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Innovation in cold-formed steel framing systems is needed for opening flexibility and application in mid-rise buildings. Hence, this study proposes a closed built-up section using four cold-formed steel (CFS) open sections with a high load bearing capacity that potentially enables the development of high-performance cold-formed steel framing systems for these. The closed section by combining four open CFS sections using fasteners can effectively enhance the load capacity of the sections under axial loading. With a specially designed intersections gusset plate this built-up section offers more potential configurations of beam-column moment connections for CFS structures. First, a heuristic optimization was performed to identify a high-performance section based on the local and distortional buckling strengths using the finite strip method. Second, a test program was developed to investigate the load bearing capacity and failure behaviors of the optimized built-up closed section under axial and eccentric loading. Third, their load bearing capacities were compared with several other closed sections such as the rectangular hollow tube (RHS) of equal cross-sectional area or equal moment of inertia to highlight the high material efficiency. This study paved the groundwork for exploring high-performance cold-formed steel framing systems with this unique closed built-up section. • Proposed a closed built-up section for two-way cold-formed steel framing systems. • Investigated the compression behavior and strength of specimens under axial and eccentric loadings. • Achieved a high load-bearing capacity of the closed built-up section. • Conducted a comparable analysis with equivalent rectangular hollow tube sections numerically. [ABSTRACT FROM AUTHOR]

High strength steel has been attracting attention in the building industry due to its superior mechanical properties. The accurate design of high strength steel structures is crucial to boost its wide application. In this paper, an accurate and unified design approach for high strength steel I-section columns with different material grades, boundary conditions, geometric dimensions (including cross-section sizes and member lengths) and failure modes is proposed based on machine learning. Firstly, 871 experimental and numerical data were collected from the literature to establish a database. Then, seven machine learning algorithms, including Decision Tree, Random Forest, Support Vector Machine, K-Nearest Neighbour, Adaptive Boosting, Extreme Gradient Boosting and Categorical Boosting, were applied to establish machine learning regression models to predict buckling resistances of high strength steel I-section columns. The model performance was then evaluated through statistic indices, with the evaluation results indicating that the Categorical Boosting trained model yields the highest level of accuracy. Based on the data in the collected database, the regression model trained by Categorical Boosting and existing codified design provisions, as given in the European code and American specification, were assessed and compared. The European code and American specification were found to yield scattered and inaccurate failure load predictions, while the Categorical Boosting trained model led to substantially more accurate and consistent failure load predictions for high strength steel I-section columns with different material grades, boundary conditions, geometric dimensions and failure modes. • A database including 871 structural performance data on high strength steel I-section columns was established. • Regression models were developed by using machine learning algorithms to predict load-carrying capacities. • The regression models were evaluated and the Categorical Boosting model provided the best performance. • The machine learning design method yielded improved design accuracy than the existing design codes. [ABSTRACT FROM AUTHOR]

Wire arc additive manufacturing (WAAM) is a method of metal 3D printing which, when strategically combined with traditional methods of manufacture, has the potential to make a significant impact on the construction sector. To illustrate this potential, an experimental investigation into the flexural buckling response of 15 hot-rolled I-section columns, strengthened by WAAM, has been undertaken and is presented herein. The WAAM material was added at the flange tips and distributed non-uniformly along the member length. Complementary tensile coupon tests on the I-section and WAAM steel material were also carried out. 3D laser scanning was employed to determine the geometry and global geometric imperfections of all specimens, while digital image correlation measurements were taken to provide a detailed insight into the surface deformation characteristics of the specimens during testing. The WAAM stiffeners provided three mechanisms of strengthening: (1) increased cross-sectional area and second moment of area, (2) enhanced local buckling capacity and (3) a more favourable residual stress pattern. Disproportionately high increases in axial capacity of between 17% and 54% for relatively modest increases of mass between 2% and 26% (of the weight of the strengthened I-section column) were achieved, demonstrating, for the first time, the substantial benefits in terms of enhanced structural efficiency and material savings, that can be realised by the combination of WAAM with traditional manufacturing methods. In the best case, the efficiency of the WAAM material (in terms of increase in load-bearing capacity per unit mass) was almost eight times that of the bare steel section. The described hybrid manufacturing concept can be employed to improve the performance and reduce the environmental impact of structures and could be a game changer in both new construction and the rehabilitation of existing infrastructure. [Display omitted] • Concept of hybrid construction featuring additive manufacturing was introduced. • WAAM stiffeners were added to I-section specimens to improve their flexural buckling strengths. • Geometric characteristics of test specimens were examined via 3D laser scanning. • Minor axis buckling tests on 15 strengthened and two bare columns were performed. • All strengthened columns were shown to exhibit enhanced structural efficiency. [ABSTRACT FROM AUTHOR]

