Column - Buckling

Buckling is a phenomenon that occurs when a slender structural member, such as a column, experiences excessive compressive forces, causing it to fail under a mode of instability. When a column is subjected to a compressive load, it tends to buckle or bend laterally.

Explanation:

1. Truss - Bending:
A truss is a structure made up of straight members connected at joints. It is primarily designed to carry axial forces (tension or compression) along its members. Bending, on the other hand, refers to the deformation of a structural member due to the application of a bending moment. Trusses are not primarily designed to resist bending forces, so the pair "Truss - Bending" is incorrect.

2. Beam - Twisting:
A beam is a horizontal or inclined structural member that is designed to resist bending forces. Bending in beams occurs when a moment is applied to the member, resulting in curvature. Twisting, on the other hand, refers to the deformation of a structural member due to torsional forces. Beams are primarily designed to resist bending, not twisting forces. Therefore, the pair "Beam - Twisting" is incorrect.

3. Column - Buckling:
A column is a vertical structural member designed to support compressive loads. When a column is subjected to a compressive load, it can fail through buckling. Buckling occurs when the column bends or deflects laterally due to excessive compressive forces. This is the correct pairing, as columns are specifically designed to resist buckling.

4. Shaft - Shortening:
A shaft is a long, slender structural member that is designed to transmit rotational motion or torque. Shortening, however, refers to the reduction in length of a structural member due to compressive forces. While shafts may experience compressive forces, they are not primarily designed to resist shortening. Therefore, the pair "Shaft - Shortening" is incorrect.

In summary, the correct pairing is "Column - Buckling" as columns are specifically designed to resist buckling, which is a mode of instability that occurs when a slender structural member experiences excessive compressive forces.