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The present work deals with the effect of beam-column joint flexibility on the elastic buckling load of plane steel frames. A simple and effective mechanical model is proposed and the corresponding stiffness matrix is presented. The model consists in the development of comprehensive approach taking into account, simultaneously, the effects of the joint rigidity, the elastic buckling load, and this for both sway and non-sway frames. As has been shown by previous research, only one element is required over the length of the element to model stability. This is a marked contribution and advantage of the proposed method, as well as its simplicity, and yet accuracy, to solve practical problem with little computational effort. Also, it includes stability functions in the stiffness matrix, something very often ignored by researchers. Numerical results are obtained for frames with various characteristics and support conditions when three illustrative examples from the literature are presented and discussed. The elastic buckling load is found to be strongly affected by semi-rigid joints and reveals that the proposed model is computationally very efficient with the expressions presented being general. The paper makes reference to the Eurocode 3 approach and those of other researchers in comparing the results. The proposed method is found to be more effective and simple to use, and yielding to very good results. [ABSTRACT FROM AUTHOR]

• Comparative analysis on variable stiffness composite cylindrical shells are conducted. • A numerical modeling method is proposed to achieve variable stiffness property. • Preloading effects on stiffness and buckling strength are investigated. • Boundary constraints and curvilinear fiber paths are analyzed to explore the design space. Composite cylindrical shell has been utilized in marine shipping industry as a reliable auxiliary wind propulsion device that can reduce fuel consumption. However, due to the special boundary constraints and complex loading cases, the vibration and buckling responses of such devices differ significantly from traditional cylindrical shells. The present research deals with the vibration and buckling behavior of composite cylindrical shells utilizing the promising variable stiffness (VS) concept. The effects of the preloading states and the design constraints were analyzed to explore the effectiveness of VS concept in cylindrical shell structures. Compared to constant stiffness (CS) composite cylindrical shells, VS cylindrical shells are less sensitive to variation in preloading states and geometric imperfections, and the buckling strength can be improved under some combination of loading sates. The effect of boundary constraints on stiffness and bucking strength is less prominent own to VS properties, in that stress concentrations near the end of the cylindrical shell structures can be smoothed out, and the strain distributions are spaced more evenly. [ABSTRACT FROM AUTHOR]

In the non-linear in-plane elastic buckling and postbuckling analyses of shallow parabolic arches, to overcome the difficulty in deriving an accurate expression for the non-linear normal strain, an approximation assumption that the derivative of the vertical coordinate with respect to the horizontal coordinate satisfies ( d y / d z ) 1 ≪ 1 has been adopted in many investigations. The merit of the assumption is that it leads to the same differential equations of equilibrium and the same solutions as those for shallow circular arches. However, the accuracy of the assumption and the limitation of the analytical solutions have not been examined and because of the approximation, the analytical solutions may lead to significant errors for the buckling loads of shallow parabolic arches in some cases. This paper investigates the effects of the approximation assumption on the accuracy of in-plane buckling and postbuckling analyses of pin-ended and fixed shallow parabolic arches by comparing the analytical solutions with their finite element counterparts. It is found that the analytical solutions based on the assumption have some limitations because the assumption holds approximately only for extremely shallow parabolic arches, but is not valid for most shallow parabolic arches. The analytical solutions for the buckling loads based on the assumption are larger than the corresponding finite element results for parabolic arches with a rise-to-span ratio greater than 0.08, the error of the analytical solution increases with an increase of the rise-to-span ratio of the arch, and the sources for the errors are identified and discussed. Hence, caution should be exercised when using the analytical solutions to predict the buckling load of shallow parabolic arches, particularly of those with a rise-to-span ratio greater than 0.08. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with buckling aspects of the design of stepped columns in mill buildings. These columns are generally loaded axially at the top and at the section where the cross section changes. These loads usually act eccentrically and thus produce column moments. Additional bending from lateral loads also has to be accounted for. Starting from these considerations, a geometrically nonlinear model for buckling behaviour analysis is proposed and formulated using the differential equations of equilibrium. The concept of equivalent (or effective) lengths of the two column segments is successfully applied. Tables to determine effective length factors are provided for a range of the following parameters: end fixities, ratio of the end axial load to the intermediate axial load, the ratio of the length and moment of inertia of the upper segment to the lower segment and the splice mechanical properties. This is followed by a study of the imperfection sensitivity to the linearly evaluated critical load. A discussion on the variation of the load carrying capacity with the level of eccentricity and lateral load acting at the step on a practical column is also presented. The findings suggest that upper and lower segments are treated as separate beam-columns. Some implications for design, in the form of interaction equations, are deduced from the presented analysis. [Copyright &y& Elsevier]

