Definition of equivalent axial load for columns with eccentricity When a column is loaded eccentrically, the “equivalent axial load” is defined as the load that produces a stress equal to which reference stress?

Introduction / Context:
Eccentric loading in columns induces combined axial compression and bending, creating a nonuniform stress distribution. To compare such a case with pure axial compression, designers sometimes use the concept of an “equivalent axial load”.

Given Data / Assumptions:

• Eccentricity about one or more axes generates bending moments.
• Equivalent axial load is a conceptual tool for comparison or simplified checks.
• We are concerned with the peak compressive stress, which governs safety.

Concept / Approach:
Under an eccentric load, the extreme fibre sees the largest compressive stress (or compression plus tension if eccentricity is large). The “equivalent axial load” is defined so that, if it acted concentrically, it would produce the same maximum compressive stress as in the real eccentric case.

Step-by-Step Solution:

Verification / Alternative check:
Equivalency is meaningful only if stresses match; using σ_max ensures conservative comparison for crushing or yield checks.

Why Other Options Are Wrong:
Most compressed fibre only is a location, not a definition; pure bending stress ignores axial part; average stress underestimates peak; shear stress is irrelevant for axial equivalence.

Common Pitfalls:
Misinterpreting “equivalent” as equal average stress; neglecting biaxial bending when eccentric in two directions.

Final Answer:
Maximum stress produced by the eccentric load