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.