About this calculator
Fatigue — not static overload — is the dominant failure mode of bolts in dynamically loaded machinery. This calculator sizes a metric screw joint for infinite fatigue life (more than 106 load cycles): it estimates the endurance strength of the threaded fastener, converts it into the largest bolt load fluctuation the thread can sustain forever, and then derives the allowable preload window — the minimum preload needed to keep the joint clamped and the maximum preload that still leaves room for the fluctuation below yield.
A bolt’s fatigue capacity is startlingly small compared with its static strength: a class 8.8 bolt rated at 800 MPa statically survives only roughly 40–60 MPa of alternating stress at the thread. Joint design therefore lives or dies by how little of the external load fluctuation actually reaches the bolt.
Theory and equations
The endurance strength (stress amplitude) of rolled-thread steel bolts is estimated with a size-dependent empirical relation — smaller bolts tolerate more alternating stress than larger ones:
The largest admissible bolt force fluctuation follows from the amplitude definition, using the stress cross-section at the mean thread diameter dm = (d2 + d3)/2:
With the joint stiffness factor Cm the clamped-part fluctuation and the total external working load are:
Finally the preload window. The lower bound guarantees the required minimum clamping force Fm survives the load cycle; the upper bound keeps the bolt below yield at peak load:
Any preload between the two bounds gives a joint that neither loses clamping nor yields, while the bolt’s alternating stress stays at the endurance limit or below. If Fi,min > Fi,max, no valid preload exists and the joint must be redesigned.
Worked example: M16, class 8.8
Inputs: M16 coarse, class 8.8, required minimum clamping force Fm = 30 kN, stiffness factor Cm = 0.25.
- Endurance strength: σe = 0.75 × (180/16 + 52) = 47.4 MPa.
- Stress area at dm: At = 156.67 mm²; load at yield F0.2 = 640 × 156.67 = 100.3 kN.
- Max bolt fluctuation: Pb = 2 × 156.67 × 47.4 = 14.9 kN.
- Clamped-part fluctuation: Pm = 14.9 × 0.75/0.25 = 44.6 kN; total admissible working load P = 59.5 kN.
- Preload window: Fi,min = 30 + 44.6 = 74.6 kN; Fi,max = 100.3 − 14.9 = 85.4 kN.
Result: tighten this joint to a preload between 74.6 and 85.4 kN (roughly 74–85% of yield) and it will carry a 59.5 kN load fluctuation indefinitely while maintaining 30 kN of clamping force. The corresponding assembly torque follows from the tightening torque calculator.
Assumptions and limitations
- The endurance formula is an empirical estimate for rolled steel threads; threads cut after heat treatment or corroded surfaces have lower limits. VDI 2230 or supplier data take precedence for critical joints.
- Pure axial fluctuation; bending of the bolt (prying, non-flat surfaces) adds alternating stress not covered here.
- Load introduction at head and nut planes; loads introduced deeper in the stack reduce the bolt share.
- Embedding losses are not deducted from the preload window — specify assembly preload near the upper bound to allow for relaxation.
Frequently asked questions
Why do bolts fail in fatigue at the first engaged thread?
The first engaged thread transfers roughly a third of the load and its root is a sharp notch (stress concentration factor 3–5). About 65% of bolt fatigue failures start there; the head fillet and thread run-out account for most of the rest.
Why is bolt fatigue strength so much lower than static strength?
Thread notch effect, surface condition, and high mean stress reduce an 800 MPa static capacity to a 40–60 MPa alternating-stress capacity. That is why design aims to keep the fluctuation reaching the bolt small, rather than relying on bolt strength.
Why does higher preload improve fatigue life?
Preload keeps the interface closed so the fluctuation keeps splitting between bolt and clamped parts. If the joint separates at peak load, the bolt suddenly carries 100% of the variation instead of ~25% — usually a fast route to failure.
What if Fi,min comes out larger than Fi,max?
No feasible preload exists. Use a larger bolt or higher strength class, lower Cm (stiffer clamped parts or a more elastic bolt), or reduce the working load per bolt — e.g. more bolts in the pattern.