In recent years, concrete-encased concrete-filled steel tube (CECFST) columns have gained popularity in structural engineering. Research studies have shown that this novel type of composite columns exhibits superior strength, ductility, stiffness, and resistance to fire and corrosion property when compared to alternative types of steel-concrete composite columns. Considering the increasing use of slender columns in practice, this study investigated structural behaviour of CECFST slender beam–columns subjected to combined compression and bending. In this paper, six pin-ended CECFST slender specimens with different section configurations, load eccentricities and slenderness ratios were tested under eccentric load. Key test results consisted of buckling mode analysis, load–deformation history, moment–curvature relationship and strain response at various locations. Results generally showed that P-δ effect deteriorated structural behaviour of CECFST slender beam–columns and this unfavourable effect should be addressed properly in the appropriate design code for composite columns. In this regard, design approaches in European code and American specification were evaluated in aspects of N–M interaction curve, moment magnification factor and effective flexural stiffness (EI) eff. It was identified that both codes tend to overestimate (EI) eff , resulting in an unconservative second-order analysis. Moreover, a parametric analysis was conducted which showed (EI) eff correlates negatively to eccentricity and slenderness, but positively to steel tube size and concrete strength. However, these relationships were not reflected in the predicted (EI) eff according to European code and American specification. • DIC was applied to analyse buckling failure modes of the tested CECFST specimens. • The moment–curvature relation of CECFST beam–columns was investigated, confirming plastic hinge formation at the midpoint. • AISC 360-16 unconservatively predicts the moment magnification factor for slender CECFST columns under eccentric load. • Parametric studies were performed through FEM to study the influence of multiple factors on effective flexural stiffness. [ABSTRACT FROM AUTHOR]

The reinforcement in marine RC structures will inevitably be corroded under long-time erosion of chloride ions, which will weaken steel mechanical properties and then structural seismic resistance. The new metallurgical technology is adopted for manufacturing high-strength steel bars (HSSB), but that may affect the corrosion resistance of steel bars at the same time. This paper experimentally investigates the effects of corrosion on monotonic and low-cycle fatigue properties of HSSB HTRB600 and normal strength steel bars (NSB) HRB400E. The HRB400E and HTRB600 steel bars were corroded to different corrosion rates by electrochemical accelerated corrosion technique. The monotonic tensile and compressive, as well as low-cycle fatigue tests of corroded steel bars were conducted to investigate the effects of corrosion on steel mechanical properties, of which corrosion levels (0–20% target corrosion mass loss), slenderness ratios (L / D =6, 8, 10, 12) and strain amplitudes (2%, 4%) are considered. Test results show that, the corrosion morphology of steel bars under electrochemical accelerated corrosion is basically consistent with that observed under natural corrosion. Compared with uncorroded HRB400E and HTRB600 steel bars, 20% corrosion mass loss leads to 38% and 35% decrease in tensile strength, as well as 33% and 28% reduction in buckling stress, respectively. The HTRB600 steel bars present slightly superior monotonic tensile and compressive corrosion resistance than HRB400E steel bars. Corrosion obviously decreases the low-cycle fatigue (LCF) life of steel bars, resulting in reductions of 44% and 36% in LCF life at 20% corrosion mass loss for HTRB600 and HRB400E steel with a L / D of 6, respectively. Moreover, the HTRB600 steel bars present more significant corrosion degradation in total hysteretic dissipated energy, compared with HRB400E steel bars. The combined effect of corrosion and inelastic buckling further exacerbates the deterioration of LCF performance of steel bars. The corresponding deterioration models are proposed to determine the LCF life and energy dissipation capacity of corroded steel bars. • Carry out monotonic and low-cycle fatigue tests of corroded HTRB600 and HRB400E steel bars. • Compare corrosion morphology between electrochemical accelerated and natural corrosion. • Establish mechanical deterioration model of corroded steel bars. • Investigate and compare the effects of corrosion on monotonic and LCF performance of HTRB600 and HRB400E steel bars. [ABSTRACT FROM AUTHOR]

