# BOLT TORQUE CALCULATION FORMULA

Formulas to calculate preload and torque of a bolt, tensile stress area of screw thread, length of engagement to prevent stripping and shear area of the internal/external threads.

 Parameter 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) (Le) 1 $${ L }_{ e }=\frac { 2\cdot { A }_{ t }{ n }_{ s } }{ 3.1416{ \cdot D }_{ 1max }\cdot [0.5+0.57735\cdot n\cdot ({ d }_{ 2min }-{ D }_{ 1max })] }$$ 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 (J) 2 $$J=\frac { { A }_{ s }\times { S }_{ ut\quad ext } }{ { A }_{ n }\times { S }_{ ut\quad int } }$$ 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.

Parameters: 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.