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StructuralEngineerLab · TOOL-008

Moment of Inertia Calculator

Calculate centroidal-axis second moments of area for five frozen section types. Ix/Iy are the primary results; Area/Centroid are secondary and Sx/Sy/rx/ry are read-only context.

Axis Convention: x = horizontal centroidal axis · y = vertical centroidal axis · Ix/Iy are centroidal-axis second moments only. Rotated-axis and principal-axis interpretation are not supported.

Section geometry

Ready.

Primary result

Second Moment of Area / Moment of Inertia

Calculate to view the inherited TOOL-002 section-property result.

Example

Doubly Symmetric I-Section: overall depth 600 mm, flange width 250 mm, flange thickness 20 mm and web thickness 12 mm. TOOL-008 reports Ix/Iy from the frozen TOOL-002 Section Properties engine.

Assumptions

  • Only five frozen section types are allowed.
  • All dimensions are converted to canonical metres before TOOL-002 is called.
  • Ix/Iy are centroidal-axis second moments of area.
  • Area/Centroid are secondary geometry outputs.
  • Sx/Sy/rx/ry are read-only TOOL-002 context.

Warnings

  • No arbitrary polygon or composite-section analysis.
  • No rotated-axis or principal-axis transformation.
  • No material-strength or code-design conclusion.
  • No utilization or PASS/FAIL conclusion.
  • I-Section requires webThickness < flangeWidth.

Method & assumptions

TOOL-008 is a focused Moment of Inertia interface over the frozen TOOL-002 Section Properties engine. It supports only Rectangle, Hollow Rectangle, Circle, Hollow Circle, and Doubly Symmetric I-Section.

  • Only Rectangle, Hollow Rectangle, Circle, Hollow Circle, and Doubly Symmetric I-Section are supported.
  • All dimensional inputs are normalized to canonical metres before the frozen TOOL-002 Section Properties engine is called.
  • Ix and Iy are centroidal-axis second moments of area.
  • Area and Centroid are secondary geometry outputs.
  • Sx, Sy, rx and ry are read-only TOOL-002 context.
  • The x-axis is horizontal centroidal and the y-axis is vertical centroidal.

Primary result: Ix and Iy

Ix and Iy are the primary TOOL-008 results. Ix is the second moment of area about the horizontal centroidal x-axis, while Iy is the second moment of area about the vertical centroidal y-axis.

Area and Centroid are secondary geometry outputs. Sx, Sy, rx and ry are read-only Context inherited from TOOL-002 and are not independently recalculated.

Axis Convention

  • x = horizontal centroidal axis.
  • y = vertical centroidal axis.
  • Ix = centroidal x-axis second moment of area.
  • Iy = centroidal y-axis second moment of area.

TOOL-008 does not support rotated-axis interpretation, principal-axis transformation, product of inertia, or arbitrary-axis second moments.

I-Section geometry rule

The authoritative frozen rule is webThickness < flangeWidth. This inherits the TOOL-002 frozen validation behavior.

Limitations

  • No arbitrary polygon sections.
  • No composite or built-up sections.
  • No transformed sections.
  • No rotated-axis calculations.
  • No principal-axis transformations.
  • No product-of-inertia output.
  • No material-strength or allowable-stress calculations.
  • No code-based design verification.
  • No utilization or PASS/FAIL conclusion.

Worked examples

Rectangle

Inputs: Width = 300 mm, Height = 600 mm

Ix is larger than Iy because the 600 mm depth is aligned with the vertical dimension. The centroid lies at the geometric center.

Circle

Inputs: Diameter = 500 mm

For a circle, Ix and Iy are equal about the centroidal x and y axes.

Doubly Symmetric I-Section

Inputs: Overall depth = 600 mm, flange width = 250 mm, flange thickness = 20 mm, web thickness = 12 mm

The strong-axis centroidal second moment Ix is larger than the weak-axis Iy. The frozen geometry rule requires webThickness < flangeWidth.

Frequently asked questions

Which section shapes are supported?

TOOL-008 supports exactly five frozen shapes: Rectangle, Hollow Rectangle, Circle, Hollow Circle, and Doubly Symmetric I-Section.

What is the primary result?

Ix and Iy are the primary TOOL-008 results. They are centroidal-axis second moments of area.

What are Area and Centroid used for?

Area and Centroid are secondary geometry outputs inherited from TOOL-002.

What are Sx, Sy, rx and ry?

They are read-only context inherited directly from TOOL-002. TOOL-008 does not independently recalculate them.

Which axis convention is used?

The x-axis is the horizontal centroidal axis and the y-axis is the vertical centroidal axis. Ix is about the centroidal x-axis and Iy is about the centroidal y-axis.

Does TOOL-008 calculate rotated or principal-axis inertia?

No. TOOL-008 V1 does not support rotated-axis transformation, principal-axis transformation, product of inertia, or arbitrary-axis second moments.

What geometry rule applies to the I-section web?

For the frozen doubly symmetric I-section, webThickness must be strictly less than flangeWidth.

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