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StructuralEngineerLab · TOOL-009

Section Modulus Calculator

Calculate elastic geometric section modulus Sx and Sy for five frozen section types. Sx/Sy are the primary results; Ix/Iy, Area, Centroid, rx and ry are read-only TOOL-002 context.

Axis Convention: x = horizontal centroidal axis · y = vertical centroidal axis · Sx/Sy correspond only to those centroidal axes.
Extreme-Fiber Distance: inherited entirely from TOOL-002. TOOL-009 does not accept or modify cx/cy. Elastic Geometric Section Modulus only; Plastic Section Modulus is not supported.

Section geometry

Ready.

Primary result

Elastic Geometric Section Modulus

Calculate to view Sx/Sy inherited from the frozen TOOL-002 Section Properties engine.

Example

Doubly Symmetric I-Section: overall depth 600 mm, flange width 250 mm, flange thickness 20 mm and web thickness 12 mm. TOOL-009 reports Sx/Sy directly 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.
  • Sx/Sy are elastic geometric section modulus values about centroidal x/y axes.
  • Extreme-fiber distance semantics are inherited from TOOL-002.
  • Ix/Iy/Area/Centroid/rx/ry are read-only TOOL-002 context.

Warnings

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

Method & assumptions

TOOL-009 is a focused Section Modulus 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 dimensions are normalized to canonical metres before the frozen TOOL-002 Section Properties engine is called.
  • Sx and Sy are elastic geometric section modulus values about centroidal x/y axes.
  • Extreme-fiber distance semantics are inherited entirely from TOOL-002.
  • TOOL-009 does not accept or modify cx/cy.
  • Ix, Iy, Area, Centroid, rx and ry are read-only TOOL-002 Context.

Primary result: Sx and Sy

Sx and Sy are the primary TOOL-009 results. They are elastic geometric section modulus values about the centroidal x and y axes.

Ix, Iy, Area, Centroid, 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.
  • Sx corresponds to the centroidal x-axis.
  • Sy corresponds to the centroidal y-axis.

Rotated-axis, principal-axis, arbitrary-axis, and product-of-inertia-based transformations are outside TOOL-009 V1.

Extreme-Fiber Distance

Extreme-fiber distance semantics are owned entirely by TOOL-002. TOOL-009 does not accept, expose, or modify user-defined cx or cy.

TOOL-009 supports Elastic Geometric Section Modulus only. Plastic Section Modulus is not supported.

I-Section geometry rule

The authoritative frozen rule is webThickness < flangeWidth.

Limitations

  • No arbitrary polygon sections.
  • No composite or built-up sections.
  • No transformed sections.
  • No rotated-axis section modulus.
  • No principal-axis section modulus.
  • No arbitrary-axis section modulus.
  • No Plastic Section Modulus.
  • No user-defined cx/cy.
  • 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

For this orientation, Sx is larger than Sy because the section is deeper about the centroidal x-axis.

Circle

Inputs: Diameter = 500 mm

For a circle, Sx equals Sy because the section is symmetric about both centroidal 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 Sx is larger than the weak-axis Sy. Extreme-fiber distance remains TOOL-002-owned, and webThickness must remain less than flangeWidth.

Frequently asked questions

Which section shapes are supported?

TOOL-009 supports exactly five frozen shapes: Rectangle, Hollow Rectangle, Circle, Hollow Circle, and Doubly Symmetric I-Section.

What are the primary results?

Sx and Sy are the primary TOOL-009 results. They are elastic geometric section modulus values about the centroidal x and y axes.

What are Ix, Iy, Area, Centroid, rx and ry?

They are read-only Context inherited from TOOL-002 and are not independently recalculated by TOOL-009.

Which axis convention is used?

The x-axis is the horizontal centroidal axis and the y-axis is the vertical centroidal axis. Sx corresponds to the centroidal x-axis and Sy to the centroidal y-axis.

How is extreme-fiber distance handled?

Extreme-fiber distance semantics are owned entirely by TOOL-002. TOOL-009 does not accept, expose, or modify user cx/cy values.

Does this calculator provide plastic section modulus?

No. TOOL-009 V1 supports Elastic Geometric Section Modulus only. Plastic Section Modulus is outside scope.

Does TOOL-009 support rotated or principal axes?

No. Rotated-axis, principal-axis, arbitrary-axis, and product-of-inertia-based transformations are outside TOOL-009 V1.

What I-section geometry rule applies?

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

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