This paper presents a three-dimensional analysis of the buckling behavior of functionally graded (FG) skew plates using a novel meshfree elastoplasticity-based formulation. To solve the nonlinear buckling problem, a Tchebychev-radial point interpolation approach, which combines radial basis functions (RBFs) with Tchebychev polynomials, is developed. The governing equations are obtained using the principle of virtual work. The Prandtl-Reuss flow rule is utilized to model incremental plastic deformation, along with the von Mises criterion and isotropic hardening. To determine the effective elastoplastic properties of the functionally graded material (FGM), the Tamura-Tomota-Ozawa (TTO) model is employed. The results demonstrate an excellent agreement with those available in the literature. Furthermore, this study explores the impact of several parameters, including inhomogeneity parameter, skew angle, thickness ratio, aspect ratio, boundary conditions (BCs), and loading ratio, on the elastoplastic buckling behavior of the FG skew plates. • Presenting the 3D elastoplastic buckling response of functionally graded skew plates. • Developing a Tchebychev-radial point interpolation approach for solving the problem. • Confirming TRPIM results through comparison with existing authentic solutions. • Investigating effects of material slopes, geometric parameters, loading ratio, and BCs. [ABSTRACT FROM AUTHOR]

This study uses the FGP-GPLs (functionally graded porous metal reinforced by graphene platelets) to rehabilitate the egg-shaped liner-pipe system. The water penetrates the cracked pipe and surrounds the thin-walled liner, resulting in hydrostatic pressure that may contribute dominantly to the buckling of the thin-walled liner. The critical buckling pressure is derived analytically by combining the thin-walled shell theory, a refined displacement function, and the energy scheme. It is found the egg-shaped FGLs liner sustains higher buckling pressure than the circular FGP-GPLs one. Furthermore, a finite element model is developed to verify the theoretical solutions. The results indicate the numerical equilibrium paths agree well with the analytical ones. In addition, the present analytical predictions are compared successfully with other close-formed solutions. Finally, parametric analyses indicate that the addition of GPLs may significantly improve the stability of the egg-shaped liner, while the increase of pores decreases the stability of the liner. The thickness of the GPLs has a slight effect on the stability of the liner when the volume of GPLs is constant. Thus, thick GPLs may be recommended in engineering practices to reduce the manufacturing cost. • An egg-shaped pipe is used to improve the hydraulic efficiency of the cross-section. • FGP-GPLs liner are employed to rehabilitate the cracked egg-shaped pipe. • Analytical schemes are developed to describe the stability of the egg-shaped liner. • The equilibrium curves are plotted for the egg-shaped FGP-GPLs liner. [ABSTRACT FROM AUTHOR]

