Glossary

Short definitions of the terms this knowledge base uses, in the sense it uses them. Each links to the page where the idea is worked through properly.

A

Accompanying action. In a load combination, a variable action present at its reduced ${\psi }_0$ value alongside the leading one. Automatic combinations.

AISC 360. The American steel specification. Elementarium's second design module checks member strength to its Chapters D to H, compression buckling included. Steel — AISC 360.

All-quad mesh. A surface mesh made entirely of quadrilaterals, with no triangles anywhere. What Elementarium's mesher guarantees, because the shell element is a four-node quad. Meshing.

Amplification factor. The arbitrary scale applied to a deformed shape or mode shape so that it is visible. Never read a displacement off the picture. Reading diagrams.

AMG — algebraic multigrid. A preconditioner for the conjugate gradient solver that resolves long-wavelength error quickly. Choosing a linear solver.

ASD — allowable strength design. The AISC method that compares nominal loads against $R_n/\Omega$. Paired with ASCE 7 §2.4 combinations. ASCE 7 combinations.

Aspect ratio. Longest side of an element over its shortest. Beyond about 3:1 bending accuracy degrades; beyond 5:1 the result is not worth quoting. Mesh quality.

B

Bar. A two-node element carrying axial force only, with three translational degrees of freedom per node. Cannot form a moment-release mechanism. Bars, beams and trusses.

Beam. A two-node element with six degrees of freedom per node, carrying axial force, two shears, torsion and two bending moments. Exact for a prismatic member under end loads and uniform load. Element formulations.

Bedding modulus. See modulus of subgrade reaction.

Buckling shape. The eigenvector of a linear buckling analysis: the form the structure takes at instability. Its amplitude is arbitrary. Linear buckling.

C

Characteristic combination. The EN 1990 serviceability combination $G+Q_{k,1}+\sum {\psi }_{0,i}{Q}_{k,i}$, for irreversible effects. Automatic combinations.

Characteristic length. $L_e=(4EI/k{)}^{1/4}$ for a beam on Winkler bedding — the distance over which a point load's effect spreads. Winkler foundations.

Cholesky factorisation. The $L{L}^{\mathsf{T}}$ direct solver, for symmetric positive definite systems. Choosing a linear solver.

Class (of a cross-section). EN 1993-1-1's four categories of steel section by susceptibility to local buckling; decides plastic or elastic resistance. Section classification.

Combination. A factored sum of load cases, one per code equation and leading action. Automatic combinations.

Completeness check. A Sturm-sequence test that the modes returned by a modal or buckling analysis are really the lowest ones, with none skipped. Modal analysis.

Conjugate gradients (CG). An iterative linear solver that converges towards the solution to a tolerance you set, rather than factorising the matrix. Choosing a linear solver.

Consistent mass. A mass matrix distributed with the element's own interpolation. Bounds true frequencies from above; the default. Modal analysis.

Convergence (mesh). The property that a result stops changing as the mesh is refined. Tested by halving the element size and comparing. Choosing element size.

Critical load factor — ${\alpha }_{cr}$. The multiple of a reference loading at which the structure buckles elastically. An upper bound, not a capacity. Linear buckling.

Cross-origin isolation. A browser security condition that lets a page share memory between threads. Where it is granted the solver runs on every core; where it is not, on one. System requirements.

D

Degree of freedom (DoF). One independent way a node can move: three translations and three rotations in a 3D model. The free plan caps the solved system at 500 of them. Supports and releases, Plans and limits.

Design strip. A width of slab over which a moment field is integrated to give the moment reinforcement is designed for. A hand calculation from the contour today; a section-cut tool is on the roadmap. Choosing element size.

Direct solver. A linear solver that factorises $K$ once and resolves cheaply for every load case. Choosing a linear solver.

Direct stiffness method. The procedure every finite element solver follows: element stiffness, transformation, assembly, constraints, solution, recovery. The direct stiffness method.

Drilling degree of freedom. The in-plane rotation about a shell element's normal. Without it a beam framing into a wall behaves as a pin. The shell element has one, tied to the membrane's own rotation (Hughes–Brezzi) rather than sprung to the ground. Element formulations.

DXF. A drawing exchange format. Imported as a reference underlay to snap against; nothing in it becomes a member. Drawings and snapping.

E

Eccentricity. An offset between a member's centreline and the node it connects to, carried by the member itself rather than by a separate rigid arm. Supports and releases.

Eigenvalue problem. $(K-{\omega }^{2}M)\varphi =0$ for modal analysis, $(K+\alpha K_g)\varphi =0$ for buckling: solved for the values ${\omega }^2$ or $\alpha$ and the shapes $\varphi$. Modal analysis, Linear buckling.

EN 1990. The Eurocode basis of design, whose equations 6.10, 6.10a and 6.10b define the ULS combinations. Automatic combinations.

EN 1993-1-1. The Eurocode for steel structures. Elementarium's first design module checks cross-section and member resistance to its §6.2 and §6.3. Steel — EN 1993-1-1.

