Approximate stress area
d₂ = d − 0.649519Pd₃ = d − 1.226869PAₛ = π[(d₂ + d₃)/2]² / 4Derived from an idealized 60° metric basic profile. Tolerances, thread rolling effects, damage, and non-standard geometry are excluded.
INDUNECT / KNOWLEDGE / RF-003PRELIMINARY REFERENCE
Bolt preload.
Torque, made visible.
Compare a nut-factor estimate with a friction-resolved tightening model. The inputs, equations and boundaries stay visible so the result can be challenged before it is used.
TWO TORQUE MODELSNO PROPERTY TABLESINPUT-DRIVEN
01REFERENCE SCOPE
ASSEMBLY STARTING POINT
See what friction does to a torque-controlled joint.
This reference estimates preload per bolt from a user-entered proof stress and utilization. It does not determine the preload required to prevent separation, slip, fatigue failure, leakage, loosening, thread stripping, or joint crushing.
INPUT / BOLT, MATERIAL & FRICTION
Input authority
No property-class, friction, washer, or tightening table is embedded. Verify proof stress, coating, lubricant, contact geometry, and friction from the applicable specification, test, and supplier documentation.
CALCULATION STATUSPRELIMINARY ESTIMATE READY
RF-003Target preload / bolt35.392 kNFM = u · Sp · As
Friction-resolved torque80.010 N·mMA = MG + MK
- Approx. tensile-stress area
- 84.267 mm² As
- Nut-factor torque
- 84.941 N·m T = K · FM · d
- Thread torque share
- 41.276 N·m MG
- Bearing torque share
- 38.733 N·m MK
- Effective bearing diameter
- 15.634 mm DKm
- Implied nut factor
- 0.188 MA / (FMd)
- Axial bolt stress
- 420.000 MPa σ = FM / As
- Simplified equivalent stress
- 566.830 MPa √(σ² + 3τ²)
- Equivalent / proof stress
- 94.5% Simplified assembly screen — not a pass/fail joint verification
02VISIBLE METHOD
EQUATIONS & ASSUMPTIONS
Two models. One preload target.
Axial target
FM = (u/100) SpAsThis is a material-utilization starting point only. It does not calculate the preload demanded by the joint function or assembly scatter.
Compact torque estimate
T = K FMdThe supplied K must represent the actual fastener, finish, lubricant, bearing surface, and tightening process.
Uniform-pressure model
DKm = ⅔(Do³ − Di³)/(Do² − Di²)The annular contact is assumed continuous and uniformly pressurized. Real contact and deformation can differ.
Helix and flank friction
φ = atan[P/(πd₂)]ρ′ = atan(μG/cos 30°)MG = FM(d₂/2)tan(φ + ρ′)Right-hand 60° metric thread, quasi-static tightening, and no prevailing torque are assumed.
Under-head or nut friction
MK = FMμKDKm/2MA = MG + MKDrive losses, prevailing torque, tool dynamics, and tightening-system calibration are excluded.
Axial plus tightening torsion
τ ≈ 16MG/(πd₃³)σeq ≈ √(σ² + 3τ²)A simplified solid-core von Mises screen. It is not a full threaded-root, fatigue, or VDI 2230 verification.
Calculation basis
1 MPa = 1 N/mm²1 N·m = 1,000 N·mmAll internal calculations use millimetres, newtons, and megapascals; displayed torque is converted to N·m.
DESIGN BOUNDARY
This is not a bolted-joint design approval.
Assembly scatter is outside the result.
Torque control produces preload scatter through friction variation, tightening method, tool accuracy, surface condition, reuse, coating, and lubrication. Determine minimum and maximum assembly preload separately.
Joint function is not checked.
External loads, load introduction, member stiffness, separation, slip, settlement, thermal effects, fatigue, self-loosening, and residual clamp load require a complete joint model.
Local failure modes remain open.
Verify internal/external thread stripping, engagement length, head and washer bearing pressure, joint crushing, flange bending, bolt bending, corrosion, temperature, and material compatibility.
Critical joints require controlled engineering.
Pressure boundaries, lifting systems, rotating equipment, structural connections, transport, and other safety-relevant applications need the applicable standard, qualified review, and validated assembly procedure.
03AUTHORITATIVE CONTEXT
VERIFY OUTSIDE THIS PAGE
Use the reference to ask better questions—not to replace the specification.
For material properties and property-class scope, consult the current authorized edition of ISO 898-1. For torque/clamp-force testing, see ISO 16047. For systematic design of highly stressed single-bolt joints, see the official VDI 2230 Part 1 listing.
Indunect does not reproduce proprietary standard tables, property-class values, friction tables, tightening tables, or standard text. Standard designations are identification links only.