Universal Thread Stress and Bolt Preload Calculator — AS8879 / UNC / UNF / Metric

Universal Thread Stress Calculator  |  AS8879 / UNC / UNF / Metric

Inputs
1. Thread Selection
2. Friction & Bearing Geometry

Collar dims = bearing contact surface under bolt head or nut face.

3. Applied Torque

Net torque available for preload = T_applied − T_prevailing − T_drag

4. Additional Axial Load (Optional)

Leave pressures at 0 for pure torque analysis.

5. Material Properties
Results

Fill in inputs on the left and click Calculate.

Margins of Safety
Load Case Total Axial Force (lb) Thread Stress σ (psi) MS Yield MS Ultimate
Intermediate Values ▶
Parametric: MS vs Friction Coefficient (at T_applied)

Preload and margins swept across μ₁ values. Selected μ₁ highlighted ◀

μ₁K₁ (in)K₂ (in) F_preload (lb)σ_preload (psi) MS YieldMS Ult
Critical Torque Limits

Maximum torque before yielding or fracture, computed by back-solving from the allowable thread stress. Includes T_prevailing and T_drag. Additional pressure load is not included here.

Method & Equations
01

Overview

When a threaded fastener is torqued, the applied torque is resisted by two mechanisms: friction on the thread faces and friction on the bearing (collar) surface under the nut or bolt head. Only the remaining torque — after overcoming thread helix and both friction components — is converted into axial clamping preload. This calculator implements the standard torque–preload relationship derived from inclined-plane and collar-friction mechanics, consistent with ASME B1.1, Shigley's Mechanical Engineering Design, and aerospace thread stress practices per AS8879.

02

Torque Balance

The total applied torque must be balanced by thread torque, collar torque, and any drag/prevailing torques:

Torque balance $$T_\text{applied} = T_1 + T_2 + T_\text{prevailing} + T_\text{drag}$$

Rearranging for the net torque available to generate preload:

Net torque $$T_\text{net} = T_\text{applied} - T_\text{prevailing} - T_\text{drag}$$
03

Thread Torque Coefficient K₁

\(T_1 = K_1 \cdot F\), where \(K_1\) is the thread torque nut factor derived from inclined-plane mechanics with Coulomb friction on the thread helix:

Thread torque coefficient K₁ $$K_1 = \frac{d_m}{2} \cdot \frac{\tan\alpha + \mu_1 \sec\beta}{1 - \mu_1 \tan\alpha \sec\beta}$$

where:

  • \(d_m\) = thread pitch diameter (in)
  • \(\alpha\) = thread lead angle (helix angle): \(\tan\alpha = \dfrac{1}{\pi \, d_m \cdot \text{TPI}}\)
  • \(\beta\) = thread half-angle = 30° for 60° unified (UN/UNJ/Metric) threads
  • \(\mu_1\) = coefficient of friction on thread faces
  • \(\sec\beta = 1/\cos\beta\) — accounts for the inclined thread flank projecting the normal force

The \(\sec\beta\) term distinguishes a V-thread from a square thread: the inclined flanks increase the normal (and therefore frictional) force compared to a flat-faced square thread with the same lead angle.

04

Collar Torque Coefficient K₂ & Preload Force

\(T_2 = K_2 \cdot F\), where \(K_2\) is derived by integrating the friction moment over the contact annulus under the bolt head or nut face:

Collar torque coefficient K₂ $$K_2 = \frac{\mu_1}{3} \cdot \frac{D_H^3 - D_h^3}{D_H^2 - D_h^2}$$

where \(D_H\) = outer diameter and \(D_h\) = inner diameter of the collar contact surface.

The resulting preload force:

Preload force $$F_\text{preload} = \frac{T_\text{net}}{K_1 + K_2}$$
Bearing / Collar Contact Geometry D H (Collar OD) D h (Collar ID) μ₁ friction zone Thread T F D_H – Collar OD D_h – Collar ID Bearing face (annulus) μ₁ acts here Fig. 1 — Bearing / Collar Contact Geometry (click to enlarge)
05

Thread Tensile Stress & Margin of Safety

Thread tensile stress $$\sigma_t = \frac{F_\text{total}}{A_s}$$

where \(F_\text{total} = F_\text{preload} + F_\text{pressure}\) and \(A_s\) is the tensile stress area from ASME B1.1 / AS8879 / ISO 898.

Margin of safety $$MS_\text{yield} = \frac{F_{ty}}{\sigma_t} - 1 \qquad MS_\text{ultimate} = \frac{F_{tu}}{\sigma_t} - 1$$

A positive MS indicates adequate design margin. A negative MS indicates failure under the applied load.

