How STATIX actually solves structures

1. Overview & philosophy

STATIX is a finite-element structural-analysis and design suite that runs entirely in a single offline browser file. Every result on this page is produced by code that ships in the app — the in-app validation suite re-runs the same production functions against closed-form benchmarks, so there is no separate "demo" maths path.

The suite is built in layers. At the centre is a direct-stiffness 3D finite element solver for frames, shells and solids. On top of that sit member-design checks to several national codes (steel, reinforced concrete, timber, masonry, composite), a component-based FEM (CBFEM) connection kernel, and geotechnical, load-generation and detailing modules. Analysis and design share one model: the forces a member-design check consumes are the forces the FEM solver computed.

Three principles guide the implementation, and they are reflected throughout this document:

• Real numerical methods, not approximations. The frame engine is a true 6-degree-of-freedom stiffness solver with an exact factorisation, not a closed-form portal-frame shortcut.
• The code clause is cited at each step. Member checks and connection components carry the standard clause they implement, so a reviewer can trace every number to a published rule.
• Honesty about maturity. Where an engine is a first version, where a result is calibrated against an established method rather than derived from first principles, or where a benchmark sits a few percent off the closed-form answer, this page says so plainly.

2. The 3D frame FEM — direct stiffness method

Frame analysis uses the displacement (direct stiffness) form of the finite element method. The structure is discretised into two-node beam elements, each carrying six degrees of freedom per node; element stiffnesses are formed in local axes, rotated to global axes, assembled into one global system, restrained at supports, and solved for nodal displacements. Member forces are then recovered element by element.

2.1 The two-node 6-DOF beam element

Each member is a prismatic 3D Euler–Bernoulli beam element. Every node carries three translations and three rotations, so an element has twelve degrees of freedom: [u_x, u_y, u_z, θ_x, θ_y, θ_z] at each end. The element stiffness matrix k is the standard 12×12 form combining four uncoupled actions — axial, St-Venant torsion, and bending about each principal axis:

where E is Young's modulus, G the shear modulus, A the section area, I_y, I_z the second moments of area, J the torsion constant and L the element length. Section properties are read from the section library for catalogue shapes, or computed from geometry for built-up and custom sections.

This is a cubic-Hermitian (Euler–Bernoulli) element: it captures bending exactly for members carrying end forces and reproduces the closed-form deflection of a prismatic beam without sub-division. Transverse-shear (Timoshenko) flexibility is not included in the bending stiffness; for the normal range of building members this is the appropriate idealisation, and deep members should be checked accordingly.

2.2 Coordinate transformation

The local axes of a member are built from its end coordinates. The first local axis runs along the member; the remaining two are formed by a Gram–Schmidt construction against a global up-vector, with a singularity guard so that vertical members fall back to a horizontal reference axis. An optional roll angle rotates the cross-section about the member axis. This yields a 3×3 rotation matrix R of direction cosines, expanded to the 12×12 block-diagonal transformation T (four copies of R). The element's global stiffness is the congruence transform:

2.3 End releases, rigid links and tension-only members

Member ends can release any of the six DOF (for example, a pinned truss member releases both end moments). Releases are applied by static condensation of the released DOF out of the element stiffness, so a released member contributes a correctly reduced stiffness rather than a numerical fudge. Semi-rigid rotational springs at the ends are supported on the same path. Rigid links are modelled as very-stiff elements with bounded amplification of EA, EI and GJ, kept stiff enough to enforce the link but bounded so the global system stays well-conditioned. Tension-only bracing is handled by a per-load-case active-set iteration that removes members which go into compression and re-solves.

2.4 Assembly, supports and springs

The global stiffness is assembled into a sparse row structure (each row a map from column to value), so large models never allocate a dense n² matrix. Each element's 12×12 global stiffness is scattered into the rows addressed by its DOF map. Nodal supports restrain DOF directly; elastic point springs (including Winkler-type foundation springs) add stiffness to the global diagonal while leaving the DOF free; and rigid floor diaphragms are enforced with a penalty multi-point constraint tying each level's in-plane motion (two translations and the vertical-axis rotation) to a master node. A safety pass auto-restrains any free DOF that ends up with zero stiffness (a dangling rotation, say), with a diagnostic message that names the offending node.

