Engineering Calculators
● Bolted Joint Calculator

Bolted Joint Calculator

Build a fastener stack-up — metric or imperial, hex or socket head, washers, nuts or tapped/insert engagement — and solve preload ↔ torque via the VDI 2230 cone-of-compression method (Shigley closed form), with fastener and clamped-member yield checks and geometry validation. Hover the ? icons for a plain-language explanation of each input and result.

1FastenerChoose the bolt size, head style, and strength grade. Together these set how much load the bolt itself can safely carry, and how big the bearing surface under the head is.
Pitch diameter dm = 7.188 mm (used in the torque-preload formula).
Bearing-face diameter (across-flats for hex, head OD for SHCS) feeds both the frustum base and bearing-stress area.
ISO 898-1 via designation formula (tensile=1st digit×100, proof=tensile×2nd digit/10); SAE J429 typical published values.
Suggested hole Ø for M8 x 1.25: 9 mm. Use the "Use suggested" button on each clamped section below to apply it.
2Clamped stack-upThe parts being squeezed together by the bolt. Their thickness and stiffness determine how much of the bolt's stretch turns into clamping force, and their bearing strength sets how much force the surface under the head/nut can take before it dents or crushes.
Section 1 (head side)
Section 2 (nut/tapped side)
Bearing/yield stress is checked at the two outer faces (section 1 and the last section) only — interior plate-to-plate interfaces have much larger nominal contact area and rarely govern.
3Hardware & thread engagementHow the bolt actually threads into the joint — through a nut, tapped directly into the material, or via a threaded insert — plus any washers, which change the bearing area and (for spring types) can add clamping compliance.
"All-metal prevailing torque" covers the K-nut / Aerotight / Aeronut / Philidas / Stover family (ISO 7042, DIN 980-V).
4Friction & tightening methodFriction between the threads/bearing face turns most of your tightening effort into heat and rubbing, not clamping force — so it strongly affects how much preload a given torque actually produces, and how consistent that preload is from one assembly to the next.
Typical αA scatter range 1.6–2.5, recommended target ≈75% of proof load. Approximate literature values — verify for critical joints.
Literature isn't unified on this convention — pick per your own tightening-method documentation.
Applied tensile load the joint must resist without separating (0 = static preload-only check).
5Solve forPick what you know and want to check: apply a torque and find the resulting preload, specify a target preload and find the torque needed, or model the turn-of-nut method (a light snug torque plus an extra measured rotation).
Results
✓ Joint design meets all checks
PreloadThe clamping tension already "built into" the joint before any external load is applied — this is what actually holds the parts together. Too low and the joint can loosen or separate under load; too high and you risk yielding or breaking the bolt.
12,319N
53% of proof load
TorqueThe twisting effort applied at the wrench. Most of it (often 80-90%) is consumed by friction under the head/nut and in the threads — only a fraction actually stretches the bolt into preload, which is why friction assumptions matter so much.
25N·m
K-factor ≈ 0.254
Yield-onset ("breakoff") torqueThe torque level that would just bring the bolt to its proof strength (before any external load), computed the same way real yield-controlled/gradient tightening tools work. Treat this as a safe ceiling — going past it starts to permanently stretch (and eventually break) the bolt.
47.54N·m
Preload scatter bandEven with a fixed target torque, the ACTUAL preload varies assembly to assembly because friction is never perfectly repeatable. This band shows the realistic range for your chosen tightening method — a good design should still pass its checks even at the low end, and not overstress the bolt at the high end.
12,319–30,797N
Bolt stress safety factorHow much margin the bolt itself has against reaching its proof strength (the point it starts to permanently stretch) once external load is added to the preload. Below 1.0 means the bolt has already exceeded proof strength — this must be fixed.
1.9
σ = 336.6 MPa
Head-side bearing SFHow much margin the material directly under the bolt head/washer has before it starts to crush or yield locally. A low value means you need a wider washer, a stronger clamped material, or a larger bolt head.
3.23
Nut/tapped-side bearing SF
2.93
Joint separation marginHow much clamping force is left squeezing the parts together once the external load is applied. If this drops to zero or below, the parts can lift apart at the joint interface — even if the bolt itself is nowhere near failing. Bigger positive numbers are safer against separation, leakage, or fretting.
12,319N
Joint separationHow much clamping force remains at the joint interface, and the safety factor against separation (Fi / [P·(1−C)], Shigley Eq. 8-29), evaluated at the nominal preload target and at the realistic min/max scatter band for your chosen tightening method.
MetricNominalMinMax
Separation Margin [N]12,31912,31930,797
- Safety Factor———
Min/max use the preload scatter band's low/high ends with the same external load — "—" means no external axial load is applied, so there's no separating tendency to compare against.
Bolt stressesPreload stress (clamping force alone), tensile stress (bolt force under the applied external load), shear stress (from the external shear force), and their von Mises combination — each at nominal preload and the min/max scatter band, with the safety factor directly underneath.
StressNominalMinMax
Preload Stress [MPa]336.6336.6841.5
- Safety Factor1.91.90.76
Tensile Stress [MPa]336.6336.6841.5
- Safety Factor1.91.90.76
Shear Stress [MPa]000
- Safety Factor———
Von Mises Stress [MPa]336.6336.6841.5
- Safety Factor1.91.90.76
Shear stress is independent of preload, so it (and the resulting von Mises value) only vary Nominal/Min/Max through their preload-driven tensile-stress component.
Thread stressA simplified thread-shear screening check (not a full thread-stripping-area derivation) — the engaged thread's shear area is approximated as half its circumferential cylinder at the relevant diameter over the engaged length.
MetricValue
External (Bolt) Thread [MPa]189.5
- Safety Factor1.95
Internal Thread (nut) [MPa]153.2
- Safety Factor2.41
Assumes a correctly matched nut (ISO 898-2: nut proof load >= bolt proof load) — nut material strength isn't modelled directly.
Clamped partsPull-through: whether the head/washer could shear-out (punch through) the top clamped section under axial load. Pin bearing: the bolt shank bearing against the clamped stack's hole wall under the external shear force. Bearing top/bottom: the existing outer-face crush checks, tabulated here alongside the others.
MetricValue
Pull-Through Stress [MPa]24.5
- Safety Factor6.5
Pin Bearing [MPa]0
- Safety Factor—
Bearing - Top (Head Side) [MPa]85.4
- Safety Factor3.23
Bearing - Bottom (Nut/Tapped Side) [MPa]85.4
- Safety Factor2.93
Pin bearing uses the total grip length against the weakest clamped section's material — "—" means no external shear force is applied.
Joint cross-section
mid-planet=10.0⌀8.5t=10.0⌀8.5grip 20.0 mm2 clamped sections · nut & bolt · dimensions in mm
Selected components
BoltISO 4762 - M8 x 1.25 - ISO 898-1 Class 8.8
Head-side washerISO 7089 - 8
Nut-side washerISO 7089 - 8
NutISO 4032 - M8