Restraints along slender structures, such as pipes conveying fluid and beams, play important roles in enhancing their bending stiffness. The current work investigates the influence of the midpoint restraint on the buckled axial force and dynamic characteristics for the first time. A continuous model is introduced by treating the midpoint restraint force as a concentrated force using Dirac function. The influence of the midpoint restraint is discussed based on modal expansion, and a partitioned model is proposed for validation. The conclusion is that the continuous model has good accuracy. Based on this model, it finds out two stable buckled states changing with the midpoint stiffness. The first stable buckled state occurs under weak midpoint restraint and has a cambered shape. The zero- and double frequency components occur in symmetric modal shapes and the response is softened along the whole beam. However, in the second stable buckled state, it turns into a whole sine function shape. The zero- and double frequency components just occur in the second modal shape, and the soften phenomenon doesn't occur at the midpoint. With increasing excitation amplitude, a bubble appears on the primary resonance peak while another resonance peak emerges nearby it. This work explains the influence of midpoint stiffness on nonlinear resonance and enhances the study of the nonlinear behavior of buckled slender structures. • The model of a beam with the midpoint flexibly restraint is established. • It finds out two stable buckled states changing with the midpoint stiffness. • Influence of the midpoint flexible restraint on dynamics of double-span beams is studied. [ABSTRACT FROM AUTHOR]

The behavior of prestressed carbon fiber reinforced polymer (CFRP)-reinforced steel columns is intricately linked to CFRP stiffness and stress; when the system is exposed to fire, the performance is more complex because of the degradation of CFRP mechanical properties. Therefore, transient fire tests are first conducted on four prestressed CFRP-reinforced steel columns under axial preloading using the ISO 834 standard curve to investigate their high-temperature performance. The entire failure process is revealed, three significant time points (i.e., CFRP failure time, buckling time, and critical time) influencing system behavior are identified, and the effect of preload and prestress level on the time points is elucidated. It is observed that CFRP plates fail with a final hair-like rupture; steel columns undergo symmetric and asymmetric failure modes, related to the initial imperfection. Subsequently, the finite element models (FEMs) are established and validated by test results, followed by a parametric analysis. It indicates that the high-temperature behavior of the prestressed CFRP-reinforced steel columns is dependent on the preload, CFRP prestress level, and initial imperfection; the buckling and critical time of such columns decrease with increasing preload and initial imperfection, while an increase in prestress leads to an increase in the buckling and critical time. Moreover, even CFRP plates without protection, and prestressed CFRP plates can improve the high-temperature performance of steel columns when the preload is not very large or the initial imperfection is not very small. These findings serve as a valuable reference for applying such columns when considering fire issues. • Transient fire tests are conducted on prestressed CFRP-reinforced steel columns using ISO834 standard curve. • Three significant time points influencing the system behavior are identified. • Effects of initial imperfection and preload on high-temperature behavior and reinforcing efficiency are discussed. [ABSTRACT FROM AUTHOR]

Metamaterial structures that exhibit negative stiffness (MSNS) behavior have shown the potential to be used as energy dissipation systems in different applications. Negative stiffness honeycomb structures consist of multiple pre-buckled beams that snapping through from one pre-buckled mode to another buckled mode, when subjected to transverse loads, displaying negative stiffness, and dissipating a significant portion of the input energy. This paper presents finite element models (FEMs) developed to investigate the performance of negative stiffness pre-buckled beams and honeycombs. The FEMs were validated using experimental results of single pre-buckled beams and honeycomb structures. The experimental testing of the pre-buckled beams was presented in the current study while the results of the honeycomb were available in the literature. The FEMs have the ability to capture the transition of the elements from one mode of buckling to another mode as well as the force thresholds, energy dissipation values, and residual displacements. The FEMs were extended to investigate the effect of different parameters such as boundary condition, apex height-to-beam thickness ratio, and constraining the second mode of buckling on the behavior of negative stiffness honeycombs. • Metamaterial structures that exhibit negative stiffness (MSNS) have potential for use in energy dissipation systems. • Finite element models (FEMs) are presented to study the performance of MSNS beams and honeycombs. • FEMs are validated using experimental results from single pre-buckled beams and honeycomb structures. • FEMs can accurately predict transitions between different modes of buckling, force thresholds, and energy dissipation. [ABSTRACT FROM AUTHOR]

