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A steel brace is effective to retrofit old reinforcement concrete (RC) buildings by increasing the horizontal load capacity of structures. However, concrete cracks that easily occur in the surrounding RC members under tension initiate early strength degradation, so this research aimed to develop a new self-centering brace (SCB) with the compression-only capacity such that no tension force is developed in the brace or to the adjoining RC members. Original SCBs have been developed to reduce the residual deformation of structures with a symmetrically flag-shaped hysteretic response. By altering the force transfer mechanism in the original SCB, a compression-only self-centering brace (C-SCB) can be developed under a symmetrically reversed cyclic loading, providing an alternative for the RC building retrofit. This paper first introduces the mechanics and deformation mechanism of the proposed C-SCB. A test program is then conducted on the cyclic tests of a buckling-restrained energy dissipating bar (EDB) to evaluate the energy dissipation. A 3,695-mm-long C-SCB is composed of posttensioning high-strength steel tendons, steel compression members, and buckling-restrained EDBs for the energy dissipation. The C-SCB in tests showed a good compression-only self-centering capability up to an axial displacement of 31 mm, with a maximum axial force of 1,530 kN. No damage of the steel tendons, compression members, or EDBs was found after three phase tests. Finite element analysis further validated the compression-only hysteretic response and mechanics of the C-SCB in a symmetrically reversed cyclic loading. [ABSTRACT FROM AUTHOR]

This paper presents a theory for the buckling of short beams considering cross-sectional distortions due to transverse shear (i.e., shear warping), based on the consistent linearization of a geometrically nonlinear planar beam. The proposed deformation field considers the warping amplitude as an independent kinematic field, and the hyperelastic material assumes that the stresses normal and tangent to the deformed cross section are linear with respect to their work-conjugate finite strains. An approximate closed-form solution to the resulting quartic equation for the critical load is provided to facilitate practical implementation. Theoretical differences giving rise to distinct buckling theories for higher-order shear beams are discussed in terms of (1) the assumed deformation field, (2) variational consistency, and (3) material constitutive relation. The proposed formulation is applied to evaluate the stability of infinite strip unbonded fiber-reinforced elastomeric isolators (FREIs) with moderate-to-high shape factor, for which shear warping is expected to have a major influence due to the flexural flexibility of the fiber reinforcement. A homogenization procedure is described to obtain effective isolator rigidities considering rubber compressibility and fiber extensibility. Next, a finite element parametric study of the buckling of unbonded infinite strip FREIs is presented, and the results are used as a benchmark to evaluate the adequacy of the proposed and existing formulations. The theory presented herein and its approximate solution exhibit the best match with the numerical results, and the latter is deemed adequate for practical application. [ABSTRACT FROM AUTHOR]

Little research has been reported that investigates the effects of plate local buckling and postbuckling on the in-plane behavior and strength of steel arches, and hitherto there has been no corresponding design guidance available. This paper presents a numerical investigation of the structural behavior of steel arches, and proposes a strength design method against their in-plane failure by considering plate local elastic-plastic buckling and postbuckling coupled with global elastic-plastic buckling. The failure modes of pin-ended steel circular arches having a box section under a uniformly distributed radial load are analyzed by using a large deformation elastic-plastic finite-element formulation. It is found that plate local buckling significantly influences the in-plane failure mode and strength of a steel arch. The arch may fail owing to local elastic-plastic buckling of its plates, global elastic-plastic buckling of the arch, or coupled local and global elastic-plastic buckling. The failure mode is found to depend on a number of factors such as the height-to-thickness ratio of the plate components, the aspect ratio of the cross section, the rise-to-span ratio, and the slenderness of the arch, as well as the yield stress of the steel. It is also found that the most important factors that influence the strength of the arch are the normalized global slenderness of the arch and the normalized height-to-thickness ratio of the plate components of the cross section. A strength reduction coefficient for estimating the in-plane strength of arches is developed based on these two most significant parameters, and a corresponding strength design method is proposed. [ABSTRACT FROM AUTHOR]

This paper presents an experimental investigation on the evaluation of the seismic performance of a new hybrid buckling restrained brace (HyBRB) under cyclic load. Detailed design steps adopted for the HyBRB design are reported in this paper. The analytical method for estimation of critical loads corresponding to buckling mode formation of the steel core inside the restrainer has been presented. The design targets achieved for the HyBRB are ease of inspection of the detachable BRB core to facilitate replacement of the steel core after a seismic event, if necessary, and enhanced energy-dissipation capacity through restrained buckling about both weak and strong axes of the core. The proposed HyBRB has displayed stable hysteretic behavior with good energy-dissipation capacity in low to high levels of the core strain range. Permanent deformation about the strong axis of the core was observed on unfastening of the restrainers, although restrained buckling of the core was observed about the weak axis in lower displacement amplitudes. Analytical simulation was carried out using a phenomenological model to simulate the experimental behavior. The simulated axial force-deformation hysteresis loops were found to be in close agreement with those obtained from experimental investigation. [ABSTRACT FROM AUTHOR]

