The proliferation of various Internet of Everything applications places urgent demand for high energy efficiency, massive connection and wide coverage for the future communication era. Motivated by this, rate-splitting multiple access (RSMA) and simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) has attracted wide publicity from industry and academia. In this paper, we consider a STAR-RIS assisted two-user RSMA network with imperfect successive interference cancellation, and all channels are modeled as Nakagami-m distribution. By adopting effective capacity (EC) as the metric, we analyze the system performance under certain quality-of-service constraint. Specifically, analytical expressions of EC for a pair of RSMA users are provided. To explore further insights, high signal-to-noise ratio (SNR) conditions are also considered. Furthermore, the effect of some specific elements on system EC performance are analyzed, and some significant conclusions are obtained as follows: (1) As SNR grows, the effective capacities of two users improve, but finally converge to constant at high SNR. (2) The increase in the amount of the STAR-RIS elements can obviously increase the effective capacities. (3) Compared to traditional STAR-RIS assisted non-orthogonal multiple access networks, STAR-RIS assisted RSMA network has distinct advantages to improve system EC performance.