Which of the following boundary conditions for a column results in the lowest effective length factor (K)?

Explanation:

• When both ends of a column are fixed, it resists rotation at both ends, providing the highest resistance to buckling. This results in the lowest effective length factor (K), which is typically 0.5 for both ends fixed.

• A lower value of K indicates a column is more resistant to buckling.

Additional Information

One end fixed and the other free

• Effective Length Factor (K = 2.0): This setup results in the highest effective length factor because the free end does not resist rotation, leading to greater flexibility and susceptibility to buckling.

• Behavior: The column behaves like a cantilever, where the free end can deflect more easily compared to a fixed end.

• Common Use: Typically found in situations where one end of the column is fixed (like in a wall or frame) and the other is exposed (like a cantilevered beam or structural element).

One end fixed and the other pinned

• Effective Length Factor (K = 0.707): The column is restrained at one end and allowed to rotate at the other. This setup offers moderate buckling resistance.

• Behavior: The fixed end resists rotation, while the pinned end allows free rotation. The column has some flexibility but is still somewhat controlled.

• Common Use: This condition is common in columns where one end is embedded in the structure (e.g., a frame) and the other is pinned, allowing for some rotation but still providing support.

Both ends pinned

• Effective Length Factor (K = 1.0): Both ends are pinned, meaning the column can rotate freely at both ends but cannot translate horizontally. This provides a moderate level of buckling resistance.

• Behavior: Since both ends can rotate, the column is not as stable as one with fixed ends but is still better than if one end were completely free.

• Common Use: Found in simple structural systems where columns are connected at both ends to beams or slabs that do not fix the column against rotation.