OpenSpecEngineering

Checks a preloaded bolt in a joint that carries a tensile load: how far the load could rise before the bolt reaches its proof load, and before the clamped parts separate. Pick a metric or inch size, its thread and the grade to get the proof load, or enter your own stress area and proof strength. Designers use it to confirm a bolt size and grade for flanges, covers, brackets and cylinder heads.

Equations

F_p = A_t·S_p     F_b = F_i + C·P     F_m = (1 − C)·P − F_i

n = (A_t·S_p − F_i)/(C·P)     n₀ = F_i/(P·(1 − C))

A_t is the tensile stress area: (π/4)(d − 0.9382p)² for a metric thread of pitch p [2], or (π/4)(d − 0.9743/N_t)² for an inch thread with N_t threads per inch [4]. S_p is the grade’s proof strength [2], [3], [5]; where the standard gives none, S_p = 0.85·S_y [1]. F_i is the preload, 75 % of F_p for a reusable joint or 90 % for a permanent one [1]. P is the external tensile load on one bolt.

C = k_b/(k_b + k_m) is the joint stiffness constant, from the bolt stiffness k_b and the clamped members’ stiffness k_m. The bolt feels only the share C of P (F_b); the rest unloads the members (F_m), which separate when F_m reaches zero [1]. n is the factor on P that brings the bolt to its proof load, and n₀ the factor that separates the joint. Both should be above 1, with a margin that suits the uncertainty in the load.

Limits and common mistakes

• C has to be worked out from the joint geometry [1]. With hard steel members it is often 0.2 to 0.3; with a soft gasket it approaches 1, and the bolt takes nearly all of P.
• The check is static. A fluctuating load needs a fatigue check of the bolt as well.
• A preload set by torque scatters widely with friction, and both factors move with it. See Bolt Torque & Preload.
• Shear loads on the joint are not covered.

Worked example

A pump cover is held by M12 class 8.8 cap screws, each carrying up to 12 kN from the internal pressure. The joint is steel on steel with C = 0.2, and it is opened for service.

1. Choose Bolt Size Metric (ISO), Size M12 and Thread M12 × 1.75.
2. Choose Bolt Grade Class 8.8 (ISO 898-1) and Preload 75 % of proof load — reusable joint.
3. Enter External Load per Bolt 12000 N and Joint Stiffness Constant 0.2, and press Solve. The Solution shows: Tensile Stress Area (At): 84.2664 mm²
   Proof Strength (Sp): 580 MPa
   Proof Load (Fp = At·Sp): 48,874.5 N
   Preload (Fi): 36,655.9 N
   Load Factor (n) — yield: 5.09109
   Load Factor (n0) — separation: 3.81832

Check: the bolt carries 36,656 + 0.2 × 12,000 = 39,056 N, well under its 48,874 N proof load. The joint separates at 36,656/0.8 = 45,820 N, which is 3.82 times the load. Separation governs, as it usually does with a high preload.