Calculating Effective Length of Compression Member

A compression member, also known as a column, supports axial compressive loads. Its strength and buckling resistance depend significantly on its length and the way its ends are supported, which are called end conditions.

The effective length of a column is an equivalent length used in buckling calculations. It represents the length of a pin-ended column having the same buckling strength as the actual column with its specific end conditions. The effective length is related to the actual length by a factor called the effective length factor, denoted by \(K\) or \(L_e/L\).

The formula for effective length is:

\(L_e = K \times L\)

Where:

• \(L_e\) is the effective length
• \(K\) is the effective length factor (depending on end conditions)
• \(L\) is the actual or centre-to-centre length

The question describes a compression member with the following details:

• Actual length (\(L\)) = 5 m
• End Condition 1: Fixed at one end
• End Condition 2: Hinged at the other end

Different end conditions result in different effective length factors. For a column that is fixed at one end and hinged (or pinned) at the other, the recommended effective length factor (\(K\)) according to various structural codes (like IS 800 for steel structures) is 0.80.

Using the formula for effective length:

\(L_e = K \times L\)

Substitute the values:

\(L_e = 0.80 \times 5 \text{ m}\)

Now, perform the multiplication:

\(L_e = 4.0 \text{ m}\)

So, the recommended effective length of the column is 4.0 meters.

Let's compare this result with the given options:

1. 3.2 m
2. 4.0 m
3. 2.6 m
4. 2.8 m

The calculated effective length of 4.0 m matches option 2.