STRESS-CONCENTRATION FACTORS FOR SHOULDER FILLETS IN ROUND AND FLAT BARS UNDER VARIOUS LOADS

The stress concentration problem of shoulder fillets in round and flat bars under various loads is often encountered in machine design of sh afts. Also it is important for test specimens used to investigate the mechanical properties of materials. Accurate stress concentration fact ors (SCFs) have been given in a recent analysis of the body force meth od. However, the results of the solutions have been presented in tabul ar form which is not suitable for engineering applications. For notche d bars, Neuber proposed the simple approximate formula K-tN which is u seful for a wide range of notch shape: 1/(K-tN-1)(m)=1/(K-ts-1)(m)+1/( K-td-1)(m) and m=2. Here, K-ts and K-td are exact solutions for shallo w and deep notches, respectively. Neuber's simple formula has been use d for >40 years in the design of notched bars because of its convenien ce. In this study, similar convenient equations K-tN are initially pro posed as an extension of Neuber's formula to the problem of shoulder f illet. In this formula new definitions of K-ts and K-td are used corre sponding to two extreme cases of shoulder fillet in round and flat bar s. Next, the most suitable exponent m is determined so as to minimize the difference between K-tN and accurate K-t, that is, the results of the body force method. Next, by applying the least squares method to t he ratio K-t/K-tN more accurate formulas are proposed. The formulas pr oposed in this paper are found to give the stress concentration factor s with better than 1% accuracy. In addition, the stress concentration factors are also provided in a graphical way, on the basis of the form ula so they can be used easily in design or research. Copyright (C) 19 97 Elsevier Science Limited.