This paper presents a simple methodology for determining the optimal design of an elastic funicular arch under point loads and selfweight for maximum in-plane buckling capacity. This class of optimization problem has hitherto not been investigated. The cross-section of the arch is assumed to be geometrically similar and constant through its entire length. The arch is assumed to be inextensible. The supporting points of the arch may be either pinned or fixed. The methodology for determining the optimal arch shape involves first finding the funicular shape of the arch under point loads and selfweight. Next, the arch is modelled by the Hencky bar chain model (HBM) for the buckling analysis. The HBM is adopted because it eliminates the requirement for formulating the governing equation for buckling and it is a straightforward model to comprehend and implement in a computer code. Each funicular arch shape is specified by a horizontal force value, and it has to be optimally selected to maximise the buckling capacity of the arch. As it is a single parameter optimization problem, the Golden Section search was used to determine the optimal horizontal force, and hence the optimal funicular arch shape. The methodology is illustrated by solving two example problems: (1) an arch under a point load and selfweight and (2) a symmetric arch under two equal point loads and selfweight. By solving the self-buckling problem of a catenary arch, the maximum spanning capacity of the catenary arch can be obtained as shown herein. • Paper outlines a method for designing elastic funicular arches to optimize buckling capacity. • Arch supportings can be pinned or fixed, offering design flexibility. • Method finds funicular arch shape under seflweight and point loads for analysis. • Paper uses Hencky bar chain model for buckling analysis, simplifying governing equations. • Method demonstrates with two examples: an arch under point load and selfweight, and a symmetric arch under two equal point loads and selfweight. [ABSTRACT FROM AUTHOR]

• - Transverse stiffeners behavior under compression; • - Experimental results of unstiffened and stiffened panels under compression (intermediate and edge stiffeners); • - Numerical analysis of transversally stiffened panels and their representative cross sections; • - Analytical analysis of the determination of the critical strength of stiffened panels. The web panels of metal sections subjected to compression have resistances that are often driven by local buckling. Transverse stiffeners are used to increase their resistance. These stiffeners can be arranged at different positions in relation to the edge of the metal section. The strength of the stiffened panel can be compared to that of a compressed element whose cross-section consists of the stiffener and a participating length of the web. To observe the behavior of these stiffened walls and to evaluate the existing analytical calculation methods, an experimental campaign was carried out on two metal sections of different heights, stiffened or not over their entire height of the web. Thus, 33 zones of stiffened or unstiffened panels are tested in double localized compression until failure. The stiffeners are placed near the edge or in the middle of the panel and welded on both sides of the web over its entire height and on the panel flanges. In parallel, a finite element model using shell elements and non-linear calculations considering the plasticity of the materials, the geometrical imperfections and the large displacements is set up. It is validated by comparing its force–displacement curves and modes of ruin with those obtained by tests. The model thus validated makes it possible to enrich the results of the experimental tests to better describe the behavior of stiffened walls subjected to compression. It also allows to discuss the observed failure modes and some analytical formulas which estimate the resistance capacities of the stiffened panels. [ABSTRACT FROM AUTHOR]

