Analytical Expression of True Cross Sectional Area of Screw Thread with the Effects of Root Radius Taken into Consideration

Abstract

The cross sectional area of threaded fastener has a complicated configuration due to the helix that characterizes its essential function of tightening structural members. When estimating the strength of threaded fasteners under external loads, the use of “stress area” is recommended in JIS B 0251. It is desired, however, to establish a procedure to calculate the true cross sectional area of screw thread by taking account of the effects of root radius in order to elucidate the various mechanical behaviors of bolted joints. In this paper, an analytical expression is presented to calculate the true cross sectional area with simple algebraic equations. Then, its “equivalent diameter” is defined and compared to effective diameter corresponding to the stress area defined in JIS B 0251.