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Compressed reinforcements on reinforced concrete (RC) and steel fibre reinforced concrete (SFRC) columns are generally submitted to cyclic and monotonic loading, which can buckle. This phenomenon can cause the reduction of both ductility and peak loads, which is why design standards propose constructive details to avoid this. Although the bibliography mentions that steel fibres in concrete can delay buckling of reinforcements, design codes do not distinguish between concrete types (with and without fibres) in these constructive details. Analytical models that determine the length and critical buckling stress of reinforcements may consider this effect. Nowadays, analytical models can be classified as discrete and distributed depending on whether they consider transverse reinforcement stiffness and the stiffness of the concrete cover that concentrates on transverse reinforcements, or if they are distributed along the element, respectively. Both discrete and distributed models are valid for small transverse reinforcement separations, while distributed models that only consider the concrete cover effect are valid for large transverse reinforcement separations. This paper proposes a mixed model to determine critical buckling loads of compressed reinforcements subjected to monotonic loading to use the stress-strain relationships of reinforcing bars, including buckling, that are found in the scientific-technical literature. This model considers transverse reinforcements discretely and concrete cover distributedly. The model can be applied to any transverse reinforcement configuration, and to any concrete type (with or without fibres). An analytical equation is also proposed to determine critical compressed reinforcement loads, whose result is presented as abaci. Finally, to calibrate the model in normal-strength concrete columns under eccentric loading, with or without fibres, a programme is presented in which the critical load of longitudinal reinforcements is experimentally determined. The proposed analytical model is calibrated and a procedure to determine critical buckling loads of compressed reinforcements under monotonic loading is proposed. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive test database of concentric compression experiments on pultruded fiber-reinforced polymer (PFRP) specimens that failed in a global flexural buckling mode published in literature between 1969 and 2016. A new closed-form equation to determine the reduction factor for global flexural buckling of PFRP structural struts under axial compression is developed on the basis of the Ayrton-Perry formula and observed initial out-of-straightness of PFRP members measured by other researchers. Recognizing that data on initial imperfections may be unavailable, a second new empirical closed-form equation is derived based upon the experimental database. Validation of the two explicit expressions is performed by both comparison to experimental data and comparison with validated numerical simulations. In addition, the accuracies of the two proposed equations are compared with those of five closed-form solutions available in the literature; both results in more accurate predictions than the extant equations. Both new proposed equations can be conveniently used by structural engineers at the preliminary engineering design stage for accurately assessing the reliability and safety of composite structures under concentric compressive loading. [ABSTRACT FROM AUTHOR]

This paper proposes a new type of buckling-restrained braces (BRBs), namely shuttle-shaped buckling-restrained braces (SS-BRBs). The proposed SS-BRB is composed of a circular steel tube as the inner core, and a shuttle-shaped thin-walled steel tube as the external restraining member. The space between them is filled by a steel-plate isolation system. The shuttle-shaped restraining member of the SS-BRB significantly improves load-carrying efficiency and saves material in its strength design. Moreover, the SS-BRB is more aesthetically appealing and can be utilized as an exposed BRB in long-span or spatial structures. In terms of the concept of restraining ratio of a BRB, no design method of an SS-BRB is available currently because it concerns the solution of the elastic buckling load of an SS-BRB. Therefore, the elastic buckling load of a pin-ended SS-BRB is initially studied by adopting the equilibrium method and is further verified through finite element (FE) method. The lateral displacement function of an SS-BRB, and the longitudinal stress at the extreme fiber of the external restraining member are derived by considering an initial geometric imperfection that is consistent with the first order overall buckling shape of the SS-BRB. A correction factor considering shear deformation has been incorporated for a more accurate prediction. The lower limit of the restraining ratio for a load-bearing type of SS-BRBs is further obtained based on yielding of the extreme fiber of the restraining member. Furthermore, the proposed formula has incorporated a strain hardening factor for the SS-BRB that experiences strain hardening of the core after its initial yielding. The proposed formulas have been validated through FE numerical analysis. The findings in this paper provide fundamentals to develop the design method for an energy-dissipation type of SS-BRBs. [ABSTRACT FROM AUTHOR]

Highlights • Experimental tests were conducted on doubly-symmetric welded Q460GJ steel beams against lateral torsional buckling. • Numerical models were developed for steel beams to quantify their lateral torsional buckling resistances. • Comparisons were made between numerical results and design curves from different national codes. Abstract This paper presents an experimental and numerical study on the global buckling behaviour of doubly-symmetric Q460GJ steel beams under three-point bending. A total of eight simply-supported beams with different slendernesses and height-to-width ratios were tested in the experimental programme. To achieve the required loading and boundary conditions, a special loading system was designed for the beams so that the vertical load applied at the mid-span through a hydraulic jack could move with the beams in the lateral direction, and a set of steel rollers was placed in the supports. All eight beams failed in lateral-torsional buckling. Finite element models were also developed for the beams, in which initial geometric imperfections and residual stresses were considered. The model was validated against experimental results, and a reasonably good agreement was obtained. A series of parametric study was carried out to gain a deep understanding of the effects of slenderness and height-to-width ratio on buckling factor. Comparisons were made between numerical data and calculated values in accordance with different national codes. [ABSTRACT FROM AUTHOR]

