the stress at which a column becomes unstable and buckles under compressive loads. It is influenced by the length, cross-sectional shape, and end conditions of the column. Buckling occurs when the compressive load causes the column to deflect laterally instead of shortening in length. Buckling can significantly reduce the load-carrying capacity of the column, making it important to consider in column design.

Rankine-Gordan formula and its components
The Rankine-Gordan formula combines the effects of direct stress and buckling stress to determine the maximum safe load-carrying capacity of a column. It is given by the equation:

P = (π²E*I)/(l/r)² + Fc/A

where P is the maximum load that the column can safely carry, E is the modulus of elasticity of the material, I is the moment of inertia of the column's cross-section, l/r is the slenderness ratio (ratio of column length to its radius of gyration), Fc is the allowable compressive stress, and A is the cross-sectional area of the column.

Conclusion
In conclusion, the Rankine-Gordan formula accounts for both direct stress and buckling stress and is applicable to intermediate columns. By considering both types of stress, the formula provides a more accurate prediction of the load-carrying capacity of the column and helps ensure its strength and stability.