The displacement demand on linear elastic single-degree-of-freedom systems for 5% damping would typically increase monotonically with increasing natural period up to the limit which is known as the second corner period (T2). The maximum displacement demand (RSDmax) and the associated T2 phenomena has great engineering significance in situations where the estimated RSDmax value is within the drift capacity of the structure as the latter can be deemed safe irrespective of its natural period properties. The earthquake magnitude dependence of T2 is well established. The displacement response spectrum model stipulated by the current Australian Standard for Seismic Actions has the value of T2 specified at 1.5 seconds based on an assumed earthquake magnitude of 7. Results presented in this paper offer support for this recommendation, but also reveal a possible influence on the value of T2 from the regionally dependent stress drop associated with the earthquake rupture. This finding offers a plausible explanation for the diverse range of T2 values that have been observed from earthquakes across the globe.