A new type of core-separated buckling-restrained braces, namely a core-separated battened buckling-restrained brace (B-BRB) has been proposed. Its load-carrying capacity and hysteretic response are investigated theoretically and experimentally in this paper. The B-BRB has a remarkable advantage over a common buckling-restrained brace (BRB), in which the newly formed cross-section of the B-BRB is spread outwards by spacing two cores, hence resulting in higher material utilization efficiency in its structural design. In addition, the two independent all-steel BRBs, each having a single plate core simply in-filled in a narrow hollow section, are connected by longitudinally distributed battens rather than continuous plates. Based on the elastic-plastic FE analysis of a B-BRB under monotonic compressive load, its ultimate resistance and failure modes are investigated numerically, considering the effect of its overall initial geometric imperfection. An interaction formula between normalized slenderness ratio and buckling factor of the B-BRB is proposed for predicting its ultimate load-carrying capacity. Consequently, the hysteretic response of the B-BRB is explored through elastic-plastic FE analysis. The maximum normalized slenderness ratios of the B-BRBs required for a load-bearing type and an energy-dissipation type are proposed in their strength designs, respectively. Ultimately, hysteretic responses of five B-BRB specimens have been experimentally investigated. The experimental results are compared with the FE numerical analysis, which considers plate local buckling of all components of the B-BRBs. The comparison has verified the rationality of the proposed design method. [ABSTRACT FROM AUTHOR]

Since economic quantities are more meaningful to decision makers than dynamic response parameters, this paper examines the economic benefits of using Buckling-Restrained Braces (BRBs) in hospitals located in the very soft soils of the lakebed zone of Mexico City. Since non-structural elements and contents are far more expensive than the structure itself, they are included in detail in the analyses. The results of analyses on three-, six-, and nine-storey frames, which represent short-period structures, show that the expected (or probable) losses and lifecycle costs are smaller when structures are equipped with BRBs. Different cases (defined by the contribution of the BRBs to the strength capacity of the structure) were analysed and compared. The best design options were identified from a comparison of lifecycle costs. As an example, a comparison of cost-benefit analysis between a bare frame and a frame designed under gravity loads and equipped with BRBs, shows that the latter is more economical; because, for the same initial cost, the lifecycle costs are significantly smaller. [ABSTRACT FROM AUTHOR]

Highlights • The differential system is solved with low computational cost. • The numerical results indicate a very good performance of the 6DE model proposed. • The 6DE model allows to obtain the equivalent properties for the beam-column model. • Practical expressions for the buckling loads exhibit an excellent agreement. Abstract Lattice towers and guyed masts are frequently used in the telecommunication industry, particularly to support antennas. These structural systems comprise a large number of elements (mainly, legs and diagonals) and for this reason, their representation by equivalent models is quite common and convenient. In a previous study, the authors derived a continuous model of a spatial lattice governed by nine differential equations (9DE). The legs trace forms a triangle and the diagonals with a zig-zag pattern are contained in three planes that join each two legs, defined as Pattern 1. Here and starting from an energy statement, the structural behavior of a 1D continuous model governed by six differential equations (6DE) which leads to a simpler representation of the lattice structure, is stated. This formulation considers the shear flexibility and the second order effect due to axial loads. Also, the inertial forces due to the legs and diagonals masses are taken into account. Numerical examples dealing with deflections, critical buckling loads and natural frequencies are solved with this 1D model. The results are compared with the outcomes found with finite element methods. A very good performance is attained with the proposed model. Finally, the equivalent properties for other patterns of diagonalization (Patterns 2, 3 and 4) different to the studied as well as the formulas to find the critical loads are included in Appendices. [ABSTRACT FROM AUTHOR]

This paper presents a numerical investigation into the buckling behaviour of cold-formed steel zed purlins when subjected to transverse distributed uplift loading. The study uses both linear and non-linear finite element methods (ABAQUS shell Finite Element analyses) to investigate the pre-buckling, buckling and post-buckling behaviour of zed-section purlins in purlin-sheeting systems. The numerical modelling strategy is carefully validated using the results of available experimental data. Influences of boundary conditions and restraints from sheeting on web shear buckling, local, distortional and lateral-torsional buckling behaviour, and the buckling interactions of the purlins are discussed. Furthermore, the strengths and failure modes of the purlins obtained from numerical results are compared with the design strengths predicted using the direct strength method (DSM) specified in the ‘North American Specification’ (AISI S100). The comparisons show that the ultimate strengths of buckling interactions are generally underestimated. Hence, the DSM is modified to cover the partially restrained zed-sections in purlin-sheeting systems. [ABSTRACT FROM AUTHOR]

This paper investigates the effects of geometric nonlinearity and temperature field on the in-plane elastic behaviour and buckling of crown-pinned circular steel arches that is subjected to a uniform radial load. Differential equations of equilibrium are derived based on the principle of stationary potential energy, and analytic solutions for the linear and nonlinear behaviour and buckling loads are derived. It is found that the nonlinearities have significant influences on the in-plane behaviour and buckling of crown-pinned arches. The nonlinear bending actions produced by the uniform radial load in crown-pinned arches are substantial, while the linear bending actions are equal to zero for three-pinned arches and are small for one-pinned arches. The nonlinear buckling loads are much lower than their linear counterparts. It is also found that the uniform temperature field influences the nonlinear elastic behaviour and buckling of crown-pinned arches, while it has no effects on the linear internal actions of three-pinned arches and small effects on those of one-pinned arches. As temperature increases, radial displacements decrease while the nonlinear buckling loads increases. It is further found that crown-pinned arches can buckle only in a symmetric mode, but not in an antisymmetric mode. Comparisons with the finite element results show that the analytical solutions derived in this paper are quite accurate. [ABSTRACT FROM AUTHOR]

Highlights: [•] Glass panels are widely used in practice as structural elements in buildings. [•] Frequently, they could be subjected to in-plane loads or multiple interacting actions. [•] The buckling response of simply supported glass panels under in-plane compressive/shearing loads is investigated. [•] The effects of imperfection shape and amplitude, aspect ratio, slenderness are highlighted. [•] A normalized interaction resistant domain is proposed for a possible verification approach. [Copyright &y& Elsevier]

