Bolt Torquing Basics: Preload, K-Factor, Torque Formula & Calculation
What is Bolt Torquing?
Bolt torquing is the process of applying a controlled rotational force to a bolt or nut to generate axial tension—known as preload—which clamps components together in flanged joints, pressure vessels, and structural assemblies. Achieving the correct preload is essential for maintaining leak-free, vibration-resistant connections in piping systems and other critical applications.
In bolted flange joints, standards like ASME PCC-1 and EN 1591 provide guidance to achieve the correct bolt preload (axial tension) without overstressing the fastener. According to PCC-1, the target bolt stress typically ranges from 40% to 70% of the bolt’s yield strength. EN 1591 uses a more detailed calculation based on flange design, gasket type, and operating conditions rather than a fixed percentage.
Common Bolt Torquing Methods
Bolts can be tightened using different methods depending on the required accuracy and application. Torque control is the most common method, but it is sensitive to friction variations. The turn-of-nut method improves consistency by rotating the nut a specified angle after snug tightening. Hydraulic tensioning provides high precision by directly stretching the bolt. For critical applications, techniques like ultrasonic elongation measurement or strain gauges verify preload.
Proper bolt sequence (star or cross pattern) and lubrication—affecting the K-Factor—are essential for uniform gasket compression and reliable joint integrity. Always follow manufacturer guidelines and engineering standards for safe bolted assemblies.
| Tightening Method | Description | Advantages | Limitations/Notes |
|---|---|---|---|
| Torque Control | Bolt tightened to a specified torque value | Simple, widely used | Sensitive to friction; torque may not equal preload |
| Turn-of-Nut Method | Nut rotated a specified angle after initial snug-tightening | More consistent preload | Requires careful angle measurement |
| Hydraulic Tensioning | Bolt elongated directly using hydraulic tools | High precision, independent of friction | Expensive equipment, slower process |
| Ultrasonic / Strain Gauge | Preload verified using ultrasonic elongation or strain measurement | Very accurate for critical applications | Specialized equipment needed |
Bolt Torque Formula
The relationship between applied torque and the resulting preload can be estimated using the following formula:
T = (K × D × F) / 12
Where:
- T = Applied torque (in ft-lb)
- K = Nut factor or K-Factor (dimensionless)
- D = Bolt diameter (in inches)
- F = Desired preload or clamping force (in pounds)
Notes:
- This formula provides an estimate and assumes standard conditions. For critical bolted joints, always verify preload through direct measurement (e.g., bolt elongation or ultrasonic methods).
- The preload (F) should not be confused with the bolt’s yield strength. Always select preload as a percentage (e.g., 40–70%) of the yield strength for optimal results.
Understanding the K-Factor in Bolt Torquing
The K-Factor (also known as the Nut Factor) defines the efficiency with which applied torque translates into axial clamping force in a bolted joint. It accounts for friction between mating surfaces and thread interfaces and is critical for accurate preload estimation.
In most engineering applications, the K-Factor typically ranges between 0.1 and 0.25:
A K-Factor > 0.25 may result in insufficient clamping force, risking joint loosening or leakage.
A K-Factor < 0.1 may produce excessive preload, potentially overstretching or damaging the bolt.
Maintaining the K-Factor within the optimal range ensures balanced load distribution, minimizes bolt fatigue, and prevents premature joint failure under operational loads like vibration or thermal cycling.
K-Factor vs Nut Factor vs Friction Factor
Although often used interchangeably, the K-Factor and Nut Factor refer to the same concept—how torque converts to clamping force. However, they differ from:
- Coefficient of Friction: Directly measures surface friction.
- Friction Factor: A more general term used in some torque-preload models.
Only the K-Factor (or nut factor) is commonly used in the standard torque equation described below.
Why Is K-Factor So Important?
An accurate K-Factor allows engineers to:
- Predict preload more reliably from applied torque
- Minimize variability caused by thread surface roughness, lubrication, or plating
- Ensure gasket integrity and joint tightness in piping and pressure systems
Factors influencing the K-Factor:
- Thread condition and pitch
- Lubrication type (e.g., anti-seize, light oil)
- Bolt coating or finish
- Reuse of bolts or nuts
- Washer type and surface finish
- Operating temperature
How to Determine the K-Factor Experimentally
There is no universal ISO or ASTM standard for K-Factor testing, but the following procedure is commonly used:
- Predict the target torque value for a given fastener.
- Install the bolt into a calibrated load cell (or measure elongation with an ultrasonic device).
- Apply lubrication to reduce unpredictable friction.
- Tighten using a calibrated torque wrench.
- Measure the resulting clamping force (preload).
Difference Between Recommended Torque and Preload per Bolt
Understanding the difference between recommended torque and preload per bolt is essential for ensuring safe, leak-proof, and reliable bolted flange connections. While they are closely related, they represent two distinct engineering parameters:
| Aspect | Recommended Torque | Preload per Bolt |
|---|---|---|
| Definition | Twisting force applied to bolt head or nut (Nm or lb-ft) | Axial clamping force generated in bolt shank (kN or lbf) |
| Purpose | Achieves proper rotational tightness to indirectly generate preload | Creates compressive force holding joint components together |
| Key Formula | T = K × d × Fₚ (Torque = friction factor × diameter × preload) | Fₚ = Aₛ × σₙ × Preload % (Preload = stress area × yield strength × preload %) |
| Units | Nm (metric) or lb-ft (imperial) | kN (metric) or lbf (imperial) |
| Depends On | Bolt diameter, lubrication (K-factor), thread friction | Bolt material grade, stress area, preload percentage |
| Engineering Goal | Prevent under/over-tightening to avoid leaks or bolt failure | Ensure joint withstands operational loads like pressure and vibration |
Sample Bolt Torquing Calculation
Given Data:
- Flange Size: 4″ Class 300 RF (Raised Face)
- Bolt Material: ASTM A193 B7 (High-Tensile Steel)
- Number of Bolts (N): 8
- Bolt Diameter (D): ¾ inch
- Bolt Stress Area (A): 0.302 in² (from ASME B1.1)
- Target Bolt Stress (σ): 25 ksi (typical for B7 bolts)
- Coefficient of Friction (μ): 0.15 (lubricated threads)
- Washer Factor (K): 0.2 (typical for lubricated bolts)
Step 1: Calculate Bolt Load (F)
The required bolt load is determined by:
F = σ x A
F = 25,000 psi × 0.302 sq.in × = 7,550 lbf per bolt
Step 2: Total Required Bolt Load (Fₜₒₜ)
F(tot) = F × N = 7,550 × 8 = 60,400 lbf
Step 3: Calculate Torque (T):
The torque required per bolt is given by:
T = K × D × F
T = 0.2 × 0.75 × 7,550 = 1,132.5 lb-in
Convert to lb-ft (divide by 12):
T = 1,132.5/12 = 94.4 lb-ft
Step:4 Final Torque Value:
Each bolt should be torqued to ~95 lb-ft (rounded for practicality).
Additional Considerations:
1. Lubrication: If using moly-based lubricant, K may drop to 0.12–0.15, reducing torque.
2. Flange Gasket Type: Soft gaskets may require multiple passes (snug, 50%, 100%).
3. ASME PCC-1: Follow recommended sequence (cross pattern).
4. Bolt Stress Limits: Ensure bolt stress does not exceed 50 ksi for A193 B7.