# BOLT TORQUE CALCULATOR - TIGHTENING TORQUE, PRELOAD AND THREAD STRENGTH CALCULATIONS FOR BOLTS AND NUTS

Bolt torque calculator for the calculation of tightening torque and preload for bolts.

In bolted joints, clamping force is usually generated by applying torque to bolt head or nut. During the bolt tightening process, the length of the bolt increases and it behaves like an extension spring. Bolt tries to turn back to its original length and exerts a force on the joint. This force is called tension force or preload. Determination of tightening torque and preload requirements for bolts and nuts is important in joint design. Fastener suppliers often give information to determine torque requirements of bolts including torque coefficient, bolt material properties and other effects.

Development of the bolt torque calculator has been done by using the theory given in the Machinery’s Handbook. Some of the key features of the calculator are summarized as follows:

- Valid for Unified inch screws threads in the size range from ¼ in to 1 ½ in and covers standard series of UNC, UNF and UNEF

- Material database for steel bolts and screws is available in the calculator. In case user wants to define different strength properties for the bolt, there is an option to not use the calculator’s database. Database is prepared by using the steel bolt properties given in the Machinery’s Handbook.

- Material database consists of ASTM and SAE steels with different grades.

- Calculates estimated required bolt tightening torque, minimum length of engagement to prevent stripping of threads and dimensional properties of bolts and nuts such as shear area of external and internal thread and tensile stress area of bolt.

Formulas used in the bolt torque calculator are given in the "List of Equations" section.

### Bolt Torque Calculator:

Note: 1 Information about this condition is needed for the calculations of thread stripping. If nut is being used as an internal thread, it's preferred to select a nut with a grade equal to or greater than the grade of the bolt being used. [Ref-2]

Note: 2 This value is required if internal thread strength < external thread strength. Otherwise not needed.

Note: 3 Recommended values: 75 % for nonpermanent connections and reused fasteners. 90 % for permanent connections.

Note: 4 Use values given by your fastener supplier and manufacturer. If these values are not available from the supplier, then see the "Supplements" section for the chart of torque factors K.

 RESULTS Parameter Value Nominal Size --- --- Threads per inch [n] --- Series Designation --- REQUIRED DIMENSIONS FOR CALCULATIONS Basic Major Diameter [d] --- in Min. Major Diameter of External Thread [dmin]1 --- Min. Pitch Diameter of External Thread [d2min]1 --- Max Minor Diameter of Internal Thread [D1max]1 --- Max Pitch Diameter of Internal Thread [D2max]1 --- Thread Tensile Stress Area [At] --- in^2 Shear Area of External Thread (Bolt) [As] --- Shear Area of Internal Thread [An] --- TORQUE & PRELOAD RESULTS Calculated Preload [Fi]2 --- lbf Estimated Required Torque [T] --- lbf*in lbf*ft Min. Length of Engagement to Prevent Stripping (including design factor ns) [Le (or Q)] --- in

Note: 1 Tolerance class 2A is used for external threads (bolts) and class 2B is used for internal threads (nuts)

Note: 2 Preload value is a calculated nominal value. Due to the different factors such as surface finish, presence of lubrication and bolt preload application method, it's possible to experience variations in this value. See the "Supplements" section for approximate accuracy of bolt preload methods.

### Definitions:

Bolt Elongation Measurements with Micrometer: A technique to control preload by measuring elongation with a micrometer. If there is an access to the head and the end of the bolt, bolt elongation can be measured by using micrometers or dial indicators. By using the elongation value of the bolt and bolt material properties, the bolt preload can be calculated.

Major Diameter: The maximum diameter of a thread which is diameter of the crest of a male thread or root of a female thread.

Minor Diameter: The minimum diameter of a thread which is diameter of the root of a male thread or crest of a female thread.

Proof load: The maximum load (force) that a bolt can withstand without acquiring a permanent set.

Torque Wrench: Torque wrench is a tool to tighten bolts, screws and nuts with a specific torque value. During tightening of a fastener with a torque wrench, torque value is measured and used as an indicator of preload of a fastener tension. Tightening fasteners with torque wrench is generally less accurate with respect to bolt tension (or elongation) measurement due to the uncertainty of the friction in threads and mating surfaces but more practical to use. There are different type of torque wrenches such as slipper type, click type, beam type, electronic and programmable type, hydraulic type and pneumatic type.