This paper deals with the effects of geometric imperfections on flexural inelastic buckling resistance of axially loaded columns with equally spaced lateral braces and presents a simplified way of forming the critical geometric imperfection for finite-element analyses, which leads to rational results for buckling resistances. First, laterally braced columns with geometric imperfections formed by the traditional single half sine wave or the eigenbuckling modes were analyzed by FEM to illustrate the effect of different imperfection shapes. Second, geometric imperfections of columns acquired from measurements in laboratory tests were adopted, and the statistical characteristic and probability distribution of initial deflections along the column length were obtained; then, extensive numerical results from finite-element analyses were obtained through random imperfection simulations. Last, the comparison was made between statistical results based on the random imperfections and those based on eigenbuckling modes to propose a critical geometric imperfection shape as a linear superposition of a limited number of scaled eigenbuckling modes, making it possible to obtain a rational buckling resistance result by one-time analysis, which is safe but not too conservative. The commonly used lowest eigenbuckling mode or equivalent sine shape for initial geometric imperfections do not provide a rational prediction for the inelastic buckling resistance of laterally braced columns. The critical geometric imperfection shape presented in this paper can be used in advanced analysis for inelastic buckling resistance of braced columns. [ABSTRACT FROM AUTHOR]

Experimental work was conducted on oriented strand board webbed wood I-joists to investigate the buckling behavior. Both lateral buckling and local web buckling were witnessed in the tests. The two types of buckling were reproduced in the finite element simulations using ABAQUS. The buckling modes and usually overestimated buckling loads of a joist were obtained from linear eigenvalue buckling analysis. The buckling modes were then introduced into a joist as initial geometric imperfections to conduct nonlinear buckling analysis, and more reliable buckling loads were obtained. Based on statistics of the analytical results, the local web buckling capacity at a support was empirically expressed by the postbuckling load. The empirical formula was extended to local web buckling under a concentrated load applied to the upper flange, where a reduction in buckling load was made to take the effect of moment into account. [ABSTRACT FROM AUTHOR]

An experimental and numerical study of the flexural buckling behavior of hot-finished high-strength steel (HSS) square and rectangular hollow section (SHS and RHS, respectively) columns is described in this paper. A total of 30 hot-finished S460 and S690 hollow section column specimens have been tested in compression with pin-ended boundary conditions. Finite element (FE) models have been developed to replicate the experiments and employed in a subsequent parametric study considering a range of member geometries. Based on the test and FE results, the applicability of the current column design curves in European, North American, Chinese and Australian structural steel design standards to hot-finished HSS SHS and RHS columns has been verified by means of reliability analyses [ABSTRACT FROM AUTHOR]

This paper presents a new design methodology for equal-width rectangular hollow section (RHS) X-joints failing by sidewall buckling. In the new approach, a slenderness parameter is defined based on the elastic local buckling stress of the sidewall, idealized as an infinitely long plate under patch loading. A Rayleigh-Ritz approximation is thereby used to obtain a closed-form solution. The proposed design equation is verified against experimental results over a wide range of wall slenderness values obtained from the literature and complemented by a brief experimental program carried out by the authors. It is demonstrated that the new design equation yields excellent results against the experimental data. Finally, a reliability analysis is performed within the framework of both the Eurocode and the AISI standards to ensure that the proposed design equation possesses the required level of safety. The newly proposed equation strongly outperforms the current Comité International pour le Développement et l'Etude de la Construction Tubulaire (CIDECT) design rule for sidewall buckling and also further extends the range of applicability to a wall slenderness ratio of up to 50. [ABSTRACT FROM AUTHOR]

This paper describes an experimental program investigating the local-global interaction buckling of stainless steel I-section beams. Three alloys were included: austenitic S30401, ferritic S44330, and lean duplex S32101. Extensive coupon tests were conducted to determine the specific properties of stainless steel sheets, including nonlinearity, anisotropy, and strain hardening. The test program encompassed six laterally braced tests and 24 unbraced tests with spans ranging between 1.9 and 4.0 m. The unbraced specimens were tested in a specially designed setup featuring clearly defined loading and support conditions. Interaction buckling was successfully achieved in the tests. The geometric imperfections, bearing capacity, and sectional and global deformations of each specimen were carefully recorded before or during the tests. Key factors affecting the test conditions were identified. The research addressed the lack of experimental data for local-global interaction buckling of stainless steel beams with open cross section and establishes the foundation for further theoretical study, as described in a companion paper. [ABSTRACT FROM AUTHOR]

This paper is concerned with the plastic buckling of Mindlin plates of polygonal plan shape and whose straight edges are simply supported. The plates are subjected to a uniform in-plane compressive stress. Two well-known competing theories of plasticity are considered here: the incremental theory of plasticity (with the Prandtl–Reuss constitutive relations) and the deformation theory of plasticity (with the Hencky constitutive relation). Based on an analogy approach, the plastic buckling stresses of such Mindlin plates are expressed in terms of their corresponding elastic buckling stresses of Kirchhoff (classical thin) plates, albeit in a transcendental form. Using this buckling stress relationship and the readily available elastic buckling solutions, one may deduce the plastic buckling stresses of the corresponding Mindlin plates. Tabulated herein are some buckling stress factors for various polygonal shaped plates with material properties defined by the Ramberg–Osgood relation. [ABSTRACT FROM AUTHOR]

When a beam is subjected to an in-plane linear temperature gradient field, the thermal effects of the temperature gradient field tend to change the curvature of the beam in the transverse direction and to expand the beam in the axial direction. The rotation and expansion of the ends of the beam may be restrained elastically by its supports or by adjacent members such as columns. The restrained thermal actions will produce bending moments and compressive forces in the beam, and when these actions reach critical values the elastically restrained beam may bifurcate from its primary in-plane equilibrium configuration to an out-of-plane buckled equilibrium configuration. This paper investigates the thermoelastic out-of-plane buckling of an elastically restrained beam with a doubly symmetric cross section that is subjected to an in-plane linear temperature gradient field. The analytical solution for the critical temperature gradient for thermoelastic out-of-plane buckling of the beam is derived. It is found that the positions of the effective centroid and shear center of a cross section subjected to a linear temperature field are different from those under mechanical loads. Beams having a doubly symmetric cross section under a linear temperature gradient field behave as beam-columns with a monosymmetric cross section, thereby rendering the thermoelastic out-of-plane buckling of an elastically restrained beam under a linear temperature gradient field more complicated than its counterpart under mechanical loading. [ABSTRACT FROM AUTHOR]