Abstract: In this paper, the first and second order derivatives of natural frequencies and buckling loads with respect to an arbitrary geometrical or physical property of a plate structure are calculated. Based on these eigenderivatives, and by using first and second order Taylor expansions, an approximate method is presented for simultaneous modification of natural frequencies and buckling loads. In the proposed method, the structural modification is considered as an inverse eigenvalue problem and calculated eigenderivatives are used for transforming this inverse problem to solving a system of algebraic equations. By solving this set of equations, the necessary changes in design parameters are calculated, in order to achieve predefined simultaneous shifts in natural frequencies and buckling loads. A plate with two boundary conditions is considered as a case study. The plate is divided into eight regions and the plate thickness in each region is considered as a design parameter. By considering several case studies, the required modification in design variables is calculated for achieving a predefined change in natural frequencies, buckling loads or simultaneous change of both. In each case, the calculated changes in design variables are implemented on the initial structure, and the changes in eigenvalues are computed using FE method. It is shown that the results from presented method compare very well with those obtained from a direct optimization procedure. [Copyright &y& Elsevier]

Abstract: A shear-flexible finite element based on an orthogonal Cartesian coordinate system is developed for the flexural and buckling analyses of thin-walled composite I-beams with both doubly and mono-symmetrical cross-sections. Using the first-order shear deformable beam theory, the derived element includes both the transverse shear and the restrained warping induced shear deformations. Governing equations are derived from the principle of minimum total potential energy. Three different types of finite elements, namely, linear, quadratic and cubic elements are developed to solve the governing equations. The geometric stiffness for the buckling analysis of axially loaded, thin-walled composite beams is developed. The resulting linearized buckling problem is solved using a shifted inverse iteration algorithm. A parametric study of the effects of the aspect ratio and the fibre orientation on the tip displacement is presented. The convergence of the elements is also investigated. The elastic buckling loads for mono- and doubly-symmetric I-beam cross-sections are compared with other results available in the literature and with solutions using shell elements in a commercially available finite element program. [Copyright &y& Elsevier]

Abstract: A simplified procedure for determining approximate values for the buckling loads of three-dimensional framed structures is developed. The procedure utilises lateral load analysis of structures and yields errors less than 10%, which may be considered suitable for design purposes. The structures with or without rigid floor diaphragms may be considered readily. Buckling loads of both regular and irregular structures may be obtained. The proposed procedure is applied to several numerical examples and it is shown that all the errors are in the acceptable range and generally on the safe side. Determining the buckling loads of structures using SAP2000 is also discussed. [Copyright &y& Elsevier]

Abstract: An approximate method for quick calculation of the critical load of tapered columns is proposed. The method is based on a series of dimensionless design-oriented charts relating the critical load of linearly tapered columns of I-section to the taper ratio and boundary conditions. These charts are derived from extensive parametric studies on the basis of an “exact”, within the limits of the Bernoulli–Euler theory, stability analysis, using a wide array of geometric characteristics of practical interest. As is demonstrated in the Numerical Examples section, these approximate calculations can yield, in a very efficient way, accurate results for single tapered columns or frames consisting of tapered elements. [Copyright &y& Elsevier]

• A large number of finite element analysis of unbounded fiber-reinforced elastomeric isolators (U-FREIs) were carried out by varying mechanical and geometric parameters of the bearings. • The behavior of the U-FREIs under simultaneous vertical and horizontal load has been thoroughly investigated. • Comparisons between numerical results and analytical formulations from literature is proposed. • Stability charts are proposed in order to define the critical pressure as well as the maximum stable horizontal displacement for a given bearing. Fiber-reinforced elastomeric isolators (FREIs) are generally installed in unbonded configurations. Because of the simultaneous application of axial loads and large lateral deformations, instability of these bearings is a major concern. This paper shows the results of a large series of 3D finite element analyses (FEAs) on square-shaped FREIs. The analyses aimed at obtaining easy to use design charts where the stability limits of these devices can be rapidly determined. The output of the analyses is compared to analytical results available in literature and the limitations of well-known closed form solutions are discussed. [ABSTRACT FROM AUTHOR]

• A novel optimization method of determining the optimal crossarm length of PSSC. • The method overcomes the drawbacks in the gradient-based optimization algorithm. • A comparison for the optimal PSSCs with different kinds of variables was performed. Prestressed stayed steel columns (PSSCs) offer a lightweight alternative for the design of slender compression columns. The stability of compression columns can be significantly enhanced by introducing crossarms. Previous research on this subject has primarily focused on load-carrying capacity estimation or analyses of the influencing factors of PSSCs. Thus, investigations of the design optimization of PSSCs remain scant. This work proposes a novel strategy for crossarm length optimization of PSSCs based on multi-dimensional global optimization algorithms. A multi-population genetic algorithm is introduced in the optimization process. The proposed optimization algorithm was demonstrated to be efficient and accurate in terms of determining the optimal crossarm length of PSSCs. [ABSTRACT FROM AUTHOR]