Documentation

This tool calculates fastener assembly torque from a two-mode failure model. The governing limit is always the lower of two independently calculated failure loads — thread stripping of the parent material, and tensile yield of the fastener itself. Whichever fails first sets the torque ceiling.

Failure Modes

Thread Stripping (Parent Material)

Thread stripping occurs when the axial fastener load exceeds the shear capacity of the threads cut into the parent material — the material the fastener threads into, not the bolt itself. The shear area is modeled as a cylinder at the pitch diameter with height equal to the engagement length. This failure mode dominates at short engagement lengths and produces a load that grows linearly with engagement.

Bolt Tensile Failure

Bolt tensile failure occurs when the axial load exceeds the fastener’s tensile capacity at its tensile stress area — a smaller effective area than the nominal shank cross-section, reduced by the thread geometry. This limit is a fixed ceiling determined entirely by bolt grade and geometry; it does not change with engagement length. It dominates when engagement is long enough that the threads are stronger than the bolt.

Governing Limit and Crossover Engagement

Below a crossover engagement length L^*, thread stripping governs and maximum torque increases with engagement. Above L^*, the bolt yield ceiling is reached first and torque no longer increases regardless of additional engagement depth. L^* is where both modes predict exactly the same failure load.

Formulas

Pitch Diameter

The pitch diameter d_m is the effective diameter of the thread engagement cylinder. For standard 60° thread forms (all ISO metric and Unified threads):

d_m = d − 0.6495 × p

Source: ISO 724 / ASME B1.1 — valid for metric (M) and unified (UNC, UNF) 60° thread forms

d: Nominal major diameter (mm)
p: Thread pitch (mm); for unified threads p = 25.4 / TPI

The constant 0.6495 comes from thread geometry: for a 60° thread, thread height H = (√3/2)p ≈ 0.866p, and the pitch diameter sits at d − (3/4)H = d − 0.6495p.

Thread Stripping Load

P_strip = (π × d_m × F_su × L) ÷ 3

Force required to strip parent material threads (N) — linear in engagement length L
Source: NASA/TM-2017-219475, Rivera-Rosario & Powell, Glenn Research Center, 2017

d_m: Pitch diameter (mm)
F_su: Ultimate shear strength of the parent material (MPa)
L: Thread engagement length (mm)

The shear area is modeled as the cylindrical surface at the pitch diameter: A_shear = π × d_m × L. The divisor of 3 is the safety factor specified in the NASA methodology. This formula, and the F_su values for each material, are taken directly from NASA/TM-2017-219475 Table 1. P_strip as computed is therefore an allowable load — not the raw shear capacity of the threads. The raw capacity is three times larger.

Tensile Stress Area

The tensile stress area A_s is the effective cross-sectional area used for bolt tensile calculations. It is smaller than the nominal shank area because the thread root reduces the net cross-section. The formula uses the average of the pitch diameter and minor diameter:

A_s = (π ÷ 4) × (d − k_s × p)²

Thread Standard	k_s	Derivation	Source
Metric ISO (M)	0.9382	(d₂ + d₃)/2 where d₂ = d − 0.6495p, d₃ = d − 1.2269p — average coefficient = 0.9382	ISO 898-1 Annex A
Unified (UNC, UNF)	0.9743	Equivalent average of pitch and minor diameter per unified thread geometry	ASME B1.1 / ASME B18.3

Bolt Tensile Capacity

P_bolt = F_ty × A_s

Maximum axial load before bolt yield (N) — constant, independent of engagement length

F_ty: Tensile yield strength of the fastener (MPa), set by the bolt grade per ISO 898-1 or SAE J429
A_s: Tensile stress area (mm²)

P_bolt is based on tensile yield strength, not tensile ultimate strength. Yield is the appropriate limit for this mode — permanent bolt elongation is the functional failure, and it occurs well before fracture. Depending on grade, there is typically 20–30% additional margin between F_ty and F_tu. No explicit safety factor is divided out at this step; the 0.65 assembly torque factor provides the working margin above the yield limit.

Governing Load

P_eff = min(P_strip, P_bolt)

The lower failure load governs. Thread stripping governs below L^*; bolt yield governs above L^*.

The crossover engagement L^* is found by setting P_strip = P_bolt and solving for L:

L^* = (3 × F_ty × A_s) ÷ (π × d_m × F_su)

Engagement at which both modes are equally loaded. Reported as the “Governing Limit” in results.

Torque

T_max = K × P_eff × d ÷ 1000

Torque at the governing allowable load (N · m). Division by 1000 converts N · mm → N · m. Not the torque at actual failure — when thread stripping governs, P_strip already embeds a 3× safety factor on shear capacity.