This paper is devoted to the mechanical buckling analysis of thick composite plates under straight single-walled carbon nanotubes reinforcement with uniform distribution and random orientations resting on an elastic foundation. To develop the fundamental equations, the finite strip method, along with third-order shear deformation theory, is employed, and the total potential energy is minimized, which leads to an eigenvalue problem. The elastic foundation is modeled by classical and two-parameter simulations. For deriving the effective modulus of composite plates reinforced with carbon nanotubes, a method is used in which each straight carbon nanotube is modeled as a fiber with transversely isotropic elastic properties. The results of the numerical experiments, including the critical buckling loads for thick rectangular composite plates reinforced by carbon nanotubes with various boundary conditions and different volume fractions of nanotubes, are provided, and the positive effect of using carbon nanotubes reinforcement in mechanical buckling of plates is illustrated. [ABSTRACT FROM AUTHOR]

This paper presents an efficient higher-order nonlocal beam theory for the thermal buckling of nanobeams. The displacement field is chosen based on assumptions that the in-plane and transverse displacements consist of bending and shear components, and the shear components of in-plane displacements give rise to the parabolic variation of shear strain through the thickness in such a way that shear stress vanishes on the nanobeam surfaces. Therefore, there is no need to use a shear correction factor. The present model is capable of capturing both the small-scale effect and transverse shear deformation effects of nanobeams, and it has strong similarities with the nonlocal Euler-Bernoulli beam theory in aspects such as equations of motion, boundary conditions, and stress resultant expressions. Using the nonlinear strain-displacement relations, the equilibrium and stability equations of nanobeams are derived. The theoretical development presented herein may serve as a reference for nonlocal theories as applied to the instability analysis of a complex nanobeam system such as a complex carbon nanotube system. [ABSTRACT FROM AUTHOR]

Part I of this work was concerned with the experimental and numerical analysis of the lateral force, or thrust, exerted by the inner core of a buckling-restrained brace (BRB) when, after buckling in compression, it arrives into contact with the external retaining case. As Part II of that study, this paper considers the case of a steel-bolted BRB, with an empty gap between core and containment struts, to attempt the derivation of engineering analytical expressions for such a thrust. It is found that the relationship between applied axial force and buckled wavelength does not obey Euler's formula. [ABSTRACT FROM AUTHOR]

As a first endeavor, the differential quadrature method in conjunction with the genetic algorithms (GAs) is applied to obtain the optimum (maximum) buckling temperature of laminated composite skew plates. The material properties are assumed to be temperature dependent and the governing equations are based on the first-order shear deformation plate theory. After discretizing the governing equations and the related boundary conditions, a direct iterative method in conjunction with GAs is used to determine the optimum fiber orientation for the maximum buckling temperature. The applicability, rapid rate of convergence, and high accuracy of the method are established by solving various examples and by comparing the results with those in the existing literature. Then, the effects of the temperature dependence of the material properties, boundary conditions, length-to-thickness ratio, number of layers, and skew angle on the maximum buckling temperature of the laminated skew plates are presented. [ABSTRACT FROM AUTHOR]

The effect of fiber orientation is studied on the failure load of a laminated curved panel subjected to uniaxial compression for a combination of simply supported and clamped boundary conditions. The failure modes are specified as buckling and first-ply failure, with the failure load defined as the minimum of these two loads. The panel is taken as a shear-deformable symmetrically laminated angle-ply laminate, and the effect of fiber orientation on the failure load is investigated by considering several laminations consisting of 0, 90, and ply angles and by determining the failure load for different aspect ratios and panel thicknesses. The best ply angles for each stacking sequence are determined to maximize the failure load and the stacking sequence giving the highest failure load. The numerical results are obtained using an eight-noded shell finite element that avoids the parasitic shear or shear locking problem. It is observed that the rotational restraints at the curved edges have a major effect on the failure load. [ABSTRACT FROM AUTHOR]

A unique formulation for the elastic torsional buckling analysis of columns is developed in this paper based on the principle of stationary complementary energy. It is well known that in displacement based numerical formulations, discretization errors lead to stiffer behavior; hence convergence from above. On the other hand, discretization errors in complementary energy based numerical formulations lead to softer behavior in linear elasticity problems, which is a desired feature from the engineering view point. However, complementary energy based formulations can only overpredict the buckling loads for the flexural buckling problems of columns unless the physical conditions are compromised. In this study a formulation based on the principle of stationary complementary energy is considered for the elastic torsional buckling analysis of columns. The complementary energy expression is obtained from the well known total potential energy functional by using Frederichs’ transformation. In contrast to flexural buckling analysis of columns, it is shown that when the principle of stationary complementary energy is used, the torsional buckling loads can be underpredicted. A mathematical proof is provided to elucidate this property. The convergence behavior of the approximate solutions is illustrated through numerical examples for several columns with different boundary conditions. [ABSTRACT FROM AUTHOR]