This paper presents an experimental study on the out-of-plane inelastic buckling strength of fixed circular steel arches under symmetric and non-symmetric loading. A test loading arrangement that allows for lateral deflections to develop freely under vertical loading is described. A finite element (FE) model consisting of the tested steel arch and the loading system is established for carrying out supplementary numerical investigation on the inelastic out-of-plane buckling strength of the fixed steel arches. The FE numerical model is validated by the experimental results. From the experimental results and supplementary FE investigation, it is found that the out-of-plane inelastic buckling strength of fixed steel arches is influenced significantly by the magnitude and distribution of initial out-of-plane geometric imperfections, as well as the out-of-plane elastic buckling modes and the in-plane loading patterns. It is also found that the out-of-plane buckling strength of a fixed steel arch under non-symmetric loading is lower than that under symmetric loading. Based on the experimental and FE results, a lower bound interaction equation is developed for predicting the out-of-plane inelastic buckling strength in the design of fixed circular steel arches against their out-of-plane failure. [ABSTRACT FROM AUTHOR]

Highlights: [•] Shear and torsional rigidities of trusses are theoretically derived. [•] Out-of-plane buckling loads of pin-ended circular truss arches are derived. [•] Effect of shear deformation on buckling loads of truss arches is included. [Copyright &y& Elsevier]

Abstract: This work examines the effect of random geometric imperfections in the buckling response of I-profile steel beam–column members as well as portal frame structures. Geometric imperfections are assumed to be non-homogeneous Gaussian random fields. Samples of these fields are generated using the spectral representation method with evolutionary power spectra derived from experimental measurements using the method of separation. A number of samples of random imperfect geometries are generated and simulated with detailed discretization with triangular shell finite elements. The stochastic buckling loads are determined in the context of brute force Monte Carlo simulation by repeated material and geometrically nonlinear finite element analyses. Single beam–column members are subjected to pure axial compression while the portal frames are tested for lateral loading. Various types of boundary conditions are implemented and histograms of bucking loads are derived for each case examined leading to useful conclusions for this type of structures, regarding imperfection triggered buckling response and buckling load variability. [Copyright &y& Elsevier]

Abstract: Arches are often supported by other structural elements which provide elastic types of restraint at both of their ends and these elastic restraints usually have different stiffnesses. This paper presents a nonlinear elastic in-plane buckling and postbuckling analysis of pin-ended shallow circular arches having elastic rotational end restraints of unequal stiffness when subjected to a uniform radial load. An energy method is used to derive the differential equations of equilibrium, and the differential equations of buckling equilibrium. The nonlinear equilibrium equation between the external load and the axial force is also established. Analytical solutions for the nonlinear in-plane behaviour and buckling loads of the arches are derived. It is found that the effects of the unequal stiffness of the rotational end restraints on the nonlinear behaviour and buckling of the arches are significant. The nonlinear buckling loads increase with an increase of the stiffness of rotational end restraints. It is also found that the pin-ended arch with elastic rotational end restraints of unequal stiffness may buckle in a limit point instability mode, but they cannot buckle in a bifurcation mode. This is different from pin-ended arches with equal rotational end restraints, which can buckle in either a limit point instability or a bifurcation mode. It is demonstrated that there exists a specific geometric parameter (as defined in the paper) that defines a switch between arches and beams curved in elevation. Comparisons with finite element results show that the analytical solutions can accurately predict the nonlinear behaviour and buckling loads of pin-ended shallow circular arches with elastic rotational end restraints of unequal stiffness. The analytical solutions are shown to reduce to those of pin-ended arches with equal rotational end restraints or without rotational end restraints, fixed arches, and pinned-fixed arches. [Copyright &y& Elsevier]

Abstract: This paper pertains to the critical load for two-hinged parabolic arches with hangers and tie. It was proved that the existence of hangers (vertical and especially slant) can lead to a significant increase of arch critical load and consequently to increase of arch capacity. It has also been shown that the convex distribution of ties (in relation to the horizontal tie) can often be very useful. The tabulated results presented in the paper allow to determine the effective (buckling) length of the arches. Furthermore, it has been noted that the recommendations of European Standard (Eurocode 3: EN 1993-2) concerning the buckling of parabolic arches with hangers and tie may quite frequently lead to unsafe design. The issues of buckling of arches presented in this paper have a practical aspect and, in author’s opinion, can find a direct application in design practice. [Copyright &y& Elsevier]

Abstract: This paper presents a mathematical model for investigating the buckling of geometrically perfect, materially and kinematically non-linear, locally weakened reinforced concrete columns. The present analytical model is based on the linearized stability theory and is capable of predicting exact buckling loads. Based on a systematic parametric analysis, the effects of the weakness location, its magnitude, the number of weaknesses and the material non-linearity of concrete and reinforcing steel on buckling loads have been investigated. The results are given in terms of graphs showing in detail that the material non-linearity of concrete and reinforcing steel and the local weaknesses have a significant influence on the buckling load. [Copyright &y& Elsevier]

Abstract: Holes are often unavoidable in webs of steel beams and in plates, due to inspection, maintenance and also aesthetic purposes. In these situations, the presence of holes may cause redistribution of plane stresses in plates with a significant reduction of stability. In this paper, linear buckling analyses of perforated plates subjected to localised symmetrical load, with circular and rectangular holes, are developed. The results show some relevant differences between the behaviour of the plate subjected to localised symmetrical load with respect to that of uniform compressive load, already known in literature, with a significant increase in the elastic critical load value. The buckling coefficient of square and rectangular perforated panels under symmetrical uniform compression assumes the same value of corresponding whole panels, and it strongly increases for localised symmetrical load, reducing its increment on the basis of the diameter of the hole. Lastly, some indications are given on the best orientation of rectangular holes when localised load are applied showing differences with the uniform compression load case. Holes with the longest edge parallel to the transverse direction of the panel subjected to uniform compression loads are preferable for stability purposes. According to present results obtained for localised loads, holes with the longest edge along the longitudinal direction are preferable. [Copyright &y& Elsevier]

