Eccentrically loaded columns – nature of stress:\nWhen a column carries an eccentric load, what kinds of stresses are induced in the cross-section?

Introduction / Context:
Columns are often loaded away from the centroidal axis due to construction tolerances or intentional eccentricity (e.g., brackets). Such eccentricity changes the internal stress state from pure compression to a combination that designers must assess for safety against crushing and buckling.

Given Data / Assumptions:

• Eccentric axial load P acting at an eccentricity e from the centroidal axis.
• Prismatic, homogeneous column section.
• Small deflection and linear elastic behavior for section stress evaluation.

Concept / Approach:
An eccentric axial load is statically equivalent to a concentric load P (causing uniform direct compressive stress) plus a bending moment M = P * e (causing a linear compressive–tensile stress distribution). The resulting stress at a fibre is the algebraic sum of direct and bending components.

Step-by-Step Solution:

Verification / Alternative check:
At the neutral axis y = 0, only direct stress remains. At extreme fibres, bending may reduce or add to direct compression, potentially producing tension if (P * e * y / I) > (P / A).

Why Other Options Are Wrong:

• Direct only / bending only: omit half of the statically equivalent effects.
• Shear only: eccentric axial loading does not create a primary shear resultant in uniform prismatic members.
• Direct and torsional: torsion requires a moment about the longitudinal axis, which is not produced by simple planar eccentricity.

Common Pitfalls:
Ignoring tension possibility on one side, or using net section area after cracking without justification. Always check maximum and minimum fibre stresses.

Final Answer:
Direct and bending stress both