Thermal buckling analysis of laminated smart composite plates subjected to uniform temperature distribution has been presented. Shape memory alloy (SMA) fibers whose material properties depend on temperature have been used as a smart material. A three-dimensional layerwise plate model has been employed in developing the system equations using variational approach. Finite-element method has been adopted for discretization of the laminate. Lagrangian interpolation functions have been used to approximate the displacement components along the thickness as well as in the in-plane direction. The actual variation of prebuckling stresses has been accounted for in the derivation of the geometric stiffness matrix of the laminates. An incremental load technique has been used in the analysis to take into account the nonlinearity in the material properties of the SMA arising due to their temperature dependence. The effects of thickness ratio, orthotropic ratio, fiber orientation, aspect ratio, stacking sequence and various boundary conditions on the critical buckling temperature have been examined in details. The results have been validated with those available in the literature. [ABSTRACT FROM AUTHOR]

The unilateral contact buckling problem of thin plates resting on tensionless foundations is investigated. Three different plate models are considered. For a plate of limited length on a tensionless elastic foundation, the plate is first simplified to a one-dimensional mechanical model by assuming a buckling mode in terms of transverse coordinates, after which a new method is employed to determine the initially unknown boundaries of the areas in contact. Based on the continuity condition on the borderline between contact and noncontact regions, the buckling mode displacements of the whole plate may be expressed through the critical load coefficient and the first half-wavelength, reducing the buckling problem to two nonlinear algebraic equations with two unknowns. This procedure has been named the transfer function method. For a very long plate with a symmetric buckling mode, an infinite plate model with two half-waves is presented. For a plate on a rigid foundation, a single half-wave buckling model is shown to be appropriate. Comparison of limiting cases with exact solutions and with ABAQUS results showed good agreement. Finally, the influences of aspect ratio and foundation stiffness are presented. [ABSTRACT FROM AUTHOR]

Approximate buckling formulas for shear–flexural buckling of cantilever columns subjected to a uniformly distributed load are derived, based on Timoshenko’s energy method. In this method the deflection curve at buckling is approximated by a trial function. Instead of trying to describe all possible buckling modes with one trial function, two trial functions are used: one to describe shear dominated localized buckling, another to describe bending dominated global buckling. It is investigated whether the bending dominated global buckling modes can best be described using polynomial functions, trigonometric functions, or a function defined by the lateral (flexural and shear) deflection of the cantilever column under uniformly distributed lateral load. The results of the derived formulas are compared to the exact solution and other approximate buckling formulas found in the literature. Attention is drawn to the fact that the shear–flexural buckling load cannot exceed the shear buckling load. [ABSTRACT FROM AUTHOR]

A Timoshenko beam model is presented in this paper for the buckling of axially loaded multiwalled carbon nanotubes surrounded by an elastic medium. Unlike the Euler beam model, the Timoshenko beam model allows for the effect of transverse shear deformation which becomes significant for carbon nanotubes with small length-to-diameter ratios. These stocky tubes are normally encountered in applications such as nanoprobes or nanotweezers. The proposed model treats each of the nested and concentric nanotubes as individual Timoshenko beams interacting with adjacent nanotubes in the presence of van der Waals forces. In particular, the buckling of double-walled carbon nanotubes modeled as a pair of double Timoshenko beams is studied closely and an explicit expression for the critical axial stress is derived. The study clearly demonstrates a significant reduction in the buckling loads of the tubes with small length-to-diameter ratios when shear deformation is taken into consideration. [ABSTRACT FROM AUTHOR]

This paper describes the buckling behavior of cold-formed steel equally lipped angle columns. The initial local imperfections, residual stresses, and corner material properties of the cold-formed steel angles have been measured experimentally and reported in this paper. An accurate finite element model was developed to carry out the buckling analysis. Both initial local and overall geometric imperfections have been incorporated in the model. The effect of residual stresses on the buckling behavior was investigated. The material nonlinearities of flat and corner portions of the angle sections were considered in the analysis. The finite element analysis was performed on equally lipped angles compressed between fixed ends for different column lengths, and column curves were obtained. The nonlinear finite element model was verified against recent experimental results. An extensive parametric study was carried out using the finite element model to study the effects of cross section geometries on the strength and behavior of lipped angle columns. The column strengths predicted by the finite element model were compared with the design strengths calculated using the North American Specification and Australian/New Zealand Standard for cold-formed steel structures. In addition, the results obtained from the finite element model were also compared with the design strengths obtained from proposed design rules. It is shown that the proposed design rules accurately predicted the column strengths for non-slender lipped angles and were quite conservative for slender lipped angles. [ABSTRACT FROM AUTHOR]

A hierarchical high-fidelity analysis methodology for predicting the critical buckling load of compression-loaded thin-walled isotropic shells is described. This hierarchical procedure includes three levels of fidelity for the analysis. Level 1 assumes that the buckling load can be predicted by the classical shell solution with simply supported boundary condition, and with a linear membrane prebuckling solution. Level 2 includes the effects of a nonlinear prebuckling solution and the effects of traditional clamped or simply supported boundary conditions. Level 3 includes the nonlinear interaction between nearly simultaneous buckling modes and the effects of boundary imperfections and general boundary conditions. Various deterministic and probabilistic approaches are used to account for the degrading effects of unavoidable shell-wall geometric imperfections. The results from the three solution levels are compared with experimental results, and the effects of the assumptions and approximations used for the three solution levels are discussed. This hierarchical analysis approach can be used in the design process to converge rapidly to an accurate prediction of the expected buckling load of a thin-shell design problem. [ABSTRACT FROM AUTHOR]

