Bolted Joint

Preload, torque, stretch, stiffness, thread strip and slip checks for a single bolted joint. Inch (UNC/UNF) and metric (ISO) bolts with SAE J429 or ISO 898-1 grade tables. Equations drawn from Shigley, Bickford, VDI 2230 and ISO 16047.

Deterministic strength checks with tightening-method scatter, probability-mode torque solver with optional Monte Carlo verification, fatigue (Goodman), pin-joint and thermal analyses, live equation derivations with citations, and parametric joint diagrams.

Report fields (names, project, notes) are in Section 11.

Bolt Selection

Bolt thread

Size

D = 6.000 mm, P = 1.000 mm, A_t = 20.12 mm²

Hardware

Bolt head style

Standard hex head (ANSI B18.2.1 / DIN 933).

Washer under bolt head

Washer under nut

Clamped member yield (MPa)

Yield strength of the clamped plates (mild steel ~240, stainless ~205, 6061-T6 aluminum ~275, AISI 1045 steel ~530).

Bolt material grade

Code

S_p 580.0 MPa

S_y 640.0 MPa

S_ut 800.0 MPa

Medium carbon, q&t; applies for sizes d <= 16 mm

Nut material grade

Code

S_p 580.0 MPa

S_y 640.0 MPa

S_ut 800.0 MPa

Medium carbon, q&t; applies for sizes d <= 16 mm

Joint geometry

Grip length L_g (mm)Unthreaded shank L_s (mm)Thread engagement L_e (mm)Hollow inner dia (mm; 0 if solid)Joint stiffness rule

Joint cross-section

Friction

PresetK (override)

Friction surfaces

Tightening Method

Tightening method

Method (sets +/- scatter band)

Preload accuracy

Recommend Torque Strategy

Recommend torque strategy

Target fraction of proof

Strategy illustration

External Load

External load (optional)

Axial L_x (N)Loading-plane factor n (0..1)Transverse shear load (N, optional)Slip friction mu (between clamped members)

Load application

Fatigue Analysis

Fatigue analysis (optional)

Enable fatigue analysis (Goodman line)

Goodman diagram

Pin Joint Analysis

Pin joint analysis (optional)

Use when peak shear load is asymmetric (large in one direction, low reversal). Checks whether the bolt survives as a pin in shear after the joint slips.

Enable pin joint analysis

Pin configuration

Thermal Effects

Thermal effects (optional)

Preload shifts when bolt and clamped members expand at different rates as temperature changes from the assembly state.

Enable thermal analysis

Differential expansion

Statistical Inputs

Statistical inputs (for probability mode)

Standard deviations used by the probability panel. Tool tolerance comes from the tightening-method scatter band above.

Friction StDev (fraction of mean, e.g. 0.15 = 15%)Yield strength StDev (fraction of mean)

Run Monte Carlo verification

Runs a direct simulation against the same input distributions to verify the analytic (delta-method) probabilities. Useful when analytic accuracy is in question or scatter is large.

Input scatter

Joint Analysis Report

Probability of failure

Bolt yield

0.580%

analytic

Thread yield

<0.001%

analytic

Slip / separation

Set shear load + slip friction to compute

Closed-form variance propagation from input scatter (friction, tool tolerance, yield strength). Thresholds: green <0.05%, yellow 0.05% to 5%, red >5%.

Recommended torque + preload

Torque (nominal)

10.50 N·m

Preload (nominal)

8.75 kN

Bolt stretch (nom)

0.067 mm

Range torque: 7.88 N·m to 13.13 N·m

Range preload: 6.57 kN to 10.94 kN

Show derivation

Preload (with tightening scatter)

F_{i}^{nom} = 0.75 \cdot S_{p} \cdot A_{t} = 8754 N; F_{i} \in [6565 N, 1.094 e + 4 N] at \pm 25%

Source: Shigley, Mechanical Engineering Design, 7th ed., 2004 — §8-7, pg. 425 (Fi = K_target * Sproof * At; K_target = 0.75 reusable, 0.90 permanent.)

Torque from preload

T = K \cdot D \cdot F_{i} = 0.2 \cdot 6.000 mm \cdot F_{i}; T^{nom} = 10.50 N\cdotm

Source: Shigley, Mechanical Engineering Design, 7th ed., 2004 — §8-7, pg. 426, formula T = K * D * Fi (Simplified Motosh / Junker form using empirical nut factor K.)

Bolt stretch (Bickford)

δ = \frac{F _{i} L _{s}}{E A _{s hank}} + \frac{F _{i} ( L _{g} - L _{s} + D )}{E A _{t}}; δ^{nom} = 0.06742 mm

Source: Bickford, Introduction to the Design and Behavior of Bolted Joints, 4th ed., 2008 — pg. 143, formula delta = Fi*Ls/(E*Ashank) + Fi*(Lg - Ls + D)/(E*At) (Two-section stretch with +1*D length adjustment for half nut + half head.)

