Documentation

This tool calculates fastener assembly torque from a three-mode failure model: stripping of the threads in the parent material, stripping of the fastener’s own external threads, or tensile failure of the fastener shank. Whichever fails first sets the maximum recommended torque.

Failure Modes

Thread Stripping (Parent Material; Internal Threads)

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.

Thread Stripping (Fastener; External Threads)

The mirror image of parent thread stripping: the bolt’s own external threads strip when the fastener material is weaker than the parent. The shear area is modeled as a cylinder at the pitch diameter d_m, the same simplified shear surface used for parent material stripping. This consistency is intentional — both modes use the NASA/TM-2017-219475 simplified cylinder model, where the 3× safety factor absorbs minor geometric differences between the two thread members. This mode is most relevant for polymer fasteners (nylon, PEEK, acetal) threaded into metal parents, but it is evaluated for all grades whenever shear strength data is available. Like parent stripping, the load grows linearly with engagement.

Bolt Tensile Failure

Bolt tensile failure occurs when the axial load exceeds the fastener’s tensile capacity. This limit dependent on the bolt grade and diameter; it does not change with engagement length. It dominates when engagement is long enough that the threads are stronger than the bolt.

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

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.

Fastener Minor Diameter

The fastener minor diameter d₁ is the root diameter of the bolt’s external thread form — the smallest diameter of the external thread profile. It is not used as a shear surface in this model; it appears only in the tensile stress area derivation below (d₃ in the k_s table), where the average of d_m and d₁ defines the effective stress diameter. For standard 60-degree thread forms:

The 1.2269 constant is the same for both metric and unified 60° thread forms and is derived from the truncated external thread profile geometry.

Thread Stripping Load (Parent Material)

d_m

Pitch diameter (mm) — shear surface for internal threads

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.

Thread Stripping Load (Fastener External Threads)

d_m

Pitch diameter (mm) — shear surface for both thread stripping modes

F_su,bolt

Ultimate shear strength of the fastener (MPa), from grade properties

L

Thread engagement length (mm)

Both thread stripping modes use the same simplified cylinder model at the pitch diameter, consistent with NASA/TM-2017 219475. The 3× safety factor is not derived from the exact thread geometry — it is a calibrated margin that absorbs geometric simplifications, thread fit variation, and shear-to-tensile ratio uncertainty. Applying the same model uniformly to both thread members is therefore more coherent than introducing a different reference diameter for one mode.

Scope note: NASA/TM-2017-219475 addresses internal thread (parent material) stripping only. P_bolt-strip extends that methodology to the fastener’s external threads by substituting F_su while keeping the same formula structure and safety factor.

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:

Bolt Tensile Capacity

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

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

When fastener stripping governs instead, the analogous crossover uses d₁ and F_su,bolt in place of d_m and F_su. Both crossover formulas share the same structure: L^* = (3 × P_bolt ) ÷ (π × d_ref × F_su,ref), where d_ref and F_su,ref are the diameter and shear strength of the governing strip mode.

Torque

K

Nut factor (torque coefficient, dimensionless) — accounts for thread friction, contact geometry, and surface finish. This tool uses K = 0.20 as the default (dry, unlubricated contact baseline). You can override K at the engagement step to reflect lubrication, coatings, or a measured value.

d

Nominal major diameter (mm)

Typical K ranges by assembly condition, approximate ranges given below:

• Dry, unlubricated (default) – 0.20
• Oiled threads – 0.13-0.15
• Anti-seize compound – 0.13-0.17
• Zinc-plated – 0.17-0.22

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

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

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 has inherent scatter. This tool defaults to K = 0.20 (dry, unlubricated contact). 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 carefully measured K value. Use the K override at the engagement step if you know your lubrication condition; otherwise the 0.20 default is a reasonable conservative estimate for dry contact. 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.

References

1. [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. [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. [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. [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. [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.