Engineering CalculatorsBolt Pattern Calculator
Aligned grid, rectangular perimeter, circular (bolt-circle), or fully custom bolt patterns, analysed under general 3-D loading — direct and torsional shear via the elastic method, axial/tension via unsymmetric bending, combined with preload and checked against the bolt's proof strength.
| Bolt | x, y (mm) | Direct (N) | Torsional (N) | Resultant (N) |
|---|---|---|---|---|
| 1 | -60, -40 | 83 | 150 | 208 |
| 2 | 0, -40 | 83 | 83 | 167 |
| 3 | 60, -40 | 83 | 150 | 208 |
| 4 | -60, 40 | 83 | 150 | 125 |
| 5 | 0, 40 | 83 | 83 | 0 |
| 6 | 60, 40 | 83 | 150 | 125 |
| Bolt | External axial (N) | Bolt tension (N) | Residual clamp (N) | Status |
|---|---|---|---|---|
| 1 | 1,167 | 22,086 | 20,919 | OK |
| 2 | 333 | 21,919 | 21,586 | OK |
| 3 | -500 | 21,753 | 22,253 | OK |
| 4 | 1,167 | 22,086 | 20,919 | OK |
| 5 | 333 | 21,919 | 21,586 | OK |
| 6 | -500 | 21,753 | 22,253 | OK |
| Bolt | Shear stress (MPa) | Tensile stress (MPa) | von Mises (MPa) | Safety factor |
|---|---|---|---|---|
| 1 | 2.7 | 380.8 | 380.8 | 1.68 |
| 2 | 2.1 | 377.9 | 377.9 | 1.69 |
| 3 | 2.7 | 375 | 375.1 | 1.71 |
| 4 | 1.6 | 380.8 | 380.8 | 1.68 |
| 5 | 0 | 377.9 | 377.9 | 1.69 |
| 6 | 1.6 | 375 | 375.1 | 1.71 |
New to Bolt Group (Elastic Method)? Read the guide: Bolt Pattern Analysis: The Elastic Method for Bolt Groups — a plain-language explainer of the standard behind this calculator.
Bolt-group ("bolt pattern") analysis using the elastic method — the classic eccentrically-loaded fastener group treatment from Shigley's Mechanical Engineering Design (bolted/riveted joints loaded in shear), Blodgett's Design of Weldments (the identical method applied to weld groups), and the AISC Steel Construction Manual's elastic method for bolt groups. All bolts are assumed identical (same size, grade and target preload) and treated as unit "point areas" — standard practice, since a bolt's own cross-section polar moment of inertia about its own centre is negligible next to the pattern's spread once bolts are more than a diameter or two apart. In-plane shear combines a direct component (shared equally, F/n) with a secondary "torsional" component from an in-plane moment Mz, distributed via the polar "moment of inertia" J=Ixx+Iyy (Mz·r/J, perpendicular to each bolt's radius from the centroid) — cross-checked against MechaniCalc's published "Bolt Pattern Force Distribution" reference. Axial (tension/compression) demand from an out-of-plane force Fz and bending moments Mx, My uses the general unsymmetric-bending formula F = Fz/n + [(Mx·Iyy−My·Ixy)(y−ȳ) + (My·Ixx−Mx·Ixy)(x−x̄)] / (Ixx·Iyy−Ixy²), which correctly handles a non-zero product of inertia Ixy for a genuinely asymmetric custom bolt layout — most published simplified treatments (including MechaniCalc's) assume Ixy=0, i.e. principal axes aligned with the pattern geometry. This reduces to the familiar Mx·y/Ixx + My·x/Iyy superposition whenever Ixy=0 (any pattern symmetric about the x or y axis). The neutral axis is taken at the pattern centroid, valid while the joint faces remain in contact under the applied moment — this is not a concrete-anchor prying/cracked-section analysis. An applied force may be entered at an offset point from the centroid (the natural way to describe a bracket or lever-arm load); the tool reduces it to an equivalent force + moment at the centroid via standard moment transfer (M = M_direct + r × F) before distributing it to the bolts. Bolt tension combines with preload via the same joint-stiffness-ratio (C) convention as this site's Bolted Joint Calculator: Fb = Fi + C·P, with separation when Fi−(1−C)·P ≤ 0 — C≈0.2 is typical for a standard steel joint without a soft gasket; use this site's Bolted Joint Calculator for an exact C from a specific clamped stack, or C=1.0 for the most conservative (no stiffness credit) check. Combined shear + tension is checked via the distortion-energy (von Mises) criterion, σ_vM=√(σ_tensile²+3·τ²), against the bolt's proof strength — matching the Bolted Joint Calculator's convention for internal consistency across the site. Torque-preload uses a single friction coefficient for both the thread and the under-head bearing face (a simplification vs. the Bolted Joint Calculator's independent thread/bearing friction). Idealisations: rigid plates (no plate bending compliance), linear-elastic response, no fatigue, vibration/self-loosening, or dynamic/impact loading. Verify a critical design against a detailed FEA or the referenced standards directly.
Validated: a 4-bolt square pattern (bolts at ±50 mm) under 1000 N direct shear plus a 200 N·m in-plane torque should split into two bolts carrying 901.4 N and two carrying 559.0 N by hand (direct shear reinforcing the torsional component on one diagonal, partly cancelling it on the other) — this calculator returns exactly those two values. The same pattern under a pure 100 N·m out-of-plane bending moment should split ±500 N by the Mx·y/Ixx superposition — this calculator also matches exactly.