Ultrasonic Bolt Measurement: According to data given in the Machinery’s Handbook, one of the most accurate tightening techniques is controlling bolt elongation with ultrasonic elongation. Ultrasonic bolt measurement is done by sending sonic wave from the one end of the bolt and measuring the time of the wave to travel forth and back through the bolt. By using material properties of the bolt and travel time of the wave, the elongation and preload of the bolt can be accurately calculated.

Unified Screw Thread: A thread form used by the United Kingdom, Canada, and the United States to obtain screw thread interchangeability among these three nations. It has 60° thread angle and dimensions are stated in inch units.

UNC (Unified National Coarse): Most commonly used type for general engineering applications. This thread form is used in materials with low tensile strength which makes threads more resistance against stripping (internal threads) .UNC give possibility for quick assembly.

UNF (Unified National Fine): External threads of this Fine Series have greater tensile stress area than comparable sizes of the coarse series. The Fine series is suitable when the resistance to stripping of both external and mating internal threads equals or exceeds the tensile load carrying capacity of the externally threaded member. It is also used where the length of engagement is short, where a smaller lead angle is desired, where the wall thickness demands a fine pitch, or where finer adjustment is needed.

UNEF (Unified National Extra Fine): Used when finer pitches than UNF are needed (Ex: Short engagement length).

### Supplements:

 Link Usage Bolt Torque Factors and Bolt Tension Measurements Supplementary tables about torque factors and preload application accuracies in bolt tightening. Steel Bolt Grades and Bolt Markings Supplementary tables about the material properties of bolts. These tables are also being stored in calculator database.

### List of Equations:

 Parameter Symbol Equation Preload Fi $${ F }_{ i }=PPS\cdot { A }_{ t }{ S }_{ p }$$ Torque T $$T=K\cdot { F }_{ i }\cdot d$$ Tensile Stress Area of Screw Thread At $${ A }_{ t }=0.7854{ (D-\frac { 0.9743 }{ n } ) }^{ 2 }$$ Length of engagement to prevent stripping (including design factor) 1 Le $${ L }_{ e }=\frac { 2\cdot { A }_{ t }{ n }_{ s } }{ 3.1416{ \cdot D }_{ 1max }\cdot [0.5+0.57735\cdot n\cdot ({ d }_{ 2min }-{ D }_{ 1max })] }$$ Shear areas of the external threads As $${ A }_{ s }=3.1416\cdot n\cdot { L }_{ e }\cdot { D }_{ 1max }[\frac { 1 }{ 2n } +0.57735({ d }_{ 2min }-{ D }_{ 1max })]$$ Shear areas of the internal threads An $${ A }_{ n }=3.1416\cdot n\cdot { L }_{ e }\cdot { d }_{ min }[\frac { 1 }{ 2n } +0.57735({ d }_{ min }-{ D }_{ 2max })]$$ Relative strength of the external and internal threads 2 J $$J=\frac { { A }_{ s }\times { S }_{ ut\quad ext } }{ { A }_{ n }\times { S }_{ ut\quad int } }$$ Required length of engagement to prevent stripping of the internal thread Q $$Q=J\cdot { L }_{ e }$$

Note: 1 If the external thread is manufactured by a material having equal or larger tensile strength than the internal thread.

Note: 2 If J is less than or equal to 1,use Le to prevent stripping. If J is greater than 1, use Q value.

 List of Parameters Symbol Definition PPS Percent of Proof Strength Sp Proof Strength n Threads per inch ns Design factor against stripping

### Reference:

• ASME B1.1-2003, Unified Inch Screw Threads (UN and UNR Thread Form)
• Oberg, E. , Jones ,F.D. , Horton H.L. , Ryffel H.H., (2016) . Machinery's Handbook . 30th edition.  Industrial Press Inc.
• Oberg, E. , Jones ,F.D. , Horton H.L. , Ryffel H.H., (2012) . Machinery's Handbook . 29th edition.  Industrial Press Inc. , pp 1521 - 1537
• Budynas.R , Nisbett.K. (2008) . Shigley's Mechanical Engineering Design . 8th edition.  McGraw-Hill
• Barrett T.R. (1990), NASA - RP - 1228, Fastener Design Manual
• Bickford J. , Nassar.S. (1998), Handbook of Bolts and Bolted Joints, Marcel Dekker Inc.