2.5 Solving K·d = F

With the free DOF identified, STATIX solves the reduced linear system

The solver is chosen automatically by problem size:

• Dense LU factorisation (Doolittle, with partial pivoting) for small models — up to about 1200 free DOF. This is the path the validation suite exercises against closed-form answers; a zero pivot is detected and reported as a precise mechanism location.
• Sparse direct LDL^T for larger models — an exact factor-once / solve-many factorisation on the compressed sparse system. A clean non-positive pivot from the direct factor pinpoints the exact unstable DOF, which is a far better diagnostic than an iterative non-convergence.
• Incomplete-Cholesky preconditioned conjugate gradient (IC(0)+PCG) as a fallback when the direct factor would be too large to store or fails.

For heavy models the factorisation can be offloaded to a web worker so the interface never blocks; the worker path returns the same factor the main thread would have computed. Because all three paths solve the same assembled system, results agree to solver tolerance.

2.6 Reaction and member-force recovery

Once the free displacements are known, the full displacement vector is assembled (restrained DOF are zero), and reactions at supports are recovered as the residual R = K·d − F. For each member, the global end displacements are rotated back to local axes and multiplied by the local stiffness to give the twelve end forces. Internal actions along the member — axial force, the two shears, torsion and the two bending moments — are then reconstructed from the end forces plus the equilibrium contribution of any distributed and point loads acting between the ends, evaluated at any station along the span.

3. Second-order, buckling and dynamic analysis

3.1 P-Δ (geometric) second-order analysis

Second-order effects are introduced through the geometric stiffness matrix. Each member's axial force from a first-order solve produces an element geometric stiffness k_g, which is assembled alongside the elastic stiffness; the system is then re-solved so that compression softens and tension stiffens members, capturing P-Δ / P-δ amplification. This is the standard linearised geometric-nonlinearity treatment used for stability-sensitive frames.

3.2 Linear buckling analysis (LBA)

The elastic critical load factor is found from the generalised eigenvalue problem that pairs the elastic and geometric stiffness matrices:

The smallest eigenvalue is the critical load factor α_cr — the multiple of the reference loading at which the structure buckles — and φ is the buckling mode shape. STATIX extracts the lowest modes by inverse power iteration with deflation (each iteration is one solve against the elastic factor; the Rayleigh quotient gives the eigenvalue, with a tight convergence tolerance and a deflation step to find higher modes). The buckling solver is dense and is intended for models up to roughly 1200 free DOF. α_cr directly feeds the code distinction between rigid, second-order and amplified-first-order analysis.

3.3 Modal analysis and mass participation

Free-vibration analysis solves the eigenproblem Kφ = ω²Mφ for natural frequencies and mode shapes, using a lumped (diagonal) mass matrix. For each mode the engine computes the participation factor, the generalised (modal) mass and the effective modal mass per global direction, then the cumulative participation ratio — the figure checked against the 90% threshold that codes require for a sufficient number of modes.

3.4 Response spectrum analysis

For seismic design, modal responses are scaled by a design response spectrum (the EN 1998-1 four-branch design spectrum, with the ground-type factors and behaviour factor q) and combined by CQC (complete quadratic combination, with the modal-correlation coefficients) or SRSS. An equivalent-lateral-force path distributes storey forces by mass and height and adds accidental-eccentricity torsion. The lumped-mass model carries translational mass only; rotational inertia is not included.

4. Shell and plate finite elements (slabs & walls)

Slabs, walls and plate fields are modelled with a four-node flat-shell element that superposes in-plane (membrane) and out-of-plane (plate bending) behaviour. The same element type is also used by the whole-frame 3D shell solver, in which I-section members are re-meshed into flange and web plates.

4.1 The flat-shell quadrilateral

The element is a four-node quadrilateral (Q4) with six DOF per node (24 per element), formed by combining three parts:

• Membrane — a standard bilinear iso-parametric plane-stress element with 2×2 Gauss integration.
• Plate bending — a thin-plate (Kirchhoff) element on the ACM (Adini–Clough–Melosh) twelve-term polynomial basis, integrated with 3×3 Gauss points. The plate constitutive matrix uses the flexural rigidity D = Et³/[12(1−ν²)].
• Drilling DOF — the in-plane (normal-axis) rotation is given a small penalty stiffness so the element couples cleanly into the 6-DOF frame assembly.

