Cross-Section Shape
Parallel Axis Offset d
0.0 mm
Distance from centroid (parallel axis theorem)
—
Ixx [mm⁴]
—
Iyy [mm⁴]
—
Area A [mm²]
—
Centroid y_c [mm]
—
Section Mod. Wxx [mm³]
| Property | Centroidal Axis | Parallel Axis (I+Ad²) | Unit |
|---|
Theory
Rectangle: $I_{xx} = \dfrac{bh^3}{12}$, $I_{yy} = \dfrac{hb^3}{12}$
Circle: $I = \dfrac{\pi d^4}{64}$, Hollow: $I = \dfrac{\pi(d_o^4 - d_i^4)}{64}$
Parallel axis theorem: $I = I_c + Ad^2$
Section modulus: $W_{xx} = \dfrac{I_{xx}}{y_{max}}$, Radius of gyration: $k = \sqrt{\dfrac{I}{A}}$
Engineering applications: FEM beam element section properties (BEAM188/BEAM189) · bending stress verification σ = M/W · flywheel and rotating disk mass moment of inertia · ANSYS Mechanical cross-section property input.