Enhanced assumed strain (EAS). Extra strain modes added inside an element and condensed out, which let a four-node membrane bend in its own plane without the parasitic shear that otherwise stiffens it. The shell element's membrane uses four. Element formulations.

Envelope. The maximum and minimum of a result quantity across a set of combinations, position by position, each with its governing combination. Not an equilibrium state. Envelopes.

Equivalent nodal forces. The nodal loads a distributed load is converted to for assembly — $wL/2$ at each end of a uniformly loaded beam, plus fixed-end moments. The direct stiffness method.

Exclusive group. A load group whose cases can never act together — wind directions, arrangements of one imposed load. Load cases.

F

Favourable action. A permanent action that relieves the effect being checked, factored at ${\gamma }_{G,inf}$ rather than ${\gamma }_{G,sup}$. Decides uplift and overturning. Automatic combinations.

Frequent combination. The EN 1990 serviceability combination $G+{\psi }_{1,1}{Q}_{k,1}+\sum {\psi }_{2,i}{Q}_{k,i}$, for reversible effects. Automatic combinations.

G

Gauss point. A numerical integration point inside an element, where stresses are most accurate. Results are carried from there to the corners by a recovery method. Element formulations.

Geometric stiffness — $K_g$. The stiffness contribution of axial force acting through lateral deflection. Assembled from a static solve for buckling; from the current state for second-order. Linear buckling.

Governing combination. The combination that produced an extreme value or a utilisation. Every check and every table carries it. Design checks.

H

Hogging. Bending that puts the top of a beam in tension — over a support, at the eaves of a portal. Whether that is a positive or a negative $M_y$ depends on which way the member's local $z$ axis points; the diagram is drawn on the tension side either way. Sign conventions.

I

Imperfection. An initial out-of-straightness or out-of-plumb applied before a second-order analysis, to EN 1993-1-1 §5.3: global sway, member bow, or a scaled buckling shape. Second-order analysis.

Incomplete Cholesky. A preconditioner for conjugate gradients built from an approximate factorisation. Choosing a linear solver.

L

$LD{L}^{\mathsf{T}}$. A direct solver that factorises symmetric matrices including indefinite ones; its negative pivots are what second-order analysis watches for instability. Choosing a linear solver.

Leading action. The variable action taking its full characteristic value in a combination, while the others accompany at ${\psi }_0$. Automatic combinations.

Line support. A support distributed along a member or a slab edge, with stiffness per unit length — the Winkler bed for a grade beam or a wall under a slab. Elastic foundations.

Linear static analysis. $Ku=f$ on the undeformed geometry with elastic material; the workhorse. Linear static.

Load case. One action, unfactored. Load cases.

Load group. Cases that share a factor and a relationship — permanent, variable exclusive, variable simultaneous, accidental. Load cases.

Local axes. A member's own $x$ along its length, $y$ and $z$ in the section, fixed by the direction it was drawn. Sign conventions.

Locking. Spurious stiffness from a constraint the element cannot satisfy. Shear locking stiffens a displacement-based plate element as it gets thin; in-plane bending locking (parasitic shear) stiffens a plain four-node membrane in a wall or deep beam. The shell element locks in neither. Element formulations.

LRFD — load and resistance factor design. The AISC strength method that compares factored loads against $\varphi R_n$. Paired with ASCE 7 §2.3.1 combinations. ASCE 7 combinations.

Lumped mass. A mass matrix concentrated on the diagonal. Usually gives frequencies below the true ones, though not as a guaranteed bound. Modal analysis.

M

Mass target. A modal analysis setting: keep extracting modes until a fraction of the mass — 0.9, per EN 1998-1 — participates. Modal analysis.

Mechanism. A structure, or part of one, that can move without resistance. Produces a singular stiffness matrix. Singular stiffness matrix.

Mid-plane. The surface a slab or wall is modelled at, as a member is modelled at its centreline. Slabs, walls and shells.

MITC4. Mixed Interpolation of Tensorial Components, four nodes: the Reissner–Mindlin bending and transverse-shear formulation of the shell element every surface in Elementarium uses, which samples the shear at the edge midpoints so that thin plates do not lock. Its membrane is enhanced separately (EAS). Element formulations.

Modal analysis. Natural frequencies and mode shapes from $(K-{\omega }^{2}M)\varphi =0$. Modal analysis.

Mode shape. The deflected form of a natural mode, normalised to unit modal mass. Only the shape means anything. Modal analysis.

Modulus of subgrade reaction — $k_s$. Contact pressure per unit settlement, kN/m³. Not a soil property: it depends on the size of the loaded area. Winkler foundations.

Moment-gradient factor — $C_b$. AISC's allowance for the shape of the moment diagram in lateral-torsional buckling. Derived per combination from the sampled forces. Steel — AISC 360.

N

National annex. A country's published choices for the parameters a Eurocode leaves open — partial factors, ψ values, permitted combination rules. National annexes.

Nationally determined parameter (NDP). One of those choices.

O

OOFEM. An open-source finite element code. Elementarium exports an OOFEM input deck for reproducing a solve independently. Import and export formats.

