Most adjoint-based optimization frameworks only consider aerodynamic performance and constraints, leading to designs that need to pass through revisions by structural requirements. Only in recent years, adjoint optimization frameworks have been extended to include structural constraints. These frameworks also make use of CAD-based parametrizations to maintain a connection to the master CAD geometry and to serve as the connection between the fluid and solid domains. In this work, a CAD-based adjoint multidisciplinary optimization framework for turbomachinery components is presented. A CAD-based parametrization is used for defining the shape freedom, from which the fluid and solid grids are generated, and a Reynolds-Averaged Navier-Stokes solver is used to compute the efficiency. The maximum von Mises stress is computed using a linear stress solver based on the Finite Element Method. The CFD and stress solvers each have adjoint capabilities, permitting an efficient computation of gradients at a cost independent of the size of the design space. An adjoint optimization of a radial turbine is performed with the objective of maximizing the aerodynamic efficiency while adhering to the structural constraints. Results show that within a reduced design time an aerodynamic optimal design can be achieved whilst keeping the mechanical stresses within range of the prescribed tolerance.