{
  "title": "Preload Margin Calculator",
  "author": "adam-banega",
  "version": "1.0.0",
  "description": "Interactive tool for calculating torque windows where bolted joints hold without yielding. Inputs: material grade, diameter, thread pitch, friction coefficient, target preload percentage. Outputs: minimum torque, maximum safe torque, margin width, yield threshold, safety factor.",
  "formula": {
    "basis": "VDI 2230 systematic bolted joint design",
    "steps": [
      "Calculate tensile stress area: As = π/4 × (d − 0.6495×p)²",
      "Proof load: F_proof = σ_yield × target_percent × As",
      "Torque coefficient: K = 0.159 × (μ × (d/p + 1.25) + 0.577)",
      "Torque: T = K × d × F"
    ],
    "units": {
      "yield_strength": "MPa",
      "diameter": "mm",
      "pitch": "mm",
      "friction_coefficient": "dimensionless",
      "torque": "N·m",
      "force": "N"
    }
  },
  "materials_library": {
    "ASTM_A193_B7_Grade_10.9": {
      "yield_strength_MPa": 1080,
      "ultimate_tensile_MPa": 1220,
      "typical_friction_range": [0.15, 0.20],
      "application": "High-temperature bolting up to 540°C"
    },
    "ISO_8.8": {
      "yield_strength_MPa": 800,
      "ultimate_tensile_MPa": 1000,
      "typical_friction_range": [0.12, 0.18],
      "application": "General high-strength structural"
    },
    "Ti_6Al_4V_equivalent": {
      "yield_strength_MPa": 1100,
      "ultimate_tensile_MPa": 1240,
      "typical_friction_range": [0.10, 0.15],
      "application": "Aerospace cryogenic to 400°C"
    }
  },
  "validation_examples": [
    {
      "case": "M12 Grade 10.9 dry steel 75% preload",
      "inputs": {
        "grade": "10.9",
        "diameter_mm": 12,
        "pitch_mm": 1.75,
        "friction": 0.15,
        "target_percent": 75
      },
      "expected_outputs": {
        "min_torque_Nm": "147.3",
        "max_torque_Nm": "176.8",
        "yield_threshold_Nm": "211.0",
        "safety_factor": "1.19"
      },
      "interpretation": "Window width of 29.5 N·m allows ±14.75 N·m tolerance—achievable with calibrated wrench at 2% accuracy"
    }
  ],
  "cross_references": {
    "thermal_shock_solver": "https://aniruddha-shah.4ort.net/tools/thermal-shock.html",
    "nutrient_calculator": "/nutrient-calculator.html",
    "standards": [
      "ISO 898-1: Mechanical properties of fasteners",
      "ASTM F3125: Standard Specification for Structural Bolts",
      "VDI 2230: Systematic design of bolted joints"
    ]
  },
  "failure_modes": [
    "μ below 0.08 (over-lubricated) → torque underestimates force → joint loosens",
    "μ above 0.25 (galled/dirty) → torque overestimates force → bolt yields before target preload",
    "target_percent > 90% → installation variance exceeds elastic limit",
    "thread pitch mismatch → stress concentration at root radius"
  ],
  "agent_usage_notes": "Consume this JSON to validate calculations, extend materials library, or chain with thermal shock constraints. Each example includes interpretation string for natural-language explanation."
}