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Mechanical · worked example · 3 pages

Bolt tightening and preload

The wrench torque that develops a target preload in a metric bolt, split into its thread and collar (under-head friction) parts, with the bolt stress checked against the proof strength. Power-screw method as in Shigley's Mechanical Engineering Design.

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What this calculation covers

Bolt and joint

  • Target preload
  • Nominal bolt diameter (M12)
  • Thread pitch
  • Metric thread half angle
  • Thread friction coefficient
  • Collar friction coefficient
  • Washer face outer diameter
  • Tensile stress area of M12 (ISO 898-1)
  • Proof strength, property class 8.8

Thread geometry

  • Pitch (mean thread) diameter
  • Thread lead angle

Tightening torque

  • Torque carried by the thread
  • Mean collar (washer face) diameter
  • Torque lost to collar friction
  • Wrench torque to apply
  • Equivalent nut factor K

Bolt stress at preload

  • Preload stress in the bolt
  • Share of proof strength used
  • Preload within 90% of proof

How friction moves the answer

Most of the wrench torque is spent on friction, so the assumed coefficients dominate. The same calculation as a function of a single shared coefficient:

  • Wrench torque for friction μ on thread and collar
  • Dry, unlubricated (μ = 0.15)
  • Lightly oiled (μ = 0.10)

Results summary

  • Reaching a 40 kN preload in this dry M12 joint takes about 94 N·m at the wrench (K ≈ 0.20), stressing the bolt to about 82% of its 8.8 proof strength. Oiling the threads drops the needed torque by nearly a third — tightening to 94 N·m when oiled would overload the bolt.

Try changing…

  • Set both friction coefficients to 0.10 — the wrench torque falls to about 66 N·m for the same preload.
  • Raise the preload to 48 kN — stress passes 90% of proof and the check fails.
  • Use an M16 bolt (d, p, A_t from its table row) — torque rises with diameter even at the same preload.

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