STANDARDS-COMPLIANT COMPUTATIONAL ARCHITECTURE

Deterministic Structural Engineering Computational Portal

StructLogic is an open-access, zero-telemetry structural engineering suite designed to provide auditable, verifiable calculations for civil and structural engineers, architects, code officials, and builders. Built on first-principles mechanics, codified against ACI 318, AWC NDS, IBC 2024, and AISC 360.

Total Engines

18 Planned

Hub Domains

5 Core Hubs

Client Telemetry

0% (Strict)

Evaluation Engine

100% Client SSG

Explore 18 Engine Specifications View Governing Formulas & Derivations

Structural Computing Philosophy

Engineering Guarantees: Open, Deterministic, Zero Runtime Leaks

01 / DETERMINISTIC RIGOR

First-Principles Calculations

No black-box AI approximations, empirical heuristics without codification, or undocumented assumptions. Every calculation yields identical floating-point results matching verified closed-form structural mechanics.

02 / AIR-GAPPED PRIVACY

Zero Client-Side Telemetry

Zero third-party trackers, zero marketing analytics, and zero database ingestion. Project dimensions, member loads, and soil parameters never cross the network boundary, ensuring proprietary engineering data protection.

03 / CODE JURISDICTION

Harmonized Code Standards

Direct mapping to current building codes including ACI 318-19, AWC NDS-2024, AISC 360-22, and IBC/IRC 2024. All reduction factors ($\phi$), load combinations, and adjustment factors ($C_D, C_M, C_t$) are transparently declared.

Mathematical Foundation & Mechanics

Governing Structural Formulas & Analytical Derivations

StructLogic computational algorithms are strictly derived from classical continuum mechanics and accepted limit state design criteria. Below are the analytical governing equations powering the suite.

CONTINUUM MECHANICS: PROOF 01

Fourth-Order Euler-Bernoulli Elastic Beam Deflection

Standard: AISC 360-22 § L3 / AWC NDS-2024 § 3.5

Euler-Bernoulli beam theory governs flexural members where plane sections remain plane and normal to the longitudinal centroidal axis under transverse loading. The fundamental governing fourth-order differential equation relating transverse displacement $w(x)$ to distributed load $q(x)$ is:

EI * (d⁴w / dx⁴) = q(x)

Direct Integration for Simply Supported Beam under Uniform Load:

For a simply supported beam of span $L$ subjected to a continuous uniform downward load $w = q_0$:

Shear Force Function $V(x)$:
V(x) = -EI * (d³w / dx³) = q₀ * (L / 2 - x)
Bending Moment Function $M(x)$:
M(x) = -EI * (d²w / dx²) = (q₀ / 2) * (L * x - x²)
Boundary Conditions: M(0) = 0, M(L) = 0. Maximum moment at mid-span: M_max = q₀ * L² / 8.
Angular Rotation Slope $\theta(x)$:
θ(x) = dw/dx = (q₀ / (24 * E * I)) * (2x³ - 6Lx² + 4L³)
Boundary Condition by symmetry: θ(L/2) = 0. End rotations: θ(0) = q₀L³ / (24EI), θ(L) = -q₀L³ / (24EI).
Transverse Elastic Deflection Curve $w(x)$:
w(x) = (q₀ * x / (24 * E * I)) * (L³ - 2 * L * x² + x³)
Boundary Conditions: w(0) = 0, w(L) = 0.

Governing Maximum Deflection Formula at Mid-Span (x = L/2):

δ_max = (5 * w * L⁴) / (384 * E * I)

Where:
• w = Distributed load per unit length (lbf/in or kN/m)
• L = Clear span length between supports (in or mm)
• E = Modulus of elasticity of structural material (psi or MPa)
• I = Second moment of area / moment of inertia of section (in⁴ or mm⁴)
• Code Limit: Residential live load deflection criterion: δ_allow = L / 360; Total load: δ_allow = L / 240.

FOUNDATION MECHANICS: PROOF 02

Concrete Continuous Wall Footing Sizing & Soil Bearing Equilibrium

Standard: ACI 318-19 § 13.2 / IBC 2024 § 1809

Continuous strip footings distribute gravity dead and live loads from foundation stem walls into supporting soil stratigraphy. The minimum footing width $B$ is determined under service load conditions to ensure the contact pressure does not exceed the net allowable bearing capacity q_allowable:

B = P_total / q_allowable = (P_dead + P_live + W_footing + W_soil) / q_gross

Service Bearing Equilibrium (ASD)

q_net = q_allowable - γ_concrete * t_f - γ_soil * h_s

B_required = (P_DL + P_LL) / q_net

Where:
• B = Required footing projection width (ft)
• P_DL, P_LL = Unfactored vertical service loads per linear foot (plf)
• t_f = Footing thickness (ft), h_s = Soil overburden depth (ft)
• γ_concrete = 150 pcf, γ_soil = 100-120 pcf