Element stiffnesses are formed in a local plate frame and rotated into global axes, then assembled into the same global stiffness matrix as the beam elements — so frames and slabs solve together in one system. Panels are auto-meshed into a grid (default density adjustable), with shared edge nodes merged on rounded coordinates so adjacent panels connect automatically; edge supports are inherited from the panel definition. The suite also includes an eight-node hexahedral solid element for solid regions, assembled with three translational DOF per node.

4.2 Stress and stress-resultant recovery

After the solve, each element recovers membrane forces N_x, N_y, N_xy from the membrane strains and bending moments M_x, M_y, M_xy from the plate curvatures (the curvatures come from the ACM basis coefficients). A combined von Mises stress is reported as the worst of the top and bottom fibre, so the controlling bending case is captured. Contours can be drawn for von Mises, the in-plane stresses and the bending moments.

4.3 Wood–Armer reinforcement and design strips

Slab reinforcement is designed from the recovered moment field. The Wood–Armer method converts the triad (M_x, M_y, M_xy) into orthogonal design moments for the top and bottom layers, including the twisting contribution and a skew-rotation option for non-orthogonal reinforcement. STATIX integrates the actual FE moment field across a transverse band (trapezoidal integration of the element field) rather than sampling a single point, then apportions the integrated moment between column and middle strips using the established flat-slab fractions (a larger share of hogging to the column strip). The per-metre design moment is converted to a bar area with the singly-reinforced lever-arm relation

with a minimum-steel floor, and the result is laid out as bar spacing in convenient increments. The same field feeds shear-wall design (an N+M layered strain-compatibility solve over the wall length with boundary-zone and web reinforcement, plus an in-plane shear check on a variable-strut truss).

4.4 Whole-frame 3D shell FEM

For detailed studies, an entire frame can be re-meshed into shells: each I-section member becomes top-flange, bottom-flange and web plates, gridded into quadrilaterals, with nodal and member loads spread onto the load-path nodes. The combined model is solved with the same dense-LU path, von Mises is recovered per element, and the peak shell deflection is sanity-checked against the beam-frame reference solution.

5. Connection design — component-based FEM (CBFEM)

The Connection Studio brings component-based finite-element connection design into the browser. The plates of a steel joint are meshed into shell elements; bolts, welds and bearing contact are introduced as nonlinear elements; and the model is pushed incrementally into the plastic range against a deformation-based limit. The connection's moment resistance is calibrated against the established EN 1993-1-8 component method — this is stated openly below.

5.1 What CBFEM is

Component-based finite element modelling sits between hand component-method calculation and full research-grade solid FE. The connecting plates carry a real finite-element mesh, so stress flow, prying and contact are captured by the model rather than assumed; the fasteners and welds are represented by nonlinear elements whose strength follows the code; and the joint is taken to its limit by an incremental, materially nonlinear solve. The result is a method that handles arbitrary geometry while remaining anchored to recognised resistances.

5.2 The CBFEM model

• Plate mesh. Each plate is subdivided into a grid of four-node shell elements; coincident edge nodes between plates are merged, and the mesh is auto-coarsened if a degree-of-freedom ceiling is reached.
• Unilateral contact. Bearing between plates (and base-plate-to-grout) is modelled as a compression-only contact with a penalty stiffness and an active-set iteration — a contact that goes into tension is released and the model re-solved, so the joint can lift off and re-bear correctly.
• Bolts. A bolt is an anisotropic spring: an axial stiffness along its shank carrying tension to the code tension resistance F_t,Rd, and a lateral law for shear that follows an elastic–slip–bearing–yield path up to the bearing resistance F_b,Rd. Prying is produced by the plate FE and contact, not baked into the spring. Tension and bearing resistances follow EN 1993-1-8 Table 3.4 with γ_M2 = 1.25.
• Welds. Fillet welds are line elements checked by the directional method of EN 1993-1-8 4.5.3.2: the throat stresses σ_⊥, τ_⊥, τ_∥ are recovered and combined as

5.3 Incremental elasto-plasticity and the 5% limit

The plates are taken into the plastic range by an incremental solve with a von Mises yield surface and a radial-return (secant-softening) update: once an element's trial stress exceeds yield, its stiffness is reduced so the stress does not exceed f_y, and its accumulated equivalent plastic strain is tracked. The ULS limit is the 5% equivalent plastic strain deformation criterion of EN 1993-1-5 / EN 1993-1-8 — the same limiting strain CBFEM methods use to define connection failure. Plate buckling of the connection plates is available as a separate linear-buckling (α_cr) check.

