Bolt Preload & Torque: How VDI 2230 Models a Bolted Joint

What VDI 2230 is

VDI 2230 is the German engineering guideline for the systematic calculation of highly stressed bolted joints. It's the reference most mechanical engineers cite when they need to defend a preload or torque number rather than just picking a value off a chart. Its central idea is that a bolted joint is a spring system: the bolt stretches, the clamped members compress, and the two share any external load in proportion to their stiffnesses.

The cone of compression

The hard part of a bolted joint is figuring out how stiff the clamped members are — the bolt is easy, but the plates don't compress uniformly. VDI 2230's model is the "cone of compression" (or frustum method): the clamping force spreads out from each bearing face into the material as a cone with roughly a 30° half-angle, so a truncated-cone (frustum) of material actually carries the load rather than the whole plate.

The common textbook realization (Shigley's Mechanical Engineering Design) chains these frustums: a two-cone model for a standard nut-and-bolt joint, or a single cone for a tapped or threaded-insert joint. Each frustum's stiffness depends on its material, its thickness, and the bearing diameter it starts from. That member stiffness, combined with the bolt's own stiffness, is what tells you how much of an external load actually shows up as extra bolt tension versus being absorbed by relieving the clamp — the whole reason a preloaded joint survives fatigue.

Torque and preload: T = K · F · d

You can't measure preload directly with a torque wrench — you measure torque and inferpreload. The relationship is captured by the nut factor equation:

T = K · F · d

where T is the tightening torque, F is the resulting preload, d is the nominal bolt diameter, and K is the "nut factor" — a lumped coefficient rolling up thread friction, under-head bearing friction, and thread geometry. For a typical lightly-lubricated steel joint (µ ≈ 0.15 on both thread and bearing), K works out to around 0.2, which is the value most torque tables implicitly assume.

The critical, non-obvious consequence: K is dominated by friction, not by the bolt. Lubricate a joint and the same torque produces substantially more preload — a torque spec written for a dry joint will badly overtighten a lubricated one. This is the single most common way bolted joints get preload wrong.

Where the simplified method applies

• The two-cone / single-cone model is an excellent general-purpose estimate, and matches full analysis well for ordinary stacks.
• On stacks with many plates of sharply different diameters, VDI 2230's own full multi-segment method can diverge from the simplified cones — treat the simple model as a screening tool there.
• Property-class strengths (ISO 898-1 / SAE J429), prevailing-torque nut values, and tightening-method scatter factors are representative values, not a substitute for your fastener supplier's certified data.