ACI 318-19 One-Way Critical Shear Section

q_u = (1.2 * P_DL + 1.6 * P_LL) / B

V_u = q_u * [ (B - b_wall) / 2 - d ]

φV_c = φ * 2 * λ * √(f'_c) * b * d

Where:
• d = Effective depth to tensile reinforcement (in)
• b_wall = Stem wall thickness (in), b = unit length (12 in)
• φ = 0.75 for shear, λ = 1.0 (normalweight concrete)
• Condition: V_u ≤ φV_c ensures plain or unreinforced shear integrity.

GEOTECHNICAL MECHANICS: PROOF 03

Rankine Active Lateral Earth Pressure Theory & Overturning Thrust

Standard: IBC 2024 § 1807 / ASCE 7-22 § C13

Rankine lateral earth pressure theory assumes an unyielding frictionless vertical wall retaining cohesionless backfill in a state of plastic limit equilibrium. When the retaining stem yields slightly outward, shear resistance mobilizes along a conjugate slip plane inclined at $(45^\circ + \phi/2)$ to the horizontal:

K_a = tan²(45° - φ/2) = (1 - sin φ) / (1 + sin φ)

Lateral Stress Distribution $\sigma_a(z)$:

σ_a(z) = K_a * γ_soil * z - 2 * c * √(K_a) + K_a * q_surcharge

For cohesionless backfill ($c = 0$) with level ground and zero surcharge: $\sigma_a(z) = K_a \gamma z$, producing a hydrostatic triangular lateral pressure wedge.

Total Resultant Thrust & Overturning Moment:

P_a = 0.5 * K_a * γ_soil * H²

M_overturning = P_a * (H / 3) = (1/6) * K_a * γ_soil * H³

Acting horizontally at centroid H/3 above the footing base. Factor of safety against overturning: FS_overturning = Σ M_resist / M_overturn ≥ 1.50.

Authoritative Structural Engineering Table 01

AWC NDS-2024 Residential Floor Joist Clear Spans

Governing standard: AWC NDS-2024 / IRC 2024 Table R502.3.1(2). Clear spans between interior/exterior structural bearings for 16-inch on-center spacing, 40 psf uniform live load, 10 psf dead load, and live deflection limit Δ_LL ≤ L/360.

Nominal Size	Actual Dim (in)	Section Modulus S_x (in³)	Moment of Inertia I_x (in⁴)	Douglas Fir-Larch #2 Max Span	Southern Pine #2 Max Span	Controlling Limit State
2 x 6	1.50 × 5.50	7.56	20.80	9 ft - 9 in (117 in)	9 ft - 11 in (119 in)	Live Load Deflection (L/360)
2 x 8	1.50 × 7.25	13.14	47.63	12 ft - 10 in (154 in)	13 ft - 1 in (157 in)	Live Load Deflection (L/360)
2 x 10	1.50 × 9.25	21.39	98.93	16 ft - 5 in (197 in)	16 ft - 6 in (198 in)	Live Load Deflection (L/360)
2 x 12	1.50 × 11.25	31.64	177.98	19 ft - 11 in (239 in)	20 ft - 7 in (247 in)	Live Load Deflection (L/360)

Douglas Fir-Larch #2 Material Properties:

Bending Stress $F_b = 900$ psi (before $C_F$ adjustment) • Modulus of Elasticity $E = 1.60 \times 10^6$ psi • Repetitive Member Factor $C_r = 1.15$ • Load Duration $C_D = 1.0$.

Southern Pine #2 Material Properties:

Bending Stress $F_b = 750 - 1000$ psi (size-dependent per SPIB) • Modulus of Elasticity $E = 1.40 - 1.50 \times 10^6$ psi • Repetitive Member Factor $C_r = 1.15$.

Authoritative Structural Engineering Table 02

ASTM C387 Dry Concrete Pre-Mix Bag Yield & Water Conversion Matrix

Governing standard: ASTM C387/C387M (Standard Specification for Packaged, Dry, Combined Materials for Mortar and Concrete). Standard volume equivalency: 1 Cubic Yard = 27 Cubic Feet = 0.764555 m³. Nominal compressive strength: 4,000 psi (27.6 MPa) at 28 days.

