# Design of Columns under an Eccentric Load

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Mechanical Engineering
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JoVE Central Mechanical Engineering
Design of Columns under an Eccentric Load
##### Vídeo anterior26.6: Design of Columns under a Centric Load

For a column loaded with an eccentric axial load in the plane of symmetry, the normal stresses due to eccentric load can be written as stresses due to an equivalent centric load and bending.

While designing columns with eccentric loadings, the maximum stress developed in the column shall not exceed the maximum allowable stress. This condition can be satisfied using two distinct approaches.

The allowable stress method assumes that the allowable stress for the eccentrically loaded column is the same as the maximum stress for the centrally loaded column. The allowable stress for the column can be expressed as a function of the slenderness ratio.

The allowable stress for centric loading is smaller than the one due to the bending moment. This results in the allowable stress method being overly conservative.

On the other hand, the interaction method considers the allowable stress due to centric loading and bending into account.

It provides an equation for the maximum stress under centric loading when there's no couple moment. Similarly, it defines the maximum stress from pure bending when there's no loading.

## Design of Columns under an Eccentric Load

Designing columns to withstand eccentric loads is a critical aspect of structural engineering, ensuring structures can support off-center loads without failure. This design process must account for the additional normal stresses introduced by eccentric loading, which can significantly influence a column's stress distribution and overall stability. An eccentric load applied to a column induces normal stresses that can be conceptualized as a combination of stresses due to an equivalent centric load and additional bending stresses. This leads to a non-uniform distribution of stress that must be carefully analyzed to prevent structural failure. Two primary methods are employed in the design of columns under eccentric loads: the allowable stress method and the interaction method.

The allowable stress method is a straightforward approach where the allowable stress for an eccentrically loaded column is equated to the maximum stress allowable for a centrally loaded column. This method simplifies the design process by treating the allowable stress as a function of the column's slenderness ratio, which is a measure of its propensity to buckle under load. However, this method assumes that the allowable stress for centric loading encompasses the additional stresses due to bending, leading to conservative designs that may not utilize the material's full potential. The conservatism inherent in this approach ensures safety but may result in larger and more expensive columns than necessary.

The interaction method offers a more nuanced approach by considering both the allowable stresses due to centric loading and the stresses arising from bending moments. This method provides a framework for calculating the maximum stress the column can withstand without a couple moment (pure centric loading) and the maximum stress due to pure bending (with no axial load). By accounting for these conditions simultaneously, the interaction method allows for a more accurate and less conservative estimation of the allowable stresses in eccentrically loaded columns.

In practice, the interaction method is often favored for its ability to balance safety with material efficiency. It requires a detailed analysis of the stress distribution within the column, considering both axial loads and bending moments.