True Cross Sectional Area of Screw Threads With Helix and Root Radius Geometries Taken Into Consideration

When evaluating the strength of threaded fasteners under external loads, stress area is commonly used. However, in order to elucidate the mechanical behavior of bolted joints more rigorously and extensively, it is desired to derive an analytical expression of the true cross sectional area of screw threads, with the effects of the helix and root radius taken into account. In this paper, a series of closed-form algebraic equations, which can calculate true cross sectional areas of internal and external screw threads, is derived. The equations obtained can be applied to both metric and inch screw threads with a coarse or a fine pitch. Then, the equivalent diameter of the true sectional area is defined and compared with the pitch diameter and stress area diameter.