P

P-Δ, P-δ. The second-order moments from gravity acting through frame sway (Δ) and through a member's own bow (δ). Second-order analysis.

Participating mass. The share of the structure's mass that moves in a given direction in a given mode; the 90% test. Modal analysis.

Partial factor. ${\gamma }_G$, ${\gamma }_Q$, ${\gamma }_{M0}$ and the rest — the safety factors applied to actions and resistances. Editable fields in the combination and set by the national annex for the check. Automatic combinations.

Patch test. A test that an element reproduces a constant strain state exactly on an arbitrary mesh. The shell element passes it in membrane and in bending. Element formulations.

Preconditioner. A transformation that makes an iterative solver converge faster — Jacobi, incomplete Cholesky or AMG. Choosing a linear solver.

Prescribed displacement. A support that moves by a set amount — settlement — rather than staying still. Load cases.

Principal moments — $m_1$, $m_2$. The extreme bending moments in a plate and the directions they act in. Results and reports.

Q

Quasi-permanent combination. The EN 1990 serviceability combination $G+\sum {\psi }_{2,i}{Q}_{k,i}$, for long-term effects. Automatic combinations.

R

Reaction. The force at a restrained degree of freedom, in global axes, acting on the structure. Their sum equals the applied load. Sign conventions.

Recovery. Carrying stresses from Gauss points to element corners — Zienkiewicz–Zhu, nodal average, area-weighted average, or none. Element formulations.

Reissner–Mindlin. Plate theory that includes transverse shear deformation, so one formulation serves thin and thick plates. Element formulations.

Release. Removal of continuity at one end of one member in one degree of freedom — fully, or partially with a stiffness. Supports and releases.

Rigid arm. A constraint tying an offset node's degrees of freedom to a master node. Not a stiff member. Supports and releases.

Rigid-body motion. Movement of the whole structure, or part of it, without strain. The pre-solve model check detects it and names the direction. Singular stiffness matrix.

S

SAF. The Structural Analysis Format — an open spreadsheet-based model exchange format read and written by SCIA Engineer, RFEM and others. Elementarium imports and exports SAF 2.2. Import and export formats.

Sagging. Bending that puts the bottom of a beam in tension — mid-span under gravity. The sign of $M_y$ follows the member's local $z$ axis, so read the diagram side, not the sign. Sign conventions.

Second-order analysis. $[K+K_g(u)]u=f$ by iteration, on the deformed geometry. Results do not superpose. Second-order analysis.

Setup (analysis). A named analysis configuration — type, solver, mesh minimums, mass sources — stored with the project and keeping its own results. Analysis types.

Shell. A surface element carrying both bending and membrane action. In Elementarium, every surface. Slabs, walls and shells.

Singular stiffness matrix. A $K$ with no unique solution — the structure contains a mechanism. Singular stiffness matrix.

Singularity (stress). A point where the elastic solution is infinite — a point support in a plate, a re-entrant corner. Refinement never converges there. Choosing element size.

Skew support. A support whose restrained directions are expressed in axes you define rather than the global ones. Supports and releases.

Sparse matrix. One that is mostly zeros, as a stiffness matrix is. The solvers exploit it. Choosing a linear solver.

Spring. A support with finite stiffness in a direction, in place of free or rigid. Linear in both directions — it resists tension. Supports and releases.

St. Venant torsion. Uniform torsion, without warping restraint. What the beam element carries. Sections and materials.

Station. One of the positions along a member at which internal forces are sampled and checks evaluated — eleven per member. Steel — AISC 360.

Sturm sequence. See completeness check.

Superposition. The property of a linear system that the response to a combination is the factored sum of the responses to its cases. Lost in second-order analysis. Linear static.

T

Tributary length. The length of a line support attributed to each analysis node along it, by which its stiffness per unit length is lumped. Elastic foundations.

U

ULS / SLS. Ultimate and serviceability limit states — strength and stability against deflection, vibration and cracking. Different combinations for each. Automatic combinations.

Utilisation ratio. Design effect over design resistance for a clause; above 1.0 the member fails it. Every one names its combination, position, clause and substituted formula. Design checks.

W

Warping (element). Out-of-plane twist of a quadrilateral's four nodes, on curved surfaces. The shell element corrects for it, so a rigid motion strains nothing, but the facet stays flat: beyond about 10° it is too coarse to quote. Mesh quality.

Warping (torsion). The out-of-plane distortion of an open section under torsion, and the restraint of it. Not modelled by the beam element. Steel — EN 1993-1-1.

WebAssembly. The binary format the C++ solver is compiled to so that it runs at native speed in a browser. System requirements.

Winkler bed. Soil idealised as independent linear springs, $p=k_{s}w$. Winkler foundations.

Z

Zienkiewicz–Zhu. An L² projection used to recover nodal stresses from element values, bounded by the element values, so it cannot invent a peak the elements do not carry. Element formulations.

ψ factors. ${\psi }_0$, ${\psi }_1$, ${\psi }_2$ — the reductions applied to accompanying variable actions in EN 1990 combinations, by action category. Automatic combinations.