Locking is a well-known phenomenon within the solution of stiff partial differential equations (PDEs). In the context of the finite element method, numerous concepts for locking mitigation have been developed over the past decades. However, the number of advanced, more complex discretization techniques is steadily evolving. In the context of shear deformable beams and plates, transverse shear locking is present for any type of discretization scheme, for any smoothness of shape functions, for both weak form Galerkin-type solution methods and collocation methods based on the Euler-Lagrange equations of the specific boundary value problem. Recently, physics-informed neural networks (PINNs) have been developed as smooth, mesh-free methods for solving PDEs. In contrast to the traditional supervised learning tasks of artificial neural networks (ANNs), PINNs are capable of solving a forward problem without the need of training data. This is achieved by incorporating physical information, for instance, residuals of the strong form of the PDE, at collocation points within the loss function. PINNs generally suffer from deteriorating convergence when solving forward problems involving stiff PDEs. The present contribution investigates the occurrence and the effects of transverse shear locking in a PDE-based PINN framework using the strong form of the boundary value problem. A two-step approach is developed to overcome transverse shear locking. First, hierarchic reparametrizations of the kinematic equations effectively enable the isolation of the shear components in the loss function. Second, a targeted scaling of the shear components enables the removal of the parameter-dependent stiffness from the loss function. Both Timoshenko beam and Mindlin plate problems are investigated in numerical experiments using PINNs. It is shown that transverse shear locking is effectively removed.