This article presents the analytical linearization of aerodynamic loads (computed with theunsteady vortex-lattice method), which is formulated as tangent matrices with respect to thekinematic states of the aerodynamic grid. The loads and their linearization are then mappedto a nonlinear structural model by means of radial-basis functions allowing for a two-waystrong interaction scheme. The structural model comprises geometrically exact beams formulatedin a director-based total Lagrangian description, circumventing the need for rotationaldegrees of freedom. The structural model is spatially discretized into finite elements andtemporally discretized with the help of an implicit scheme that identically preserves momentaand energy. The resulting nonlinear discrete equations are solved by applying Newton’smethod, requiring calculating the Jacobians of the whole aeroelastic system. The correctnessof the linearized loads is then shown by direct comparison with their numerical counterparts.In addition, we employ our strongly-coupled aeroelastic model to investigate the nonlinearstatic and dynamic behavior of a suspension bridge. With this approach, we successfully investigatethe numerical features of the aeroelastic system under divergence and flutter conditions.