Bolted joint strength combines material limits, preload control, joint stiffness, and failure mode checks. This cheat sheet helps engineering students organize the core formulas used to size and evaluate bolted connections. It is especially useful when comparing bolt grades, estimating tightening torque, and checking whether a joint can safely carry tension, shear, or cyclic loads.
Key Facts
- The proof load of a bolt is Fp = Sp At, where Sp is proof strength and At is tensile stress area.
- A common target preload for static joints is Fi = 0.70 Sp At for reusable bolts and Fi = 0.75 Sp At for permanent structural joints, when allowed by standards.
- The torque-preload estimate is T = K Fi d, where K is the nut factor, Fi is desired preload, and d is nominal bolt diameter.
- The joint stiffness factor is C = kb / (kb + km), where kb is bolt stiffness and km is member stiffness.
- For an external tensile load P on a preloaded joint, the added bolt load is Pb = C P and the reduced clamping load is Pm = (1 - C) P.
- Joint separation begins when P >= Fi / (1 - C), because the external load has removed all remaining clamp force.
- Average bolt shear stress is tau = V / A, using the shear area A through the shear plane, and it must be compared with the allowable shear stress.
- A simple fatigue check for bolt tensile stress uses Goodman form sigma_a / Se + sigma_m / Sut <= 1 / n, where n is the factor of safety.
Vocabulary
- Proof strength
- The maximum stress a bolt can withstand without permanent set under a specified proof load.
- Tensile stress area
- The effective threaded area At used to calculate tensile stress and proof load in a bolt.
- Preload
- The initial tensile force Fi placed in a bolt during tightening to clamp joint members together.
- Nut factor
- The empirical coefficient K in T = K Fi d that accounts for thread friction, bearing friction, and geometry.
- Joint stiffness factor
- The fraction C of an external tensile load that increases bolt load in a preloaded joint.
- Joint separation
- The condition where external tensile load removes all clamping force between joint members.
Common Mistakes to Avoid
- Using nominal bolt area instead of tensile stress area is wrong for threaded tensile loading because the threads reduce the effective load-carrying area.
- Assuming torque directly equals preload is wrong because friction dominates tightening behavior, so the same torque can produce different preload values.
- Ignoring preload in a tension joint is wrong because preload changes how much external load is carried by the bolt and how much clamp force remains.
- Checking only bolt tension while ignoring shear and bearing is wrong because a joint can fail by bolt shear, plate bearing, tear-out, or slip before tensile rupture.
- Using static strength formulas for cyclic loading is wrong because fatigue depends on alternating stress, mean stress, surface condition, size, and stress concentration.
Practice Questions
- 1 A bolt has Sp = 830 MPa and At = 58 mm^2. Find the proof load Fp in kN.
- 2 A joint uses a bolt with d = 12 mm, desired preload Fi = 30 kN, and K = 0.20. Estimate the tightening torque T in N·m.
- 3 For a preloaded joint with Fi = 25 kN and C = 0.25, find the external tensile load P that causes joint separation.
- 4 Explain why increasing bolt preload can improve fatigue performance in a joint even though it increases the initial tensile stress in the bolt.