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Tensile Stress Area of a Bolt

When you select Calculated tensile stress area (Connector-Bolt PropertyManager), the program calculates the tensile stress area (At), which is the mimimum area of the threaded section of the bolt, according to the formula: At = [(d3 + d2) / 2)]2 * π /4

  • P = pitch, axial distance between two adjacent threads
  • n = 1 / P, number of bolt threads per inch (ANSI) or millimeter (ISO)
  • d = nominal bolt shank diameter
ISO Bolt threads
  • d3 = d - 1.2268 * P
  • d2 = d - 0.6495 * P
The formula for the tensile stress area becomes: At = 0.7854 * [d - (0.9382 * P)]2

Substituting P = 1 / n results to At = 0.7854 * [d - (0.9382 / n)]2, where d is given in mm, and n is given in threads/mm.

ANSI threads

A similar approach is followed for the calculation of the tensile stress area:

At = 0.7854 * [d - (0.9743 / n)]2, where d is given in inches, and n is given in threads/inch.

Reference: Machinery's Handbook published by Industrial Press.

The table below provides the nominal bolt diameter and pitch values for the main ISO M large thread bolts.
Table 1. ISO M Metric Bolt Threads, ISO 724 (DIN 13 T1)
Nominal Diameter d (mm) Pitch P (mm)
M 1.60 0.35
M 2.00 0.40
M 2.20 0.45
M 3.00 0.50
M 4.00 0.70
M 4.50 0.75
M 5.00 0.80
M 6.00 1.00
M 8.00 1.25
M 10.00 1.50
M 12.00 1.75
M 16.00 2.00
M 20.00 2.50
M 24.00 3.00
M 30.00 3.50
M 36.00 4.00
M 42.00 4.50
M 48.00 5.00
M 56.00 5.50
M 64.00 6.00

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