Engineering software manual for the 54 product modules shipped under /products/*. This document describes purpose, governing methods, design-code support, UI maturity, and known gaps. It complements the homogenization contract in Homogenization-Roadmap.md.

Audience: engineers evaluating PhyCalcPro for design work, and developers extending modules.

Disclaimer: All modules produce indicative results unless explicitly marked beta with implemented code checks. Nothing here replaces licensed professional review or official code compliance certification.

Equations (authoring): Use LaTeX in $…$ for inline math and `

for display blocks (or$ … $/$\dots$). The site converts these to KaTeX. List items like - Torque: $T = …$` render as labeled display equations.

Table of contents

1. Platform architecture
2. Module inventory
3. Structural engineering
4. Machine design
5. Fasteners & connections
6. Materials & sections
7. Pressure systems
8. Dynamics & vibrations
9. Manufacturing
10. Area properties (profiles)
11. Maturity & numerical methods
12. Gaps & roadmap

1. Platform architecture

1.1 Navigation and layout

• Single sidebar: src/app/products/layout.tsx renders the category sidebar. Category layouts are passthrough wrappers — no nested sidebars.
• Module chrome: Each calculator page uses CalculatorLayout with a two-column workspace beside the sidebar:
  • Inputs column — parameters, mesh controls, calculate/save (CalculatorInputPanel where adopted).
  • Results column — plots, metric cards, engineering checks, export (CalculatorResultsShell / ExportableReport).
• Legacy three-slot API: Some pages still pass left / center / right; CalculatorLayout merges left+center into the inputs column and maps right → results. Migration to explicit inputs / results props is in progress.

1.2 Calculation pipeline

Standard module contract (see homogenization roadmap):

page.tsx
  useStandardCalculation(moduleId, onRegionUnits?)   // or useCalculatorModule
  CalculatorLayout(moduleId, inputs, results)
  calculate → solver engine → wrapResult(output)
  *Results → ExportableReport(moduleId=…)

• wrapResult attaches a CalculationSpec with design-code checks via withCalculationSpec.
• Specialized evaluators (full check mapping): beams, columns, gears, combined-loading, welds.
• Generic evaluator (evaluators/generic.ts): all other catalogued modules — checks are declared but mapped from indicative outputs.

1.3 Design codes

Global selector: US / EU / ISO / Indicative (DesignCodeContext).

Changing design code sets default units via useDesignCodeUnits / moduleProfiles.ts (on code change, not every render). Field unit selectors still expose all units for the dimension unless restrictToProfile is set.

1.4 Units

• Field definitions: src/lib/units/moduleProfiles.ts (expansion modules profiled; legacy gaps remain for trusses, cost-estimator, cam-toolpaths).
• Preferred input widget: CalculatorUnitField + calculatorNumberInputClass.
• Metric display: CalculatorMetricCard / formatEngineeringValue for auto scientific notation when $|v| \ge 1000$ or $|v| < 0.01$.

1.5 Export

ExportableReport with moduleId enables:

• PDF capture of results (plots tagged data-export-plot, diagrams data-export-diagram).
• Default CSV rows from solver output.
• Quality checklist from moduleQualityDefaults.
• Engineering checks panel when calculationSpec is present.

Charts use EngineeringPlot with separate yLabel, unitLabel, xLabel, xUnit.

1.6 Release tiers

CalculatorLayout shows catalog validationStatus and a computed release tier from benchmark stats (ReleaseTierBadge). Benchmark solvers exist for a subset (gears, columns, combined-loading, impact, fatigue, corrosion, suspension, rotation).

2. Module inventory

Homogenization snapshot

Validation catalog status

3. Structural engineering

3.1 Beam Analysis (beams) — beta

Purpose: 2D Euler–Bernoulli beam analysis — deflection, moment, shear, bending stress for common supports and arbitrary point/UDL/moment loads.

Method: FEM — 2-node Hermite beam elements; mesh-refinable (meshSegments). Not a full 3D or Timoshenko model.

Key relations:

• Element stiffness from $EI/L^3$; curvature–moment:

\sigma = M,c/I

P_{cr} = \frac{\pi^2 E I}{L_e^2}, \quad L_e = k L

M_x = -D(\partial^2 w/\partial x^2 + \nu,\partial^2 w/\partial y^2), \quad D = \frac{E t^3}{12(1-\nu^2)}

\sigma_{ax} = \frac{P}{A}, \quad \sigma_b = \frac{M c}{I}, \quad \tau_t = \frac{T c}{J}, \quad \tau_v = \frac{V}{A}

\sigma_{vm} = \sqrt{(\sigma_{ax}+\sigma_b)^2 + 3\tau_t^2}

T = \dfrac{60P}{2\pi n}

\sigma_b = \dfrac{F_t}{b,m,Y}

P = X F_r + Y F_a, \quad L_{10} = \left(\frac{C}{P}\right)^3 \times 10^6 \text{ rev}

E_k = \tfrac{1}{2} I \omega^2, \quad \sigma_\theta \approx \rho \omega^2 r^2

A_t = a_t \times L \times n_w

\sigma_{eq} = \sqrt{\tau^2 + \sigma^2}

\sigma_{vm} = \sqrt{\sigma_n^2 + 3(\tau_v^2 + \tau_t^2)}

E_L = E_f V_f + E_m V_m, \quad \frac{1}{E_T} = \frac{V_f}{E_f} + \frac{V_m}{E_m}

f_y(T) = f_{y,0}(1 - k_y \Delta T), \quad f_E(T) = E_0(1 - k_E \Delta T)

\sigma_a \le S_e \left(1 - \frac{\sigma_m}{\sigma_u}\right), \quad N \propto \left(\frac{S_e}{\sigma_a}\right)^3

t_{req} = t_0 + \dot{c}, t_{life},(1 + \text{margin})

\sigma_h = \frac{p r}{t}, \quad \sigma_l = \frac{p r}{2t}

F_{ext} = p A_{piston}, \quad F_{ret} = p (A_{piston} - A_{rod})

\dot{Q} = \dot{m}h c{p,h}(T_{h,in} - T_{h,out}), \quad \text{LMTD} = \frac{\Delta T_1 - \Delta T_2}{\ln(\Delta T_1/\Delta T_2)}

\varepsilon = f(\text{NTU}, C_r), \quad \text{NTU} = \frac{UA}{C_{min}}

(K - \omega^2 M),\phi = 0

J = m,\Delta v, \quad F_{avg} = \frac{J}{\Delta t}, \quad \sigma_d = \frac{F_{avg}}{A}

M_{roll} = F_y \frac{WB}{2}, \quad \phi = \frac{M_{roll}}{K_{roll}}, \quad \Delta W = F_y \frac{h_{cg}}{t_{track}}

\text{WC} = \sum t_i, \quad \text{RSS} = \sqrt{\sum t_i^2}

C_{min} = D_{min}^{hole} - D_{max}^{shaft}, \quad C_{max} = D_{max}^{hole} - D_{min}^{shaft}