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Accidental moment for column

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The ACI Code specifies that even when a column is subjected to a nominally concentric load, a minimum moment (often referred to as the accidental moment) must be considered in design.

This requirement ensures that the column can safely resist small eccentricities that may occur in practice due to various unavoidable factors.

Reasons for Specifying a Minimum Moment (Accidental Moment)

  1. Construction Tolerances:
    During construction, a column may not be placed exactly at the intended centerline. Such positional deviations cause an eccentricity between the applied load and the column centroid, inducing a bending moment known as the accidental moment.

  2. Load Eccentricity:
    Eccentricity may also occur due to:

    • Misalignment of columns between successive stories.

    • Imperfect placement of beams or slabs.

    • Slight variations in material or loading conditions.

These effects, although minor, must be accounted for to ensure realistic and safe column design.

Axial Load Capacity for Concentric Loading

For a truly concentric load (no eccentricity), the nominal axial load capacity of a column as per ACI is given by:

Pn=0.85fc′(Ag−Ast)+fyAst


where:

  • fc′= specified compressive strength of concrete

  • fy = yield strength of reinforcement

  • Ag = gross area of column section

  • Ast = area of longitudinal steel reinforcement

However, the ACI Code limits this ideal concentric load capacity by applying reduction factors to account for the minimum accidental eccentricity.

Reduction Factors to Account for Minimum Eccentricity

To reflect the practical occurrence of small eccentricities, ACI reduces the maximum usable axial capacity as follows:

  • For Tied Columns:

    Pn=0.80×[0.85fc′(Ag−Ast)+fyAst]
    • For Spiral Columns:
Pn=0.85×[0.85fc′(Ag−Ast)+fyAst]

The reduction factors (0.80 for tied columns and 0.85 for spiral columns) ensure that even if a column is designed for concentric loading, it can safely resist minor bending moments due to construction and loading imperfections.
These moments—though small—are collectively referred to as the accidental moments, ensuring a practical and conservative design as per the ACI Code.




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