bolt-fastener

name	bolt-fastener
description	Bolted joint analysis — preload, joint stiffness, separation, fatigue, torque-tension, gasketed joints, bolt patterns under eccentric loads. VDI 2230, Shigley Ch.8.
metadata	{"priority":8,"promptSignals":{"phrases":["bolt","fastener","preload","bolted joint","torque","joint separation","bolt fatigue","clamping force"],"minScore":4}}

Bolted Joint Analysis — Complete Skill

Bolt Geometry & Stress Area

Tensile stress area: A_t = π/4·((d_p+d_r)/2)² ≈ π/4·(d - 0.9743/n)² Where n = threads per inch (TPI), d_p = pitch diameter, d_r = root diameter Standard areas: M8=36.6mm², M10=58.0mm², M12=84.3mm², M16=157mm² 1/2-13: A_t=0.1419in², 1/2-20: A_t=0.1599in²

Proof Load & Strength

• S_p = proof strength (bolt can sustain without permanent set)
• S_y ≈ 1.1·S_p (typically)
• SAE Grade 5: Sp=85ksi, Sy=92ksi, Sut=120ksi
• SAE Grade 8: Sp=120ksi, Sy=130ksi, Sut=150ksi
• Metric 8.8: Sp=600MPa, Sy=660MPa, Sut=830MPa
• Metric 10.9: Sp=830MPa, Sy=940MPa, Sut=1040MPa
• Metric 12.9: Sp=970MPa, Sy=1100MPa, Sut=1220MPa

Preload

Target preload: F_i = 0.75·F_p = 0.75·A_t·S_p (reused joints) F_i = 0.90·F_p (non-reused, permanent) F_i = 0.50·F_p (gasketed joints, soft gaskets)

Torque to achieve preload: T = K·d·F_i K = nut factor: 0.20 (no lube, dry), 0.15 (lubricated, cadmium plated), 0.12 (waxed MoS2) This is only ±25-35% accurate — use direct tension indicators or ultrasonic for precision

Joint elongation: δ_b = F_i·L/(A_t·E_b) Member compression: δ_m = F_i·Σ(L_k/A_k·E_k)

Joint Stiffness Constants

Bolt stiffness: k_b = A_t·E_b/L_b (for threaded section) For mixed shank+thread: k_b = A_d·A_t·E/(A_d·L_t + A_t·L_d)

Member stiffness (Wileman formula, steel-on-steel): k_m = A_b·E_m·0.5774·π/(2·ln(5·(0.5774L+0.5d)/(0.5774L+2.5d))) Or: k_m = EdA/(1.813L) for first approximation

Stiffness ratio: C = k_b/(k_b + k_m) Typical C: 0.15-0.35 (soft gasket→rigid flange)

Load Distribution (Joint Analysis)

Applied tensile load P per bolt:

• Force in bolt: F_b = F_i + C·P (bolt sees only fraction C of external load)
• Force in members: F_m = F_i - (1-C)·P

Separation: Joint separates when F_m = 0 → P_sep = F_i/(1-C) [load at which joint opens] Design: P < P_sep/n_sep, where n_sep ≥ 1.2-1.5

Bolt Fatigue

Alternating bolt load: F_a = C·P_a/2 (P_a = alternating external load per bolt) Mean bolt load: F_m = F_i + C·P_m

Alternating stress: σ_a = F_a/A_t Mean stress: σ_m = F_m/A_t

Endurance limit of bolt: S_e ≈ 18.6 ksi (SAE Gr.5), 23.2 ksi (SAE Gr.8) (Bolts have very low endurance limits due to thread stress concentration)

Goodman: σ_a/S_e + σ_m/S_p = 1/n (use S_p not Sut for bolts) Note: High preload keeps σ_a small — preload is the best fatigue protection

Bolt Patterns Under Eccentric Load

For a bolt group under moment M and direct shear V:

Direct shear per bolt: V_i = V/N (equal for all bolts)

Shear due to moment (torsional): r_i = distance from centroid of pattern to bolt i τ_M = M·r_i/J_p where J_p = Σ(A_b·r_i²)

Total shear: R_i = √(V_x,total² + V_y,total²) — worst bolt is farthest from centroid at worst angle

Shear Joints (Bolts in Shear)

Bearing stress: σ_b = F/(d·t) ≤ 1.35·Sut (AISC) Shear stress: τ = F/A_s ≤ 0.577·Syb Tearout/shear-out: τ = F/(2·t·e) ≤ 0.577·Sy_plate Net tension: σ = F/((w-d)·t) ≤ Sy_plate

Slip-critical joints (friction): F_s = μ·N_bolts·F_i (μ ≈ 0.35 clean steel, 0.15 painted)

Gasketed Joints (ASME Sec. VIII)

Additional bolt force to seat gasket: W_g = 2b·π·G·m·p (seating load) Where m = gasket factor (0.5-6.5), b = effective gasket width, G = mean gasket diameter Total bolt area required: A_m = max(W_op, W_g)/S_b

Output

Provide: F_i (preload), T (torque), C (joint constant), F_b,max, n_separation, n_fatigue (if cyclic), governing failure mode.