In this paper, the buckling response of glass panels linearly supported along the top and bottom edges, under the action of in-plane shear loads, is investigated by means of analytical and Finite-Element (FE) methods. The typical buckling behaviour is first assessed in the hypothesis of fully neglecting the possible deformability contribution of adhesive linear supports, while successively the effects of linear, flexible sealant joints on the overall structural response of the same panels are also properly taken into account and highlighted. Based on extended parametric FE linear buckling and nonlinear incremental simulations, the influence of initial geometrical imperfections with various shapes and amplitudes, adhesive stiffnesses and glass types is investigated, both for monolithic and laminated glass panels. In the latter case, the accuracy of an equivalent thickness approach derived from early contributions is also demonstrated. Analytical approximating curves are proposed for the fitting of numerically derived buckling coefficients, so that they could represent a practical tool in the calculation of the expected Euler’s critical load. A normalized buckling curve for ideally simply supported glass panels under in-plane shear loads is finally recalled from past research projects and proposed as a rational design method for the examined loading and boundary condition. [ABSTRACT FROM AUTHOR]

Abstract: The load-resisting capacity of buckling-restrained braces (BRB) composed of an H-shaped core element and an external tube was investigated in this study by component testing. A study was carried out on the effect of the design parameters such as the thickness of the constraining tube and the length of the unconstrained length of the core ends on the maximum strength and the energy dissipation capability. The performance of the BRB was evaluated by comparing the test results with the recommended provisions for BRB. It was found that the thickness of the external tube and the unconstrained part of the core had a significant effect on the strength and hysteretic behavior of the BRB; with the correct thickness of external tube and unconstrained length, the BRB behaved stably throughout the cyclic loading history until the cumulative plastic deformation reached 330, which far exceeded the value of 200 required by the recommended provisions. [Copyright &y& Elsevier]

Abstract: In this study, linear buckling analysis of unstiffened plates under interacting patch loading and bending moment is developed. The study focuses on estimation of the elastic critical load due to patch load, and concomitant linearly variable compressive stress in the normal direction, with analysis of mechanisms of plate instability. The present work proposes simple design equations for the elastic critical load of rectangular plates subjected to both patch load, and uniform compressive stress, and also patch load with linearly varying compressive stresses for the serviceability limit state. The proposed analytical relationship, obtained on the basis of parametric numerical analyses, is validated by comparing analytical predictions with experimental tests from the literature, and full numerical models; good agreement was obtained for practical situations in steel bridge design, such as the erection of steel bridges with the launching construction technique. In the launch phase, web panels of the open-section girders are subjected to concentrated loads applied to the lower flange, and considerable bending moment. [Copyright &y& Elsevier]

Abstract: Torsional bracing systems have been used widely in I-girder bridges to increase the flexural-torsional buckling strength and distribute the load to the adjacent girders. To evaluate the required stiffness of the bracing and the flexural-torsional buckling strength of the I-girder with a multiple torsional bracing system, the equivalent continuous torsional bracing concept is often adopted regardless of the type of torsional bracing system. However, a previous study on the I-girder with discrete torsional bracings under uniform bending reported that the equivalent continuous torsional bracing concept has certain limitations on discrete torsional bracing problems and it needs to be investigated for general loading cases. This article presents an analytical solution for the elastic flexural-torsional buckling strength and stiffness requirements of I-girders with discrete torsional bracings under various loading conditions. First, a review was performed of the previous study on the elastic critical buckling moment and torsional stiffness requirement of the I-girder with discrete torsional bracings under uniform bending. This solution was then extended for various loading conditions. From the derived analytical solutions, the equivalent moment factor was proposed for practical engineering purposes and the proposed solutions were verified by comparing them with the results of finite element analysis and those of other previous studies. Finally, non-linear finite element analyses including the effects of the initial imperfection and residual stresses were conducted to examine the inelastic buckling strengths of I-girders with discrete torsional bracings under various loading conditions. The results showed that the buckling curves from the current design specification provide reasonably conservative flexural-torsional buckling strengths of the I-girder with discrete torsional bracings when the proposed elastic solutions are applied to obtain the buckling parameters. [Copyright &y& Elsevier]

Abstract: An analytical approach for the buckling analysis of rectangular plates under mixed boundary conditions is presented. In order to solve the partial differential equation governing the problem at hand a method of separation of variables is here adopted, by introducing the displacement field as a result of the scalar product of two vectors which combine prescribed and unknown scalar functions. By following this strategy, exact buckling solutions for a wide class of problems, in which mixed boundary conditions can be assigned relaxing some usual constraints, are determined, and buckling load of plates, where biaxial tensile and compressive loads are applied in presence of piecewise clamped and partially supported sides, obtained analytically. Several cases of engineering interest are finally analyzed, and comparisons of the theoretical outcomes with literature data and Finite Element-based numerical results are also shown, in order to highlight the effectiveness of the proposed strategy. [Copyright &y& Elsevier]

The reliability of doubly-symmetric wide flange steel beams designed to the AISC Specification for Structural Steel Buildings subjected to elastic lateral torsional buckling was evaluated when considering variation in moment gradient and load height. The analysis considers continuous loads on spans subjected to various end moments with supports that are torsionally fixed and laterally supported, without additional intermediate restraints. Dead load, occupancy live load, and beam resistance random variables were considered. Beam lateral torsional buckling resistance was evaluated from numerical solution of a fundamental differential equation that accounts for the effect of moment gradient and load height. In some cases, it was found that use of the AISC design procedure results in significant inaccuracies for estimation of elastic lateral torsional buckling resistance, where underestimations occur in regions of reverse curvature bending and when loads are placed below the beam shear center, while large overestimations can occur when loads are placed above the beam shear center. These discrepancies result in significant variation in beam reliability. However, the use of accurate equivalent uniform moment factors can restore uniformity in notional reliability level. [ABSTRACT FROM AUTHOR]

