Studies of human-robot interaction in dynamic and unstructured environments show that as more advanced robotic capabilities are deployed, the need for cooperative competencies to support collaboration with human problem-holders increases. Designing human-robot systems to meet these demands requires an explicit understanding of the work functions and constraints that shape the feasibility of alternative joint work strategies. Yet existing human-robot interaction frameworks either emphasize computational support for real-time execution or rely on static representations for design, offering limited support for reasoning about coordination dynamics during early-stage conceptual design. To address this gap, this article presents a novel computational framework for analyzing joint work strategies in human-robot systems by integrating techniques from functional modeling with graph-theoretic representations. The framework characterizes collective work in terms of the relationships among system functions and the physical and informational structure of the work environment, while explicitly capturing how coordination demands evolve over time. Its use during conceptual design is demonstrated through a case study in disaster robotics, which shows how the framework can be used to support early trade-space exploration of human-robot coordination strategies and to identify cooperative competencies that support flexible management of coordination overhead. These results show how the framework makes coordination demands and their temporal evolution explicit, supporting design-time reasoning about cooperative competency requirements and work demands prior to implementation.