A practical model has been developed to predict, for a given level of lateral deformation, the likelihood that longitudinal bars in a reinforced concrete column will have begun to buckle. Three relationships linking plastic rotation, drift ratio, and displacement ductility with the onset of bar buckling were derived based on the results of plastic-hinge analysis, moment-curvature analysis, and the expected influence of the confinement reinforcement. These relationships, which account for the effective confinement ratio, axial-load ratio, aspect ratio, and longitudinal bar diameter, were calibrated using observations of bar buckling from cyclic tests of 62 rectangular-reinforced and 42 spiral-reinforced concrete columns. A version of the drift ratio relationship is proposed for earthquake engineering applications. The ratios of the measured displacements at bar buckling to the displacements calculated with the proposed model had a mean of 1.01 and a coefficient of variation of 25% for rectangular-reinforced concrete columns. The corresponding mean and coefficient of variation for spiral-reinforced columns were 0.97 and 24%, respectively. [ABSTRACT FROM AUTHOR]

This paper presents experimental and numerical results of the elastic–plastic response and buckling of S3×5.7 steel and aluminum I-beams subjected to cyclic pure bending. A special four-point bending device was designed and built for this purpose. The emphasis of the work is on the description of the response and buckling of the beams. The numerical results were obtained using a commercial finite element program that implements the nonlinear kinematic hardening plasticity model. The results indicate that the beams considered, most of which had length-to-height ratio of 5, buckled first in a global mode involving either twisting or lateral deflections of the beams. The prevailing deflection mode seems to be determined by the nature of the initial geometric imperfections. The deformations induced by the global deflections could induce a local buckle at mid-span. The finite element predictions yield results that qualitatively reproduce the development of most of the aspects of the response of the beams, but generally at a slower rate. [ABSTRACT FROM AUTHOR]

Recently, passive vibration control design has gained popularity. The aim of this design is to absorb most of the seismic energy by using additional dampers while maintaining the elasticity of the main structure. Buckling restrained braces (BRBs) are used as one of the elastoplastic dampers in this design and, therefore, the cumulative deformation capacity of BRBs to the point of fatigue fracture is an important benchmark for their performance. The estimation of this value under a random amplitude is complicated however, as this value is affected by the loading history. In this study, past experiments on BRBs are revisited in order to investigate the relation between the cumulative deformation capacity and the applied loading history. Based on these analyses, a simple method is proposed for predicting the cumulative deformation and energy absorption capacities of BRBs under random amplitudes. In contrast to Miner’s method, the proposed method does not require analyses of the individual amplitudes, and the values of interest are directly determined from the response indexes. [ABSTRACT FROM AUTHOR]

This paper is concerned with the buckling analysis of simply supported rectangular Reissner–Mindlin plates subjected to linearly varying edge loads. An analytical solution is developed and the effect of load intensity variation on the critical load is investigated. The solution is verified with the commercial computer code ANSYS. It is observed that the results of the present solution are in excellent agreement with those of ANSYS. The inaccuracy of the currently cited data in some design handbooks is highlighted. [ABSTRACT FROM AUTHOR]

A total of 23 tests were conducted to study the cyclic loading performance of links in steel eccentrically braced frames. The objectives of these tests were to reevaluate flange slenderness limits and overstrength factors for links. The effect of loading history on link performance was also investigated. Link specimens were constructed from five different wide-flange sections, all of ASTM A992 steel, with various lengths ranging from short shear yielding links to very long flexural yielding links. In addition to providing data on the effects of flange buckling and overstrength, these tests also showed some unexpected failure modes. The paper provides an overview of this experimental investigation, describing the overall research program, as well as details of the test specimens and test results. The paper concludes with a number of design recommendations for links in eccentrically braced frames. [ABSTRACT FROM AUTHOR]

The paper deals with the effect of moisture and temperature on the buckling response of a laminated composite plate subjected to hygrothermomechanical loadings. Mechanical loading consists of uniaxial, biaxial, and shear. The distribution of temperature and moisture on the surface is considered to be uniform. The degradation in material properties due to moisture and temperature is taken into account using a micromechanical model. The mathematical formulation is based on higher order shear deformation theory and von Karman's nonlinear kinematics. A C0 finite-element method based on higher-order shear deformation plate theory is used for deriving the standard Eigenvalue problem. ATaylor series based mean-centered first-order perturbation technique is used to find out the second-order statistics of the hygrothermal buckling loads. The effects of temperature rise, moisture concentration, fiber-volume fraction, and plate parameters on buckling response of the plate are presented. [ABSTRACT FROM AUTHOR]

The analytical solution of a buckling force of a pretwisted delaminated composite column with a proper consideration of the extensional and bending stiffness coupling and transverse shear effect is presented. The system of homogenous linearized differential equations with nonconstant coefficients obtained for this problem is solved with the help of the mathematical theory of analytic differential systems. The parametric studies are presented considering the effect of slenderness, the length of delamination, the asymmetrical position of delamination, and the transverse shear on the critical buckling force. [ABSTRACT FROM AUTHOR]

The present study estimates the critical/buckling loads of laminated composite rectangular plates under in-plane uniaxial and biaxial loadings. The formulation is based on the first-order shear deformation theory and von-Karman-type nonlinearity. Chebyshev series is used for spatial discretisation and quadratic extrapolation is used for linearization. An incremental iterative approach is used for estimation of the critical load. Different combinations of simply supported, clamped and free boundary conditions are considered. The effects of plate aspect ratio, lamination scheme, number of layers and material properties on the critical loads are studied. [ABSTRACT FROM AUTHOR]

