Glossary

Engineering terminology used across Integraph's design tools -- section properties, buckling modes, design methods, and code-level definitions.

How to use this glossary

This page defines the engineering vocabulary that appears across multiple Integraph tools. Terms are grouped by topic. Each entry gives a plain-language definition, the canonical symbol (where one exists), units, and which tool(s) reference it.

Tool docs link bold specialist terms to this page on first use. If you land here from a tool page and want more depth, follow the references in each entry to the relevant theory section.

Section properties

Geometric properties derived from a cross-section’s outline and reinforcement layout. These are the building blocks of every flexural, axial, and shear capacity calculation.

Area

The cross-sectional area enclosed by the section outline (minus voids). Symbol: $A$. Units: mm². Used in axial capacity, weight, and stiffness calculations. Used by: ACS, LGS, Section Analyzer.

Centroid

The geometric centre of the cross-section — the point about which the first moments of area sum to zero. Symbol: $(\bar{x}, \bar{y})$. Units: mm. The neutral axis under pure bending passes through the centroid for elastic, homogeneous sections. Used by: ACS, LGS, Section Analyzer.

Second moment of area

A geometric measure of a section’s resistance to bending about a given axis. Symbols: $I_x$, $I_y$ (about centroidal axes), $I_{xy}$ (product of inertia). Units: mm⁴. Also called “moment of inertia” in informal use. Used by: ACS, LGS, Section Analyzer.

Principal axes

The pair of orthogonal centroidal axes about which the product of inertia $I_{xy}$ is zero and the second moments of area reach their extreme values. Symbols: $u$, $v$ for the principal directions; $I_u$, $I_v$ for the principal second moments of area. For doubly-symmetric sections the principal axes coincide with the geometric axes; for asymmetric sections they are rotated. Used by: LGS, Section Analyzer.

Section modulus

The ratio of second moment of area to the distance from the neutral axis to the extreme fibre. Defines the elastic bending stress for a given moment. Symbols: $S_x$, $S_y$ (also $Z_x$, $Z_y$ in some jurisdictions). Units: mm³. Used by: ACS, LGS, Section Analyzer.

Plastic section modulus

The first moment of area of the cross-section above the plastic neutral axis, used to compute the fully plastic moment capacity. Symbol: $Z_x$, $Z_y$ (also $S_x$, $S_y$ in some jurisdictions — the symbol convention is reversed between AS and AISC). Units: mm³. The ratio of plastic to elastic modulus is the shape factor. Used by: LGS, Section Analyzer.

Radius of gyration

The distance from the centroidal axis at which the entire area could be concentrated to give the same second moment of area. Symbols: $r_x$, $r_y$. Units: mm. Appears in slenderness ratio definitions ($L/r$) for compression members. Used by: LGS.

Thin-walled and cold-formed steel

Properties specific to thin-walled open and closed sections, where warping and shear-centre eccentricity affect torsional and lateral-torsional behaviour.

Warping constant

A sectorial property that measures a thin-walled open section’s resistance to non-uniform torsion (warping torsion). Symbol: $I_w$ (sometimes $C_w$ in US conventions). Units: mm⁶. Combined with $J$ in the Vlasov differential equation for restrained torsion. Used by: LGS.

Shear centre

The point in the cross-section plane through which a transverse load must pass to produce pure bending without twisting. Coincides with the centroid for doubly-symmetric sections; offset for channels, angles, and asymmetric sections. Symbol: $(x_s, y_s)$. Units: mm. The eccentricity between the shear centre and the load application point governs flexural-torsional response. Used by: LGS.

Principal sectorial coordinate

The sectorial area function $\omega(s)$ evaluated relative to the shear centre and normalised to make its average zero. Building block for the warping constant. Units: mm². Used by: LGS.

St. Venant torsion constant

The torsional constant that governs uniform (St. Venant) twist of a member. Symbol: $J$ (sometimes $I_t$). Units: mm⁴. For thin-walled open sections, $J = \sum b_i t_i^3 / 3$ over each rectangular element. Used by: LGS.