• The buckling of carbon fiber composite cylindrical shells with annular ribs under external pressure is investigated numerically and experimentally. • The effects of rib cross-sections, rib geometry and distribution on buckling load and buckling mode are explored. • The overall stability of the ribbed CF-CCS is sensitive to the rib section parameters, distance and thickness-radius ratio. • The numerical results obtained by nonlinear buckling analysis agree well with the experimental results. The buckling of carbon fiber composite cylindrical shells (CF-CCSs) with annular ribs under external pressure was investigated numerically and experimentally. The effects of rib cross-sections, rib geometry and distribution on buckling load and buckling mode were analyzed numerically. In addition, the ribbed polymer composite cylindrical shell was fabricated and tested. The geometry, thickness, buckling load and final collapse mode of the ribbed polymer composite cylindrical shell were measured. Finally, a nonlinear buckling analysis with geometrical imperfections was carried out based on the measured data; the numerical results were in agreement with the experimental results. The results show that different rib cross-sections have limited influence on the load carrying capacity of CF-CCSs, but the distribution of the ribs and the geometry of the ribs have a greater influence on CF-CCSs. [ABSTRACT FROM AUTHOR]

This article focuses on the buckling response of columns formed by pre-twisting a flat, narrow and straight material strip of a rectangular cross section. The experimental analysis accomplished for birch plywood strips covers twisting up to 90 degrees. The corresponding computational analysis covers the twisting process (geometrically nonlinear analysis) and the subsequent compression (linear buckling analysis, including the residual stresses from the twisting process) and includes comparisons for 3D solid and 2D shell finite elements within orthotropic linear elasticity. A further finite element analysis provides findings up to twisting angles of 400 degrees and includes nonlinear post-buckling analyses for the compression subsequent to twisting, in addition to the linear buckling analyses. These sets of analyses reveal some new findings regarding this classical problem. Most importantly, there are four characteristic twisting angles which are associated to mode jumps in buckling, to a plateau in the curve relating the critical load and the twisting angle and, finally, to a loss of stability during the twisting process. The influence of the twisting-induced stresses on the buckling response is investigated as well. • Compression response of twisted (by up to 90 degrees) plywood strips is studied experimentally. • 3D solid and shell FE models confirmed significant increase in critical buckling load. • FE analyses (for twisting up to 400 degrees) revealed four characteristic angles associated to: • (1) Mode jumps in buckling, (2) A plateau in the curve relating critical load and twisting angle, (3) A loss of stability during the twisting process. [ABSTRACT FROM AUTHOR]

• The mechanical properties of carbon/epoxy composite faces reinforced with 0–1 wt% multi-walled carbon nanotubes were experimentally determined. • High-order shear deformation theory was used for the core while considering continuity conditions between the faces and core. • The generalized differential quadrature method was employed to determine the critical buckling load of the sandwich plates. • Incorporating 0.5 wt% multi-walled carbon nanotubes into the composite faces improved the critical buckling load by up to 17.83% due to enhanced mechanical properties. • The effects of nanoparticle loading, geometry, and boundary conditions on the buckling behavior were explored, providing insights for designing optimized nanocomposite sandwich structures. The current investigation aims to examine the buckling behavior of sandwich structures reinforced with faces containing varying weight percentages (wt.%) of multi-walled carbon nanotubes (MWCNT), through the combined employment of experimental and numerical analysis techniques. In particular, the numerical analysis is executed through the implementation of the generalized differential quadrature method (GDQM). The study first determines the mechanical properties of the pure and reinforced samples via experimental tests. The buckling equations of the sandwich plate are then derived using the Frostig approach and a high-order shear deformation theory (SDT) for the flexible core. The continuity conditions between the faces and the core are considered to obtain the structural equations of the system, and Lagrange coefficients are introduced to enhance the accuracy of the governing equations. Subsequently, the study investigates the impact of various parameters, such as core thickness, aspect ratio, different boundary conditions (BC), and the addition of MWCNT nanoparticles on the critical buckling load of the system, utilizing the mechanical properties obtained for the composite faces. The present investigation reveals that the incorporation of MWCNT into the composite matrix brings about notable enhancements in the mechanical characteristics of sandwich structures. Specifically, the elastic modulus and ultimate strength of the faces are found to increase following the addition of MWCNT. Additionally, the critical buckling load of the sandwich plates is observed to rise with an increase in aspect ratio and length-to-thickness ratio, while a decrease in axial load yields similar results. The clamped boundary condition has higher critical buckling loads than the simply supported boundary condition. The addition of MWCNT nanoparticles decreases the dimensionless critical buckling force as the b/a ratio increases. Finally, the reported results of the current investigation present noteworthy findings about the advancement and improvement of sandwich composite structures to meet various application requirements. [ABSTRACT FROM AUTHOR]

