Coexisting equilibria and stability of a shallow arch: Unilateral displacement-control experiments and theory

• The deflection of a shallow arch is constrained unilaterally by a displacement-control device.
• Remote coexisting equilibria, snap-through, and mode jumping are observed.
• Stability boundaries for the primary and secondary force–deflection branches are determined.
• The arch is modeled via constrained minimization of the strain energy.
• Good agreement is attained between experimental data and theoretical results.

The equilibria and stability of a shallow prestressed arch (beam–column) are investigated theoretically and experimentally. The deflection of the arch is unilaterally constrained by a displacement-control device. Both snap-through and remote coexisting equilibria are observed. Force–deflection curves for primary and secondary equilibrium branches are measured for varying constraint locations. The effect of the constraint location on the critical condition at which stability is lost, resulting in a jump to a remote equilibrium, is investigated. Good agreement is attained between experimental data and theoretical results (based on minimization of the constrained strain energy and an inextensibility assumption).