Column : Buckling

Explanation:

Column:
A column is a structural member that primarily carries axial compression loads. It is designed to provide vertical support to the imposed loads and transfer them to the foundation. Columns are commonly used in buildings and other structures to support the weight of the structure and resist compressive forces.

Buckling:
Buckling is a structural failure mode that occurs when a slender column or beam, under compression, fails due to instability. It is characterized by a sudden lateral deflection or bending of the column or beam. Buckling can occur when the compressive load exceeds the critical load, which depends on the column's length, cross-sectional properties, and the material's modulus of elasticity.

Matching:
The correct matching pair in the given options is "Column : Buckling." Columns are primarily susceptible to buckling failure, especially when they are slender and subjected to compressive loads.

Incorrect Options:

a) Truss : Bending
A truss is a structural framework composed of triangular units connected at joints. Trusses are commonly used to support roofs, bridges, and other structures. However, trusses are primarily designed to resist axial forces, such as tension and compression, rather than bending moments.

b) Beam : Twisting
A beam is a structural element that primarily resists bending moments. Beams are used to support loads and transfer them to the columns or walls. Twisting is not a typical failure mode for beams. Beams are more prone to bending and shear failures.

d) Shaft : Shortening
A shaft is a long, cylindrical structural element used to transmit torque and rotational motion. Shortening is not a characteristic failure mode for shafts. Shafts are designed to withstand torsional and bending loads, rather than compressive loads that lead to shortening.

Therefore, the correct matching pair is "Column : Buckling."