Developing a full range S–N curve and estimating cumulative fatigue damage of steel elements

•Simplified formula for full range S–N curves for medium strength steels is proposed.•Formula was developed using empirical formulae and a mathematical function.•Formula needs only tensile strength and hardness for developing S–N curves.•Accuracy of the formula was verified by using six medium strength steels.•A case study (steel connection) was used to show the significance of the formula. The need for material specific monotonic test based full range stress – life curves is discussed. Combining monotonic test based empirical fatigue formulae and a Wholer field mathematical model, a new formula for developing full range stress life curves for medium strength steels is proposed. The accuracy of the proposed formula is verified using experimental fatigue data of six steels. The cumulative fatigue damage and future life of a connection detail of a steel bridge is estimated using a full range S–N curve developed by employing the proposed formula. For this estimation, stress concentration factors of the connection detail are determined using a finite element model and, cumulative damage is evaluated using both miner rule and sequential law. The damage and future life so estimated are compared with those estimated using the code provided conventional method; the importance of employing material specific S–N curves with appropriate stress concentration factors for special connection details and correct damage accumulation methods is highlighted.