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In deterministic time-aware networks, such as TTEthernet (TTE) and Time Sensitive Networking (TSN), time-triggered (TT) communication are often routed and scheduled without taking into account other critical traffic such as Rate-Constrained (RC) traffic. Consequently, the impact of a static transmission schedule for TT traffic can prevent RC traffic from fulfilling their timing constraints. In this paper, we present a general framework for routing, scheduling and formal timing analysis (FTA) in deterministic time-aware networks (e.g. TSN, TTE). The general framework drives an iterative execution of different modules (i.e. routing, scheduling and FTA) searching for a solution that fulfills an arbitrary number of defined constraints (e.g. maximum end-to-end RC and TT latency) and optimization goals (e.g. minimize reception jitter). The result is an iteratively improved solution including the routing configuration for TT and RC flows, the static TT schedule, a formal analysis for the RC traffic, as well as any additional outputs satisfying user constraints (e.g. maximum RC jitter). We then do a performance evaluation of the general framework, with a proposed implementation of the necessary modules for TTEthernet networks with mixed time-triggered and rate-constrained traffic. The evaluation of our studied realistic use case shows that, using the general framework, the end-to-end latency for RC traffic can be reduced up to 28.3%, and the number of flows not fulfilling their deadlines divided by up to 3 compared to existing methods.