Abstract: Because of evident aesthetic, lighting and architectural advantages, glass curtain walls are largely used to clad modern buildings. Since these elements are considered to constitute purely architectural systems, they are essentially designed to resist loads acting orthogonally to the plane of the façade (e.g. wind loads). Contrarily, glass elements are frequently used as structural components able to sustain in-plane loads (e.g. columns, stiffening fins, beam elements, stairs, etc.), thus to preserve their integrity a buckling verification could assume great importance. In order to overcome these problems, an analytical formulation is proposed for the estimation of the buckling resistance of flat laminated glass panels under in-plane compression or shear. Two different design approaches are taken into account and compared: the first one directly derives from the theory of sandwich panels, whereas the second one is based on the approximate concept of equivalent thickness. As discussed in the paper, this last approach constitutes a useful design expedient for the deformability and resistance check of buckled laminated panels under in-plane compression or shear, in presence of different boundary conditions. Since the resistance of such brittle elements directly depends on the level of connection between the glass panes offered by the interlayer, the effects of possible temperature and time-loading variations are highlighted. The obtained analytical results are in agreement with sophisticated numerical simulations. [Copyright &y& Elsevier]

The present study uses the isogeometric analysis (IGA) to investigate the post-buckling behavior of functionally graded (FG) microplates subjected to mechanical and thermal loads. The modified a strain gradient theory with three length scale parameters is used to capture the size effect. The Reddy third-order shear deformation plate theory with the von Kámán nonlinearity (i.e., small strains and moderate rotations) is employed to describe the kinematics of the microplates. Material variations in the thickness direction of the plate are described using a rule of mixtures. In addition, material properties are assumed to be either temperature-dependent or temperature-independent. The governing equations are derived using the principle of virtual work, which are then discretized using the IGA approach, whereby a C 2 -continuity requirement is fulfilled naturally and efficiently. To trace the post-buckling paths, Newton’s iterative technique is utilized. Various parametric studies are conducted to examine the influences of material variations, size effects, thickness ratios, and boundary conditions on the post-buckling behavior of microplates. [ABSTRACT FROM AUTHOR]

Highlights: [•] The flexural–torsional buckling shapes of fixed arches are studied thoroughly. [•] Buckling loads of fixed arches are derived by using two methods theoretically. [•] Approximate formulas of buckling loads of fixed arches are presented. [•] ‘Effective length’ method is verified to be unsuitable for arches. [Copyright &y& Elsevier]

Highlights: [•] An analytical model on instability of bearings affected by cavitation is elaborated. [•] A procedure to calculate buckling load in tension with cavitation is developed. [•] The analysis is conducted on long strip bearings and circular bearings. [•] The effects of cavitation on both compressive and bending stiffness are described. [Copyright &y& Elsevier]

Abstract: Simplified methods for approximating the global, distortional, and local critical elastic buckling loads of cold-formed steel columns and beams with holes are developed and summarized. These methods provide engineering approximations appropriate for design, but are intended to be general enough to accommodate the range of hole shapes, locations, and spacings common in industry. The simplified methods are developed as a convenient alternative to shell finite element eigen-buckling analysis, which require laborious and subjective visual identification methods as well as commercial software not generally accessible to the engineering community. Global buckling of cold-formed steel beams and columns, including the influence of holes, is predicted with approximate “weighted average” cross-section properties formulated from classical energy-based stability solutions. Distortional and local buckling of a cold-formed steel member with holes are determined with the semi-analytical finite strip method, considering appropriate modifications to the element thickness and choice of buckling half-wavelength. The proposed methods are verified with shell finite element eigen-buckling studies. Unambiguous, simple methods for elastic buckling prediction of members with holes is central to the extension of the Direct Strength Method (DSM) for cold-formed steel member ultimate strength determination. [Copyright &y& Elsevier]

Single-layer reticulated domes are typical structures with high degree of static indeterminacy. The stability of the reticulated dome structures is complicated and closely related to both the member buckling and the overall buckling of the structure. However, little theoretical research work deals with this very complex phenomenon. Meanwhile, for the statically indeterminate structures, it is a common belief that the local failure would occur first and result in the change of internal force paths, while the structure could support load continually before the overall collapse of the structure. In this paper, the interaction between the member buckling and the overall buckling of the structure was investigated, and this common belief was explored. The geometrically and materially nonlinear analyses (GMNA) were carried out for the reticulated domes with eight types of different grid forms, and the examination of member buckling for each dome was conducted based on the examination method of the P – δ end curve or the P – δ mid curve of the member. The relationship between the member buckling and the global instability of the structure was obtained by evaluation results of member buckling. Consequently, for the common reticulated domes, two instability patterns were identified, i.e. progressive instability and synchronous instability. In the case of progressive instability, the member buckling occurs in advance of the overall buckling of the structure. Then the number of the instable member increases, and finally the overall buckling of the structure occurs. In the case of synchronous instability, the member buckling and the overall buckling of the structure happen simultaneously. The interaction mechanism between the member buckling and the global instability of the structure was analyzed for both instability patterns. [ABSTRACT FROM AUTHOR]