06

Critical Torque (Back-Solved)

The maximum torque before yielding or fracture is found by back-solving from the material allowable stress:

Critical torque — back-solve $$F_\text{allow} = F_{ty} \text{ (or } F_{tu}\text{)} \cdot A_s$$ $$T_\text{critical} = F_\text{allow} \cdot (K_1 + K_2) + T_\text{prevailing} + T_\text{drag}$$
07

AS8879 Thread Note

AS8879 (formerly MIL-S-8879) specifies UNJ (coarse) and UNJF (fine) aerospace threads. These differ from standard UN threads by having a controlled radius root on the external thread, which significantly improves fatigue life by reducing stress concentration at the thread root. AS8879 threads are the preferred aerospace thread form for structural fasteners per NAS and military standards.

Friction Coefficient Reference

Friction Coefficients for Common Fastener Material Pairs

The friction coefficient \(\mu_1\) has a dominant effect on the torque–preload relationship. Values below are sourced from Engineering Toolbox, Shigley's (Table 8-15), and Bickford's Bolted Joints.

Material 1Material 2Condition / Lubricantμ staticμ kineticFastener Relevance
PTFE / Solid Film / Graphite Lubricants
PTFE (Teflon)PTFEDry or greased0.040.04PTFE-coated fasteners; extreme low-friction baseline
SteelSteelGraphite lubricant—0.058Graphite-lubricated threads (kinetic)
Carbon (hard)CarbonDry0.16—Carbon-coated contact surfaces
GraphiteSteelDry0.10—Graphite-coated steel threads
Greased / Well-Lubricated Metal Pairs
CadmiumCadmiumGreased0.05—Cad-plated fasteners, greased
CopperCopperGreased0.08—Copper-alloy thread inserts, greased
SteelSteelGreased ★0.16—Typical value for lubricated steel/SS threaded fasteners
NickelMild SteelGreased—0.178Nickel-alloy into mild steel, greased
Lightly Lubricated / Oiled
SteelSteelLight mineral oil (static)0.23—Lightly oiled threads (use static for install)
SteelSteelCastor oil (kinetic)0.150.081Castor-oil lubricated threads
CopperSteelOleic acid / light oil—0.18Copper anti-seize / light oil on steel
Dry / Unlubricated Metal Pairs
ChromiumChromiumDry0.41—Chrome-plated fasteners, dry
BrassSteelDry (static)0.510.44Brass nut on steel bolt, dry
Cast IronSteelDry (static)0.400.23CI nut on steel, dry
AluminumMild SteelDry (static)0.610.47Aluminum fastener into mild steel, dry
SteelSteelDry (static)0.5–0.80.42Steel fasteners, unlubricated — large scatter, do not rely on
NickelNickelDry (static)0.7–1.10.53Nickel-alloy fasteners, unlubricated — galling risk
References & Important Notices
  • ASME B1.1 — Unified Inch Screw Threads. Defines UN, UNC, UNF thread geometry and tensile stress areas.
  • AS8879 (SAE) — Screw Threads — UNJ Profile, Inch Controlled Radius Root with Increased Minor Diameter. Aerospace UNJ/UNJF thread standard.
  • ISO 898-1 — Mechanical Properties of Fasteners Made of Carbon Steel and Alloy Steel. Metric thread stress areas and property classes.
  • Shigley, J.E. & Mischke, C.R. — Mechanical Engineering Design, 10th Ed. McGraw-Hill. Torque-preload equations, Chapter 8.
  • Bickford, J.H. — An Introduction to the Design and Behavior of Bolted Joints, 3rd Ed. Marcel Dekker.
  • MMPDS-10 / MMPDS-13 — Metallic Materials Properties Development and Standardization. Material properties for aerospace alloys.
  • Engineering Toolbox — Friction Coefficients for various Materials. engineeringtoolbox.com
  • NASM8846 — Insert, Screw Thread, Helical Coil. Prevailing torque values for helicoil inserts.
  • Friction coefficient uncertainty. The friction coefficient μ₁ has a dominant and highly variable effect on predicted preload. It is sensitive to surface finish, lubricant type and quantity, plating condition, coating wear, and assembly speed. The scatter in dry steel-on-steel values alone spans 0.5–0.8 (static). For flight-critical or pressure-boundary fasteners, torque-tension testing on representative hardware under production assembly conditions is strongly recommended.
  • Torsional stress not included. This calculator computes tensile (axial) thread stress only. During installation, the fastener also experiences torsional shear stress from thread and collar friction. The combined von Mises stress is approximately 10–15% higher than the tensile stress shown. Conservative practice per Shigley's applies a proof-strength check on the combined stress; this calculator is appropriate for comparative margin analysis but should not replace a full combined-stress check for critical applications.
  • For informational use only. This calculator is provided as an engineering aid. Results must be verified by a qualified engineer before use in any safety-critical or flight application. KasperCalc assumes no liability for design decisions made using these results.