| 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.