Abstract: Presented in this paper is an analytical investigation on column stability of unbraced multi-storey frames with accounting for initial geometric imperfections, namely, out-of-straightness of columns and out-of-plumbness of the frame. Within the context of storey-based buckling and using the end-fixity factor to characterize the beam-to-column rotational restraints, the lateral stiffness of axially loaded columns in unbraced frames with consideration of the effects of the imperfections is derived. The formulations and procedure of calculating storey-based column effective length factors with explicit accounting for the initial geometric imperfections are then proposed. Numerical examples with parametric studies are presented to illustrate the effects of the out-of-straightness and the out-of-plumbness on the column effective length factors and column strengths. The proposed method enables the practitioners to explicitly evaluate column strengths for any given values of the initial geometric imperfections, which is not available in the current design practice. [Copyright &y& Elsevier]

Codes of practice rely on the effective length method to assess the stability of multi-storey frames. The effective length method involves isolating a critical column within a frame and evaluating the rotational and translational stiffness of its end restraints, so that the critical buckling load may be obtained. The non-contradictory complementary information (NCCI) document SN008a (Oppe et al., 2005) to BS EN 1993-1 (BSI, 2005) provides erroneous results in certain situations because it omits the contribution made to the rotational stiffness of the end restraints by columns above and below, and to the translational stiffness of end restraints by other columns in the same storey. Two improvements to the method are proposed in this paper. First, the axial load in adjoining columns is incorporated into the calculation of the effective length. Second, a modification to the effective length ratio is proposed that allows the buckling load of adjacent columns to be considered. The improvements are shown to be effective and consistently provide results within 2% of that computed by structural analysis software, as opposed to the up to 80% discrepancies seen using the NCCI (Oppe et al., 2005). [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: The aim of this paper is to provide a consistent virtual work formulation for the nonlinear and postbuckling analysis of steel frames at high temperatures. Central to this study is the derivation of the virtual work terms for the thermal stage, in addition to those for the loading stage, based on the updated Lagrangian formulation. The incremental stiffness equation derived for the beam element, considering both the geometrical and thermal effects, is qualified by the rigid body test. The generalized displacement control (GDC) method is adopted as the path-tracing scheme for postbuckling response. Eurocode-3 reduction factors and transformed section method are both adopted for steel I-sections. Two loading cases are studied. For structures loaded gradually under constant temperature, the critical or ultimate loading strength is obtained from the load-deflection curve. For structures heated gradually under constant loading, the critical or maximum temperature that can be sustained by the structure is computed. Conclusions are drawn for the examples studied in this paper. [Copyright &y& Elsevier]

Abstract: This paper examines the stability and natural frequencies of the transverse vibrations of a slender articulated column with a pair of collocated piezoactuators. Buckling of the column can occur as one of the supports is subjected to a prescribed displacement, shortening the length of the system. The phenomenon can be counteracted by the tensile force generated by the actuators. The residual tensile force for a column with both ends restrained against longitudinal displacements and an arbitrary number of collocated actuators is derived by a variational principle, and applied to the considered system. The influence of such a created stress, along with the location of the hinge and adjacent piezoactuators of different lengths, on the stated objectives are numerically investigated after solving the boundary value problem. Any change in the relation between the axial stiffnesses of the piezo-column system and the core column affects the induced tensile force and also influences the adequate bending stiffnesses and mass per unit length of the structure, which is reflected in the numerical results. The absolute and relative enhancements in the critical force are presented for different geometrical parameters of the column. It is shown that the determined vibration modes can be employed to explain and interpret the first and second critical loads. Additional results show how a second pair of piezoactuators changes the courses of the natural vibration curves and affects the buckling force of the system. [Copyright &y& Elsevier]

Buckling is one of the typical failure modes for single-layer reticulated shells (SLRSs). To prevent buckling, it is necessary to predict the critical buckling load and post-buckling path of the structure, and hence, structural stability analysis should be carried out. Unlike ideal structures, SLRSs with stochastic imperfections could experience different failure modes with varied post buckling paths. In the present paper, a stochastic imperfection modal superposition method is proposed for SLRS with stochastic imperfections. The SLRS structure is modeled using Timoshenko beams. Considering several possible buckling modes and random variables, Monte Carlo simulations are performed to analyze the superposition of buckling modes of the structure with stochastic imperfections. The modal combination factor is treated as a random variable and different distributions types are used for comparisons, such as uniform distribution, Gaussian distribution, T-Gaussian distribution, and triangular distribution. Based on parametric study results and comparisons with other traditional stability analysis method, the proposed method is found to provide good accuracy at considerably less computation cost. [ABSTRACT FROM AUTHOR]

The behaviour of monosymmetric steel sections when they become fully plastic under the action of an axial force P and a bending moment M applied in the plane of symmetry is considered. Attention is focused on the cross sectional strength, the possibility of local buckling occurring being ignored. The interaction curve that relates the co-existing values of P and M when the section becomes fully plastic is derived. The conditions that this curve must satisfy are established and a procedure for obtaining the curve is given. Interaction curves available for some T -sections are discussed; some anomalies are found in these curves. These are investigated and it is found that they exist because of the procedure used to obtain these curves; they disappear when the procedure proposed in this paper is used instead. If the procedure used previously in the analysis of monosymmetric sections is used to analyse eccentrically loaded doubly symmetric sections, the same anomalies are encountered; these also disappear when the proposed procedure is used. [ABSTRACT FROM AUTHOR]

Highlights: [•] Preloaded arch with rotational end restraints is susceptible to dynamic buckling. [•] Arch with equal end restraints has upper and lower dynamic buckling loads. [•] Arch with unequal end restraint has only one dynamic buckling load. [•] Effects of preloading, arch shape and stiffness of end restraints are significant. [•] Energy approach is effective for dynamic buckling of shallow arches. [Copyright &y& Elsevier]

