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Dezi et. al (2010)
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Welcome to our moment of inertia calculator! This page is specifically for finding the moment of inertia for a trapezoidal section. Enter the height (H), bottom base width (B), upper base width (a) and distance between the ends of the lower and upper base from the left (B2) of your section below, and see the results in the output section below.
This tool calculates Ixx and Iyy about the centroidal axis, as well as Iyy0, the moment of inertia of the sections taken about the base horizontal axis..

Calculations

Inputs



H
:200mm​



B
:225mm​



a
:169mm​



B2
:45mm​



B3
:11mm​



Outputs

Moment of inertia


Iyy0
:703961567mm4​



Ixx
:130448957mm4​



Iyy
:130939510mm4​

Dimensions


Area
:39400mm2​



xc
:120.597293mm​



yc
:95.2622673mm​



Explanation

The moment of inertia of a trapezoidal section can be calculated using the equations shown to the right. H is the height of the section, a and B are the base widths of the section, and B2 and B3 are the horizontal distances between the bases.
Iyy0 is the moment of inertia of the section about its base. The parallel axis theorem is applied to this value to determine the moment of inertia about the section centroid, Iyy.

Ixx=H336a2+4aB+B2a+B Iyy=Iyy0−Axc2 Iyy0=H12B3−3B23−B33−2B3(3B−B3)236I_{xx} = \frac{H^3}{36} \frac{a^2+4aB+B^2}{a+B} \\\ \\ I_{yy} = I_{yy_{0}} - Ax_{c}^2 \\\ \\ I_{yy_{0}} = H\frac{12B^3-3B_{2}^3-B_{3}^3-2B_{3}(3B-B_{3})^2}{36}


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