Bolt Fatigue Under Alternating Load Calculator

The alternating stress a preloaded bolt actually sees — Φ times the external load range, not the range itself — against VDI 2230’s endurance amplitude and Shigley’s endurance strength through Goodman, with the counter-intuitive result shown rather than asserted: raising preload usually improves fatigue life, because it stops the joint separating.

Last updated 24 Sep 2026

Bolt fatigue

Preload, Φ and load cycle → margin and range

Thread sizeVDI 2230’s endurance amplitude falls with diameter as 0.85(150/d + 45), so a big bolt has a lower allowable amplitude than a small one — a size effect, and a real one.

Property class or gradeNote how little the class buys in fatigue. Shigley’s endurance strengths rise only 47% from class 8.8 to 12.9 while the tensile strength rises 53% and the PERMISSIBLE amplitude rises less still, because the higher preload raises the mean stress.

Preload, % of the proof stressThe input to watch. Raising it does NOT raise the alternating stress while the joint stays closed, and it raises the load at which the joint separates — which is why higher preload usually improves fatigue life.

Load factor Φ of the jointFrom the joint stiffness page. 0.15 to 0.25 for a steel joint; much higher with a soft member or a gasket, and a high Φ is bad here — the bolt feels more of the load range.

External load on the joint, minimum (N)Per bolt. Zero for a load that comes and goes completely, which is the worst case for a given peak.

External load on the joint, maximum (N)Per bolt, at the peak of the cycle. If this exceeds the separation load the amplitude jumps by roughly 1/Φ and the page says so loudly.

How the thread was madeA rolled thread has compressive residual stress and favourable grain flow at the root. Cambridge’s DANotes give the fatigue stress-concentration factor as 2.2 rolled against 2.8 cut below class 5.8, and 3.0 against 3.8 at 8.8 and above — both ratios 1.27, which is the check that the pairs were read off the right rows.

Not a circuit: the bolt's load, on one axis in per cent of its proof load, for the SAME external load cycle at two different preloads. The shaded block is the range the bolt's tension actually swings through; its height is twice the alternating stress and its middle is the mean stress. The left-hand column is a low reference preload of 30 per cent of proof, and the right-hand one is the preload you chose. The point of the picture is that the right-hand block is usually SHORTER as well as higher. Raising the preload lifts the mean, which every fatigue diagram says is bad, and it shortens the block, which is what actually decides whether the bolt survives. The mechanism is separation: at low preload the joint opens at the top of the cycle and the bolt takes the whole external load, so the block stretches down to near the preload itself; once the preload is high enough to keep the joint closed the bolt only ever feels Φ of the load range, and the block collapses to that. The line near the top is the proof load, which neither block should cross.

23.6kNExample

M10 class 8.8 preloaded to 75% of proof in a steel joint with Φ = 0.24, carrying an external load that cycles between 0 and 30 kN per bolt, thread rolled before heat treatment

One expression carries the whole result

F_bolt = max(F_i + ΦF_A, F_A) · σ_a = (F_bolt,max − F_bolt,min)/(2A_s) · σ_m = (F_bolt,max + F_bolt,min)/(2A_s) · σ_ASV = 0.85(150/d + 45) · σ_ASG = σ_ASV(2 − F_Sm/F_0.2min) · σ_a,allow = S_e(1 − σ_m/R_m) [Goodman]

max(·,·): the whole of the separation behaviour. While the joint is closed the bolt carries F_i + ΦF_A; once it has opened it carries F_A. The larger is always the right one, so no separation test is needed and the corner comes out of the arithmetic
Φ: load factor, from the joint stiffness page. It scales the amplitude directly — halve Φ and you halve the alternating stress, which is why a soft member is a fatigue problem
σ_a: alternating stress amplitude at the thread root, nominal. Both published limits on this page are nominal-stress limits with the stress concentration already inside them, so K_f is not applied again
σ_ASV: VDI 2230’s endurance amplitude for a thread rolled before heat treatment. Note it depends only on the diameter — not on the property class, which is deliberate and is one of the more surprising things in the guideline
σ_ASG: … and for a thread rolled after heat treatment, where the benefit is a decreasing function of the mean load
S_e: Shigley’s fully corrected endurance strength for a rolled thread: 129 N/mm² for class 8.8, 140 for 9.8, 162 for 10.9, 190 for 12.9. A zero-mean limit, so it needs the Goodman step
F_0.2min: the load at the minimum 0.2% proof strength, A_s · R_p0.2

