In-Plane Stability And Design Method Of Steel Circular Arches With Rigid And Elastic Restraints

Steel arches, with their elegant shapes, reasonable mechanical characteristics and relatively good economic have been widely used in engineering projects. When a slab encases the top flange of the arch and is mechanically anchored to it, or there are some lateral supports to provide restraints, in-plane stability of steel arches is needed to be concerned. Until recently, the in-plane ultimate load-carrying capacity of steel arches has been studied by several researchers, and the strength design methods with interaction equation are established. The applicability and normalization of these formulas need to be further examination.In this thesis, in-plane inelastic stability behavior and strength design of three-hinged, two-hinged and fixed steel circular arches with I-section are studied systematically. Based on the results of finite element method (FEM), fitted values of linear elastic critical compression when arches subject to hydrostatic load are presented, and the obtained results are compared with classic buckling theory. The relationship between the arch stability coefficients and the normalized slenderness ratio which is defined using the critical compression is established in the form of Perry-Roberson formula. Second-order effect of axial compression due to the large displacement will lead to the increase of moment. This thesis studies the moment amplification factor of three-hinged arches and proposes the corresponding formulas. The interaction formula composed of compression and bending which are obtained by a first order analysis is proposed for the in-plane strength design of circular arches. Compared to other research, innovations of this thesis are:(1) axial compression and bending moment are internal forces of controlling section using first-order linear elastic analysis, rather than the maximum compression and maximum bending which dose not necessarily appear in the same cross-section. This approach is consistent with the habits of the engineering design.(2) in the formula, supporting condition, distribution of moment, geometric second-order effect and plastic capacity of cross-section are considered by some factors. Moreover, existing design formulas proposed by other researchers are verified in the thesis.An arch is often connected with other structures that provide elastic restraints to the arch. It can be considered to be supported elastically at both ends by horizontal springs. These elastic restraints significantly influence its behavior. Analytical solutions of horizontally elastically supported arches that are subjected to several vertical symmetric uniformly distributed loads are obtained based on linear equilibrium equations. A dimensionless elastic flexibility factor is introduced. By analyzing the linear analytical solutions and using the flexibility factor, criterions that distinguish between arches and arched beams are suggested. The effects of the stiffness of the horizontal end restraint on the distribution of internal forces are studied. By FEM, a limiting flexibility factor that distinguishes between in-plane linear elastic anti-symmetric bifurcation mode and symmetric snap-through mode is presented, and formulas for critical load and mid-span axial forces in term of elastic flexibility factor are proposed.In this thesis, an elasto-plastic finite element model is established to study the in-plane stability behavior and ultimate strength of steel circular arches with horizontal elastic restraints using large deformation theory by FEM. Initial geometric crookedness, residual stress and material inelasticity are considered in the investigation. In six load cases, the effects of the stiffness of end restraints on the bearing capacity of arches with I-section and horizontal displacement of supports in the limit state of load-carrying are studied. Based on the numerical results, formulas for dimensionless ultimate strength and displacement of supports in terms of elastic flexibility factor are proposed. The design formulas for pin-ended arches proposed by other researches are used for elastically supported arches, and a simplified design criterion is presented.This thesis investigates the deformation characteristics and mechanical properties of compressed bars with biaxial symmetric I-section. Based on the large deformation theory, a finite-element program of3D-Steel-Struct developed by the authors is used in the analysis. Initial geometric crookedness, residual stress and material inelasticity are considered in the investigation. Second order elastic and second order rigid-plastic analysis are carried out for imperfect members, and relation between axial compression and deformation are deduced. Analytical expressions of axial compression and deflection at mid-span and of axial compression and axial shortening are presented, and comparison shows the excellent agreement between the proposed explicit expressions and the numerical results.The axial ductility of compressed members is defined. This thesis studies the ductility of compressed bars with I-section revolving round the maximum and the minimum principal axes of inertia of an area, with tube section, and with L-section revolving round the minimum principal axis of inertia of an area and parallel axis respectively. Formulas relating the ductility to the slenderness are proposed.Second order elastic and second order rigid-plastic analysis are carried out for imperfect beams and beam-columns with biaxial symmetric I-section, and relation between load and deformation are deduced. Initial geometric crookedness, residual stress and material inelasticity are considered in the investigation. Based on the results of FEM, analytical expressions with good accuracy of relationship between load and deformation of beams and beam-columns are presented.