In particular, the automatic cutting and automatic increment techniques needed for the incremental/iterative procedure are described in detail. The effects of geometry, boundary condition, shear deformation, loading condition as well as the material characteristics on the instability behavior of both the elastic and elasto-plastic arches are numerically investigated. | Vietnam Journal of Mechanics, VAST, Vol. 27, No. 3 (2005), pp. 158 - 170 INSTABILITY BEHAVIOR OF ARCHES UNDER QUASI-STATIC CONCENTRATED LOAD NGUYEN DINH KIEN Institute of Mechanics Abstract. The present paper investigates the instability characteristics of arch structures under quasi-static concentrated load. The arches are idealized as equivalent frameworks and analyzed by the finite element method using the nonlinear co-rotational beam elements. The numerical algorithms for computing the limit load and tracing the equilibrium path are presented. In particular, the automatic cutting and automatic increment techniques needed for the incremental/iterative procedure are described in detail. The effects of geometry, boundary condition, shear deformation, loading condition as well as the material characteristics on the instability behavior of both the elastic and elasto-plastic arches are numerically investigated. 1. INTRODUCTION Arch structures play an important role in civil engineering, and basic arch constructions have been known and used successfully for centuries. The analysis and design of arches based on the concepts of linearities have been described in some textbooks [1, 2]. However, with the invention of new material the arches can be designed more slender and withstanding more loads. Consequently, the instability problem of arches has been received much attention in the field of structural mechanics. From practical point of view, most instability phenomena happen under quasi-static loads, in which a considerable change in the structural geometry is occurred with a steady increase in the external load. Furthermore, nearly all the steel arches that have been built lie in vertical plane [2] . Accordingly, a 2D analysis can be employed when the external loads also act in the vertical plane. The present work assumes the arch is loaded by quasistatic concentrated loads in its plane, so that the instability analysis in the vertical plane can be adopted. In the
