Mechanical Fasteners, Bolted Joint Assembly & Structural Reliability
Bolt Torque Preload Tension, Nut-Factor K & Proof Formula
Calculate ISO Metric Bolt Tensile Proof Load (kN), Achieved Clamp Preload Tension F_i (kN) from Wrench Torque T = K*D*F_i, Proof-Load Utilization (%), and Anti-Seize Yield Gate.
Applying MoS2 anti-seize to a dry-torque spec stretches bolts +67% past proof load!
Nearly 90% of wrench torque applied to a dry nut overcomes thread and under-head friction, leaving only ~10% to stretch the bolt into clamping tension! Under Shigley’s empirical Torque-Tension Equation T_Nm = K * (D_mm / 1,000) * (F_i_kN * 1,000) = K * D_mm * F_i_kN, Achieved Clamp Preload is F_i_kN = T_Nm / (K * D_mm), where the dimensionless Nut Factor K averages ~0.20 for dry as-received steel, ~0.15 for lubricated phosphate/oil, and ~0.11–0.12 for MoS2 / copper anti-seize paste! Reusable non-permanent joints target F_i ≈ 75% of Proof Load (F_proof_kN = A_t_mm2 * S_proof_MPa / 1,000); lubricating threads with MoS2 without lowering wrench torque spikes F_i by 0.20 / 0.12 = 1.67x, yielding or snapping the bolt during assembly!
Verify on an M20x2.5 ISO Class 10.9 Structural Flange Bolt—Nominal_Diameter D = 20.0 mm (B2), Tensile_Stress_Area A_t = 245.0 mm² (B3), Class_10_9_Proof_Strength = 830 MPa (B4 -> Proof Load F_p = 245 * 830 / 1,000 = 203.35 kN in E2), Specified_Wrench_Torque T = 600.0 N·m (B5), and Dry_Steel_Nut_Factor K = 0.20 (B6): Achieved Clamp Preload equals 600 / (0.20 * 20) = 150.00 kN (E3), utilizing 150 / 203.35 = 73.76% of Proof Load (E4), with Status "SAFE: <=100% Proof" (E5)!
| Bolted Preload Assembly KPI (M20 Class 10.9, At=245 mm², Sp=830 MPa, T=600 N·m) | Formula | Verified Output |
|---|---|---|
| Bolt Tensile Proof Load F_p (kN) | Stress_Area_mm2 * Proof_MPa / 1000 | 203.35 kN |
| Achieved Clamp Preload F_i (kN) | Torque_Nm / (Nut_Factor_K * Diam_mm) | 150.00 kN (250.00 kN @ MoS2!) |
| Proof-Load Utilization (%) | (Achieved_Preload_kN / Proof_Load_kN) * 100 | 73.76% (122.94% @ MoS2!) |
| Assembly Plastic-Yield Gate | IF(Pct_Proof > 100, "OVER PROOF: Bolt Yields!", "SAFE: <=100% Proof") | SAFE: <=100% Proof |
Shigley Nut-Factor Preload & Proof-Utilization Formula
Validate Diameter_mm > 0, Stress_Area_mm2 > 0, Proof_Strength_MPa > 0, Torque_Nm > 0, and Nut_Factor_K in [0.08, 0.35]!
=LET(dm_m, B2, at_m, B3, sp_m, B4, tq_n, B5, nf_k, B6, IF(OR(dm_m <= 0, at_m <= 0, sp_m <= 0, tq_n <= 0, nf_k < 0.08, nf_k > 0.35), "Invalid Fastener Input", LET(fp_k, at_m * sp_m / 1000, fi_k, tq_n / (nf_k * dm_m), ROUND((fi_k / fp_k) * 100, 2))))Unauthorized MoS2 Anti-Seize Over-Torque Yield Check (Set Nut Factor K = 0.12)
Simulate a millwright brushing MoS2 anti-seize onto the threads (B6 = 0.12) while still pulling the 600 N·m dry torque spec: Clamp Preload E3 surges from 150.00 kN to 250.00 kN (122.94% of proof load E4), firing "OVER PROOF: Bolt Yields!" in E5!
=IF(ISTEXT(E4), E4, IF(E4 > 100, "OVER PROOF: Bolt Yields!", "SAFE: <=100% Proof"))Try the example
Use the original values or change them to test your understanding.