Representative standard designations (ISO/DIN number + size + variant) for cross-referencing against a supplier's current catalog — not a guaranteed live vendor SKU.

Reference & assumptions

New to VDI 2230? Read the guide: Bolt Preload & Torque: How VDI 2230 Models a Bolted Joint — a plain-language explainer of the standard behind this calculator.

Clamped-member stiffness uses the standard simplified two-cone (nut & bolt) or single-cone (tapped/ threaded-insert) frustum method — a 30° half-angle cone of compression spreading from each bearing face, chained across multiple clamped sections where the mid-plane (or, for tapped joints, the mid-point of thread engagement) falls inside a plate. This is the standard textbook realization (Shigley's Mechanical Engineering Design) of VDI 2230's cone-of-compression concept; VDI 2230's own full multi-segment method may give different results on stacks with many plates of sharply different diameters — treat this as a good general-purpose estimate, not a replacement for full VDI 2230 analysis on complex stacks. Bearing/ yield stress is checked only at the two outer bearing faces, not interior plate-to-plate interfaces. Minimum thread engagement length is a first-principles-scaled estimate (proof-strength-to-yield-strength ratio, floored at 1× nominal diameter), not a full thread-shear-area derivation. The thread-stress, pull-through, and pin-bearing checks are simplified cylindrical shear-area screening calculations — thread shear area is approximated as half the thread's circumferential cylinder over the engaged length, and a 0.577 (1/√3) distortion-energy factor converts tensile proof/yield strength to an estimated shear strength — not full Machinery's-Handbook thread-stripping-area derivations. Bolt-length mode derives the engagement length as the entered bolt length minus the thickness of every clamped section ahead of the tapped/insert one. Property-class strength values (ISO 898-1 designation formula, SAE J429 typical published grades), all-metal prevailing-torque nut torques, and tightening-method scatter factors (αA) are typical/representative — verify against the current official standards and, where required, physical testing before certification use.

