Many selective pressures influence the shape of bird wings and their adaptation to the myriad of flight behaviors known from extant species. While some of these pressures may be synergistic, functional demands may also result in opposing pressures, and morphological diversification may be constrained. For example, wings must have an aerodynamically appropriate shape for flight, but also be strong enough to resist the aerodynamic and inertial loads they experience. The balance of these pressures differs among species with different flight styles and ecologies, and wing morphology is expected to vary accordingly. Two-dimensional (2D) shape traits, such as aspect ratio, and three-dimensional (3D) attributes of wing morphology including camber and thickness contribute to aerodynamic function and vary significantly among species. In prior work, we found that a combination of high aspect ratio and high camber produced high coefficients of lift (C_L), while high aspect ratio and moderately low camber produced higher lift-to-drag ratios (C_L/C_D). A morphological survey of bird wings found that long-distance gliding birds trended toward high camber, contrary to predictions that their wings would be adapted to produce high C_L/C_D. We hypothesize that the structure of bird wings may exclude them from the seemingly more efficient configuration of high aspect ratio and low camber. We propose that because camber in birds is intrinsically linked to the cross-sectional thickness of the wing, that the thickness required to resist bending forces also imposes a minimum bound on wing camber, potentially constraining morphological evolution. We explore the relationship between wing thickness and camber among birds, and use a beam-theory model of structural stiffness to describe how structural demands constrain the evolution of wing morphology.