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?
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ABy 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
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BBy adding the axial load and eccentric load and then subtracting the product of bending moment and the bending factor
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CBy dividing the sum of axial and eccentric loads by the product of bending moment and bending factor
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DNone of these
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E—
Answer
Correct 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
Explanation
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