Preloaded bolted joints under an axial load: bolt and member stiffness, load factor, bolt force and remaining clamp force, separation, margin to proof load, fatigue (Goodman), slip under a transverse load, preload scatter and embedding loss, with the joint diagram. Metric bolts M6 – M24, classes 8.8, 10.9 and 12.9.
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Scatter: torque wrench ±20 – 25 %, angle-controlled ±10 %. Embedding: about 3 – 5 µm per interface for machined faces (VDI 2230 table values are higher for rough faces); 0 = ignore.
The bolt is a spring in tension, the clamped parts a stiffer spring in compression. An external load first unloads the members; only the fraction C of it reaches the bolt, until the parts separate. Then the bolt carries all of it.
ISO 898-1 strengths: 8.8 Sp 580 / Rm 800 MPa up to M16, 600 / 830 MPa above; 10.9 830 / 1040; 12.9 970 / 1220 MPa. Tensile stress areas per ISO 898-1. Method after Shigley's Mechanical Engineering Design, chapter 8 (fatigue limits table 8-17). It is a simplified concentric model, not a VDI 2230 calculation: no load-introduction factor (the external load is assumed to act under the head and nut, which is conservative for the bolt), no eccentric loading or prying, no thermal loads, no thread stripping or bearing pressure checks. Head and nut compliance are neglected (grip-only stiffness).
This calculator analyses a preloaded bolted joint loaded along the bolt axis, the way machine designers check flanges, covers, bearing caps and brackets. Choose the thread (M6 – M24), property class, clamped material, grip, bolt length and preload, and enter the external load per bolt. It returns the bolt and member stiffness, the joint constant C (the share of the load the bolt sees), the bolt force and remaining clamp force, the load at which the joint separates, the margin to the proof load, a Goodman fatigue factor for a load cycling from zero, the tightening torque estimate and, with a transverse load, the slip safety. Preload scatter and embedding loss show how much the real clamp force can fall short.
The joint stays closed up to 31.6 kN, three times the working load, and the bolt is safe in fatigue (2.92). Only a fifth of the external load reaches the bolt – the reason a well-preloaded bolt survives loads that would break it if it were loose.
Tightening stretches the bolt and squeezes the clamped parts. An external load first relieves the squeeze on the parts, so the bolt force rises only by the fraction C = kb/(kb + km) of the load. Clamped parts are usually several times stiffer than the bolt, so C is often 0.1 – 0.4.
Once the external load exceeds Fi/(1 − C), the clamped surfaces open. From then on the bolt carries the whole load, the joint can leak or move, and the bolt sees much larger stress changes, so fatigue life drops sharply. Designs keep a separation margin of 1.5 – 2 or more for dynamic loads.
Typically 70 – 75 % of the proof load for reusable joints and up to 90 % for permanent ones. More preload keeps the joint closed and improves fatigue life, but leaves less margin for the external load and for tightening scatter.
Not very: with a torque wrench the achieved preload typically scatters ±20 – 25 % because most of the torque is lost in thread and head friction. Angle-controlled or yield-controlled tightening, or direct tension indicators, reduce the scatter. Enter the scatter to see the minimum clamp force and maximum bolt force.
After tightening, the surface roughness peaks under the head, nut and between the plates flatten, so the joint shortens by a few micrometres and part of the preload is lost. The loss is fZ times the series stiffness kb·km/(kb + km). Short, stiff joints lose the most.
No. It is the simplified concentric method from Shigley's Mechanical Engineering Design, chapter 8, with preload scatter, embedding and a slip check added. VDI 2230 adds load-introduction factors, eccentric loading, thermal effects, thread stripping and bearing pressure; use it for safety-critical joints.
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