Moment of Inertia and Centroid of a Square Channel

Section properties of a Square Channel: area, centroid location and second moment of area (moment of inertia) about the centroidal axes and about the base and left edge. These values are used to size beams and columns, compute bending stresses (σ = M·y/I) and deflections.

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Square Channel cross section with its dimensions and centroid
  • dd = height
  • bb = width
  • tt = web thickness
  • ss = flange thickness
PropertySymbolFormula
AreaAA2bs+t(d−2s)2bs + t(d-2s)
PerimeterPP2d+4b−2t2d + 4b -2t
Centroid from the left edgexˉ\bar{x}2b2s+t2(d−2s)4bs+2t(d−2s)\frac{2b^2s + t^2(d-2s)}{4bs + 2t(d-2s)}
Centroid from the bottom edgeyˉ\bar{y}d2\frac{d}{2}
Moment of inertia about the centroidal x-axisIˉx\bar{I}_xIx−yˉ2AI_x - \bar{y}^2A
Moment of inertia about the centroidal y-axisIˉy\bar{I}_yIy−xˉ2AI_y - \bar{x}^2A
Moment of inertia about the baseIxI_xtd33+s(b−t)(3d2−3ds+2s2)3\frac{td^3}{3} + \frac{s(b-t)(3d^2 - 3ds + 2s^2)}{3}
Moment of inertia about the left edgeIyI_y2b3s3+t3(d−2s)3\frac{2b^3s}{3} + \frac{t^3(d-2s)}{3}

The origin is the bottom-left corner of the bounding box. The moments of inertia about the base and the left edge follow from the parallel axis theorem: Ix=Iˉx+Ayˉ2I_x = \bar{I}_x + A\bar{y}^2.

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Enter the dimensions and get the area, centroid and moments of inertia instantly, with the section drawn to scale. Metric and imperial units.

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