Bolt Preload

A bolt is a spring you tighten on purpose

The instinct that a bolt "holds two parts together" is half right. What actually holds the parts together is the clamp force — the compression squeezed into the members — and that clamp force comes from the bolt being stretched. Tightening the nut draws the bolt out a few hundredths of a millimetre; the bolt, behaving as a long stiff spring, pulls back with a force called the preload F_i. The members push back equally, and the joint settles into a self-balanced state of bolt-in-tension, members-in-compression, with no external load present at all.

That stored tension is the whole game. A correctly preloaded joint behaves as a single rigid lump: external loads are mostly absorbed by changes in the clamp force rather than passed straight into the bolt. A loosely preloaded joint behaves like a hinge with a loose pin — every load cycle rattles straight through the bolt, and it fatigues, fretts and backs off.

The torque-tension relationship

Because you cannot see tension, almost all field tightening sets preload indirectly through torque. The workhorse relationship is the short-form torque equation:

T = K · d · F_i

where:
  T   = tightening torque        (N·m)
  K   = nut factor / torque coeff. (dimensionless, ~0.20 dry steel)
  d   = nominal bolt diameter     (m)
  F_i = preload (clamp tension)   (N)

K bundles up the thread geometry and — dominantly — friction. A fuller derivation splits it into three terms: torque to climb the thread helix, torque to overcome thread friction, and torque to overcome friction under the rotating nut/head bearing face:

T = F_i · [ p/(2π) + (μ_t·r_t)/cos(β) + μ_n·r_n ]
     \____helix___/  \___thread friction__/  \_bearing_/

  p   = thread pitch        r_t = mean thread radius
  μ_t = thread friction     β   = half thread angle (30° for ISO)
  μ_n = bearing friction    r_n = mean bearing radius

The unsettling consequence: of the total tightening torque, only about 10–15% does the useful work of stretching the bolt. Roughly 40% is lost in thread friction and 50% under the nut face. That is why a tiny change in lubrication — a dry galvanized bolt versus the same bolt with a smear of anti-seize — can swing the achieved preload by a factor of two for the same torque wrench setting.

Worked example: torque for an M12 8.8 bolt

Suppose we want to preload an M12 grade 8.8 bolt to 75% of its proof load. The proof strength of an 8.8 bolt is 580 MPa and the tensile stress area of an M12 thread is A_s = 84.3 mm². How much torque do we set, dry?

Proof load  F_p = σ_proof · A_s
                = 580e6 Pa × 84.3e-6 m²
                = 48,900 N  ≈ 48.9 kN

Target preload F_i = 0.75 × F_p
                   = 0.75 × 48.9 kN
                   = 36.7 kN

Torque  T = K · d · F_i
          = 0.20 × 0.012 m × 36,700 N
          = 88 N·m

So roughly 88 N·m on a torque wrench. Lubricate the threads (K ≈ 0.13) and the same 88 N·m would now produce about 56 kN — well past proof, into yield. The number on the wrench is meaningless without knowing the friction condition it was calibrated for.

The bolted-joint diagram: sharing the load

Once the joint is preloaded, an external tensile load P does not all go into the bolt. The bolt (stiffness k_b) and the clamped members (stiffness k_m) sit in parallel, so they share the new load in proportion to their stiffness. The fraction the bolt takes is the joint stiffness constant:

C = k_b / (k_b + k_m)            (joint stiffness ratio)

Bolt tension under load:   F_b = F_i + C·P
Clamp force under load:    F_m = F_i − (1 − C)·P

Members are short and fat (high k_m); bolts are long and thin (low k_b). Typical metal-to-metal joints land at C = 0.15 to 0.25, meaning the bolt feels only 15–25% of any added load — the rest simply unloads the clamp. This is the single most important and least intuitive fact about bolted joints: adding load to a preloaded bolt barely increases its tension.

The danger is the other side. As P grows, clamp force F_m falls. When F_m reaches zero the joint separates, and beyond that the bolt suddenly carries the entire load (C effectively jumps to 1). The separation load is:

P_sep = F_i / (1 − C)

Design rule: keep the maximum service load below P_sep with margin, so the clamp never fully relaxes. A gasketed joint that separates leaks; a structural joint that separates slips into bearing and may shear its bolts.

