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# Tensile Stress Area vs. Root Area Of A Threaded Fastener

The effective cross-sectional area of the threaded rod that resists rod fracture is the tensile stress area. It has been observed during the testing of threaded rod that an unthreaded rod, having a diameter equal to the mean of the pitch diameter and the minor diameter has the same tensile strength as the threaded rod. This cross-sectional area called the tensile stress area is used for the purposes of calculating the tensile strength of the rod.

## Tensile Stress Area

For metric series, the tensile stress area (for steel) = (PI/4)*(D-0.938194P)2

For inch series, the tensile stress area (for steel) = (PI/4)*[D-(0.9743/n)]2

where D = nominal diameter, P = thread pitch, n = threads per inch, PI = 3.1416

## Root Area

Don’t be confused with Root area – a more conservative stress area that is still widely used such as in ASME B31.1 code. Root area is based on the root or minor diameter of the threads, and therefore its stress area is smaller than the tensile stress area. Root area is not based on experimental data. It is designed to introduce a factor of safety in thread strength calculations. The designer pruposely assumes a “root” stress area smaller than the “real” tensile stress area to be sure that the rod isn’t overstressed in service.

For metric series, the root area = (PI/4)*(D-1.3P)2

For inch series, the root area = (PI/4)*[D-(1.3/n)]2