Related Resources: Design and Engineering General

Threaded Fastener Design and Analysis

Machine Design Applications, Equations and Calculators
Structural Deflection Equations and Stress
Fastener, Bolt and Screw Design Torque and Force Calculations

Engineering Fundamentals of Threaded Fastener Design and Analysis
Ralph S. Shoberg, P.E.,

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Open: Engineering Fundamentals of Threaded Fastener Design and Analysis

The process of tightening threaded fastener assemblies, especially for critical bolted joints, involves controlling both input torque and angle of turn to achieve the desired result of proper preload of the bolted assembly. Understanding the role of friction in both the underhead and threaded contact zones is the key to defining the relationship between torque, angle, and tension.

There can be as many as 200 or more factors that affect the tension created in a bolt when tightening torque is applied (refer to paragraph 2.2). Fortunately, torque-angle signature curves can be obtained for most bolted joints.

By combining the torque-angle curves with a few simple calculations and a basic understanding of the engineering mechanics of threaded fasteners, you can obtain the practical information needed to evaluate the characteristics of individual fastener tightening processes. The torque-angle curves can also provide the necessary information to properly qualify the capability of tightening tools to properly tighten a given fastener.


Introduction: Engineering Fundamentals of the Tightening Process
Energy Transfer
Modeling the Tightening Process
Where Does the Torque Go?
Elastic Torque-Tension Relationship
Stress/Strain vs. Torque/Tension
Correlation of Stress-Strain and Turn.7
Force-Deformation and Torque-Angle Diagrams 8
Preload-Preload Efficiency Factor
Torque-Tension Correlation Coefficient
Thread/Underhead Friction Measurements
Automated Tightening Process
Torque-Angle-Tension Control
Torque-Angle Signature Analysis
Tightening Curve
Elastic Origin
Loosening Curve
Beyond Yield
Loosening Tendencies
Accurate Measurement
Torque-Angle Signature Analysis Summary
Clamp Force/Strength Considerations
Modeling the Tightening Process
Torque-Tension Coefficient: Nut Factor, K
Experimental Determination of Friction Coefficients8
Thread/Underhead Friction Coefficient Measurements
M-Alpha Diagram
FM-Alpha Diagram
Estimating the Tension-Angle Coefficient
Ultrasonic Stretch
Strain-Gaged Bolt
Force Washer
Model-Calculation: Estimate of Angle-Tension Coefficient
Laboratory Measurement of Friction Coefficients
Material Property-Yield
Torque-Angle Tension Control Summary
Torque-Tension Audits
Hand Torque Audit-Tool Torque Capability
Tool Torque Capability/ISO 5393
Release Angle-Tension Audit
Loosening-Embedment or Loss of Preload
Measurements Verify Fastener Torque and Tension
Other Strategies
Prevailing Torque Locknut Signature Analysis 4.3
Hand Torque Tightness Quality Audits
Redefining The Audit
Hand Torque Audit Qualification
Using Torque Angle Records to Determine Joint Stiffness
Material Yield Point
Glossary of Important Terms 8.0