Since bolts and nuts stretch slightly under load, the distribution of stress on the threads is not uniform. Theoretically, the first thread takes a third of the load, the first three threads take three-quarters of the load, and the first six threads take nearly the whole load. The percentage of total load carried by engaged full threads is roughly:
1st = 34%, 2nd = 57%, 3rd = 73%, 4th = 84%, 5th = 93%, 6th = 100%.
The exception to this is when softer nut material (or internal threads in aluminum, for example) are involved. Relaxation of the first threads under high loading distributes the load more uniformly among the remaining engaged threads. Nuts with National Coarse threads typically have 5 threads in them, whereas nuts with National Fine threads have about 8 threads.
Thread and Bolt Stress Area tables show thread-stripping areas in square inches (or mm) for a length of thread engagement equal to one nominal diameter of the bolt (the common length for thick or heavy hex nuts). A regular hex nut has a thread length equal to 0.875 times the nominal diameter of the bolt.
The tensile stress areas may be calculated with the following formulas: As = 0.7854*(D – (0.9743/n)^2, where D = the nominal inch diameter & n is the number of threads/inch.
As = 0.7854*(D – .938p)^2, where D = the nominal metric diameter and p is the pitch length in mm.
(Super-conservatively, use the minimum root diameter of the fastener for the tensile stress area, using A = 0.7854*D^2)
Axial or strip-out shear strengths are approximately 60% of the minimum tensile strength of steel fasteners (55% for stainless steel). This is the mode of failure generated by over-tightening a bolt until the bolt or nut threads strip.
Rule of Thumb: The nut’s proof load should approximately equal the ultimate tensile strength of the bolt. If absolute safety is a design prerequisite, select a nut with a specified proof stress about 20 % greater than the specified minimum tensile strength of the mating bolt, screw or stud.
The thread stripping areas (Ats) defined in the formulas for recommended lengths of thread engagement are based on twice the tensile stress areas (As) of the thread. To ensure that the screw fails before the thread strips it is necessary that the shear area is at least 2 times the tensile stress area: Ats = 2 x As. These calculations vary, depending upon whether the bolt material is stronger than the nut material; the nut material is stronger than the bolt material or both are made from the same material.
Occasionally, the designer won’t have sufficient room in the assembly to follow the rules of thumb above. In the next installment, I’ll show how the minimum length of thread engagement required to develop full strength may be calculated.