Wagner asymmetry parameters

Sectorial integrals $\beta_x$, $\beta_y$, $\beta_\omega$ that capture the coupling between bending and torsion in monosymmetric and asymmetric sections. They appear in the cubic stability equation governing the elastic flexural-torsional buckling load. Units: mm. Used by: LGS.

Buckling

Loss-of-stability phenomena in thin-walled, slender, or otherwise compression-loaded members. The mode and the corresponding elastic critical stress depend on the geometry, the loading, and the support conditions.

Buckling

The general phenomenon where a member loses geometric stability under compressive load (or compressive stress at any fibre) before reaching its material yield strength. Modes are classified by characteristic wavelength: local, distortional, global. Used by: LGS.

Local buckling

Buckling at short wavelength where individual plate elements (flange, web, lip) deform out-of-plane while the cross-section corners remain fixed. Symbol for the critical load: $P_{crl}$. Used by: LGS.

Distortional buckling

Buckling at intermediate wavelength where the cross-section distorts — typically the flange-lip system rotates as a rigid body about the flange-web junction. Symbol for the critical load: $P_{crd}$. Most pronounced in lipped channels and zeds with intermediate stiffeners. Used by: LGS.

Global buckling

Buckling at long wavelength where the entire cross-section translates and/or rotates without distortion. Includes flexural, torsional, and flexural-torsional modes. Symbol for the critical load: $P_{cre}$. Used by: LGS.

Flexural-torsional buckling

A global buckling mode where the member simultaneously bends and twists. Governs for monosymmetric and asymmetric open sections (channels, zeds, angles) under axial compression. Used by: LGS.

Lateral-torsional buckling

A global buckling mode under flexure where the compression flange of a beam buckles laterally accompanied by twist of the cross-section. Symbol for the critical moment: $M_{cr}$. Used by: LGS.

Signature curve

The plot of elastic critical buckling stress (or load) versus half-wavelength produced by the Finite Strip Method. Local minima identify the critical local, distortional, and global buckling modes; the LGS signature curve viewer makes these visible. Used by: LGS.

Half-wavelength

The longitudinal length of one half-wave in the buckled mode shape. Symbol: $L_{cr}$ (the half-wavelength at which the critical stress is minimum for a given mode). Units: mm. Used by: LGS.

Elastic critical stress

The compressive stress (or extreme-fibre bending stress) at which a member becomes elastically unstable, ignoring material yielding. Symbol: $f_{cr}$ for the local/distortional mode, $f_{oc}$ for global. Units: MPa. Used by: LGS.

Direct Strength Method

A unified design method for cold-formed steel that maps elastic buckling stresses directly to nominal strengths, replacing the older effective-width approach for many cases.

Direct Strength Method

The cold-formed steel design methodology that takes the elastic critical buckling load for each mode (local, distortional, global) and applies a calibrated strength curve to obtain the nominal capacity. Codified in AISI S100 and AS/NZS 4600. Used by: LGS.

DSM

Abbreviation for Direct Strength Method. Used by: LGS.

Slenderness ratio

In the DSM context, the square root of the ratio of yield load to elastic critical load for a given buckling mode: $\lambda_l = \sqrt{P_y / P_{crl}}$, $\lambda_d = \sqrt{P_y / P_{crd}}$, $\lambda_c = \sqrt{P_y / P_{cre}}$. Dimensionless. Determines whether a strength curve returns yield-controlled, post-buckling, or elastic-buckling capacity. Used by: LGS.

Winter strength curve

The post-buckling strength formula used in DSM for local and distortional modes: $P_n / P_y = 1 - 0.15 (P_{crl} / P_y)^{0.4}$ for $\lambda_l > 0.776$ (analogous form for distortional). Based on Winter’s empirical post-buckling research. Used by: LGS.