T_assembly = 0.65 × T_max

Recommended assembly torque — 65% of limit (safety factor ≈ 1.54)

K: Nut factor (torque coefficient, dimensionless) — accounts for thread friction, contact geometry, and surface finish. Typical values: 0.15–0.20 (lubricated), 0.20–0.25 (dry/clean). This tool uses K = 0.20 for all materials.
d: Nominal major diameter (mm)

The 0.65 factor applies on top of whichever mode governs, but the two modes enter the calculation at different points on the material response curve — so the implied margins against actual failure differ:

Governing mode	Reference strength	Effective margin at T_assembly
Thread stripping	F_su — ultimate shear	≈ 4.6× against shear failure (FoS 3 in P_strip, then × 0.65)
Bolt tensile	F_ty — tensile yield	≈ 1.54× against bolt yield; additional 20–30% margin to fracture depending on grade

This asymmetry is intentional. Thread stripping is a sudden, catastrophic failure against an ultimate strength — a higher margin is warranted. Bolt yield is a ductile, well-characterised failure against a yield limit, with visible warning before fracture. Applying the same numerical factor to both modes would not produce equivalent safety; it would just move the inconsistency out of sight.

Symbol Reference

Symbol	Description	Units
d	Nominal major diameter	mm
p	Thread pitch	mm
d_m	Pitch diameter — d − 0.6495p	mm
L	Thread engagement length	mm
L^*	Crossover engagement length	mm
F_su	Parent material ultimate shear strength	MPa
F_ty	Fastener tensile yield strength	MPa
K	Nut factor (torque coefficient)	—
A_s	Bolt tensile stress area	mm²
k_s	Stress area coefficient (0.9382 metric · 0.9743 unified)	—
P_strip	Thread stripping load (parent material governs)	N
P_bolt	Bolt tensile capacity at yield	N
P_eff	Effective governing load — min(P_strip, P_bolt)	N
T_max	Torque at the governing allowable load (100%)	N · m
T_assembly	Assembly torque — 0.65 × T_max	N · m

Limitations

Non-critical applications only. This tool is not appropriate for flight hardware, structural preload calculations, pressure-boundary joints, safety-critical connections, or any application where joint failure could result in injury, loss of life, or significant property damage. Always verify against applicable design standards and consult a qualified engineer for safety-critical applications.

Nut factor K is fixed at 0.20. This is a common dry-contact value but K varies significantly in practice — from ~0.12 (well-lubricated, waxed) to ~0.30+ (rough, dry, or corroded threads). The torque-to-preload relationship has inherent scatter of ±25% even with a correct K value. Torque-angle or direct tension measurement methods achieve better preload accuracy.
Full thread engagement is assumed. The model assumes clean, undamaged threads fully engaged for the specified depth. Cross-threading, partial engagement, thread damage, or interference fits are not accounted for.
No joint relaxation or embedment. Initial preload is reduced after installation due to surface embedding and thread relaxation, typically 5–15% in metallic joints and more in soft or gasketed assemblies.
Static loading only. The calculated limits are static failure loads. Cyclic, dynamic, or impact loading require separate fatigue analysis and typically necessitate reduced torque values.
Thread fit is not considered. Class of fit (e.g. 6H/6g, 2A/2B) affects both the actual engagement geometry and friction behavior but is not modeled here.
Single shear plane assumed. The thread stripping model assumes one shear plane. Double-shear or through-bolt configurations require separate analysis.

References

[1] Rivera-Rosario, G. & Powell, T. (2017). Threaded Fastener Torque/Preload Relationships. NASA/TM-2017-219475. NASA Glenn Research Center. — Primary source for the thread stripping load formula, F_su values, and the methodology governing both failure modes.
[2] ISO 898-1:2013. Mechanical properties of fasteners made of carbon steel and alloy steel — Part 1: Bolts, screws and studs with specified property classes. International Organization for Standardization. — Source for the tensile stress area formula for metric threads (Annex A).
[3] ASME B1.1-2003. Unified Inch Screw Threads (UN and UNR Thread Form). American Society of Mechanical Engineers. — Source for unified thread geometry and the k_s = 0.9743 tensile stress area constant.
[4] ISO 724:1993. ISO general-purpose metric screw threads — Basic dimensions. International Organization for Standardization. — Source for the pitch diameter formula and thread geometry constants.
[5] ISO 261:1998. ISO general-purpose metric screw threads — General plan. International Organization for Standardization. — Basis for the metric thread size series (M1.6 through M64) covered by this tool.