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Calculate bolt preload and clamping force from applied torque using the torque-tension relationship. Determine clamping force, bolt stress, and safety factors for bolted joints.
Select surface condition to estimate friction coefficient
Where T = torque, k = nut factor (approx. μ + 0.05), d = bolt diameter, F = preload force
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Clamp force (or clamping force) is the force exerted by a bolt on the joint members it holds together. When a bolt is tightened, it creates tension (preload) in the bolt itself, which generates an equal and opposite clamping force on the joined parts.
The clamp force keeps the joint together and resists separation under external loads. Proper clamp force is critical for:
Key Relationship
Torque applied to a bolt creates tension in the bolt, which manifests as clamp force on the joint:
The fundamental relationship between applied torque and bolt tension is expressed by the torque-tension formula:
Where the nut factor (k) accounts for:
Given:
• Bolt diameter: 1/2 inch
• Applied torque: 100 lb-ft
• Friction (dry): μ = 0.15
• k = 0.15 + 0.05 = 0.20
Solution:
T = k × d × F
1200 = 0.20 × 0.5 × F
F = 12,000 lbs preload
The friction coefficient (μ) varies based on bolt and surface conditions. Use these typical values:
| Surface Condition | Friction Coefficient (μ) | Nut Factor (k) | Notes |
|---|---|---|---|
| Dry (unlubricated) | 0.15 | 0.20 | Steel on steel, as received |
| Lubricated (oiled) | 0.12 | 0.17 | With light machine oil |
| Anti-seize coated | 0.18 | 0.23 | High-temperature applications |
| Plated (cadmium/zinc) | 0.13 | 0.18 | Factory plated bolts |
Important: Friction varies with material, surface finish, temperature, and lubrication. These values are typical averages. For critical applications, test with your specific materials.
Common bolt grades with their strength properties:
| Grade | Yield Strength | Tensile Strength | Common Uses |
|---|---|---|---|
| Grade 2 | 57 ksi | 74 ksi | General purpose, light loads |
| Grade 5 | 85 ksi | 120 ksi | Most common, automotive, machinery |
| Grade 8 | 130 ksi | 150 ksi | High-strength, critical applications |
| Metric 4.6 | 58 ksi | 87 ksi | General purpose metric |
| Metric 5.8 | 87 ksi | 145 ksi | Common metric applications |
| Metric 8.8 | 116 ksi | 173 ksi | High-strength metric |
Preload is the tension created in the bolt itself when tightened. Clamp force is the pressing force this tension exerts on the joint members. In a simple joint, they are approximately equal in magnitude but opposite in direction.
Friction under the bolt head and in the threads accounts for about 50-70% of applied torque. The same torque applied to different surfaces (dry vs. lubricated) results in very different preloads. A 10% change in friction can cause a 15-20% change in preload.
Safety factor is the ratio of bolt yield strength to actual bolt stress. A factor of 2.0 means the bolt could withstand double the current stress before yielding. Most applications target 1.5-2.0 for static loads and 2.0-3.0 for dynamic loads.
Use adequate clamp force (maintain safety factor), use lock washers or thread-locking compound, and consider nylon-insert lock nuts. Loose clamp force is the primary cause of vibration loosening. Maintain 70-80% of yield strength as preload.
No. Different materials and grades have different yield strengths. The same torque applied to Grade 2 and Grade 8 bolts will produce different stress levels. Always check bolt specifications and use the correct torque for the grade and condition.
Torque and preload are approximately proportional: T = k × d × F. The proportionality constant (k) depends primarily on friction. Higher friction means more torque is lost to friction (less efficient), so you get less preload per unit torque applied.
Higher temperatures can reduce clamp force due to thermal expansion and stress relaxation. Cold temperatures increase friction, requiring more torque for the same preload. Always apply torque at the expected operating temperature when possible.
This calculator provides estimates using the standard torque-tension formula. Actual results vary based on bolt geometry, material variation, and surface conditions. For critical applications, perform physical testing or consult engineering specifications. Consider a 15-20% margin of error.