Validated: the frustum (cone-of-compression) stiffness formula was checked by independently re-deriving it from the documented equation across three different geometries/materials — all matched the calculator's own function to within floating-point precision. The torque-preload relationship round-trips exactly (10,000 N of preload → 25.80 N·m → back to exactly 10,000 N through the inverse function), and for typical friction (µ = 0.15 thread and bearing) it implies a K-factor of 0.215 in T = K·F·d — squarely in the ~0.2 range Shigley documents for this friction regime. Thread minor diameters and minimum engagement length both matched hand calculation from the standard ISO 68-1 and proof/yield-ratio formulas exactly.

Contact resistance (if enabled) uses Holm's single-spot constriction + film contact-resistance model — the foundational, widely-cited model for bolted electrical joints — with empirical roughness/ flatness correction factors standing in for full multi-spot asperity clustering. It's a trend/order-of- magnitude estimate: real bolted-joint measurements commonly deviate 2-5x from a single-spot analytical prediction due to surface contamination, real multi-spot clustering, and aging, which is exactly why standards such as IEC 61238-1 and ASTM B667 require physical contact-resistance qualification testing for critical joints rather than relying on calculation alone.

Calculation steps
1. Bolt (fastener) stiffness
k = A·E/L per segment (unthreaded shank + threaded engagement), combined in series
Unthreaded shank: A=50.3 mm², L=13.6 mm, k=739,198 N/mm; Threaded engagement: A=36.6 mm², L=6.4 mm, k=1,143,750 N/mm
k_bolt = 449,008 N/mm
2. Clamped-member stiffness (frustum / cone-of-compression method)
k = (0.5774·π·E·d) / ln{[(1.155t+D−d)(D+d)] / [(1.155t+D+d)(D−d)]}, per segment, combined in series
head: t=10, D=16, k=1,945,764 N/mm; nut: t=10, D=16, k=5,648,081 N/mm
k_members = 1,447,203 N/mm, joint stiffness parameter C = 0.237
3. Preload achieved for target torque (Shigley closed form, inverted)
T = F·dm/2·[(l+π·f·dm·sec30°)/(π·dm−f·l·sec30°)] + F·fc·dc/2
dm=7.188 mm, l=1.25 mm, f=0.15, fc=0.15
F = 12,319 N, T = 25 N·m (thread term 10.22 + bearing term 14.78), K-factor ≈ 0.254
4. Preload scatter band (Torque wrench (calibrated, hand tool), αA ≈ 1.6–2.5)
min = F (nominal target), max = F·αA
12,319–30,797 N (53% of proof load at nominal)
5. Load sharing under external axial load
F_bolt = F_preload + C·P, F_member = F_preload − (1−C)·P
P = 0 N, C = 0.237
F_bolt = 12,319 N, F_member = 12,319 N
6. Fastener tensile stress vs. proof strength
σ = F_bolt / As, SF = proof / σ
σ = 336.6 MPa, SF = 1.9 (target 1.5) — pass
7. Shear stress and combined (von Mises) stress
τ = V / A_shank, σ_vm = √(σ_tensile² + 3τ²), SF = proof / σ_vm
V = 0 N, A_shank = π/4·d² = 50.3 mm²
τ = 0 MPa, σ_vm = 336.6 MPa, SF = 1.9 at nominal preload
8. Yield-onset ("breakoff") torque
F_yield = proof × As, then T_yield via the same torque-preload formula
T_yield = 47.54 N·m — a safe ceiling regardless of tightening method
9. Bearing stress — head side (al6061t6)
σ = F_bolt / [π/4·(D_bearing² − d_hole²)], SF = yield / σ
σ = 85.4 MPa, SF = 3.23 — pass
10. Bearing stress — nut/tapped side (steelGeneric)
σ = F_bolt / [π/4·(D_bearing² − d_hole²)], SF = yield / σ
σ = 85.4 MPa, SF = 2.93 — pass
11. Thread shear stress (external/bolt and internal thread)
A ≈ π·D·Le·0.5 (simplified — half the thread circumference over the engaged length), τ = F_bolt / A, SF = 0.577·strength / τ
Le = 6.4 mm, bolt minor Ø used for the external check, nominal Ø for the internal check
External: τ = 189.5 MPa, SF = 1.95. Internal: τ = 153.2 MPa, SF = 2.41.
12. Pull-through and pin-bearing checks
Pull-through: A = π·D_bearing·t_top, σ = F_bolt/A. Pin bearing: A = d·L_grip, σ = V/A. SF = 0.577·yield / σ
Pull-through σ = 24.5 MPa (SF 6.5); pin bearing σ = 0 MPa (SF —)