Stress concentration formulae useful for any shape of notch in a round test specimen under tension and under bending

In this work stress concentration factors, K-t, for a round bar with a circ ular-are or V-shaped notch are considered on the basis of exact solutions f or special cases and accurate numerical results. Then, a set of K-t formula e useful for any shape of notch is proposed. The conclusions can be summari zed as follows. (i) For the Limiting cases of deep (d) and shallow (s) notches, the body fo rce method is used to calculate the K-t values. Then, the formulae are obta ined 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 notch is deep or blunt. (iii) On the other hand, if the notch is sharp or shallow K-t is mainly con trolled by K-ts, and the notch depth. (iv) The notch shape is classified into several groups according to the not ch radius and notch depth. Then, the least-squares method is applied for th e calculation of K-t/K-td and K-t/K-ts. (v) Finally a set of convenient formulae is proposed that are useful for an y shape of notch in a round test specimen. The formulae give SCFs with <1% error for any shape of notch.