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The buckling of isotropic rings under external pressure has attracted the interest of researchers since late 1950s. The formula for critical fluid buckling pressure of thin rings is very well known. This formula was directly extended to account for homogeneous orthotropic rings as well. The buckling of orthotropic cylindrical shells was also a subject of interest since the 1960s. However, the formulations developed, to date, require numerical solutions to obtain the critical pressure. In this work, a generalized closed form analytical formula for the buckling of thin orthotropic multi-angle laminated rings/long cylinders is developed. Standard energy based formulation is used to express the kinematics and equilibrium equations. Classical lamination theory is implemented to introduce the constitutive equations of thin shells. These equations are statically condensed, in terms of the ring's boundary conditions, to produce effective axial, coupling and flexural rigidities for the cases of rings and long cylinders. The critical buckling pressure may be calculated by hand using the derived equation in terms of these effective elastic rigidities. Comparisons are made with some existing results. Parametric studies are conducted to compare the present results with those of the buckling equations implemented by design standards. Various fiber orientations and stacking sequences are considered.

This paper reviews the research on the theory of elastic stability published at the end of the 19th century, with emphasis on the work by G. H. Bryan in Cambridge. The state of the studies on structural stability previous to Bryan is reviewed, and two lines of work are identified: one is a general stability of rigid bodies and the other is a collection of case studies of elastic stability. Bryan's theory is discussed next, presenting his arguments based on first energy principles, which led him to strong conclusions. The importance of the word "general" and the idea of having solved the problem in each case are explained. The impact of the contributions made by Bryan, together with the critiques that this generated, is also discussed.

To investigate the elastic buckling behavior of self-anchored suspension bridges subjected to proportionally increasing dead loads, a new stability procedure is proposed based on the deflection theory. For this purpose, a finite element buckling analysis is performed using the initial state solution based on the unstrained length method (ULM) (Ref. 1). The finite element solutions are compared with those by the deflection theory. It is shown that both the main girder and tower of the self-anchored suspension bridge are under compression, but their fundamental buckling modes are tower-dominant. Importantly, it is observed that local buckling within the main girder supported by hangers occurs without any geometric change of the main cable, in the higher buckling modes of the self-anchored suspension bridge.

Following the empirical-computational methodology, the contemporary investigations deal with inelastic stability and dynamics of concrete beam-columns. Even under service loads, the concrete structures exhibit physical nonlinearity due to presence of axio-flexural cracks. The objective of the present paper is to analyze the static and dynamic stability of conservative physically nonlinear fully cracked flanged concrete beam–columns. In this paper, using proper reference frames, analytical expressions are developed for the lateral displacement and stiffness of a flanged concrete cantilever under axial compressive and lateral forces. Two critical values of both the axial and lateral loads are identified. For constant lateral force smaller than its first critical value, the concrete beam–columns exhibit brittle buckling mode. Higher lateral forces lesser than the second critical value introduce alternate stable and unstable domains with increase in axial force. The lateral stiffness is predicted to vanish when the axial loads reach the critical values and when the limiting displacement is reached for axial load exceeding its second critical value. The load-space is partitioned into stable and unstable regions. Accessibility of these equilibrium states in the load space has been investigated. Such distinguishing aspects of the predicted behavior of elastic concrete beam–columns are discussed. Their dynamic stability is investigated in second part of the paper.

In this paper, the incremental equilibrium equations and corresponding boundary conditions for the isotropic, hyperelastic and incompressible shells are derived and then employed in order to analyze the behavior of spherical and cylindrical shells subjected to external pressure. The generalized differential quadrature (GDQ) method is utilized to solve the eigenvalue problem that results from a linear bifurcation analysis. The results are in full agreement with the previously obtained results and the effects of thickness and mode number are studied on the shell’s stability. For the spherical and cylindrical shells of arbitrary thickness which are subjected to external hydrostatic pressure, the symmetrical buckling takes place at a value of ${\alpha }_1$ which depends on the geometric parameter $A_1/A_2$ and the mode number $n$, where $A_1$ and $A_2$ are the undeformed inner and outer radii, respectively, and ${\alpha }_1$ is the ratio of the deformed inner radius to the undeformed inner radius.

To provide practical calculation method for analyzing the out-of-plane stability of single tube CFST arch bridge and the out-of-plane elastic stability of typical single tube CFST arch bridge was analyzed by finite element method. Firstly, the basic structural data and statistic parameters of 25 single tube CFST arch bridges were collected and analyzed using statistical approaches. Secondly, on the basis of the existing data, the finite element models of three types of typical single tube CFST arch bridges with span lengths of 50∼59 m, 60∼69 m and 70∼79 m were established and their safety performance were examined. The basic assumption of using elastic stability coefficient to analyze the outof- plane elastic stability of typical arch bridge and the calculation methods for vertical and transverse loads were provided. Different finite element methods were adopted to analyze the out-of-plane stability of typical arch bridges and the finite element calculation methods for out-of-plane stability of typical arch bridges were determined. The results indicate that the finite element model of the typical single tube CFST arch bridge established based on the statistic data is able to reflect the actual condition of the structure, and it is proper to use stability coefficients of dead and live loads to calculate the out-of-plane load bearing capacity and the ultimate load bearing capacity of typical arch bridges.