What the AI can calculate

Check of a rectangular reinforced concrete column under biaxial bending + axial force (EN 1992-1-1 §5.8.9). Data: b, h [mm], d1 [mm], As_x (reinforcement per face on the X axis), As_y (per face on the Y axis) [mm²], fck, fyk [MPa], NEd [kN], MEdx, MEdy [kNm]. Returns M_Rd,x / M_Rd,y at NEd, the exponent 'a', the biaxial ratio (≤1 = OK) and the Mx-My envelope at NEd (series).

N-M interaction diagram of a rectangular reinforced concrete column with symmetrical reinforcement (EN 1992-1-1). Data: b, h [mm], As (reinforcement area per face) [mm²], d1 (cover to the bar centre) [mm], fck, fyk [MPa], NEd [kN], MEd [kNm], L (column length) [mm]. Returns N_Rd_max, M_Rd at NEd, the amplified moment M_Ed_dim, the utilisation and the N-M capacity CURVE (series).

Moment-curvature curve (M-κ) of a rectangular reinforced concrete section — non-linear behaviour up to failure. Data: width, height [mm], fck, fyk [MPa] + 2 reinforcement layers (bottom/top). Returns the M-κ curve (series) and the yield and ultimate moments/curvatures. Requires the section analysis microservice (Python, :8001).

Section properties (gross + cracked) for a rectangular reinforced concrete section: area, gross and cracked second moment of area, modulus Ecm, axial capacity and pure moment. Data: width, height [mm], fck, fyk [MPa] + 2 reinforcement layers (bottom/top). Requires the section analysis microservice (Python, :8001).

Crack width check of a reinforced concrete slab (EN 1992-1-1 §7.3), 1 m strip. Data: B (width, default 1000), H (thickness) [mm], fck, fyk [MPa], Md (service moment) [kNm/m], bottom/top reinforcement (diameter, spacing, cover) [mm], w_lim [mm]. Returns w_k and the check w_k ≤ w_lim. Requires the section analysis microservice (:8001).

3D SOLID FEA of a WELDED beam-to-column CONNECTION made of I/H sections (CalculiX through the Desktop Agent, Gmsh mesh, weld = monolithic solid via BooleanUnion). ⚠️ AGENT function — asynchronous and long; requires the JointLib agent (gmsh.exe + ccx.exe). Data (mm, N): column dimensions col_h/col_b/col_tf/col_tw and beam dimensions beam_h/beam_b/beam_tf/beam_tw, F (vertical force at the beam end), mesh_size. Returns mesh3d (deformed, coloured by stress) + maximum von Mises stress and displacement.

3D SOLID FEA (CalculiX through the Desktop Agent, automatic Gmsh mesh) for an L×H×W box. ⚠️ AGENT function — asynchronous and long; requires the JointLib agent running (gmsh.exe + ccx.exe), suited to workflows rather than instant calculation. Data (mm, N): L (length, X), H (height, Y), W (width, Z), F (vertical force at the end, downwards), mesh_size. Fixed at Y≈0, force at X≈L. Returns mesh3d (displacements + stresses) + maximum von Mises stress, maximum displacement, number of nodes/elements.

3D SOLID FEA of a BOLTED END-PLATE beam-to-column connection (CalculiX through the Desktop Agent). Solid plate + welded beam stub, moment applied as a flange couple, bolts as tension springs, compression flange bearing on the column. ⚠️ AGENT function — asynchronous and long; requires the JointLib agent (ccx.exe). Data (mm, kNm, N/mm²): plate bp/hp/tp, beam beam_h/beam_bf/beam_tf/beam_tw, y_c (beam axis on the plate), bolts n_rows/bolt_dx/bolt_y1/bolt_pitch, M_Ed and f_y. Returns the plate utilisation from stress (area percentile, singularities filtered out), σ_rep/σ_max, maximum displacement and the coloured 3D mesh.

Single-span beam on FEALiTE2D. End supports (support_left/right: 0=free, 1=pinned, 2=fixed) + loads (uniform q, point P at x=a, moment M0 at x=aM). Cases: simply supported / cantilever / propped / fixed. Returns reactions + M/V/deflection.

Continuous beam over 2..6 spans (simply supported) with a uniform load q, on FEALiTE2D. Spans: L1..L6 (the first n_spans are used). Returns the span and support moments and the M/V/deflection diagrams over the whole length.

2D portal frame (single bay, single storey: 2 columns + rafter) on FEALiTE2D. Bases: base_fixed 1=fixed, 0=pinned. Loads: uniform q on the rafter (downwards), horizontal H at the top-left corner. Returns reactions, axial force in the columns, the lateral displacement and the bending moment diagrams for the rafter and the column.

Soil pressures under a rectangular isolated footing — the simplified method of NP 112 Annex E (zones by eccentricity: full contact / partial in one direction / biaxial partial, closed form). Data: B, L [m], N [kN] (compression), Mx, My [kNm], p_conv [kPa]. Returns p_max, p_min, the eccentricities, the active area, the effective dimensions and the pressure profile along L.