Worked example

M10 class 8.8 preloaded to 75% of proof in a steel joint with Φ = 0.24, carrying an external load that cycles between 0 and 30 kN per bolt, thread rolled before heat treatment
Preload = 0.75 × 57.99 × 580 = 25.23 kN, and separation is at F_i/(1 − 0.24) = 33.19 kN
At the top of the cycle: F_i + ΦF_A = 25.23 kN + 0.24 × 30 kN = 32.43 kN, against F_A = 30 kN. The larger is 32.43 kN, so the joint is still closed — just
At the bottom the external load is zero, so the bolt is at its preload, 25.23 kN
σ_a = (32,425 − 25,225)/(2 × 57.99) = 62.08 N/mm², and σ_m = 497 N/mm². Note what σ_a is NOT: the 30 kN external range over the area, which would be 259 N/mm². The joint divided it
VDI 2230: σ_ASV = 0.85(150/10 + 45) = 51.0 N/mm². Shigley: S_e = 129 N/mm² for a class 8.8, and Goodman at σ_m = 497 gives 129(1 − 497/800) = 48.8 N/mm². Two published methods, 4% apart
Safety factor = 48.8/62.08 = 0.79. VDI recommend at least 1.2 on this check and many houses use 1.5, so this joint is marginal and would not pass a 1.5 requirement
NOW DROP THE PRELOAD TO 40% and watch what happens. Separation falls to 17.7 kN, the 30 kN peak is well past it, and the bolt now carries the whole 30 kN at the top of the cycle against 13.45 kN at the bottom. σ_a becomes 142.7 N/mm² — 2.3 times worse — and the bolt fails. LOWERING the preload destroyed it. That is the result, and it is why a loose bolt in a vibrating joint breaks and a tight one does not

The counter-intuitive result, tabulated: one fixed load cycle, rising preload

An M10 class 8.8 with Φ = 0.24, carrying an external load that cycles from zero to 30 kN. Read down the alternating-stress column: at 10% preload it is 247 N/mm² and the bolt has no chance; at 75% it is 62 and the bolt survives. The mean stress has gone UP and the bolt is better off, which is the result that makes people stare. The mechanism is in the fourth column. Below about 65% of proof the joint separates at the top of the cycle, and once it has separated the bolt carries the whole 30 kN with nothing sharing it; above that it stays closed and the bolt only ever feels Φ × 30 kN = 7.2 kN of range. The floor the blue column falls to is Φ·ΔF/2A_s, and once you are on it more preload does nothing for the amplitude — it only eats the Goodman allowable by raising the mean. That is where the optimum is, and it is well above half of proof. This is a first-pass calculation on an idealised part — uniform section, static load, no stress raisers beyond those stated, and room-temperature material properties. Real parts have fillets, keyways, surface finish and duty cycles that a closed-form answer cannot see.
Preload (% of proof)	Preload (kN)	Separation load (kN)	Separated at 30 kN?	σ_a (N/mm²)	σ_m (N/mm²)	VDI limit	Goodman limit	Safety factor
10	3.4	4.4	yes	229.7	288	51.0	82.6	0.22
20	6.7	8.9	yes	200.7	317	51.0	77.9	0.25
30	10.1	13.3	yes	171.7	346	51.0	73.3	0.30
40	13.5	17.7	yes	142.7	375	51.0	68.6	0.36
50	16.8	22.1	yes	113.7	404	51.0	63.9	0.45
60	20.2	26.6	yes	84.7	433	51.0	59.2	0.60
70	23.5	31.0	no	62.1	468	51.0	53.5	0.82
75	25.2	33.2	no	62.1	497	51.0	48.8	0.79
80	26.9	35.4	no	62.1	526	51.0	44.2	0.71
90	30.3	39.8	no	62.1	584	51.0	34.8	0.56