In this paper, stability analysis of thick annular sector plates under mechanical and thermal loads based on third-order shear deformation theory (TSDT) is investigated. The equilibrium and stability equations based on TSDT are obtained and solved analytically by doing some mathematical manipulation. Then, for nine possible boundary conditions, the buckling load and temperature are calculated and compared with those obtained using different plate theories. As the results show, for boundary conditions that include simply supported and clamped edges, the minimum value for buckling load and temperature is predicted by first-order shear deformation theory (FSDT) and maximum value is predicted by classical plate theory (CPT). Also, for boundary conditions containing free edges, the value obtained by TSDT is larger than that obtained using CPT and FSDT for some values of thickness/length ratio. It is worthy to mention that the results obtained from CPT for boundary conditions containing free edges in a wide range of thickness/length ratio are acceptable. [ABSTRACT FROM AUTHOR]

The local buckling behavior of longitudinal reinforcing steel, which occurs between two transverse hoops, is examined using rational mechanics, taking into account the full plastic behavior of the steel and the effects of true stress and strain. A computational fiber element analysis is used to compute the coupled effect of axial compression and lateral buckling. The results of the computational analysis are then used to develop a simple model for the compressive behavior of longitudinal reinforcing steel in engineering stress-strain coordinates. Although several models exist that are capable of predicting compressive behavior with a moderate degree of precision, these models are generally computationally intensive and therefore of little practical use to structural designers. Other existing simple models either have a high degree of built-in empiricism or are based on overly simplified assumptions about the plastic behavior of the steel. The minimalist model developed in this study is compared with available experimental results. A statistical study shows favorable correlation between the proposed analytical model and experimental results. [ABSTRACT FROM AUTHOR]

Tubular-section members are commonly used as seismic-resistant braces because they have a higher moment of inertia than open cross sections of equivalent area. However, the cumulative cyclic deformation capacity of tubular sections after buckling is smaller than that of open sections, such as H-shaped sections, because fracture is initiated by local buckling of circular tubular sections. To evaluate the seismic performance of such diagonal braces, it is essential to predict the cumulative cyclic deformation capacity of these braces before any fracturing. In this study, the cumulative cyclic deformation capacity of circular tube braces under local buckling was assessed by performing cyclic loading tests for a range of slenderness and diameter-to-thickness ratios. The mechanism of strain concentration in the tubular braces was studied in various types of analysis, and a method is proposed for assessing the cumulative deformation capacity before fracture based on the entire axial deformation of the braces. [ABSTRACT FROM AUTHOR]

This paper presents a study of buckling and postbuckling behaviour of simply supported composite plates subjected to nonuniform in-plane loading. The mathematical model is based on higher order shear deformation theory incorporating von Kármán nonlinear strain displacement relations. Because the applied in-plane edge load is nonuniform, in the first step the plane elasticity problem is solved to evaluate the stress distribution within the prebuckling range. Using these stress distributions, the governing equations for postbuckling analysis of composite plates are obtained through the theorem of minimum potential energy. Adopting Galerkin's approximation, the governing nonlinear partial differential equations are reduced into a set of nonlinear algebraic equations in the case of postbuckling analysis, and homogeneous linear algebraic equations in the case of buckling analysis. The critical buckling load is obtained from the solution of associated linear eigenvalue problem. Postbuckling equilibrium paths are obtained by solving nonlinear algebraic equations employing the Newton-Raphson iterative scheme. Explicit expressions for the plate in-plane stress distributions within the prebuckling range are reported for isotropic and composite plates subjected to parabolic in-plane edge loading. Buckling loads are determined for three plate aspect ratios (a/b=0.5, 1, 1.5) and three different types of in-plane load distributions. The effect of shear deformation on the buckling loads of composite plate is reported. The present buckling results are compared with previously published results wherever possible. [ABSTRACT FROM AUTHOR]

A sandwich beam buckling problem is studied here using two-dimensional elasticity to model the beam constituents. The global and local instability of such a beam with orthotropic constituents under various boundary conditions are investigated. The face sheet and the core are assumed to be linear elastic orthotropic continua. General buckling deformation modes of the sandwich beam subjected to uniaxial compressive loading are considered. The appropriate incremental stress and conjugate incremental finite-strain measure for the instability problem of the sandwich beam, and the corresponding constitutive model are addressed. It is shown that a sandwich beam having a core with a negligible stiffness compared to the face sheets is prone to fail by edge buckling. The present analysis is compared with several previous analytical studies and corresponding experimental results. Finite-element analyses are carried out for comparison against the theoretical predictions. The formulation used in the finite-element code is discussed in relation to the formulation adopted in the theoretical derivation. [ABSTRACT FROM AUTHOR]

The paper presents a model for the inelastic buckling behavior of steel braces. The model consists of a force-based frame element with distributed inelasticity and fiber discretization of the cross section. With this approach, the response of the element can be derived by integration of the uniaxial stress-strain relation of the fibers and can account for kinematic and isotropic hardening as well as the Bauschinger effect of the material. The interaction between axial force and bending moment is thus accounted for. Even though the element only accounts for small deformations in the basic system, large displacement geometry is included in the nonlinear transformation of the force-deformation relation of the basic element following the concept of the corotational formulation. With this approach, two elements for each brace suffice to yield results that match an extensive set of experimental data of braces with different cross sections and slenderness ratios. Even though the model does not account for the effect of local buckling, this phenomenon does not seem to appreciably affect the global response of braces with compact sections. [ABSTRACT FROM AUTHOR]

