Question

Compression members always tends to buckle in the direction of

• A. Horizontal axis
• B. Vertical axis
• C. Minimum cross section
• D. Least radius of gyration

Hint:

Think of it like trying to bend a ruler. It's very easy to bend it about its thin axis (low moment of inertia) but very difficult to bend it about its wide axis (high moment of inertia).
A column behaves the same way under compression - it will buckle in its "flattest" or weakest direction, which corresponds to the axis with the least radius of gyration.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
The question asks about the direction or axis around which a compression member (a column) will buckle.

Step 2: Detailed Explanation:
Buckling is a failure mode characterized by a sudden lateral deflection. A column under compression will always buckle in the way that is easiest for it to do so, which is the direction of its least resistance to bending.
The resistance of a column to bending (and thus buckling) is determined by its flexural rigidity, $EI$. For a given material ($E$), the resistance depends on the moment of inertia, $I$.
A column's cross-section will generally have different moments of inertia about its different principal axes (e.g., $I_{xx}$ and $I_{yy}$ for a rectangular or I-section). The column will buckle by bending about the axis with the

minimum moment of inertia ($I_{min}$).
The

radius of gyration ($k$) is defined as $k = \sqrt{I/A}$. Since the area $A$ is constant for the cross-section, the axis with the minimum moment of inertia ($I_{min}$) is also the axis with the

least radius of gyration ($k_{min}$).
Therefore, a column always tends to buckle about the axis corresponding to its least radius of gyration, as this is its weakest direction.

Step 3: Final Answer:
Compression members always tend to buckle in the direction of the least radius of gyration.