Two published methods, and why they look so different until you account for the mean stress

Shigley’s Table 8-17 gives a class 8.8 bolt an endurance strength of 129 N/mm² and VDI 2230’s formula gives an M10 an endurance amplitude of 51. They look irreconcilable and they are not: Shigley’s figure is a zero-mean endurance limit that you then take through a Goodman line at the actual mean stress, and VDI’s is already the amplitude at a preloaded bolt’s high mean stress. Do the Goodman step and the two land within a few per cent at most sizes, as the last column shows. Note also what the VDI formula says about size: 0.85(150/d + 45) falls from about 70 N/mm² at M4 to 42 at M36, so a big bolt has a LOWER allowable amplitude than a small one. That is a real size effect — more material, more chance of the critical defect — and it is why a fatigue problem is rarely solved by going up one size. The same designation can mean different dimensions in different standards families — ANSI against ISO, inch against metric, one national standard against another. The family used here is named beside every figure; check which one your part was made to.
Size	VDI 2230 σ_ASV (N/mm²)	Shigley Se, class 8.8 (N/mm²)	… through Goodman at the mean stress below	σ_m at 75% preload (N/mm²)	Goodman ÷ VDI
M4	70.1	129	55.5	456	0.79
M5	63.8	129	55.5	456	0.87
M6	59.5	129	55.5	456	0.93
M8	54.2	129	55.5	456	1.02
M10	51.0	129	55.5	456	1.09
M12	48.9	129	55.5	456	1.14
M14	47.4	129	55.5	456	1.17
M16	46.2	129	55.5	456	1.20
M18	45.3	129	55.7	472	1.23
M20	44.6	129	55.7	472	1.25
M22	44.0	129	55.7	472	1.26
M24	43.6	129	55.7	472	1.28
M27	43.0	129	55.7	472	1.30
M30	42.5	129	55.7	472	1.31
M36	41.8	129	55.7	472	1.33

Rolled, rolled-after-heat-treatment, and cut

The two published K_f pairs give exactly the same ratio — 2.8/2.2 = 1.273 and 3.8/3.0 = 1.267 — which is the check that they were read off the right rows, and it is the 21% knock-down this page applies to a cut thread. The middle row is the one with a catch worth understanding. Rolling after heat treatment is the standard trick for a fatigue-critical bolt and it genuinely works, but VDI 2230’s own model makes its benefit a decreasing function of mean load, so it and high preload are partly competing strategies. Where the load range is large relative to the preload, take the preload; where the preload is already near yield, the rolled-after bolt has little left to give. This is a first-pass calculation on an idealised part — uniform section, static load, no stress raisers beyond those stated, and room-temperature material properties. Real parts have fillets, keyways, surface finish and duty cycles that a closed-form answer cannot see.
Thread	K_f, class 5.8 and below	K_f, class 8.8 and up	Effect on the endurance amplitude	Why
Rolled before heat treatment	2.2	3.0	the baseline	Cold forming the root gives favourable grain flow and work hardening. The commercial standard, and what VDI 2230’s 0.85(150/d + 45) assumes.
Rolled after heat treatment	—	—	higher at low mean load, falling to the baseline as the mean rises	The rolling leaves compressive residual stress at the root that the heat treatment cannot relieve, and compressive residual stress is what resists a fatigue crack opening. VDI 2230 models it as σ_ASV(2 − F_Sm/F_0.2min), so the advantage is consumed by mean load — a bolt preloaded to 90% of yield gets almost none of it.
Cut or ground	2.8	3.8	reduced by 21%	A cut root severs the grain and leaves tensile residual stress and tool marks. Cambridge’s DANotes put it plainly: “a rolled thread is less prone than a cut thread to fatigue damage, due to better grain orientation and surface work hardening conferred by manufacture”.