Abstract: This paper presents an exact method for obtaining column’s designs with the maximum possible critical buckling load while maintaining the total structural mass at prescribed value equal to that of a known baseline design. The developed optimization model dealt with slender elastic columns that are axially graded in either material or wall thickness. The first type of columns with material grading is constructed from uniform segments that are fabricated from two different materials, making the physical and mechanical properties change piecewisely in the axial direction. Design variables include the volume fraction of the constituent materials as well as the length of each segment composing the column. The other type considers piecewise axial grading of the cross-section wall thickness of columns constructed from uniform homogeneous isotropic segments. The associated design variables include the wall thickness and length of each segment composing the column. The buckling load analysis in either case is performed via an exact method, which ensures the attainment of the global maximum critical load under the imposed equality mass constraint for any number of segments, type of boundary conditions, type of cross section and type of material of construction. Numerical examples and detailed results, which are based on dimensionless analysis, are given and useful design charts have been developed for the cases of simply supported and cantilevered columns. Actually, the given approach can be beneficial to guide structural engineers for choosing the significant design variables in a proper and efficient way without violating economic feasibility requirements. [Copyright &y& Elsevier]

Inelastic behavior of diagonally braced moment resisting frame (DBMRF) dual systems are investigated to determine their yield mechanisms and failure modes, and to quantify the load sharing between the moment frame and the gusset–brace subsystems. An improved performance is sought through new balanced design criteria that will increase a DBMRF system’s ductility, and permit yielding in multiple secondary stages at selected performance levels. The presented balanced design approach is based on a non-dimensional formulation, which addresses both tensile yielding and compressive buckling phases of DBMRF systems and considers the participation of all system constituents. The satisfaction of the proposed balanced design criteria is achieved through parametric studies carried out with high-fidelity three-dimensional finite element (FE) models that are globally and locally validated/verified against experimental data/numerical simulations available in open literature. Using the validated FE models, the collapse behavior of a representative set of DBMRF systems are examined, and the influences of the brace elements’ demand-to-capacity ratios, as well as the gusset plate connection types/sizes on the yield mechanisms and the failure modes are scrutinized. Both pushover and cyclic analyses are carried out; and the overall system ductility and energy dissipation values are investigated for different width-to-height ratios. The responses of system constituents are evaluated using the specified, as well as the expected material properties. The worked examples clearly demonstrate the utility of the proposed balanced design criteria in improving the DBMRF systems’ ductility, and in avoiding premature failure modes. [ABSTRACT FROM AUTHOR]

Abstract: This research paper aims to evaluate the influence of different vent hole geometries and welding on the strength of galvanized rectangular hollow sections K-joints typically used in tubular warren lattice girders. On the one hand, four different hole geometries were considered in this study, taking into account the standard recommendations and manufacturers suggestions. On the other hand, residual stresses derived from welding thermal loads on the RHS K-joints between tubular profiles were taken into account. Next, a nonlinear buckling analysis for each type of hole was undertaken and the numerical results have been validated in comparison with Eurocode 3-Part1.8. Finally, a design of experiments based on the previous FEM models was developed and a hundred different nonlinear buckling analyses were calculated, showing clearly the different joint failures, both in chord and braces. Surface response from each DOE analysis is presented and the most important conclusions of this work are exposed. [Copyright &y& Elsevier]

Abstract: In the present paper the focus is on the compressive response of short high strength reinforced concrete members having circular transverse cross-sections and reinforced with longitudinal steel bars and transverse spirals or hoops. An analytical model is proposed which allows one to estimate the confinement pressures exerted by transverse steel and by longitudinal bars during the loading process, taking into account the interaction of the hoops or spirals with the inner core both in the plane of the transverse steel and in the space between two successive hoops. Yielding of steel spirals or hoops and longitudinal bars including buckling phenomena and damage to the concrete core are also considered by means of variation in the elastic modulus and in the Poisson’s coefficient. The proposed mechanical model is able to reproduce the load-shortening curves of compressed members; it gives good agreement with several experimental data and with analytical results obtained by using other recent models available in the literature. [Copyright &y& Elsevier]

Abstract: The results of a finite element study on the behavior and capacity of W-shape steel beams reinforced with welded plates while under load are presented. The finite element model was verified using test results obtained from a concurrent experimental study involving the testing of six beam specimens reinforced while under load. The verified model was then used to investigate the effect of several influential parameters with the focus on reinforcing patterns, preload magnitudes at the time of welding, and initial imperfections of the unreinforced beam. Numerical results show that an increase in the preload magnitude at the time of reinforcing resulted in a reduction in the ultimate capacity of reinforced beams failing in lateral-torsional buckling. This reduction was more significant for a beam reinforced with a plate welded to its tension flange than that reinforced with a plate welded to each of its flanges. The variation of initial imperfections of unreinforced beams was also shown to affect the ultimate capacity of the reinforced beam. For beams failing by yielding, the effects of preload magnitudes and initial imperfections were marginal. [Copyright &y& Elsevier]

Long runs of cold-formed steel Z-section purlins are often segmented due to assemblage and transportation issues. The segments are commonly connected by bolts to a short cold-formed steel member similar to the purlin; this short member is typically called a sleeve; from a structural point of view, it does not guarantee a state of full continuity to the purlin. This study reports a series of 15 experiments on cold-formed steel Z-sections purlins with sleeved bolted connections tested in bending. These experiments vary cross-section height, thickness and length of sleeve, and span. This parametric experimental study seeks to better understand the flexural-buckling strength, collapse mechanism, and moment-rotation behavior of purlin-sleeve systems. Since the design of purlins with sleeved bolted connections is often limited by the serviceability limit state, in this case excessive displacement, special attention is given to accurately determining and understanding the moment-rotation behavior of purlin-sleeve systems. Based on the experimental results, an expression is proposed to predict non-linear moment-rotation behavior; the proposed expression is compared to expressions previously proposed in the literature. The proposed moment-rotation expression, when used in a simple rotation spring-beam model, leads to accurate prediction of displacement and bending moment in the purlin-sleeve system at any load stage. [ABSTRACT FROM AUTHOR]