Bag Net Weight	Metric Mass	Yield per Bag (ft³)	Yield per Bag (yd³)	Exact Bags / 1 yd³	+5% Safety Buffer	+10% Waste Buffer	Water Demand / Bag
80 lb Bag	36.29 kg	0.600 ft³	0.02222 yd³	45.0 Bags	48 Bags	50 Bags	3.0 - 3.5 Quarts (2.8 - 3.3 L)
60 lb Bag	27.22 kg	0.450 ft³	0.01667 yd³	60.0 Bags	63 Bags	66 Bags	2.25 - 2.5 Quarts (2.1 - 2.4 L)
50 lb Bag	22.68 kg	0.375 ft³	0.01389 yd³	72.0 Bags	76 Bags	80 Bags	1.8 - 2.1 Quarts (1.7 - 2.0 L)

Geometric Volumetric Equations for In-Situ Pour Sizing:

Rectangular Slab / Footing:

Volume (yd³) = (Length[ft] × Width[ft] × Depth[ft]) / 27

Cylindrical Sonotube / Pier:

Volume (yd³) = (π × (Diameter[in]/24)² × Depth[ft]) / 27

Continuous Wall Trench:

Volume (yd³) = (Perimeter[ft] × Trench Width[ft] × Depth[ft]) / 27

Authoritative Structural Engineering Table 03

Governing Structural Engineering Standards Matrix

Multi-body standards taxonomy governing StructLogic calculation algorithms. Incorporates deterministic design coefficients, resistance reduction factors ($\phi$), and serviceability limit states.

Standard	Issuing Authority	Regulatory Scope	Primary Limit States	Safety / Reduction Coeffs
ACI 318-19	American Concrete Institute	Reinforced concrete beams, continuous wall footings, slabs, two-way punching shear	Ultimate flexural yield, one-way beam shear, punching shear, rebar bond	φ_flexure = 0.90, φ_shear = 0.75, φ_bearing = 0.65
AWC NDS-2024	American Wood Council	Solid sawn lumber, glulam timber, joists, rafters, timber post buckling, fastener shear	Allowable stress flexure (F'_b), horizontal shear (F'_v), bearing (F'_c⊥), deflection	C_D, C_M, C_t, C_L, C_F, C_r (Repetitive member = 1.15)
IBC 2024 / IRC 2024	International Code Council	Jurisdictional building codes, minimum occupancy live loads, stair geometry (R311.7)	Serviceability deflection (Table 1604.3: L/360, L/240), frost penetration depth	Maximum stair riser = 7.75 in, Minimum tread = 10.0 in
AISC 360-22	American Institute of Steel Construction	Structural steel W-shapes, hollow structural sections (HSS), column buckling, steel connections	Lateral torsional buckling (LTB), compression column buckling, web local crippling	LRFD: φ_b = 0.90, φ_c = 0.90; ASD: Ω_b = 1.67, Ω_c = 1.67
ASCE 7-22	American Society of Civil Engineers	Minimum design loads: wind velocity pressures, roof ground snow loads, seismic spectral acceleration	ASD & LRFD load combinations: 1.2D + 1.6L + 0.5S, 1.4D, 0.9D + 1.0W	Risk Category I-IV Importance factors (I_w, I_s, I_e)

Full Architectural Specification

18 Planned Calculation Engines Across 5 Specialized Hubs

The complete matrix of computational tools under active development. Each engine runs strictly client-side, generates verifiable equation outputs, and guarantees deterministic results matching certified standards.

Hub 1: Concrete & Footing Mechanics

Standard: ACI 318-19 / IBC Chapter 18

ENGINE 01ACI 318-19 § 13.2

Continuous Wall Footing Sizing

Determines width $B$ and thickness $T$ for strip footings based on unconfined soil bearing, stem wall width, and service line loads.

Target URL: /calculators/continuous-footing-calculator

ENGINE 02ACI 318-19 § 13.4

Isolated Spread Footing & Bearing Pressure

Sizes square and rectangular column footings against two-way punching shear ($\phi V_c$) and one-way flexural crack control.

Target URL: /calculators/isolated-footing-calculator

ENGINE 03ASTM C387 / ACI 301

Concrete Slab & Footing Volume / Bag Yield

Cubic yardage volumetric calculator with 50/60/80 lb dry premix bag conversions and adjustable compaction buffers.

Target URL: /calculators/concrete-calculator

ENGINE 04ACI 318-19 Chapter 9

Reinforced Concrete Beam Flexure & Shear

Computes nominal moment capacity $\phi M_n$, steel reinforcement ratio $\rho$, stirrup spacing $s$, and minimum crack limits.

Target URL: /calculators/rebar-beam-calculator

Hub 2: Timber Framing & Joist Spans

Standard: AWC NDS-2024 / IRC 2024

ENGINE 05NDS-2024 / IRC Table R502.3.1

Residential Floor Joist Clear Span Engine

Full species catalog (DF-L, SP, HF, SPF) evaluation across 12", 16", 19.2", and 24" O.C. spacings and live load deflection caps.