Where a bolt actually cracks, and the load the threads share

The engaged-thread load shares are measured figures, not a model: Croccolo and colleagues in *Mechanics & Industry* report about 38 / 24 / 15 / 11 per cent on the first four threads of a preloaded M10 × 1 with a standard nut, following Sopwith’s 1948 analysis. Two practical consequences. A nut designed to even out that distribution — a tapered first thread, a compressed or a differential-pitch nut — buys real fatigue life, which is why such nuts exist. And anything that adds bending to the bolt loads the first engaged thread on one side much harder than the average, which is why a non-perpendicular bearing face is a fatigue problem and not just an assembly one. This is a first-pass calculation on an idealised part — uniform section, static load, no stress raisers beyond those stated, and room-temperature material properties. Real parts have fillets, keyways, surface finish and duty cycles that a closed-form answer cannot see.
Location	Share of failures	What raises the stress there
The first thread engaged in the nut, on the loaded side	the majority	It carries about 38% of the axial load on its own, against 24% for the second and 15% for the third, and it sits at a sharp root with a stress concentration factor of 3.0 for a rolled class 8.8 thread. Croccolo and colleagues state the consequence directly: failure “generally takes place in the first thread turn in contact between the bolt and nut”.
The thread runout, where the thread meets the shank	common on partially threaded bolts	A geometric discontinuity with no load sharing to relieve it. It matters when the runout lies inside the grip or at a member interface rather than clear of the joint.
Under the head, at the head-to-shank fillet	less common but characteristic	A stress concentration of 2.1 to 2.3, lower than the thread root’s, but the whole load passes through it. A generous fillet radius and a hardened washer that keeps the bearing pressure uniform are the mitigations.

Why tightening a bolt harder makes it last longer

A preloaded bolt in a fluctuating load does not see the fluctuation. It sees Φ times it, where Φ is the load factor from the joint stiffness page — typically 0.2 for a steel joint. So the alternating stress amplitude is Φ·ΔF/2A_s, about a fifth of what an unclamped bolt would suffer. That is the first thing worth saying, and it is why bolted joints under vibration work at all.

The second thing is the one that makes people stare: raising the preload usually makes the fatigue life longer, not shorter. It raises the mean stress, which every fatigue diagram says is bad, and it still wins. The reason is that Φ only applies while the joint is closed. Once the external load exceeds F_i/(1 − Φ) the members have no compression left, the bolt carries the entire external load, and the amplitude jumps by roughly 1/Φ — a factor of four or five. Raising preload pushes the separation point above the peak load and cuts the amplitude to its floor. On this page’s default M10 joint, dropping the preload from 75% of proof to 40% multiplies the alternating stress by about four and turns a bolt that survives into one that does not. The whole behaviour comes out of one expression, F_bolt = max(F_i + ΦF_A, F_A), with no separation test written anywhere.

Two published methods, and they reconcile. VDI 2230 gives the endurance amplitude at the thread root directly as 0.85(150/d + 45) N/mm² for a thread rolled before heat treatment — 51 N/mm² for an M10, and notably independent of the property class. Shigley’s Table 8-17 gives fully corrected endurance strengths of 129, 140, 162 and 190 N/mm² for classes 8.8, 9.8, 10.9 and 12.9. Those look irreconcilable until you notice that Shigley’s is a zero-mean limit that has to go through a Goodman line at the actual mean stress. Do that at 75% preload and it gives 49 N/mm² against VDI’s 51. This page computes both, reports both, and takes the lower.

Where the bolt cracks, and why the first thread matters. The first engaged thread on the loaded side carries about 38% of the axial load on its own — 24% on the second, 15% on the third, 11% on the fourth, per Croccolo and colleagues following Sopwith’s 1948 analysis — and it sits at a root with a fatigue stress concentration factor of 3.0 for a rolled class 8.8 thread. That is why most bolt fatigue failures are there, why a nut that evens out the thread load buys real life, and why anything that bends the bolt loads one side of that thread much harder than the average. A cut thread costs about a fifth of the endurance amplitude: the published K_f values are 3.0 rolled against 3.8 cut above class 8.8, and 2.2 against 2.8 below, whose ratios agree at 1.27.