5.4 Calibration against the component method — the honest part

A coarse shell mesh has a well-known weakness for capacity: the elastic stress peak under a bolt is a near-singularity, so reading the moment resistance straight off the elastic stress field is unreliable. STATIX therefore calibrates the connection capacity against the EN 1993-1-8 component method. The calibrated path computes each bolt-row resistance from the actual code components — the end-plate and column-flange T-stub modes 1/2/3 (EN 6.2.6), bolt tension and punching (Table 3.4), and column-web tension/compression — then ramps the joint moment, distributing it to the rows by lever arm until a row reaches its component cap, and assembles the moment resistance as a top-down plastic mechanism:

An independent in-app auditor re-derives M_j,Rd from its own EN primitives and compares. On the bolted extended end-plate benchmark the calibrated CBFEM result tracks the component method within roughly 1–2% for the governing case, and the validation pack requires the agreement to stay inside a defined tolerance band, with no bolt row permitted above its component cap. The FE mesh still does the geometric and contact work; the capacity number is anchored to the recognised component resistances rather than to a singular elastic peak.

6. Steel member design

Member checks read the forces from the frame solver and apply the cross-section and stability rules of the selected code. The same model can be checked to several standards; the codes give genuinely different capacities, not cosmetic relabelling.

6.1 Cross-section classification

Sections are classified (Class 1–4) from the width-to-thickness ratios of the flange and web outstands, scaled by ε = √(235/f_y) against the EN 1993-1-1 Table 5.2 limits (with equivalent rules for the other codes). The class selects the section modulus used downstream — plastic W_pl for Class 1–2, elastic W_el for Class 3, and an effective modulus for Class 4.

6.2 Axial buckling

Flexural buckling uses the column-curve reduction factor. For Eurocode the engine computes the Euler load N_cr = π²EI/L_cr², the non-dimensional slenderness λ̅ = √(Af_y/N_cr), and

with the imperfection factor α chosen from the buckling curve appropriate to the section (EN 1993-1-1 6.3.1). The SANS/CSA path uses the equivalent additive column formula with its own resistance factor. Flexural-torsional and torsional buckling are added for sections that need them — single and double angles, tees, cruciforms and cold-formed channels — via the elastic critical-load cubic, with the governing mode replacing the flexural reduction.

6.3 Lateral-torsional buckling

For laterally unrestrained beams the elastic critical moment is

with the moment-gradient factor C₁ from the end-moment ratio. The LTB reduction χ_LT follows the same curve form as axial buckling (EN 1993-1-1 6.3.2.3), giving the buckling resistance M_b,Rd = χ_LT W f_y / γ_M1.

6.4 Shear and combined actions

Shear resistance is checked on the shear area, and combined axial-plus-bending is evaluated with the code interaction expression — the EN 1993-1-1 6.3.3 interaction with the k_yy, k_zz factors for Eurocode, or the additive beam-column interaction for SANS/CSA/AISC. The governing utilisation across the sampled stations is reported. Serviceability deflection is computed by Hermite interpolation of the member deflected shape, taking the chord-relative sag against the span/limit ratio, and it governs over strength when larger.

Specialist steel checks — plate girders, crane runway beams, fire and the cold-formed and fatigue routes — are layered on the same member pipeline.

7. Reinforced concrete

7.1 Beams

Flexural design uses the rectangular stress block. The lever-arm relation K = M/(bd²f_cu) gives z and hence the tension steel A_s = M/(0.87 f_y z) (SANS 10100 / BS 8110 form), with compression steel added when K exceeds the singly-reinforced limit. Moment redistribution couples the redistribution ratio to the neutral-axis depth limit for ductility (EN 1992 5.5 / SANS), and re-establishes span moments from equilibrium after the supports are redistributed.

7.2 Columns — N–M interaction and biaxial bending

Column capacity is built from a strain-compatibility section solve. Sweeping the neutral-axis depth, the engine integrates the rectangular concrete stress block (stress 0.447 f_cu, ultimate strain ε_cu = 0.0035) and the bar forces (bounded by the design yield) to trace the uniaxial N–M interaction curve, the squash load N₀ and the balanced point. Slenderness adds a nominal-curvature additional moment. Biaxial bending is checked with Bresler's reciprocal-load rule and the load-contour interaction:

7.3 Punching shear and cracked deflection

Flat-slab punching is driven directly from the FE results: the engine locates columns landing on slab nodes, pulls the design shear from the reactions, reads the effective depth and reinforcement ratio, classifies the perimeter as internal/edge/corner, and applies the code v_Rd,c / v_Rd,max checks. Deflection uses a cracked-versus-uncracked stiffness selection.

