threaded-fasteners

name	threaded-fasteners
description	Threaded fastener design — preload, torque-tension, bolt stiffness, joint separation, proof load, fatigue, torque coefficients, VDI 2230, ASME bolting.
metadata	{"priority":8,"promptSignals":{"phrases":["bolt preload","threaded fastener","bolt torque","torque tension","VDI 2230","bolt joint","proof load","bolt tightening"],"minScore":3}}

Threaded Fastener Design — Complete Skill

Thread Standards

Unified (UNC/UNF): inch; designation: 1/4-20 UNC (diameter-TPI) Metric (M): ISO 68-1; designation: M10×1.5 (dia × pitch [mm]) Standard pitch (coarse): M10→1.5mm; M12→1.75mm; M16→2mm; M20→2.5mm

Stress area (ISO): A_s = π/4 × [(d_2+d_3)/2]² A_s approximate: M10: 58 mm²; M12: 84.3 mm²; M16: 157 mm²; M20: 245 mm²; M24: 353 mm²

Preload and Tightening Torque

Preload: F_i = K_i × F_proof or design to F_i = 0.65–0.85 × A_s × S_p S_p = proof strength (0.85–0.92 × S_y for bolts)

Torque-Tension (short Kellermann-Klein): T = K × d × F_i

K (nut factor / torque coefficient):

• K = 0.20 (as-received steel, no lubrication — standard)
• K = 0.15 (lightly oiled, or zinc-plated)
• K = 0.12 (molybdenum disulfide lubrication)
• K = 0.10 (PTFE-coated)
• K = 0.25 (corroded, no lubrication)

Full Shigley torque equation: T = F_i [( d_m/2)(tan λ + μ_t/cos α_n) + μ_c r_c] d_m = mean thread diameter; λ = lead angle; α_n = half-angle; μ_c = collar friction

Bolt and Joint Stiffness

Bolt stiffness (threaded + unthreaded sections): 1/k_b = L_t/(E A_s) + L_d/(E A_d) L_t = threaded length in grip; L_d = unthreaded length; A_d = shank area

Joint stiffness (frustum method, Wileman): k_j = (E_j π d tan α) / (2 ln[(2t tanα + d_w - d)(d_w + d) / ((2t tanα + d_w + d)(d_w - d))]) Standard half-angle: α = 30° Approximate: k_j ≈ 3 to 10 × k_b (joint much stiffer for steel-to-steel)

Joint compliance ratio: C (bolt fraction) = k_b / (k_b + k_j) Typical C ≈ 0.1–0.3

Load Sharing and Joint Separation

External force P adds to bolt: F_b = F_i + C×P External force P reduces clamping: F_c = F_i - (1-C)×P

Joint separation condition (F_c → 0): P_sep = F_i / (1-C)

Design requirement: P_max < P_sep / n_sep (n_sep ≥ 1.5 typical)

Bolt Grades and Strength

Metric property classes:

Class	S_p [MPa]	S_y [MPa]	S_u [MPa]
4.6	225	240	400
8.8	600	660	830
10.9	830	940	1040
12.9	970	1100	1220

SAE grades (inch): SAE 5: S_p = 85 ksi (585 MPa); SAE 8: S_p = 120 ksi (825 MPa)

Fatigue of Bolts

Fatigue critical section: thread root (first engaged thread, run-out point) Rolled threads: 30–40% better fatigue life than cut threads (compressive residual stress) Endurance limit (SAE J429): ≈ 23 ksi (160 MPa) for SAE Grade 8

Modified Goodman for bolt fatigue: σ_a / S_e + σ_m / S_u ≤ 1 σ_a = C × P_a / A_s; σ_m = F_i / A_s + C × P_m / A_s Good design: C small (stiffer joint) reduces fatigue amplitude

VDI 2230 Procedure

German standard for systematic bolt joint analysis (11 steps):

1. Determine required clamp load F_Kerf (from friction, sealing, or separation criteria)
2. Calculate tightening torque with scatter: F_i = F_Kerf / α_A (α_A = 1.2–1.8 for scatter)
3. Check bolt utilization under tightening + working loads
4. Verify against fatigue limit

Tightening method and scatter α_A:

• Torque wrench: α_A = 1.4–1.8
• Torque-angle: α_A = 1.2–1.4
• Yield control: α_A = 1.05–1.1
• Hydraulic tensioning: α_A = 1.0–1.05

Locking Devices

Spring washers: poor — not recommended (NASA TM 108377) Prevailing torque nuts (Nyloc, all-metal): reliable; torque specified separately Thread locker (Loctite): good for low-torque; check chemical compatibility Cotter pin / castellated nut: reliable for safety-critical Nord-Lock washer: wedge-locking; high vibration resistance

Output

Provide: bolt grade and size, A_s [mm²], S_p [MPa], F_i [N] (% of proof load), T_tighten [N·m], K, C (compliance), F_b and F_c at max load [N], P_sep [N], fatigue safety factor, locking method.