Deformation and stability of a pinned shallow arch constrained by a rigid plate and loaded by a concentrated moment

This paper studies the behavior of a pinned half-sine arch, with a center rigid constraint plate, under a static concentrated moment. Under proper loading conditions, the arch will be in contact with the constraint plate at discrete points. This type of configurations is referred to as the contact equilibrium configuration. Geometric restrictions on the deformation of the arch at the contact point are derived. Then, the method of mode expansion is used to solve the force equilibrium equations together with the geometric restrictions for the equilibrium configuration. Due to the restrictions on the deformation of the arch imposed by the constraint plate, the classical potential energy method cannot be directly applied to determine the stability of the contact equilibrium configuration. A modified potential energy method is proposed for overcoming this problem. With the proposed method, the effects of the magnitude and location of the applied moment on the deformation and stability of the arch are investigated thoroughly. We find that, in the presence of the constraint plate, the arch possesses more complicated deformation patterns. Finally, experiments are conducted to validate the theoretical results.