8. Timber, masonry and composite

8.1 Timber (EN 1995-1-1 / SANS 10163)

Timber design carries a library of strength classes (the C-classes, glulam and SA pine grades) with their characteristic values. Design values follow X_d = k_mod X_k / γ_M, with k_mod from service class and load duration. Bending includes the lateral-torsional k_crit, compression includes the buckling factor k_c, shear uses the cracked-section factor, and combined tension/compression-plus-bending uses the code interaction with the k_m cross-coupling factor.

8.2 Masonry (EN 1996-1-1 / SANS 10164)

Characteristic compressive strength is built from the unit and mortar strengths via f_k = K f_b^0.7 f_m^0.3. Vertical capacity applies the slenderness and eccentricity reduction factor Φ (the Annex-G form), with in-plane shear on the compressed length and an out-of-plane flexural check; partial factors follow EN (and the SANS value where that code is selected).

8.3 Composite steel–concrete (EN 1994-1-1)

Composite beams compute the effective slab width, then the plastic moment M_pl,Rd from the plastic neutral-axis position (in slab or steel). Shear-connector resistance is the lesser of stud-shank shear and concrete crushing; the degree of shear connection interpolates between the steel and full-composite resistance for partial connection. Deflection uses the short-term modular ratio with cracked/uncracked transformed sections.

9. Cold-formed sections & fatigue

9.1 Cold-formed effective section (EN 1993-1-3 / EN 1993-1-5)

Thin-walled lipped C, Z and sigma sections are handled with an effective-width treatment for local and distortional buckling, with a corner-radius correction, so that Class-4 plate slenderness reduces the effective area and modulus before the member check runs.

9.2 Fatigue (EN 1993-1-9)

Fatigue uses the standard S–N detail-category catalogue. The direct-stress curves are bilinear (slope m = 3 down to the constant-amplitude fatigue limit at 5×10⁶ cycles, then m = 5 to the cut-off at 10⁸); shear details use a single m = 5 slope. Endurance is read from the appropriate branch, and variable-amplitude spectra are accumulated with Palmgren–Miner damage D = ∑ n_i/N_R,i ≤ 1, with the equivalent constant-amplitude range reported.

10. Geotechnics & foundations

10.1 Bearing capacity

Shallow-foundation bearing capacity uses the classic three-term equation with the Terzaghi and Meyerhof bearing-capacity factors:

with shape, depth and load-inclination factors, a water-table correction on the effective unit weight, and an allowable capacity from a factor of safety.

10.2 Piles and retaining walls

Pile capacity sums shaft friction (the α-method in clay, the β-method in sand) and end bearing, with a Converse–Labarre group-efficiency factor. Retaining walls use Coulomb active earth pressure (with a Rankine backup), full overturning / sliding / bearing factor-of-safety checks, a first-pass RC stem-and-base design, and an EC7 Design-Approach-1 partial-factor envelope (reducing tanφ and raising surcharge).

11. Loads & combinations

STATIX generates limit-state load combinations for several codes — the EN/SANS partial-factor combinations, the AISC/ASCE LRFD and ASD sets, the CSA/NBCC companion-action combinations and the AS/NZS set — including the uplift/reversal cases. Wind pressures from the wind generator are resolved onto members as line loads by tributary width (windward, leeward and roof uplift zones), with a nodal fallback for bare frames. Seismic equivalent-lateral forces are distributed over storey nodes by mass and height with accidental-eccentricity torsion, and the response-spectrum path (section 3.4) provides the modal route.

12. Detailing — bar bending schedules (SANS 282)

Reinforcement detailing produces bar bending schedules to BS 8666 / SANS 282: shape codes, mandrel radii, bend deductions and centre-line cutting lengths, with project-unique bar marks running across all RC members, mass totals, and export to DXF. Slab reinforcement from the Wood–Armer design (section 4.3) is scheduled as straight mats per direction, with welded-mesh options to SANS 1024.

13. Validation & verification

A built-in validation suite re-runs the production engines against closed-form benchmarks and prints a pass/fail report. Crucially, the benchmarks call the same functions the app uses — there is no separate demonstration code path.

