Statics and strength

Calculate section properties

Determine area, second moments of area, and section moduli for rectangles, circles, and hollow sections.

I / WSI
01

Section

Dimensions and centroidal axesRectangle
xybhS

S = area centroid; x and y are the axes for Iₓ, Iᵧ, Wₓ and Wᵧ. Diagram not to scale.

02

Results

ƒ(x)

Set the inputs and run the calculation.

Inputs and method

Section properties for design

Calculate area, second moments of area and section moduli for idealized sections.

Inputs

Shape and dimensions such as width, height, diameter and wall thickness define geometry.

Height places material farther from the neutral axis and therefore has a stronger bending effect. This is why a taller slender section raises I and W more than an equally heavy widening.

Calculation

The area distribution gives I and W; W = I/yₘₐₓ feeds bending stress σ = M/W.

Example

Doubling rectangle height at constant width roughly quadruples I and doubles W.

Sources and limits: Classical section theory; include radii, cut-outs and local buckling for real geometry.

Purpose

What the calculator is for

Dimensions are converted into the geometric basis for stress, stiffness, and preliminary sizing. For example, a rectangular beam's section modulus can feed the bending-stress calculator directly.

Limits

What still needs checking

The calculation uses ideal nominal geometry. Profile radii, tolerances, local buckling, and plastic reserve are excluded.