Methods of setting preload, ranked by accuracy

Method	What it controls	Typical scatter on F_i	Cost / use
Feel / impact wrench, no spec	Nothing reliable	±35% or worse	Free; non-critical only
Torque control	Applied torque	±25–35%	Cheap, ubiquitous; friction-sensitive
Torque + angle (turn-of-the-nut)	Torque then rotation past snug	±15%	Engine, structural; partly bypasses friction
Torque-to-yield (TTY)	Stretch into yield plateau	±8–10%	Head/rod bolts; usually single-use
Bolt stretch / micrometer length	Measured elongation ΔL	±5%	Large flanges; needs both ends accessible
Ultrasonic / strain-gauge bolt	Direct tension measurement	±1–3%	Critical joints; instrumented, expensive

Notice the pattern: every step up in accuracy moves closer to measuring the thing you actually care about — tension or stretch — and further from the friction-corrupted proxy of torque. Stretch is gold because Hooke's law ties it directly to force: ΔL = F_i·L_grip / (A·E), so a measured elongation of, say, 0.10 mm over a 50 mm grip on a steel bolt of area 84 mm² maps straight to a preload (F_i = ΔL·A·E/L_grip ≈ 0.10e-3 × 84e-6 × 200e9 / 50e-3 ≈ 33.6 kN) with no friction guesswork.

Preload and fatigue: the counterintuitive part

Fatigue cracks grow under alternating stress, not steady stress. In a preloaded joint subjected to a fluctuating external load swinging from 0 to P, the bolt's stress only swings by C·P/A_s — a small fraction of what an unpreloaded bolt would see. Raise the preload and (within the elastic range) you do not raise the cyclic amplitude at all; you only raise the steady mean. That is why aerospace and engine bolts are deliberately preloaded high: a high mean stress with a tiny alternating component sits in a benign corner of the Goodman/Haigh diagram.

Concretely, for a connecting-rod bolt seeing a 20 kN peak inertial load each revolution: unpreloaded it would cycle over a 0→20 kN range (stress amplitude ≈ 10 kN); preloaded with C = 0.2 the bolt tension swings by only 0.2 × 20 = 4 kN (amplitude ≈ 2 kN) about a high mean — a 5× smaller stress amplitude, which on a steel S-N curve can mean a 10–50× longer fatigue life. The most common cause of bolt fatigue failure is not too much load — it is too little preload.

Self-loosening: the Junker mechanism

The other way a joint dies is by backing off. Counterintuitively, the dominant cause is not vibration shaking the nut "unscrewed," but transverse slip. Gerhard Junker showed in 1969 that when sideways motion makes the thread and bearing surfaces slip relative to each other, the friction that normally locks the nut is momentarily cancelled, and the bolt's own helix torque ratchets the nut loose a fraction of a turn each cycle. Once preload starts dropping, slip gets easier, and the loss accelerates.

• Keep preload high. A joint kept above its slip threshold never enters the Junker regime — high preload is the first and best locking feature.
• Reduce embedment. Fresh surfaces bed in and lose 2–10% of preload in the first hours; re-torque after settling, or use hardened washers under the turning element.
• Add a secondary lock only as backup. Prevailing-torque (nylon-insert) nuts, thread adhesives (anaerobic threadlockers), and wedge-locking ramp washers resist rotation; spring and split washers are largely ineffective against transverse slip.

Failure modes and trade-offs

• Under-preload. Joint slips, leaks, frets, and the bolt fatigues under the full alternating load. By far the most common real-world failure — and usually a tightening-process problem, not a bolt-strength problem.
• Over-preload past yield. The shank necks down; combined with the residual torsional stress from tightening, equivalent stress can exceed 100% of proof and the bolt strips or snaps during installation, or fails early in service.
• Embedment relaxation. Rough or soft mating surfaces, paint, or gaskets compress over time, bleeding off preload. Designers either re-torque, avoid soft elements in the grip, or use longer (more compliant) bolts so a given embedment loss is a smaller fraction of stretch.
• Hydrogen embrittlement. High-strength bolts (grade 10.9/12.9, ≥ 1000 MPa) electroplated or used in corrosive service can crack delayed under sustained preload. Mitigate with baking after plating or mechanical zinc coatings.
• Stress relaxation / creep at temperature. Hot flanges (steam, exhaust) lose preload as the bolt creeps; use creep-resistant alloys and re-tension during commissioning.
• The compliance trade-off. A longer, thinner bolt lowers C (good for fatigue and embedment tolerance) but stores the same energy over more stretch, so it needs a finer tightening method to hit target accurately. Stiff short bolts are easy to torque but unforgiving of any preload loss.

Bolt grade comparison (ISO metric, coarse thread)

Property	Grade 8.8	Grade 10.9	Grade 12.9
Proof strength	580 MPa	830 MPa	970 MPa
Tensile strength (UTS)	800 MPa	1040 MPa	1220 MPa
M12 proof load (A_s = 84.3 mm²)	~48.9 kN	~70 kN	~82 kN
Typical target preload (75%)	~36.7 kN	~52 kN	~61 kN
M12 dry torque ≈ K·d·F_i (K=0.2)	~88 N·m	~125 N·m	~147 N·m
Hydrogen-embrittlement risk	Low	Moderate	High
Typical use	General structural, machinery	Engines, suspension, flanges	High-duty engine, tooling