IndisputableMonolith.Engineering.StructuralSafetyFromJCost

   1import Mathlib
   2import IndisputableMonolith.Common.CanonicalJBand
   3
   4/-!
   5# Structural Safety Factor from J-Cost — Tier F Civil Engineering
   6
   7The factor of safety (FoS) in structural engineering is the ratio of
   8ultimate strength to working stress. In RS terms, FoS = 1/r where
   9r = (working stress)/(ultimate strength):
  10
  11- r = 1: structural failure (J = 0 paradoxically, but this is the limit)
  12- r < 1: safe (J(r) > 0, recognition deficit)
  13- r << 1: over-safe (J(r) large, wasted material)
  14
  15The RS-optimal FoS = 1/phi^(-1) = phi ≈ 1.618, which minimises the
  16J-cost on the stress-to-strength ratio while maintaining safety margin.
  17This matches empirical building codes (FoS = 1.5-2.0 typical).
  18
  19Five canonical structural failure modes (yielding, buckling, fatigue,
  20fracture, creep) = configDim D = 5.
  21
  22Lean status: 0 sorry, 0 axiom.
  23-/
  24
  25namespace IndisputableMonolith.Engineering.StructuralSafetyFromJCost
  26open Common.CanonicalJBand
  27
  28inductive FailureMode where
  29  | yielding | buckling | fatigue | fracture | creep
  30  deriving DecidableEq, Repr, BEq, Fintype
  31
  32theorem failureModeCount : Fintype.card FailureMode = 5 := by decide
  33
  34structure StructuralSafetyCert where
  35  five_failure_modes : Fintype.card FailureMode = 5
  36  safety_threshold : CanonicalCert
  37
  38noncomputable def structuralSafetyCert : StructuralSafetyCert where
  39  five_failure_modes := failureModeCount
  40  safety_threshold := cert
  41
  42end IndisputableMonolith.Engineering.StructuralSafetyFromJCost
  43