Concrete design

Vocabulary for ULS and SLS analysis of reinforced and prestressed concrete cross-sections.

Moment-curvature

The full nonlinear relationship between applied moment and section curvature, traced from uncracked through cracking, yielding, and ultimate. Symbol: $M-\kappa$. Used to evaluate ductility, deflection multipliers, and post-yield behaviour. Used by: ACS.

M-N interaction

The set of $(M, N)$ pairs that bring a concrete section to its ultimate limit state, plotted as an interaction diagram. For biaxial cases the locus is a 3D surface $(M_x, M_y, N)$. Used by: ACS.

Neutral axis

The line through the cross-section where the longitudinal strain (and therefore the longitudinal stress for elastic-homogeneous sections) is zero. Symbol for the depth from the extreme compression fibre: $d_n$ (or $c$ in some jurisdictions). Units: mm. Used by: ACS.

Ductility parameter

A non-dimensional measure of how under-reinforced (and therefore ductile) a flexural section is at ultimate. AS 3600 uses $k_u = d_n / d$; ACI 318 uses the net tensile strain $\varepsilon_t$ at extreme tension steel. Each code sets a minimum to ensure ductile failure. Used by: ACS.

Effective moment of inertia

A smeared section stiffness used to compute short-term deflections of cracked reinforced concrete members, interpolating between gross and fully-cracked stiffness based on the applied moment relative to the cracking moment. Symbol: $I_{ef}$ (AS 3600) or $I_e$ (ACI 318, Branson’s equation). Units: mm⁴. Used by: ACS.

Stress-strain model

The mathematical relationship between concrete compressive stress and strain used in the section analysis. Common choices include the rectangular stress block (ULS only), Hognestad’s parabola, Mander’s confined model, parabolic-rectangular (EC2), bilinear, Kent-Park modified, Popovics/Thorenfeldt, and FIB Model Code 2010. The chosen model must be compatible with the analysis type — the rectangular block is valid for ULS capacity only, not for fibre-based moment-curvature. Used by: ACS.

General terms

Code-level definitions and design-method vocabulary that span every tool.

Limit state

A specific condition beyond which a structure or member fails to satisfy a design requirement. The two principal families are ultimate limit state (collapse, instability) and serviceability limit state (deflection, crack width, vibration). Fire is treated as an additional limit-state family in most codes. Used by: ACS, LGS.

ULS

Abbreviation for ultimate limit state — the design check against collapse, instability, or loss of structural integrity. Loads are factored up; material strengths are factored down. Used by: ACS, LGS.

SLS

Abbreviation for serviceability limit state — the design check against deflection, vibration, crack width, and other non-collapse performance criteria. Generally uses unfactored or characteristic loads. Used by: ACS, LGS.

Partial safety factor

A multiplicative factor applied to a load (load factor, $\gamma_G$, $\gamma_Q$) or to a material strength (capacity reduction factor, $\phi$, or material factor, $\gamma_M$) to ensure a target reliability level. Different codes split the total safety margin between load and material side differently. Used by: ACS, LGS.

Characteristic strength

A statistically-defined material strength typically corresponding to the 5% lower fractile of measured test results. Symbols: $f'_c$ (characteristic concrete cylinder strength), $f_y$ (characteristic yield strength of reinforcement), $f_{yk}$ (characteristic yield strength in EC). Units: MPa. Used by: ACS, LGS.

Design action

A load effect (moment, shear, axial force) computed from factored loads and used in ULS capacity checks. Notation distinguishes design actions from capacities by an asterisk in Australian conventions ($M^*$, $V^*$, $N^*$) or by a subscript $d$ in Eurocodes ($M_{Ed}$, $V_{Ed}$, $N_{Ed}$). Used by: ACS, LGS.

Related pages

• Platform overview
• Getting started
• Advanced Concrete Section — concrete design vocabulary in context
• Light Gauge Steel (coming soon) — cold-formed steel buckling and DSM in context