Bolted joint
Torque coefficient from friction. Load sharing, bearing pressure, and margins against slip and shear.
Find the preload from the tightening torque, and check bolt stress, residual clamp force, bearing pressure under the head and the margin against shear — all in one place.
The torque coefficient K is not a fixed number here; it is calculated from the friction at the thread and under the head. Most of the tightening torque is spent on friction, so the same torque produces a very different preload once the lubrication changes.
Up to three clamped parts can be stacked, each with its own material, and they are treated as spring elements. That makes the way an axial external load divides between the bolt and the parts — the load factor — visible in the joint diagram. For external shear, the margin against slip at the faying surface and the margin against bolt shear are evaluated separately.
1st part (bolt head side)
2nd part
3rd part (nut side; 0 = not used)
Enter the external load carried by one bolt.
| Torque coefficient K (from μ) | – |
|---|---|
| Pitch diameter d2 | –mm |
| Tensile stress area As | –mm² |
| Bolt axial stress σb (after load) | –MPa |
| Proof stress Rp0.2 | –MPa |
| Margin to yield (safety factor) | – |
| Grip length Lg (total thickness) | –mm |
|---|---|
| Bolt stiffness Kb | –N/mm |
| Parts stiffness Kc (in series) | –N/mm |
| Equivalent area of the parts Ac | –mm² |
| Load factor φ = Kb/(Kb+Kc) | – |
| Taken by the bolt φ·We | –N |
| Taken by the parts (1−φ)·We | –N |
| External load at separation | –N |
| Bearing contact area Aw | –mm² |
|---|---|
| Allowable bearing pressure (lower of head / nut side) | –MPa |
| Bearing pressure utilisation | –% |
| Force transmissible by friction μs·Fc·n | –N |
| Safety factor against slip | – |
| Bolt shear stress τ | –MPa |
| Shear yield τy = Rp0.2/√3 | –MPa |
| Safety factor against shear | – |
Axial direction
Shear direction
Is the torque coefficient K the same as the friction coefficient?
No, they are different things. K is not a friction coefficient; it is a dimensionless coefficient that gathers up how efficiently tightening torque turns into preload. It combines three things.
1. The lead of the thread (the work of climbing the incline, needed even with zero friction). 2. Friction at the thread, μth. 3. Friction under the head, μw.
This tool computes K = [ p/(2π) + μth·d2/(2cos30°) + μw·Dw/2 ] / d. Most of the tightening torque is in fact consumed by friction; only something like 10 to 20 per cent becomes preload. That is why the preload changes so much with the friction condition, at the same torque.
The often-quoted K = 0.2 corresponds roughly to a dry condition with μth = μw = 0.15. Note that lubricating lowers K, so the same torque gives more preload — which means over-tightening.
How to read the joint diagram
The horizontal axis is deflection, the vertical axis is force. The line rising to the right from the origin is the bolt (it extends; slope Kb). The line that appears to rise to the right from the far side is the clamped parts (they compress; slope Kc, read from the right edge leftwards). The height at which the two meet is the initial preload Ff.
Apply an axial external load We and the meeting point moves to the right. The force in the bolt rises by φ·We and the force in the parts falls by (1−φ)·We. The diagram shows directly that the whole external load does not go into the bolt. The stiffer the parts (the larger Kc), the smaller φ becomes and the easier the bolt has it.
Where the line for the parts reaches zero is separation. Beyond that point the entire external load falls on the bolt, the slope changes abruptly, and it heads for failure quickly.
How shear is treated (slip and bolt shear)
When a bolted joint carries shear, the correct design is one in which the bolt does not carry shear at all. The preload presses the parts together and the friction between them transmits the shear (a friction connection). The force that can be transmitted is μs · Fc · n, where n is the number of faying surfaces and Fc is the residual clamp force after the axial external load has been applied.
Once slip occurs, the bolt bears against the edge of the hole, and only then does the bolt itself carry shear (a bearing connection). That state is outside the design intent, so treat the bolt shear calculation as a check on the last line of defence. Shear yield is evaluated as τy = Rp0.2/√3 (von Mises).
If the shear plane falls on the threads, the tensile stress area is used; on the shank, the area of the nominal diameter. As a rule, avoid designs that put the threads in the shear plane.
This is a simplified calculation intended for first-pass sizing. Stress concentration, buckling, fatigue, welds, dynamic loading and temperature effects are not included. Yield, proof and allowable stress figures are representative guide values and are not guaranteed to match the standards themselves. Always carry out your own verification before building and manufacturing real hardware. We accept no liability for loss arising from the results of this tool.
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