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Figure 1: A bolted joint works like a stiff spring. Tightening the nut stretches the bolt (tension) and compresses the parts (clamping force).
1. Bolt Selection for Required Clamping Force
The primary goal of a bolted joint is to provide a required clamping force (F) between mechanical components to prevent separation or sliding.
If a set of n bolts is used, and the total load is distributed equally, the required clamping load per bolt is:
P = F / n
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Defining Material Limits (Proof Strength)
Bolts are selected from standard grades (e.g., SAE J429 Grade 5 or 8, ASTM A325). Instead of designing to the yield strength, bolt design uses Proof Strength (σ).
Engineering Insight: Proof vs. Yield
Proof strength is slightly lower than yield strength. It is the maximum tensile stress a bolt can withstand without experiencing any permanent set. Designing to proof strength ensures the bolt remains entirely elastic during assembly.
Proof strength is slightly lower than yield strength. It is the maximum tensile stress a bolt can withstand without experiencing any permanent set. Designing to proof strength ensures the bolt remains entirely elastic during assembly.
We design the bolt to operate at a specific percentage, K%, of its proof strength. This parameter K is the demand factor (typically 75% to 90% for preload).
The allowable tensile stress (σa) and minimum required tensile stress area (At) are calculated as:
σa = K × Ïƒ
At = P / σa
Using standard thread tables, select a bolt size with a tensile stress area equal to or greater than the calculated At.
2. The Tightening Torque Requirement
We cannot easily measure clamping force directly on the assembly line. Instead, we measure the tightening torque applied to the nut and correlate it to the desired preload.
Figure 2: Torque is used as a proxy for preload. Accurate torque application is critical for joint integrity.
The short-form equation to estimate required torque is:
T = k1 × D × P
- T = Required tightening torque (in-lb or N-m)
- D = Nominal outside diameter of the thread (in or m)
- P = Desired clamping load per bolt (lb or N)
- k1 = Torque coefficient (Nut Factor)
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3. The Torque Coefficient (k₁) & Lubrication
The torque coefficient, k1, is the most critical and variable part of the equation. It represents friction in the threads and under the nut face. Nearly 90% of applied torque is lost to friction; only about 10% actually stretches the bolt.
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Figure 3: The condition of the threads drastically changes the required torque. Lubrication lowers friction, requiring less torque for the same preload.
Typical values for k1 generally accepted in industry:
- k1 ≈ 0.15 (Lubricated): For average commercial conditions where any lubrication is present, including residual cutting fluids or intentional anti-seize application.
- k1 ≈ 0.20 (Dry): For clean, dry, unlubricated steel threads.
⚠️ Critical Warning: The Danger of Lubrication
If a torque specification is calculated for a "Dry" condition (k=0.20), but the installer lubricates the bolt (k=0.15), applying the specified dry torque will result in significant over-tightening, potentially yielding or breaking the bolt.
If a torque specification is calculated for a "Dry" condition (k=0.20), but the installer lubricates the bolt (k=0.15), applying the specified dry torque will result in significant over-tightening, potentially yielding or breaking the bolt.
4. Advanced Considerations
This guide covers the fundamental mechanics of bolt selection. However, critical joint design requires analyzing several more complex failure modes:
- Thread Stripping: Ensuring the nut or tapped hole is strong enough to withstand the load without the threads shearing off.
- Fatigue Failure: Bolts subjected to cyclic loading (vibration) need careful fatigue analysis, not just static strength checks.
- Preload Relaxation: Over time, gaskets creep and threads settle, causing a loss of clamping force (embedding).
Related article: Overview of Bolts, Nuts, Screws, and Studs
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