Preloaded Bolted Joint Separation — Worked Example

1. Problem

An M10 bolt (property class 10.9) clamps two steel plates with an initial preload of 35 kN. An external tensile load is applied to the joint. Determine the bolt load, clamp force and separation load as the external load increases.

2. Given

3. Required

• Joint stiffness factor n
• Bolt load and clamp force at P_ext = 20 kN
• Separation load P_sep
• Bolt load after separation at P_ext = 30 kN

4. Assumptions

• The joint remains clamped (no separation) for the first part of the calculation
• Linear elastic behaviour of bolt and members
• The external load is applied within the clamped region (between the plates)
• Member stiffness k_m is from the frustum (cone) model
• No eccentricity — concentric loading

5. Governing Equations

Joint stiffness factor:
  n  =  k_b / (k_b + k_m)

Before separation:
  ΔF_bolt  =  n × P_ext         (load into bolt)
  ΔF_clamp  =  (1 − n) × P_ext    (loss of clamp force)

  F_bolt  =  F_pre + n × P_ext
  F_clamp  =  F_pre − (1 − n) × P_ext

Separation occurs when F_clamp = 0:
  P_sep  =  F_pre / (1 − n)

After separation:
  F_bolt  =  P_ext    (bolt carries full external load)

6. Calculation

Step 1: Joint stiffness factor.

n  =  k_b / (k_b + k_m)  =  290 / (290 + 1450)  =  290 / 1740  =  0.167

6. Calculation (continued)

Step 2: At P_ext = 20 kN (before separation — verified below).

ΔF_bolt   =  0.167 × 20  =  3.3 kN
ΔF_clamp  =  (1 − 0.167) × 20  =  0.833 × 20  =  16.7 kN

F_bolt   =  35 + 3.3  =  38.3 kN
F_clamp  =  35 − 16.7  =  18.3 kN   (still > 0 → joint clamped)

6. Calculation (continued)

Step 3: Separation load.

P_sep  =  F_pre / (1 − n)  =  35 / 0.833  =  42.0 kN

6. Calculation (continued)

Step 4: At P_ext = 30 kN (still before separation since 30 < 42).

F_bolt   =  35 + 0.167 × 30  =  35 + 5.0  =  40.0 kN
F_clamp  =  35 − 0.833 × 30  =  35 − 25.0  =  10.0 kN   (still clamped)

7. Result

Joint stiffness factor n = 0.167 — only 17% of external load goes into the bolt before separation. At P_ext = 20 kN: F_bolt = 38.3 kN, F_clamp = 18.3 kN. Separation load P_sep = 42.0 kN. After separation, the bolt carries the full external load.

8. Check

• Bolt stress at P_ext = 20 kN: σ = 38,300 / 58.0 = 660 MPa < Fty = 940 MPa (MS = +0.42) — bolt is safe
• The stiffness factor n = 0.167 is typical for a steel-steel joint with k_m >> k_b — physically reasonable
• At P_sep = 42 kN: F_bolt = 35 + 0.167 × 42 = 42.0 kN, σ = 42,000/58 = 724 MPa — still below yield
• After separation at P_ext = 50 kN: F_bolt = 50 kN, σ = 862 MPa < Fty (MS = +0.09) — close to yield
• Dimensional check: kN/mm × mm = kN — consistent

9. Interpretation

The key insight is that before separation, only 17% of the external load enters the bolt — the rest reduces the clamp force. This is why preloaded joints are so effective at reducing bolt fatigue: the bolt stress range is a small fraction of the external load range. After separation (P > 42 kN), the bolt suddenly carries the full load — the stress jumps from 42 kN to the full external load, creating a large stress range that can cause rapid fatigue crack initiation.

For fatigue-critical joints, the design goal is to keep P_ext < P_sep under all service loads. If separation occurs in service, the bolt should be re-sized or the preload increased to prevent it.

10. Limitations

• Member stiffness k_m uses the frustum cone model — actual stiffness depends on geometry and may differ
• No eccentricity — offset joints have additional bending loads
• No temperature effects — differential thermal expansion can change the preload
• No creep or relaxation — preload decreases over time in some materials
• The separation is assumed to be abrupt — in reality, progressive partial separation can occur
• No gasket or seal effects

11. Related Resources

• Bolt Tensile and Shear Stress Area (Reference Library)
• How to Define Bolt Preload
• How to Check a Bolted Joint
• How to Determine Whether a Joint Will Separate
• How to Extract Bolt Loads from an FE Model
• Bolt Strength Calculator