A bolted joint works by stretching the bolt like a spring and compressing the clamped parts like another spring. The initial tightening force, called preload, is often much larger than the external service load. This matters because a well preloaded joint can stay clamped, resist slipping, and reduce damaging cyclic stress in the bolt.
Bolted joint analysis helps engineers choose bolt size, grade, torque, washer area, and safety factors.
Key Facts
- Bolt stiffness can be estimated by k_b = A_b E_b / L_b, where A_b is tensile area, E_b is elastic modulus, and L_b is effective grip length.
- Member stiffness k_m depends on material, thickness, washer or head diameter, and the compression cone through the clamped parts.
- Joint stiffness factor C = k_b / (k_b + k_m), so the bolt receives C P of an external tensile separating load P.
- Bolt load under external tensile load is F_b = F_i + C P, where F_i is preload.
- Remaining clamp force is F_c = F_i - (1 - C) P, and joint separation begins when F_c = 0.
- Approximate torque-tension relation is T = K F_i d, where T is tightening torque, K is nut factor, F_i is preload, and d is nominal bolt diameter.
Vocabulary
- Preload
- The tensile force intentionally created in a bolt when it is tightened.
- Clamp force
- The compressive force squeezing the joined members together due to bolt preload.
- Joint stiffness factor
- The fraction of an external tensile load carried by the bolt in a preloaded joint.
- Proof load
- The maximum tensile load a bolt can support without permanent deformation according to its specification.
- Nut factor
- An empirical factor in the torque-tension equation that accounts for thread and bearing friction.
Common Mistakes to Avoid
- Adding the full external load to the bolt preload is wrong because only the fraction C P increases bolt tension before separation.
- Ignoring loss of clamp force is wrong because the joint can separate or slip even when the bolt itself has not failed.
- Using tightening torque as an exact measure of preload is wrong because friction variations can cause large preload scatter for the same torque.
- Assuming higher preload always solves fatigue is wrong because preload must stay below proof load and must not crush the clamped material.
Practice Questions
- 1 A bolt has stiffness k_b = 250 MN/m and the clamped members have stiffness k_m = 750 MN/m. Find the joint stiffness factor C and the added bolt load if the external separating load is P = 12 kN.
- 2 A bolted joint has preload F_i = 30 kN and stiffness factor C = 0.25. For an external separating load P = 20 kN, find the final bolt load F_b and remaining clamp force F_c.
- 3 Two identical joints see the same fluctuating external tensile load. One is properly preloaded and the other is only finger-tight. Explain which bolt is more likely to fail by fatigue and why.