• The seismic behaviour of LRS FRP-wrapped non-ductile RC columns was experimentally investigated. • The advantage of LRS FRP-wrapped RC columns in seismic retrofit was demonstrated. • The influence of FRP confinement stiffness on seismic performance was studied. • The accuracy of cyclic compression model model of LRS FRP-strengthened concrete was verified. This paper presents experimental studies and numerical simulations of circular reinforced concrete (RC) columns wrapped with Polyethylene Naphthalate fiber reinforced polymer (PEN FRP, a kind of large-rupture-strain FRP) and conventional CFRP. A total of seven columns were designed and fabricated, including a control column, three columns strengthened with CFRP, and three columns strengthened with PEN FRP. All columns were subjected to cyclic lateral load and a constant high axial load. The effectiveness of PEN FRP strengthening was systematically analyzed and discussed regarding the failure mode, displacement ductility, lateral cyclic load–displacement curve, stiffness degradation and energy dissipation capacity. The test results indicated that the control column exhibited inferior ductility and peak lateral strength, while FRP-strengthened columns possess better energy dissipation capacity and ductility. Further study found that PEN FRP was preferred to CFRP with similar tensile stiffness in seismic strengthening. Finally, based on the cyclic compression model of LRS FRP-strengthened concrete, the improved tensile model of FRP-strengthened concrete, and the cyclic stress–strain model of reinforcing steel, numerical simulations for seismic performance were carried out in OpenSees. It was found that the numerical simulation results of all FRP-strengthened RC columns were in excellent agreement with the test results. To better understand the effect of FRP confinement stiffness on the seismic performance of circular columns, parametric analysis was performed. Results showed that the numerical simulations need to consider the buckling of longitudinal reinforcement for accurately predicting the seismic behavior of FRP-strengthened columns of lower confinement stiffness. [ABSTRACT FROM AUTHOR]

• Yielding in steel beams varies with moment distribution and residual stresses. • Yielding reduces effective in-plane and out-of-plane section rigidities. • In-plane moment distribution in continuous beams is affected by reduced rigidities. • Lateral buckling resistance is affected by moment distribution and reduced rigidities. • Buckling prediction requires iterative numerical analysis. The inelastic behaviour of a steel beam is complicated by reductions in the section rigidities which depend on the moment distribution and residual stress pattern. The inelastic beam is effectively tapered and mono-symmetric, and iterative numerical methods need generally to be used for the analysis. The in-plane moment distribution in an inelastic continuous beam lies between the commonly assumed rigid-plastic "plastic" path and a "yield" moment path. The yield path is the more critical for lateral buckling of the continuous beams considered in this paper. Approximations of the inelastic out-of-plane moduli of continuous beams developed from closed form lateral buckling solutions for simply supported beams in uniform bending can be used in a computer program for the buckling analysis of tapered mono-symmetric beams. Residual stresses cause significant reductions in the inelastic buckling resistance. The AISC design code predicts strengths which are similar in shape but significantly higher in magnitude than the inelastic buckling resistances of simply supported beams in uniform bending. The predictions for beams with central concentrated loads are much higher than the corresponding inelastic buckling resistances. Closer but still conservative approximations are obtained by using the method of design by inelastic buckling, which can also be used for continuous beams. This method is much simpler than those used to obtain accurate predictions. [ABSTRACT FROM AUTHOR]