Stiffness

K_b = 129.83 MN/m

K_j = 1168.45 MN/m

Show derivation

Bolt stiffness

K_{b} = (\frac{L _{s}}{E A _{s hank}} + \frac{L _{g} - L _{s} + D}{E A _{t}})^{- 1} = 1.298 e + 8 N/m

Source: Shigley, Mechanical Engineering Design, 7th ed., 2004 — §8-3, pg. 416, formula Kb = Fi / delta

Joint stiffness

K_{j} = 9 \cdot K_{b} = 1168.45 MN/m

Source: Shigley, Mechanical Engineering Design, 7th ed., 2004 (Rule-of-thumb estimates: Kj ~ 3*Kb for clamped aluminum, ~9*Kb for clamped steel.)

Strength check (utilization)

Bolt tensile (proof)93.8%

Bolt tensile (yield)85.0%

Bolt tensile (ultimate)68.0%

Bolt thread strip (yield)53.3%

Nut thread strip (yield)37.4%

Bearing: Under bolt head (onto plate)129.0%

Bearing: Under nut (onto plate)129.0%

First failure mode at peak preload: Bolt fractures in tension

Show capacity equations

Bolt proof force

F_{b p} = S_{p} \cdot A_{t} = 580.0 MPa \cdot 20.12 mm^{2} = 1.167 e + 4 N

Source: Shigley, Mechanical Engineering Design, 7th ed., 2004 — §8-7, pg. 425 (Fi = K_target * Sproof * At; K_target = 0.75 reusable, 0.90 permanent.)

Bolt yield force

F_{b y} = S_{y} \cdot A_{t} = 640.0 MPa \cdot 20.12 mm^{2} = 1.288 e + 4 N

Bolt ultimate tensile force

F_{b t} = S_{u t} \cdot A_{t} = 800.0 MPa \cdot 20.12 mm^{2} = 1.610 e + 4 N

Bolt thread yield force

F_{b t y} = 0.577 S_{y, b o l t} A_{s} = 20.54 kN

Source: Shigley, Mechanical Engineering Design, 7th ed., 2004 (Distortion energy theory: tau_yield ~ 0.577 * Sy (von Mises).)

Nut thread yield force

F_{n t y} = 0.577 S_{y, n u t} A_{n} = 29.24 kN

Source: Shigley, Mechanical Engineering Design, 7th ed., 2004 (Distortion energy theory: tau_yield ~ 0.577 * Sy (von Mises).)

Bolt thread strip (ultimate)

F_{b tt} = 0.5 S_{u t, b o l t} A_{s} = 22.25 kN

Source: Shigley, Mechanical Engineering Design, 7th ed., 2004 (Maximum shear stress theory: tau_ult ~ 0.50 * Sut.)

Nut thread strip (ultimate)

F_{n tt} = 0.5 S_{u t, n u t} A_{n} = 31.67 kN

Source: Shigley, Mechanical Engineering Design, 7th ed., 2004 (Maximum shear stress theory: tau_ult ~ 0.50 * Sut.)

Thread sizing

A_s (bolt) = 55.62 mm²

A_n (nut) = 79.17 mm²

J = 0.702

Q (required L_e) = 3.474 mm

Show derivation

External (bolt) thread shear area

A_{s} = π L_{e} D_{1} (0.5 + 0.57735 (d_{2} - D_{1}) / P) = 55.62 mm^{2}

Source: Bickford, Introduction to the Design and Behavior of Bolted Joints, 4th ed., 2008 — formula As = pi * n * Le * Knmax * (1/(2n) + 0.57735*(Esmin - Knmax)) (Bickford external (bolt) thread shear area with Class 2A allowance.)

Internal (nut) thread shear area

A_{n} = π L_{e} D (0.5 + 0.57735 (D - d_{2}) / P) = 79.17 mm^{2}

Source: Bickford, Introduction to the Design and Behavior of Bolted Joints, 4th ed., 2008 — formula An = pi * n * Le * Dsmin * (1/(2n) + 0.57735*(Dsmin - Enmax)) (Bickford internal (nut) thread shear area with Class 2B allowance.)

Relative material strength J

J = \frac{A _{s} S _{u t, b o l t}}{A _{n} S _{u t, n u t}} = 0.702

Source: Bickford, Introduction to the Design and Behavior of Bolted Joints, 4th ed., 2008 — formula J = (As * Sut_bolt) / (An * Sut_nut) (If J > 1, weaker nut threads control; multiply Le by J.)

Corrected required engagement Q

Q = 3.47 mm (set L_{e} \geq Q)

Source: Bickford, Introduction to the Design and Behavior of Bolted Joints, 4th ed., 2008 — formula Le = 2*At / (pi*Knmax*(0.5 + 0.5773*n*(Esmin - Knmax))) (Engagement length so bolt fails in tension before threads strip (equal materials).)

Torque Spec Sheet

Report details

These fields appear on the downloaded torque specification sheet (PDF). Typed names print above their signature lines; the lines themselves stay blank for wet-ink signing.

ProjectPart numberJoint IDRevisionPrepared byChecked byApproved byLubrication conditionTool (model, range, calibration)

Assembly sequence / notes

Lubrication must match the friction inputs in Section 2 - the printed torque is only valid for the friction condition it was computed with.

The link (and the QR code on the sheet) reopens this exact configuration, including these report details.