Eccentrically loaded columns – defining an equivalent axial load for design How is the equivalent axial load commonly determined for an eccentrically loaded column to reflect the effect of the produced bending moment?

Introduction / Context:
Eccentric axial load P acting at an eccentricity e produces a combined effect: direct compression and bending with moment M = P * e. Some design approaches convert this combined action into an “equivalent axial load” using a bending factor to simplify checks against allowable stress.

Given Data / Assumptions:

• Column subjected to axial load P with eccentricity e.
• Bending moment M = P * e considered.
• Working-stress context using equivalent load concepts.

Concept / Approach:
The extreme-fibre stress is usually checked as σ = P/A ± M/Z. Equivalently, some handbooks propose a transformed axial load by adding a term proportional to M (via a bending factor) to P to maintain a single check against allowable compressive stress.

Step-by-Step Solution:
Compute M = P * e.Introduce a bending factor α reflecting section properties and stress distribution.Define P_eq ≈ P + α * M to represent the combined effect conservatively.

Verification / Alternative check:
Direct stress interaction (P/A + M/Z ≤ σ_allow) provides the exact check; the equivalent-load approach with α * M is an expedient that parallels interaction.

Why Other Options Are Wrong:

• Subtracting or dividing by M and a factor has no rational basis for a conservative equivalent load.
• Hence option (a) is the only reasonable description.

Common Pitfalls:
Relying only on “equivalent load” without verifying combined-stress interaction can miss critical tension on one face.

Final Answer:
By adding the axial load and the contribution due to eccentricity, i.e., axial load plus the product of bending moment from eccentricity and an appropriate bending factor