Target URL: /calculators/joist-span-calculator

ENGINE 06NDS-2024 / IRC Table R802.4

Ceiling Joist & Rafter Span Engine

Attic live load and roof snow load evaluations with slope pitch adjustment factors and collar tie thrust mechanics.

Target URL: /calculators/rafter-span-calculator

ENGINE 07NDS-2024 Chapter 3 & 5

Wood Beam & Girder Sizing

Multi-ply solid-sawn, LVL, and glulam girder sizing with lateral stability (C_L), duration (C_D), and bearing stress (F_c_perp).

Target URL: /calculators/wood-beam-calculator

ENGINE 08NDS-2024 § 3.7 Ylinen Formula

Wood Column / Post Axial Buckling

Evaluates solid and built-up timber posts under concentric/eccentric axial compression using the Ylinen column stability factor $C_P$.

Target URL: /calculators/timber-column-calculator

Hub 3: Roof & Stair Geometry

Standard: IBC 2024 / IRC Section R311 & R802

ENGINE 09Trigonometric Framing Geometry

Common Rafter Length, Plumb Cut & Rake Pitch

Exact line length, birdsmouth seat cut depth, plumb cut angles, and ridge deduction for any unit rise/run ratio.

Target URL: /calculators/rafter-pitch-calculator

ENGINE 10Compound Angle Framing

Hip & Valley Rafter Compound Mitre Engine

Calculates 17-inch unit run hypes, backing angles, side cheek cuts, and jack rafter offset increments.

Target URL: /calculators/hip-valley-calculator

ENGINE 11IRC § R311.7 / Blondel Formula

IBC/IRC Code Stair Stringer Rise & Run

Enforces max 7.75" rise, min 10.0" run, Blondel rule (2R + T = 24 to 25 inches), headroom clearance, and stringer throat shear.

Target URL: /calculators/stair-stringer-calculator

ENGINE 12TPI 1 / ANSI Design Criteria

Roof Truss Pitch & Structural Span Envelope

Determines Fink, Howe, and Pratt web geometry, heel height overhangs, and bottom chord tension forces.

Target URL: /calculators/roof-truss-calculator

Hub 4: Geotechnical & Earth Retention

Standard: IBC Section 1807 / Rankine & Coulomb Mechanics

ENGINE 13Rankine & Coulomb

Lateral Earth Pressure Retention

Active ($K_a$), passive ($K_p$), and at-rest ($K_0$) pressure coefficients with slope surcharge corrections.

Target URL: /calculators/earth-pressure-calculator

ENGINE 14IBC § 1807.2 / ACI 318

Cantilever Retaining Wall Stability

Overturning ($FS \ge 1.5$), sliding ($FS \ge 1.5$), shear key design, and toe soil bearing eccentricity ($e \le B/6$).

Target URL: /calculators/retaining-wall-calculator

ENGINE 15Terzaghi / Meyerhof

Soil Bearing Capacity & Settlement

Terzaghi bearing factors ($N_c, N_q, N_\gamma$) and 1D consolidation settlement estimation under foundation footprints.

Target URL: /calculators/soil-bearing-calculator

Hub 5: Fasteners & Connection Shear

Standard: AWC NDS Chapter 11-12 / ACI 318 Chapter 17

ENGINE 16NDS-2024 Yield Limit Mode

Timber Fastener Lateral Shear & Withdrawal

European Yield Model (EYM Modes $I_s$ through $IV$) for nails, wood screws, and through-bolts in single and double shear.

Target URL: /calculators/fastener-shear-calculator

ENGINE 17ACI 318-19 Chapter 17

Anchor Bolt Tension & Concrete Breakout

Cast-in-place and post-installed anchor tension breakout, steel tensile failure, pryout, and edge distance reduction.

Target URL: /calculators/anchor-bolt-calculator

ENGINE 18ASTM D7147 / ICC-ES

Joist Hanger & Metal Connector Rating

Face-mount and top-flange joist hanger allowable downward and uplift ratings with nail schedule modification factors.

Target URL: /calculators/hanger-shear-calculator

Deterministic Architecture

Transparent, Peer-Auditable Structural Algorithms

StructLogic calculations are executed in memory inside the client browser. No backend computational servers, third-party APIs, or telemetry daemons are involved. Every calculation produces step-by-step symbolic intermediate expressions, allowing licensed structural engineers to audit every formula and design coefficient prior to official plan submission.

TypeScript 5 StrictReact 19 Server ComponentsStatic Site Generation (SSG)WCAG 2.1 AAA Contrast