What this calculation leaves out. Constant amplitude, concentric loading, no bending, no slip between the members, nominal stresses, room temperature, and the nominal preload rather than the band you will actually achieve — a fatigue check should really be made at the BOTTOM of the preload band, where separation is closest, and the preload accuracy by tightening method calculator says how low that is. VDI 2230’s own R-sequence handles eccentric loading, and for anything with a real load spectrum this is a screening calculation and not a life prediction.

Frequently asked questions

Does higher preload improve or worsen bolt fatigue life?

Usually it improves it, which surprises people because higher preload means higher mean stress. Two things are happening. While the joint stays closed, the alternating stress is Φ·ΔF/2A_s and does not depend on the preload at all. And raising the preload raises the separation load, which keeps the joint closed — and separation is what really hurts, because past it the bolt carries the whole external load and the amplitude jumps by about 1/Φ. So the curve of alternating stress against preload falls steeply and then goes flat, and the optimum is well above half of proof load. The chart on this page plots it.

Why do rolled threads last longer than cut ones?

Cold rolling the thread form leaves compressive residual stress at the root and aligns the grain flow around it rather than cutting through it, and it work-hardens the surface. A cut root severs the grain, leaves tensile residual stress and carries tool marks. Cambridge’s DANotes quantify it through the fatigue stress-concentration factor: 2.2 rolled against 2.8 cut for class 5.8 and below, 3.0 against 3.8 for 8.8 and above — both ratios 1.27, so a cut thread loses about 21% of its endurance amplitude. Rolling AFTER heat treatment is better still, but VDI 2230 models that benefit as shrinking with mean load, so it and hard preloading partly compete.

What alternating stress can a class 8.8 bolt take?

About 51 N/mm² of amplitude for an M10, by VDI 2230’s 0.85(150/d + 45), and that figure does not depend on the property class — which is one of the more surprising things in the guideline and a useful corrective to the instinct that a 12.9 bolt solves a fatigue problem. It does depend on diameter, falling from about 70 N/mm² at M4 to 42 at M36. Shigley’s route gets to a similar number: 129 N/mm² zero-mean for a class 8.8, which through Goodman at a 75%-preload mean stress comes to about 49.

Where do bolts usually break in fatigue?

At the first thread engaged in the nut, on the loaded side. That thread carries about 38% of the axial load on its own and sits at a sharp root; Croccolo and colleagues state that failure “generally takes place in the first thread turn in contact between the bolt and nut”. The other two sites are the thread runout where the thread meets the shank, which matters on a partially threaded bolt when the runout lies inside the grip, and the head-to-shank fillet, whose stress concentration is lower at 2.1 to 2.3 but which carries the whole load.

Should I use Goodman or the VDI method?

Use both, which is what this page does, and take the lower. They are not alternatives so much as the same physics entered at different points: VDI 2230 gives you the permissible amplitude for a preloaded bolt directly, and Shigley gives you a zero-mean endurance strength that you then take through a Goodman (or Gerber, or ASME-elliptic) line at the actual mean stress. Mosedal’s comparison of Shigley, Juvinall and Spotts on the same M10 joint gets endurance limits of 129, 373 and 387 N/mm² for it — a factor of three — precisely because the three define the limit at different places in the Haigh plane. The number alone means nothing without the method.

Does a bigger bolt fix a fatigue problem?

Less than you would hope. The stress area grows, which cuts the amplitude, but VDI 2230’s permissible amplitude FALLS with diameter — 0.85(150/d + 45), so from 51 N/mm² at M10 to 46 at M16 to 42 at M36 — and a bigger bolt is also a stiffer bolt, which raises Φ and gives it a larger share of the external load. Going from one M10 to two M8s often beats going from one M10 to one M14, because it cuts the load per bolt and keeps Φ low. The changes that help most are usually not to the bolt: lower Φ, higher preload up to the point where separation stops governing, and a better thread.

