A wide flange section for a 4 m long column (hinged at both ends) has the following properties: 

Cross-sectional area = 6,000 mm² 
Radius of gyration, rx = 150mm
Radius of gyration, ry = 100mm
Modulus of Elasticity, E = 200,000 MPa

Determine the value of effective length.

For a column that is hinged at both ends, the **effective length** is given by:

\[
L_{\text{effective}} = K \cdot L
\]

where:

- \( K \) is the effective length factor, which depends on the end conditions of the column. For a column hinged at both ends, \( K = 1 \).
- \( L \) is the actual length of the column.

Given:

- \( L = 4 \, \text{m} = 4000 \, \text{mm} \) (converting from meters to millimeters).

Since \( K = 1 \), the effective length \( L_{\text{effective}} \) is:

\[
L_{\text{effective}} = 1 \cdot 4000 \, \text{mm} = 4000 \, \text{mm}
\]

### Answer:
The effective length of the column is **4000 mm**.

Would you like additional details or have further questions?

### Related Questions:
1. How would the effective length change if one end were fixed and the other hinged?
2. How do you calculate the critical load for buckling with given column properties?
3. What is the impact of radius of gyration on a column's stability?
4. How does changing the modulus of elasticity \( E \) affect a column’s critical load?
5. Can we calculate the slenderness ratio of this column based on the given data?

**Tip:** The effective length factor \( K \) varies with end conditions and affects the buckling behavior significantly.

A wide flange section for a 4 m long column (hinged at both ends) has the following properties:

Cross-sectional area = 6,000 mm²
Radius of gyration, rx = 150mm
Radius of gyration, ry = 100mm
Modulus of Elasticity, E = 200,000 MPa

Determine the value of effective length.

Find the effective length of a 4 m long column with hinged ends, cross-sectional area of 6,000 mm², and a modulus of elasticity of 200,000 MPa. Explore concepts like effective length, radius of gyration, and column stability using key structural engineering formulas.

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