The instability behaviour of eccentrically loaded circular masonry columns is investigated. Two approaches are considered for the analysis. One is based on a semi-analytical formulation of the relevant boundary-value problem for a no-tension material response; the other employs a plastic-damage-contact constitutive model, the CraftS model, to capture the complex microstructural behaviour of the material. The latter has been implemented in the finite element program LUSAS and has been already successfully employed to describe progressive instability in eccentrically loaded brickwork wallettes of rectangular cross section. Equilibrium paths and limit load estimates are computed for both analysis approaches for a range of column aspect ratios and load eccentricities. It is shown that the type of material response becomes less important for specimens with height-to-diameter aspect ratios greater than 7.5 and for loads applied to points in the kernel of the cross section, while for higher eccentricities the presence of a tensile strength increases considerably the limit load. The damage evolution predicted by the models is also investigated for selected cases, showing that the formulation based on the no-tension material is able to capture with good agreement the damaged zone of the column for loads with low eccentricities. For the same type of loading, a useful design formula is provided. [ABSTRACT FROM AUTHOR]

Abstract: Based on a seven-degree-of-freedom shear deformable beam model, analytical solutions are derived for the lateral stability analysis of cross-ply laminated thin-walled beams subjected to combined axial and bending loads. The model includes shear deformability in a full form, i.e. shear flexibility due to both bending and nonuniform warping is considered. The theory is formulated in the context of large displacements and rotations, considering moderate bending rotations and large twist. Composite is assumed to be made of symmetric balanced laminates and especially orthotropic laminates. The closed-form analytic expressions obtained in this paper are valid for simply supported bisymmetric beams. These fundamental solutions explicitly identify the influence of geometric nonlinear effects due to the prebuckling deformation. The numerical results are compared with the bifurcation loads of the postbuckling response. In addition, the effects of the variation of load height parameter and fiber angle orientation are investigated. [ABSTRACT FROM AUTHOR]

Creep in structural steels at high temperatures has been widely observed in experiments; however its inclusion in numerical simulations has been limited due to lack of experimental creep data and the corresponding constitutive model for ASTM A992 structural steels. Recently published experimental creep data for ASTM A992 steels (Morovat et al., 2012) helped alleviate the first problem and this paper addresses the second issue related to modeling of high temperature creep. To this end, first the physical mechanisms underlying the creep phenomenon in metals are revisited and the frameworks for modeling high temperature creep are discussed. A hyperbolic sine model is then used to fit the experimental creep data for ASTM A992 steel and the corresponding best fit parameters are provided. Finally, high temperature creep buckling of ASTM A992 steel columns is examined and it is shown that creep can play an important role, especially at high temperatures and/or loads. [ABSTRACT FROM AUTHOR]

Steel plate shear walls with beam-connected web plates (B-SPSWs) are an alternative configuration of steel plate shear walls (SPSWs) where web plates are connected to the beams only. Detaching web plates from columns and introducing simple beam-column connections in B-SPSWs eliminate flexural demands in the columns resulting from web plate tension field action; consequently, the columns of B-SPSWs are designed primarily for axial loads. A recent study, however, showed that the columns of B-SPSWs resist significant flexural demands during earthquake shaking due to differential interstory drifts that result in significant column rotations at floor levels. Typical design methods (i.e., the Equivalent Lateral Force method and Modal Response Spectrum analysis) do not capture these rotations associated with differential drifts that might lead to column instability. A two-phase numerical study is conducted to evaluate the behavior and stability of B-SPSW columns. In the first phase, three-dimensional nonlinear response-history analyses are conducted to investigate the column stability for eighteen B-SPSWs with different geometric characteristics designed following two design approaches. The results suggest that column buckling is a possible mode of failure for one of the design approaches. In the second phase, a parametric study is undertaken to further investigate potential column buckling failure modes in B-SPSW columns and to establish an upper-bound estimate for the column buckling strength reduction due to column rotations at floor levels that are not considered in traditional design approaches. [ABSTRACT FROM AUTHOR]

Highlights: [•] The AEM could analyze the I35-W bridge behavior till its complete collapse. [•] The cause of collapse was obtained from the analysis and was found to be in very good agreement with the investigations of the collapsed bridge. [•] The failure of the gusset plates at connections L11 and U10 was found to initiate the collapse of the bridge. Their failure was initiated by their buckling. [•] The under-designed thickness of the plates, their corrosion, and the over loading were the reasons for the bridge collapse. [Copyright &y& Elsevier]

Highlights: [•] Critical review of design methods for slender RC panels under eccentric axial load. [•] Experimental campaign on cracked and uncracked centrally reinforced panels. [•] Improved capacity prediction using a computational model with lumped plasticity. [•] Testing and calculations combined with a Design Assisted by Testing (DAT) approach. [•] Novel and more efficient design capacity curve derived using the DAT procedure. [Copyright &y& Elsevier]

Abstract: The failure mode of a previously analyzed reinforced concrete (RC) hyperbolic cooling tower is re-investigated by means of the Finite Element Method (FEM), however, with another computer program. Furthermore, the original design of this cooling tower is changed. The changes include use of ultra-high-strength-fiber concrete (UHSF-concrete), reduction of the thickness of the shell, and consideration of imperfections of the original geometry of the structure. The main conclusion drawn from the numerical results is that the cooling tower would still fail by loss of strength, characterized by the existence of an ultimate load and of yielding of the reinforcement. [Copyright &y& Elsevier]