This paper is concerned with an application of the Ritz method for elastic, axisymmetric, buckling analysis of moderately thick, rotational orthotropic shells under uniform external pressure. In order to capture the effect of transverse shear deformation, which is significant for thick shells, the Mindlin shell theory is used. In applying the Ritz method, the displacement components of the shell are approximated by the product of one-dimensional polynomial functions, and the boundary equations are raised to the appropriate powers so as to ensure the satisfaction of geometric boundary conditions a priori. The validity of the method, convergence and accuracy of solutions are demonstrated using spherical shells, which is a special case of rotational shells, where closed-form solutions exist for some cases. A parametric study is conducted on spherical and parabolic shells, considering the effects of height-to-base-radius ratios, thickness-to-radius ratios, and different support conditions on the buckling solutions. The new solutions should be useful to researchers and engineers who are developing analytical tools and designs of shells. [ABSTRACT FROM AUTHOR]

When subject to combinations of internal pressure and axial compression, experience shows that the often thin cylindrical shell walls of tanks and silos are prone to a local form of buckling failure that is essentially axisymmetric and is strongly influenced by the nature of the end or intermediate support conditions. This paper will outline the basis of an analytical solution to the inherently nonlinear elastic–plastic buckling into axisymmetric modes, in which end constraints and arbitrary radial pressure loading are modeled as essentially loading imperfections on an otherwise linear, classical, critical buckling formulation. Closed form analytical expressions for the imperfect behavior, including geometric imperfections, are then used to predict either first surface or full section plasticity, allowing buckling failure to be summarized in a form that is closely analogous to the Ayrton–Perry formula for the buckling of columns. It is suggested that a suitably simplified form of this general approach to axisymmetric buckling, when combined with similarly simple methods for the buckling into nonaxisymmetric modes, could provide an important alternative to the current procedures for the buckling design of thin-walled, cylindrical, tanks and silos. [ABSTRACT FROM AUTHOR]

This paper is concerned with the elastic buckling problem of circular Mindlin plates with a concentric internal ring support and elastically restrained edge. In solving this problem analytically, the circular plate is first divided into an annular segment and a core circular segment at the location of the internal ring support. Based on the Mindlin plate theory, the governing differential equations for the annular and circular segments are then solved exactly and the solutions brought together by using the interfacial conditions. New exact critical buckling loads of circular Mindlin plate with an internal ring support and elastically restrained edge are presented for the first time. The optimal radius of the internal ring support for maximum buckling load is also found. An approximate relationship between the buckling loads of such circular plates based on the classical thin plate theory and the Mindlin plate theory is also explored. [ABSTRACT FROM AUTHOR]

The numerical solution of problems of curved rods can be formulated using rod elements developed within the context of the theory of a Cosserat point. It is well known that the buckling of shallow arches presents a formidable challenge to theoretical models because it necessarily requires accurate modeling of the nonlinear coupling of membrane and bending effects as well as the accurate prediction of prebuckled deformations. This paper shows that the Cosserat theory predicts buckling loads and deformed shapes of elastic clamped circular arches which are in excellent agreement with the experiments over the full range of arch geometries that were tested. This success suggests that the Cosserat theory can be used to obtain reliable results for nonlinear deformations of curved elastic rods. Moreover, the analysis of these experiments indicates that variations in the thicknesses of shallow arch structures due to standard tolerances have a strong influence on buckling loads and should be measured and controlled in accurate buckling experiments. [ABSTRACT FROM AUTHOR]

Current models to determine the local buckling stress of inelastic plates under in-plane loading are based on plastic deformation theory and semirational or empirical relationships. A successful J2 flow theory describing inelastic local buckling of initially perfect plates needs to avoid two well-known pitfalls known as the “inelastic column buckling paradox” and the “plastic buckling paradox.” While the former problem, which found its origin in 1895 in Engesser’s double modulus approach, was resolved by Shanley in the late 1940s, a convincing solution of the plastic buckling paradox has not yet been presented. This paper proposes a modification to the J2 flow theory which hinges on the determination of the shear stiffness from second-order considerations. A differential equation is derived which describes the incremental plate deformations at the inelastic local buckling load. The differential equation is studied for two cases of boundary conditions: a plate simply supported along four edges and a plate simply supported along three edges with one longitudinal edge free. [ABSTRACT FROM AUTHOR]

Building codes and common design practices generally assume that the lateral support provided by the soil is sufficient to prevent buckling of fully embedded piles. As small diameter grouted piles (micropiles) have evolved from relatively low capacity friction piles to current applications that include high capacity elements, there is a need to revisit the issue of potential buckling of these very slender piles when embedded in soft soils. Pile buckling loads obtained from a semiempirical relationship are compared to the allowable loads permitted by current and proposed codes and design guidelines. It is concluded that buckling is generally not a concern for the most common types of micropile design, but there are some designs permitted under the codes and design guidelines for which buckling may be a controlling design factor. [ABSTRACT FROM AUTHOR]

This paper addresses the buckling behavior and strength of hybrid pultruded short profiles subjected to uniform compression. Since the design of glass fiber-reinforced polymer (GFRP) pultruded profiles is often governed by deformations and buckling phenomena, the introduction of carbon fibers in GFRP (hybrid) profiles has been proved to increase both strength and stiffness of flexural members. In the context of short compression members (columns), experimental, numerical, and analytical studies were carried out, with particular attention being given to the local buckling. Two series of 660-mm-long I-section profiles () were tested under uniform compression. In order to evaluate the advantages of introducing carbon fiber reinforcement in the flanges, two profile types were tested: bare GFRP profile (reference column) and carbon fiber reinforced polymer (CFRP) strengthened GFRP profile (hybrid column). Shell finite-element (SFE) models were developed and validated, based on experimental data. After that, and in order to predict the critical buckling loads of the tested columns, a study was performed using analytical solutions based on the orthotropic plate theory. Both numerical and analytical results presented a good agreement with experimental data. Results obtained show that the critical load, the ultimate load, and the axial stiffness considerably increase with the introduction of CFRP sheets in the flanges of the GFRP profile. [ABSTRACT FROM AUTHOR]

