Stress concentration formula useful for any dimensions of shoulder fillet in a round bar under tension and bending

In this work stress concentration factors (SCFs), K-t for a round bar with a fillet are considered on the basis of exact solutions, now available for special cases, and accurate numerical results. Then, a convenient K-t formula useful for any dimensions of the fillet is proposed. The conclusions can be summarised as follows: (i) For the limiting cases of deep (d) and shallow (s) fillet, the body force method is used to calculate the K-t values. Then, the formula are obtained as K-td and K-ts. (ii) On the one hand, upon comparison of K-t and K-td, it is found that K-t is nearly equal to K-td if the fillet is deep or blunt. (iii) On the other hand, if the fillet is sharp or shallow, K-t is mainly controlled by K-ts and the fillet depth. (iv) The fillet shape is classified into several groups according to the fillet radius and fillet depth. Then the least squares method is applied for calculation of K-t/K-td and K-t/K-ts. (v) Finally, a convenient formula is proposed that is useful for any dimensions of fillet in a round bar. The formula give SCFs with less than 1% error in most cases for any dimensions of fillet under tension and bending.