Sign and axis conventions

How Integraph AEC defines coordinate axes, the sign of moments, stresses, and curvatures across every tool. Read once and trust it everywhere.

Why this page exists

Every structural design package has to choose a sign convention for moments, stresses, and curvatures. Different design standards (AS 3600, ACI 318, Eurocode 2, AISI S100, AS/NZS 4600) are deliberately silent on which face is the “positive” face for biaxial bending — the choice is left to the software author.

This page is the one authoritative answer for Integraph. Every tool — ACS Concrete Designer, GCS Section Analyzer, LGS Light Gauge Steel, and any future tool — follows the conventions on this page exactly. If you ever see a Integraph output that appears to contradict this page, it is a bug and we want to know about it.

If you are an engineer accustomed to a different convention (in particular, the AISI/AISC steel-design textbook convention), see the LGS deviation at the bottom of this page.

The convention at a glance

Every Integraph canvas displays a small Y↑ X→ axis indicator in the bottom-left corner so the orientation is unambiguous while you work.

Combined biaxial loading — the canonical example

If you enter M*x = +50 kN·m and M*y = +50 kN·m together, the peak compressive stress lands in the top-left quadrant of the section:

• M*x alone compresses the top → top in compression
• M*y alone compresses the left → left in compression
• Combined → peak at top-left

If you ever see peak compression land at the bottom-left or top-right under combined positive M*x and M*y, you are looking at a bug. File it with a screenshot and the load combination.

The strain field

Internally, every Integraph stress / strain analysis uses the unified strain field:

ε(x, y) = ε₀ + κx · (y − y_ref) − κy · (x − x_ref)

Where:

• ε₀ is the strain at the section centroid
• κx is the curvature about the X axis (positive κx ↔ positive M*x, compression at top)
• κy is the curvature about the Y axis (positive κy ↔ positive M*y, compression at left)
• y_ref, x_ref are the centroid of the gross section

You’ll see this strain field referenced in the Theory sections of each tool’s documentation.

Neutral axis depth

NA depth (sometimes written dn or c in the AS 3600 / ACI 318 / EC2 textbooks) is always measured from the compression face:

• For positive M*x (sagging): NA depth is the distance from the top face downward to the neutral axis.
• For positive M*y: NA depth is the distance from the left face rightward to the neutral axis.

The Integraph report PDF cites NA depth in this convention.

Section properties

For any cross-section you analyse, the section-property outputs follow standard engineering definitions consistent with this convention:

• Ixx = ∫ y² dA — second moment of area about the X axis (its kernel is y², so it is sensitive to a section’s vertical extent).
• Iyy = ∫ x² dA — second moment about the Y axis.
• Ixy = ∫ xy dA — product of inertia.
• Sx_top = Ixx / (yMax − y_centroid) — elastic section modulus at the top fibre (smallest under sagging).
• Sx_bot = Ixx / (y_centroid − yMin) — at the bottom fibre.
• Sy_left, Sy_right — analogous for the Y-axis bending.

The naming is physical — Sx_top is the modulus at the top face — so a glance at the report tells you which fibre the modulus belongs to.

A note for cold-formed steel engineers

The strict mathematical engineering-mechanics convention (and the AISI S100 / AISC 360 textbook convention) is σ > 0 = tension, which produces positive M*x → bottom flange in compression for a section in sagging.

Integraph deliberately departs from this convention for LGS and uses the unified platform convention: σ > 0 = compression, positive M*x → top flange in compression.

We made this choice so that engineers switching between ACS (concrete), GCS (section properties), and LGS (cold-formed steel) in the same project never have to context-switch on the sign of M*x or σ. The cost is that LGS worked examples in AISI Specification Cl. F-series, AS/NZS 4600 commentary, or the Cold-Formed Steel Design textbook (Yu & LaBoube) will display the opposite sign when transcribed directly into Integraph. The conversion is straightforward — flip the sign of M*x and M*y when transcribing from an AISI/AISC worked example — but you have to remember to do it.

When the LGS tool launches, its worked examples in the Integraph documentation will be presented in the platform convention throughout, so you can use them directly. The LGS Vlasov analysis theory — including its sign-convention deviation from AISI, which walks through how to transcribe an AISI / AS-NZS 4600 worked example — is coming soon.

See it in practice

Each design tool’s documentation includes a worked example you can follow end-to-end with the canonical convention applied throughout:

• ACS (Concrete Designer) — RC beam worked example — sagging $M^*_x$ produces top-fibre compression in the slab; reinforcement at the bottom takes the tension.
• GCS (Section Analyzer) — Composite section worked example — section moduli Sx_top and Sx_bot are read at the physical top and bottom fibres of the composite as drawn.
• LGS (Light Gauge Steel) — C-channel purlin worked example (coming soon) — wind uplift puts the unrestrained bottom flange in compression, entered as negative $M^*_x$ under the canonical. The same example also shows how the sign differs from the AISI textbook version.

References

• AS 3600:2018 Cl 8.1.4 — basis of strength calculations (the sagging convention is the implicit textbook convention used in Cl 8 and Cl 10 worked examples)
• AS 3600 Supplement 1:2022 — commentary supporting the sagging convention
• ACI 318-19 Cl 22.2 — design assumptions; uses the sagging convention in Cl 9 / Cl 22 worked examples
• EN 1992-1-1:2023 Cl 8.2 — bending design; uses the sagging convention in worked examples
• Park & Paulay (1975), Reinforced Concrete Structures, §3.4 — foundational text using the sagging convention
• The Concrete Centre — How to Design Concrete Structures using Eurocode 2 — uses the sagging convention
• Concrete Institute of Australia — practice guides to AS 3600:2018 — use the sagging convention

When this page changes

The conventions on this page are stable. They will not change at the whim of an individual PR. Any change would be a breaking change affecting every saved design in the platform; it would be announced and accompanied by a migration guide for affected designs.

If you spot a place where Integraph behaviour appears to contradict this page, please file an issue with the load combination and a screenshot of the canvas. We treat these as high-priority bugs.