Calculate Column Slenderness Ratio

The slenderness ratio is a critical measure for columns, indicating their tendency to buckle under load. It relates the column's effective length to its radius of gyration.

Slenderness Ratio Formula

The formula for the slenderness ratio is:

$ \text{Slenderness Ratio} = \frac{L_e}{r} $

Where $L_e$ is the effective height and $r$ is the least radius of gyration.

Column Radius of Gyration (r)

For a circular cross-section, the radius of gyration ($r$) is calculated using the diameter ($D$):

$ r = \frac{D}{4} $

Given the diameter $D = 300 \text{ mm}$:

$ r = \frac{300 \text{ mm}}{4} = 75 \text{ mm} $

Column Effective Height (Le)

The effective height $L_e$ is given as $3 \text{ m}$. We need consistent units, so convert meters to millimeters:

$ L_e = 3 \text{ m} \times 1000 \frac{\text{mm}}{\text{m}} = 3000 \text{ mm} $

Determine Slenderness Ratio

Substitute the calculated values of $L_e$ and $r$ into the slenderness ratio formula:

$ \text{Slenderness Ratio} = \frac{3000 \text{ mm}}{75 \text{ mm}} $

$ \text{Slenderness Ratio} = 40 $

The calculation yields an integer value.