Moment of Inertia and Centroid of a Tapered Channel

Section properties of a Tapered 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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Tapered Channel cross section with its dimensions and centroid
  • dd = height
  • bb = width
  • tt = web thickness
  • ss = flange thickness
  • nn = maximum flange depth
PropertySymbolFormula
AreaAAbd−(b−t)(d−n−s)bd - (b-t)(d-n-s)
PerimeterPP2(d+b+s−n+(n−s)2+(b−t)2)2(d+b+s-n+\sqrt{(n-s)^2+(b-t)^2})
Centroid from the left edgexˉ\bar{x}2b2(n+2s)+2b(n−s)t+(3d−4n−2s)t26A\frac{2b^2(n+2s) + 2b(n-s)t + (3d-4n-2s)t^2}{6A}
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 baseIxI_xd3t3+(b−t)(3d2(n+s)−2d(n2+ns+s2)+(n+s)(n2+s2))6\frac{d^3t}{3} + \frac{(b-t)(3d^2(n+s)-2d(n^2+ns+s^2)+(n+s)(n^2+s^2))}{6}

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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