On non-linear behavior and buckling of arch-beam structures

Abstract

This paper investigates analytical predictions for non-linear behavior and buckling of pin-ended arch-beam structures. The nonlinear in-plane equilibrium is derived based on the principle of virtual work and the force balance condition of the ends of arch-beam structures. A new calculation method of the stationary point of inflexion is proposed and used to develop the symmetric buckling requirement for arch-beam structures. The asymmetric buckling requirement as well as all the possible nonlinear buckling behaviors and corresponding buckling requirements for arch-beam structures are also investigated analytically. The accuracy of proposed analytical solutions is validated through the comparisons against finite element analysis results. The major findings of this theoretical investigation are: (1) the analytical solution of the symmetric buckling requirement for arch-beam structures is thoroughly different from that for the single arch structures; (2) a stable bifurcation phenomenon can be observed in the nonlinear asymmetric buckling of arch-beam structures, in which buckling load increases as the asymmetric buckling occurs; (3) the symmetric buckling requirement and the asymmetric buckling requirement of arch-beam structures are independent of each other and the asymmetric buckling can occur before the stationary point of inflexion; and (4) the nonlinear buckling behavior of arch-beam structures is more complicated than the behavior of single arch structures, and six different buckling phenomena can be observed by changing the parameters of compression stiffness ratio between the beam and the arch, modified slenderness and rise-to-span ratio.