Soil pressures under a rigid rectangular isolated footing on a Winkler bed (no tension) — continuous model, valid also for partial contact (uplift). Data: B, L [m], N [kN] (compression), Mx, My [kNm], p_conv [kPa]. Returns p_max, p_min, the eccentricities, the active contact area, the effective dimensions and the pressure profile along L.

Slope stability (critical slip circle method), homogeneous soil layer. Data: height (slope height) [m], angle (inclination from the horizontal) [degrees], gamma (unit weight) [kN/m³], phi (angle of internal friction) [degrees], c (cohesion) [kPa], surcharge [kN/m²], water_table (water level above the base) [m]. Returns the factor of safety FOS, the critical circle and the FOS vs. angle curve. Requires the geotechnics microservice (:8001).

Soil (elastic half-space) with a rectangular footing bearing on it, through 3D finite elements (CalculiX, parametric hexahedral mesh). ⚠️ AGENT function — asynchronous; requires the JointLib Desktop Agent running (ccx.exe). Data (m, kPa): B, L (footing sides), q (contact pressure), E (soil modulus), nu (Poisson), density (0=coarse/1=medium/2=fine). Returns: the vertical stress bulb σz as a 2D map (section through the centre), the σz profile on the vertical, the settlement at the centre, σz at the surface, number of elements. The bulb follows Boussinesq/Newmark theory in the near-surface zone.

Finite element analysis of a rectangular slab (PyNite) — deflection and moments as 2D MAPS. Data: Lx, Ly [m], t (thickness) [m], fck [MPa], q (load) [kN/m²], nx, ny (mesh divisions), edges edge_s/edge_n/edge_w/edge_e (0=pinned, 1=fixed, 2=free). Returns the field2d fields Dz (deflection), Mx, My + the maximum values. Requires the slab analysis microservice (:8001).

Moments in a rectangular two-way slab supported on all four edges with the corners held down — BS 8110-1:1997 Table 3.14, the nine support cases, interpolated linearly on k = l_y/l_x (1.0…2.0). Data: q (DESIGN load) [kN/m²], lx (short span) [m], ly (long span) [m], support_case (0=interior, 1=one short edge discontinuous, 2=one long edge discontinuous, 3=corner panel, 4=both short edges discontinuous, 5=both long edges discontinuous, 6=three discontinuous with one long edge continuous, 7=three discontinuous with one short edge continuous, 8=simply supported on all four sides). Returns the span moments (M_x, M_y), the support moments (M_x_sup, M_y_sup) [kNm/m], the β coefficients used and k. NOTE: BOTH moments are referred to l_x² (the SHORT span) — that is the table's convention. The support moment is 0 on a discontinuous edge. Above k = 2 the table does not apply — the slab spans one way.

Section properties for EN steel profiles, selected NUMERICALLY (no strings): family 0=HEA,1=HEB,2=HEM,3=IPE,4=UPN,5=SHS,6=RHS,7=CHS; size = the nominal figure in the designation [mm] (the depth of the I/U profile — e.g. 300→HEA300; the SHS side; the larger RHS side; the CHS outer diameter); t = wall thickness [mm] (hollow sections only); b = the smaller side [mm] (RHS only). Picks the closest profile and returns A, Iy, Iz, Wel, Wpl, i_y, i_z (radii of gyration), IT, mass, h, b.

Stability of cold-formed thin-walled sections (C/Z/U) with pyCUFSM (finite strip). Data (mm, N, MPa): section_type (0=C, 1=Z, 2=U), h (web), b (flange), c (lip; 0 for U), t, r (internal radius), fy, N (axial force [N]), M (moment [N·mm]), L (member length [mm]), end_condition (0=pinned-pinned, 1=fixed-fixed, 2=fixed-pinned, 3=cantilever). Returns the signature curve, local/distortional/global Pcr, the governing mode and the EN 1993-1-3 resistance. Requires the pyCUFSM microservice/agent running.

Local buckling of a compressed plate (EN 1993-1-5) + section classification (EN 1993-1-1 Tab. 5.2). Data: fy [MPa], b (plate width) [mm], t (thickness) [mm], plate_type (0=internal kσ=4, 1=outstand kσ=0.43, 2=stiffened kσ=6.97), ksigma (optional, overrides kσ). Returns σcr, the slenderness λp, the section class and — for Class 4 — the reduction factor ρ and the effective width b_eff.

Buckling reduction factor χ (EN 1993-1-1 §6.3.1): Φ=0.5·[1+α·(λ̄−0.2)+λ̄²], χ=1/(Φ+√(Φ²−λ̄²)) ≤ 1. Data: lambda_bar (relative slenderness λ̄), alpha (imperfection factor; curves a0=0.13, a=0.21, b=0.34, c=0.49, d=0.76). For LTB use λ̄_LT and α_LT. Returns χ (≤1) and the curve χ(λ̄). Compose it with Ncr and λ̄ computed through equations for the resistance Nb,Rd.

Beam with a point load: bending moment diagram M(x) and shear force V(x). cantilever=0 → simply supported; cantilever=1 → cantilever fixed at the left end.