When you tighten a bolt with torque, the thread root carries axial tensile stress from the preload and torsional stress from the thread torque at the same time. Change the preload, bolt size and friction to check in real time that the combined stress stays below the proof strength.
Parameters
Bolt size (ISO coarse)
Sets pitch, pitch diameter and stress area
Property class
Sets the proof strength σ_p
Preload F
kN
Thread friction μ_th
Dry steel ~0.14, lubricated ~0.10
Underhead friction μ_b
Friction under the bolt head / nut face
Target proof utilization
%
VDI 2230 guideline is 90%
Results
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Tensile stress σ (MPa)
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Torsional stress τ (MPa)
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Combined stress σ_red (MPa)
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Proof utilization (%)
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Tightening torque T_a (N·m)
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Allowable preload F_max (kN)
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Bolt stress state
During tightening the bolt carries axial tension (blue) and torsion (orange) at once. The right square is the stress element at the thread root. Colour shows the proof utilization (green = margin / red = over).
The von Mises equivalent stress. Tightening is OK when this stays within the target fraction of the proof strength σ_p. Tightening torque is T_a = T_th + μ_b·F·D_km/2 (D_km: effective bearing diameter).
What is the Bolt Thread Root Combined Stress Simulator?
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Isn't a bolt just "pulled" when you tighten it? What is torsional stress doing there?
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Good question. Picture tightening a bolt with a wrench. The turning effort builds preload by working against thread friction and the thread "ramp" (the lead). To overcome the thread friction, the bolt shaft itself gets twisted a little. So the moment you finish tightening, the bolt carries tension from the preload and torsion from part of the tightening torque at the same time. That is the combined stress.
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So checking only the tensile stress and saying "below proof, OK" is risky?
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Exactly. You might think you are at 90% in tension, but with the torsion added the combined stress can pass 100% and the bolt has already yielded. Raise "Thread friction μ_th" on the left — the torsional stress τ jumps up and the gap between the combined stress σ_red and the tensile stress σ widens. More friction means more torsion. That is why tightening control must always check the combined stress against the proof strength.
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In the torque breakdown chart the pitch part is only 10%. Is the rest just wasted?
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Not "wasted" so much as "lost to friction". Of the torque you put in, only the pitch part — about 10% — actually does the work of creating preload. About 40% goes to thread-flank friction and about 50% to underhead (below the head) friction as heat. This matters: if the friction coefficient scatters by 20%, the preload at the same torque scatters by 20-30%. That friction scatter is why a torque wrench does not give very accurate preload.
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If friction is unpredictable, is there a more accurate way to set preload?
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Yes. The "angle method" controls preload by the turn angle after the joint seats, and is more accurate than the torque method. The "yield-point tightening" method deliberately tightens close to yield to stabilise preload. Ultrasonic measurement of bolt elongation is another option. All of them cost time or equipment, so many shops still use the torque method — which is exactly why you check here that the combined stress keeps a margin to the proof strength even with friction scatter.
Frequently Asked Questions
When you tighten a bolt with the torque method, the turning effort works against thread friction and the thread lead to build up preload. The torque T_th needed to overcome the thread friction remains in the bolt shank as torsion. So immediately after tightening, the bolt carries axial tensile stress from the preload and torsional stress from the thread torque at the same time. This tool combines the two into an equivalent stress.
Find the axial tensile stress σ = F/A_s (A_s is the tensile stress area) and the torsional stress τ = T_th/W_p (W_p is the polar section modulus), then combine them with the von Mises equivalent stress σ_red = √(σ² + 3τ²). VDI 2230 keeps the tightening σ_red to about 90% of the proof strength σ_p. τ is often 25-35% of σ, so the combined stress is about 10-15% larger than the tensile stress alone.
Tightening torque T_a splits three ways: (1) the thread lead — the net work that creates preload, about 10%; (2) thread-flank friction, about 40%; (3) underhead (bolt head / nut face) friction, about 50%. So roughly 90% of the input torque is consumed by friction and only about 10% becomes preload. Because friction scatter feeds straight into preload scatter, the torque method has limited accuracy.
The torsional stress is largest just after tightening and partly relaxes over time; re-tightening or a small back-off can reduce it too. The design basis is to verify that the combined stress just after tightening does not exceed the proof strength. For fatigue under cyclic external load, the torsional part usually matters little, and the tensile stress amplitude from preload variation governs instead.
Real-World Applications
Basic verification of bolted joints: In engines, pressure vessels and structural connections that use bolts at high preload, it is essential to confirm that the thread root does not yield right after tightening. The combined stress from this tool compares directly with the VDI 2230 control limit of "up to about 90% of proof at tightening" and helps decide how high the preload can go.
Friction control and tightening-method choice: With the torque method, friction scatter becomes preload scatter. Sweep μ_th in this tool and you see how much the torsional and combined stresses move. If the proof margin is short once scatter is allowed for, consider a more accurate method such as the angle method or yield-point tightening.
Evaluating lubrication and surface treatment: At the same torque, lubrication or surface treatment that lowers friction raises the preload and lowers the torsional stress. Changing μ_th and μ_b here shows that lubrication delivers "more preload" and "less torsion" together. Over-lubrication, however, can push the preload high enough to yield the bolt, so the torque must be re-set.
Troubleshooting: When "the bolt broke / loosened even though it was tightened to spec", a wrong friction assumption is often the cause. Re-entering the actual friction coefficient in this tool separates the two cases: the combined stress had exceeded the proof strength (over-tightened) or the preload was too low (under-tightened).
Common Misconceptions and Pitfalls
The most common mistake is to check the proof strength with the tensile stress alone. The bolt also carries torsion just after tightening, so even when the tensile stress σ is at 90% of proof, the combined stress σ_red can be over 100%. σ_red = √(σ²+3τ²) is about 13% larger than σ even when τ is only 30% of σ. Always evaluate with the combined stress. This tool shows both side by side in the result cards.
Next, the assumption that tightening torque and preload are proportional, so all is well. The two are linked through the friction coefficient, and that friction easily varies by 20-30% with surface condition, lubrication, plating and repeated tightening. At the same torque the preload scatters widely, and in the worst case an excessive preload yields the thread root. The safe approach allows for the upper and lower friction bounds and checks the combined stress at the maximum-preload case.
Finally, forgetting the thread-root stress concentration. This tool works with the average stress over the effective section, while the actual thread-root notch creates a stress concentration (factor of about 3-5). For static, ductile materials local yielding redistributes the stress, so the average-stress evaluation is enough; but for fatigue under cyclic load this thread-root stress concentration becomes the failure origin. Fatigue must be assessed separately, accounting for the stress concentration and the difference between rolled and cut threads.