Related calculators

References

VDI 2230 Blatt 1, Systematic calculation of highly stressed bolted joints — Joints with one cylindrical bolt. Cited by clause and table; the guideline is copyrighted and was not reproduced. The tightening-torque terms used here are its own form, M_A = F_M[0.16 P + 0.58 d₂ μ_G + 0.5 D_Km μ_K], where the 0.58 is 0.5/cos 30° written out. Table A8 gives the tightening factor α_A; clause R12 gives the endurance limit; clause R4 gives the embedding amount f_Z.
R. G. Budynas and J. K. Nisbett, Shigley’s Mechanical Engineering Design, chapter 8. Cited for the frustum member-stiffness model, the stiffness constant C = k_b/(k_b + k_m) with the note that “a good design target is around 0.2”, and Table 8-17’s fully corrected endurance strengths for rolled threads. The one Table 8-17 value this batch could confirm from a second document is 129 N/mm² for an M10 class 8.8, which A. Mosedal’s Three textbook analyses of fatigue in the bolted tension joint reproduces with K_f = 3.0.
A. Mosedal, Three textbook analyses of fatigue in the bolted tension joint (Texas Tech). Sets Shigley’s, Juvinall’s and Spotts’ treatments of the same M10 × 1.5 class 8.8 joint side by side and gets endurance limits of 129, 373 and 387 N/mm² for it — because the three define the limit at different points in the Haigh plane. It is the source for the alternating and mean stress forms used here, σ_a = ΦP/2Aₛ and σ_m = Fᵢ/Aₛ + σ_a.
University of Cambridge DANotes, Threaded fasteners: Bolt fatigue. Source for the fatigue stress-concentration factors — rolled thread 2.2 and cut thread 2.8 for class 5.8 and below, rolled 3.0 and cut 3.8 for class 8.8 and above — and for the statement that “a rolled thread is less prone than a cut thread to fatigue damage, due to better grain orientation and surface work hardening conferred by manufacture”. The two ratios are identical, 2.8/2.2 = 3.8/3.0 = 1.273, which is the check that the pairs were read off the right rows.
D. Croccolo, M. De Agostinis, S. Fini, G. Olmi et al., Achieving uniform thread load distribution in bolted joints using different pitch values, Mechanics & Industry 21 (2020) 607. Source for the load share of the engaged threads of a preloaded M10 × 1 bolt with a standard uniform-pitch nut: about 38% on the first thread, 24% on the second, 15% on the third and 11% on the fourth. It states that “in a preloaded bolt the first threads in contact withstand most of the axial load, and consequently the failure generally takes place in the first thread turn in contact between the bolt and nut”, and cites D. G. Sopwith, The Distribution of Load in Screw Threads, Proc. I.Mech.E. 159 (1948) 373, as the classical analytical model.
ISO 898-1:2013, Mechanical properties of fasteners made of carbon steel and alloy steel — Part 1: Bolts, screws and studs with specified property classes. Cited by clause; the standard is copyrighted and was not fetched. Clause 9.1.6.1 defines the nominal stress area as the circle on the mean of the pitch diameter d₂ and the minor diameter d₃ of the basic profile, which is where the 0.938194 on this page comes from — it is derived here from d₂ = d − 0.649519 P and d₃ = d − 1.226870 P, not copied. Table 3 carries the property classes.
Kova Fasteners. ISO 898 Part 1 – 2013 (Extract). The source for the minimum tensile strength R_m, the minimum yield or 0.2% proof strength, and the stress under proof load S_p for every property class used here. It also carries the note that for classes 4.8, 5.8 and 6.8 “the values for R_pf min are under investigation” — which is why the second digit of those three designations is a label and not a property.
Sandia National Laboratories, SAND2008-0371, Guideline for Bolted Joint Design and Analysis: Version 1.0, as reproduced by the Engineering Library. Source for the target preload rule, attributed there to Machinery’s Handbook: “use 75% of the proof strength … for removable fasteners and 90% of the proof strength for permanent fasteners”; for the torque-wrench accuracies by lubrication state (unlubricated ±35%, cadmium plated ±30%, lubricated ±25%); and for Shigley’s frustum form of the member stiffness with the statement that the cone half-angle “should be between 25 and 33 degrees and in general recommends 30 degrees”.