Bolted Joint Strength Calculator mechanism

Model scope

The instrument can be labeled only as a simplified static axial-joint calculator unless the missing shear, safety-factor, separation, stiffness, and torque definitions are added. The torque outputs above are explicitly conditional on K=0.2 and are not independently justified by the supplied specification.

• σ=F/At is correct for nominal axial bolt stress only; it does not calculate shear stress, combined loading, thread stripping, bending, or stress concentration effects.
• The preload relation Fi=0.75·Fproof is a stated typical simplification, not a universal design rule. Proof strength is a stress, so preload force must be calculated as Fi=0.75·Sproof·At.
• The stiffness relation C=kb/(kb+km) is correct for compatible stiffness units and a linear elastic concentric joint, but the specification does not define how kb and km are obtained.
• Joint separation requires an explicit criterion and load model. For a concentric tensile external load P, the usual simplified criterion is Psep=Fi/(1-C), but this is not stated.
• No formula is supplied for the claimed joint safety factor. The vectors use the conditional definition SF=Sproof/σbolt; yield, ultimate, fatigue, slip, separation, and proof-load criteria could produce different safety factors.
• No formula is supplied for recommended torque. A torque estimate requires an explicit nut factor K and nominal diameter, typically T=K·Fi·d, and is highly dependent on friction, lubrication, threads, and bearing surfaces.

Units and conventions

• Stress and proof strength are in MPa with tensile stress area in mm² for metric vectors; 1 MPa·mm²=1 N.
• The stiffness values kb and km use the same force-per-length units, so C is dimensionless.
• External applied load P is an axial tensile load shared by one bolt and the joint model is concentric and linear elastic.
• The conditional torque calculation uses dimensionless nut factor K and nominal bolt diameter d; metric torque is N·m and inch torque is lbf·in unless converted.
• The conditional safety factor is against proof stress only: SF=Sproof/σbolt.
• No shear load is included in these vectors because the specification does not define a shear-area method.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "bolt": "M10 x 1.5",
    "grade": "ISO property class 8.8",
    "applied_axial_load_N": 20000,
    "tightening_method": "nut-factor estimate",
    "K": 0.2,
    "nominal_diameter_m": 0.01,
    "kb_N_per_mm": 100000,
    "km_N_per_mm": 900000
  },
  "expected_outputs": {
    "tensile_stress_area_mm2": 58,
    "proof_strength_MPa": 600,
    "preload_N": 26100,
    "C": 0.1,
    "bolt_load_N": 28100,
    "bolt_tensile_stress_MPa": 484.482759,
    "proof_based_SF": 1.238434,
    "separation_load_N": 29000,
    "remaining_clamp_force_N": 8100,
    "conditional_torque_N_m": 52.2
  },
  "reference_data": {
    "tensile_stress_area_mm2": 58,
    "proof_strength_MPa": 600,
    "source_convention": "ISO 898-1 standard table values for M10 property class 8.8; widely tabulated standard value"
  },
  "working": "At=58.0 mm² and Sproof=600 MPa. Fi=0.75×600×58.0=26100 N. C=100000/(100000+900000)=0.100000. Incremental bolt load=C×P=0.1×20000=2000 N. Total bolt load=26100+2000=28100 N. σ=28100/58.0=484.482759 MPa. SF=600/484.482759=1.238434. Psep=Fi/(1-C)=26100/0.9=29000 N. Remaining clamp force=Fi-(1-C)P=26100-0.9×20000=8100 N. Conditional torque T=K×Fi×d=0.2×26100×0.01=52.2 N·m."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The stiffness-ratio calculation divides by kb + km and becomes undefined when the stiffness sum is zero; the instrument should reject that input. The specification also lacks the torque coefficient or a torque lookup, so recommended torque is undefined for torque-based tightening inputs.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche7/tranche7-results.json
• BOUNDARY_HAZARD_CATALOG.json