Warping restraining devices can result in substantial improvements in the girder elastic buckling capacity; however, calculating this increase can be complex. This paper presents a simplified method to evaluate the increase in elastic buckling strength and corresponding unbraced length due to improved warping restraint provided by split pipe stiffeners located at the ends of doubly symmetric W-shapes. The solution is based on analytical studies and results from a finite-element parametric study validated using large-scale laboratory tests. The laboratory tests include specimens exposed to concentrated loads with split pipe warp-restraining devices and others with standard plate stiffeners. The proposed analytic method is based on uniform moment and shows that warping restraint can increase the elastic buckling capacity of a girder by 30-100%. The improved warping stiffness can result in increases in the unbraced length in the range of 20-35% compared with systems with plate stiffeners. [ABSTRACT FROM AUTHOR]

Presents a study which applied a 2-dimensional higher-order shell theory to the buckling problems of a thick circular cylindrical shell subjected to axial compression. Analysis of buckling problems of a simply supported circular cylindrical shell subjected to axial compression; Principle of virtual displacements; Comparison of the obtained buckling stresses with those of the existing theories.

An unconstrained gusset connection for buckling restrained braces in reinforced concrete frame structures is proposed and tested as an effort to mitigate the complicated and usually harmful interactions between the steel gusset plate and the adjoining reinforced concrete column. Local damage control incorporating the rearrangement of beam flexural strength is also proposed to enhance the reliability of the gusset connection by moving the potential plastic hinge of the beam away from the connection region. Two different connecting methods, one with posttensioned steel rods and the other embedded stud groups, were considered. The results of the cyclic loading tests on reinforced concrete (RC) beam-gusset connection subassemblies confirmed that both connecting methods are available as long as the local damage control is implemented, which is not only helpful in eliminating the unfavorable deformation loss at the connection, but more importantly, can prevent the buckling restrained braces (BRBs) from being dislocated as a result of the beam end failure in extreme earthquake events. [ABSTRACT FROM AUTHOR]

Although steel single angle sections are commonly used as beams to support distributed loads which cause biaxial bending and torsion, their behavior may be extremely complicated, and the accurate prediction of their strengths very difficult. Further, many design codes do not have any design rules for torsion, while some recommendations are unnecessarily conservative, or are of limited application, or fail to consider some effects which are thought to be important. This paper is one of a series on the behavior and design of single angle section steel beams. Two previous papers have studied the biaxial bending behavior of restrained beams, a third has studied the lateral buckling of unrestrained beams, and a fourth the biaxial bending of unrestrained beams. In each paper, simple design methods have been developed. In this present paper, an approximate method of predicting the second-order deflections and twist rotations of steel equal angle beams under major axis bending and torsion is developed. This method is then used to determine the approximate maximum biaxial bending moments in such beams, which are then used with the section moment capacity proposals of the first paper of the series and the lateral buckling proposals of the third paper to approximate the member capacities. This method is extended to steel unequal angle beams in a companion paper. [ABSTRACT FROM AUTHOR]

A structural engineer wishing to determine the buckling load of unequal-leg angle columns receives conflicting information from published literature because researchers offer two radically different models for their analyses of thin-walled open-profile bars. One model considers the bar to be a continuum whereas the American Institute of Steel Construction adopts a noncontinuum multifilament model. Furthermore, the continuum model defines the normal planes of the deflected bar with the line of centroids whereas the multifilament model uses the shear center line. A test program based on 5×3×1/4 in. (127×76×6 mm) steel angles is proposed to resolve the issue by determining which model produces computed buckling loads that better correlate with collapse loads obtained from tests. The possibility that neither method produces a buckling load that correlates with collapse loads is not ruled out. [ABSTRACT FROM AUTHOR]

In this paper, buckling delamination around interface inner cracks contained within the simply supported elastic and viscoelastic rectangular sandwich plate under biaxial loading is studied. It is assumed that the materials of the face layers are viscoelastic and the material of the core layer is pure elastic. Moreover, it is assumed that the material of the core layer is stiffer than the materials of the face layers. Within these assumptions it is supposed that between the face and core layers there are rectangular inner cracks, the locations of which are symmetric with respect to the plate geometry. The edge surfaces of the cracks have insignificant initial imperfections before the loading. The evolution of these initial imperfections with the flow of time is investigated within the scope of the three-dimensional (3D) geometrically nonlinear field equations of the theory of viscoelasticity. For determination of the values of the critical parameters (buckling force, time, and buckling mode), the initial imperfection criterion (i.e., the case where the size of the initial imperfection starts to increase and grows indefinitely) is used. Mathematical modeling of the corresponding boundary value problem is formulated within the framework of the piecewise homogeneous body model. To solve the corresponding boundary-value problems, boundary form perturbation techniques, the Laplace transform, 3D FEM modeling and the Schapery method are used. The numerical results related to the influence of the materials or geometrical parameters of the plate on the critical parameters and critical time are presented and analyzed. [ABSTRACT FROM AUTHOR]