Understanding Slenderness Ratio for a Supported Steel Column

The question asks for the slenderness ratio of a steel column that is supported throughout its entire length by a masonry wall. Let's break down what the slenderness ratio means and how the support affects it.

What is Slenderness Ratio?

In structural engineering, the slenderness ratio is a critical parameter used to determine a column's susceptibility to buckling under axial load. Buckling is a sudden failure mode where a slender structural member bends sideways under compression, even if the stress is below the material's yield strength.

The slenderness ratio is generally defined as the ratio of the effective length of the column to its least radius of gyration. Mathematically, it can be expressed as:

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

Where:

• $K$ is the effective length factor, which depends on the column's end conditions (how it's supported at the top and bottom).
• $L$ is the actual unsupported length of the column.
• $r$ is the radius of gyration of the column's cross-section (specifically, the least radius of gyration, which represents the weakest axis for buckling).

Impact of Continuous Masonry Wall Support

The key information here is that the steel column is supported throughout its length by a masonry wall. This means the wall provides continuous lateral support along the entire height of the column.

Continuous lateral support significantly restricts the column's ability to buckle sideways. If a column cannot buckle, its effective length ($KL$) approaches zero.

Consider the formula: $ \text{Slenderness Ratio} = \frac{KL}{r} $.

• Because the column is supported continuously, the potential for buckling is eliminated.
• This continuous support effectively makes the unsupported length relevant to buckling ($L$ in the context of buckling) very close to zero, or it drastically reduces the effective length factor ($K$) towards zero.

When the effective length ($KL$) approaches zero, the slenderness ratio also approaches zero. A slenderness ratio of zero implies infinite resistance to buckling.

Conclusion

For a steel column that receives continuous support along its entire length from a masonry wall, the potential for buckling is eliminated. Therefore, its slenderness ratio, which quantifies this buckling potential, is considered to be zero.

Comparing this conclusion with the given options:

• zero: This aligns with our analysis, as continuous support prevents buckling.
• 10: A small but non-zero value, implying some buckling potential.
• 100: A higher value, indicating significant slenderness and buckling risk.
• infinity: This would imply a column with zero radius of gyration or infinite length, which is not the case here.