Stresses in Column with Biaxial Eccentric Loading

When vertical load on the column is not coincide with center of gravity of column cross section and does not act on either axis (X and Y axis), then the column is called biaxially eccentric loaded column.

Load Acting Eccentric to Both Axes

If the axial load P is placed at a point (ex, ey) eccentric to both x-axis and y-axis as shown in Figure, then the system can be assumed to consist of

(i) a direct compressive force P acting at the centroid,

(ii) a couple(Bending Moment) P x ey, about the x-axis and

(iii) a couple P x ex, about the y-axis.

The moment of P about these axes are respectively.

Mx = P.ey and My= P.ex

As seen for the case of load acting eccentric to one axis, the stress at any point can be written as

σ = σa + σbx + σby

σ = P/A + Mx/Zx + My/Zy

The maximum or minimum fiber stress will occur at the corner point A, B, C or D in the given figure.

If the load is in first quadrant ie. ex and ey are +ve, then the stresses will be calculated as below

σ = σa + σbx + σby

σA = σa + σbx - σby

σB = σa - σbx - σby

σC = σa - σbx + σby

σD = σa + σbx + σby

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