Alongside the benchmarks, a model audit checks connectivity, coincident nodes and mechanism stability; a per-node moment-equilibrium residual is reported; and around 150 in-app regression hooks back the "how to verify it" for every engine. A mechanism is reported with the exact node and DOF responsible.

14. Methods, assumptions & limitations

Read this section before relying on any output. STATIX is a design aid; the items below are where judgement is most needed.

• Beam theory. Frame elements are Euler–Bernoulli (no transverse-shear flexibility). Deep members, where shear deformation matters, should be checked accordingly.
• Linearity. The standard solve is linear-elastic. Second-order (P-Δ), buckling and tension-only effects are available but are added on the geometric-stiffness / active-set basis described above, not a full large-displacement nonlinear solver.
• Solver size. The dense and buckling paths target models up to ~1200 free DOF; larger models use the sparse direct / PCG paths. Tension-only active-set runs on small dense models (a warning is issued and the members are analysed two-way above the limit, which may be unconservative for braces).
• Shell FE. First version, thin-plate (Kirchhoff) only — no Mindlin/MITC thick-plate element. Validated for simply-supported fields to a few percent; clamped-edge hogging is read soft and extrapolated. Verify thick slabs and steep clamped edges.
• CBFEM capacity. Connection moment resistance is calibrated against the EN 1993-1-8 component method, not read from the elastic stress peak. No automatic M–φ curve or rigid/semi-rigid classification is produced. Other connection benchmarks sit within defined (wider) tolerance bands.
• Seismic / response spectrum. First-pass. Lumped translational mass only; spectra, behaviour factors and combinations must be verified to the governing seismic code.
• Specialist material engines. Timber, masonry, composite, cold-formed, fatigue, moment redistribution and the geotechnical engines are first-version, textbook-form implementations and are not yet independently production-validated.
• RC code variants. The concrete path is built on the rectangular stress block (SANS 10100 / BS 8110 form); it is not a separate full EN 1992 parabolic-rectangular engine.
• Units and conventions. The engine works in SI internally; sign conventions for moments and the hogging-positive slab convention are documented in-app. Imperial display is a presentation layer.

15. References

Design codes implemented or referenced

• SANS 10160 — Basis of structural design and actions for buildings and industrial structures.
• SANS 10162-1 — The structural use of steel: limit-states design of hot-rolled steelwork.
• SANS 10100 — The structural use of concrete.
• SANS 10163 / SANS 10164 / SANS 282 / SANS 1024 — Timber, masonry, bar bending and welded mesh.
• EN 1990 — Eurocode: Basis of structural design.
• EN 1991 — Eurocode 1: Actions on structures.
• EN 1992-1-1 — Eurocode 2: Design of concrete structures.
• EN 1993-1-1, 1-3, 1-5, 1-8, 1-9 — Eurocode 3: steel (general, cold-formed, plated, joints, fatigue).
• EN 1994-1-1 — Eurocode 4: composite steel and concrete structures.
• EN 1995-1-1 — Eurocode 5: design of timber structures.
• EN 1996-1-1 — Eurocode 6: design of masonry structures.
• EN 1997 (Eurocode 7) — Geotechnical design.
• EN 1998-1 — Eurocode 8: design of structures for earthquake resistance.
• AISC 360 (LRFD & ASD) and ASCE 7; CSA S16 and NBCC; AS 4100 / AS–NZS 1170; BS 8110 / BS 8666.

Finite-element and structural-mechanics texts

• Cook, R. D., Malkus, D. S., Plesha, M. E. & Witt, R. J. — Concepts and Applications of Finite Element Analysis.
• Bathe, K.-J. — Finite Element Procedures.
• Zienkiewicz, O. C., Taylor, R. L. & Zhu, J. Z. — The Finite Element Method.
• Timoshenko, S. P. & Woinowsky-Krieger, S. — Theory of Plates and Shells.
• Przemieniecki, J. S. — Theory of Matrix Structural Analysis.
• McGuire, W., Gallagher, R. H. & Ziemian, R. D. — Matrix Structural Analysis.
• Wood, R. H. — The reinforcement of slabs in accordance with a predetermined field of moments (the Wood–Armer method).
• Wald, F. et al. — published work on the component-based finite element method (CBFEM) for steel connections.

Written by the STATIX design team. Back to top ↑