• Buckling behavior of hybrid composites tubes. • Modal behavior or hybrid composites tubes before and after failure. • Analysis of variance of the structural responses in composites tubes with ply drop-off. • The results revealed that the hybrid structure with drop-offs is an appropriate option that offers the best cost-benefit. A comparative study of the static and dynamic behavior of a new type of tubular structure with drop-offs used in lower limb prostheses is presented in this paper. Composite structures that present mass reduction, low cost, and excellent performance are a great challenge for many researchers. In order to overcome these difficulties, numerical and experimental methods are performed, generating results regarding natural frequencies, damping loss factors, and maximum compression load for five different setups for tubes with drop-offs. For the manufacture of the structures, three types of fabrics are considered: carbon, glass, and a carbon/aramid hybrid fabric. Beyond the three types of tubes, two more setups are created considering hybridization, with the inner ply manufactured with glass fabric, the outer ply of the first setup manufactured with carbon fabric, and the outer ply of the second setup manufactured with carbon/aramid hybrid fabric. The structural hybridization and insertion of drop-offs provide a reduction in the cost of material. Firstly, an optimization strategy using the Lichtenberg algorithm is executed, aiming at the basic material properties in relation to elasticity modulus, strain modulus, Poisson ratio, and density. Then, it is possible to perform numerical modal analysis using the Finite Element Method in Ansys® software with the aim of obtaining the first natural frequencies for each setup. Modal experimental tests before and after failure obtained in the compression test are performed to measure the first natural frequency and damping loss factor for each setup, providing a comparison between the dynamic behavior of the undamaged and damaged structures, and, posteriorly, the numerical and experimental modal results before failure are compared. The compression test is performed to measure the maximum compression load supported by each structure. The results revealed that the hybrid structure with drop-offs is an appropriate option that offers the best cost-benefit for pylon tubes. [ABSTRACT FROM AUTHOR]

This study presents the results of a parametric analysis on a wide range of geometries of bridge natural rubber bearings for the definition of consistent limit states. This range, defined as a matrix depending on the shape factor, slenderness ratio, and device width, ensures maximum homogeneity of the studied population based on values typically found in practice for bridge applications. The effects of typical axial loads are also considered. Numerical analyses are performed on a finite element model previously developed by the authors that is capable of simulating shear failure and buckling limit states. Each specimen undergoes a numerical pushover analysis to obtain the critical shear strain and the type of ultimate limit state achieved. The results of the numerical analyses are first presented to show the influence of the investigated parameters on the type of limit state and the corresponding value of critical deformation. Design charts are constructed for practicing engineers. In addition, this work addresses the framework of performance-based design of bridges, with the objective of defining convenient damage states for the construction of bridge fragility curves. For this purpose, the statistical importance of each studied bearing pad or seismic isolator with respect to the whole population is taken into account to develop probabilistic capacity models. A slenderness threshold is validated for isolators to distinguish between potential limit states. • Fragility models are built for performance assessments of bearings and isolators. • Slenderness shows a crucial role on the type of limit state and respective strain. • A relationship to transform instability curves is defined for different width values. • Design charts are proposed for natural rubber bearings and isolators. • A problematic region for bearings under loads greater than 7 MPa is identified. [ABSTRACT FROM AUTHOR]

This work aims to evaluate the critical buckling load of panels made of cross-laminated timber, considering finite element simulations and different analytical methods of calculating the effective bending and shear stiffness. In addition, the effect of openings, pre-cracks, and adhesive strength on the critical buckling load is analyzed. Results indicate that the approach with thin external faces is both simpler and more effective. When estimating the bending and shear stiffness, the methods that show the least difference are the γ -method and the shear analogy method, with the first of them being more conservative. The corrected Timoshenko method tends to overestimate the critical load. Moreover, using cohesive zone models embedded in finite element simulations, the critical load is reduced by an average of 10% due to the stiffness of the adhesive. Furthermore, when panels have adhesive-free edges, the critical load can be reduced by more than 50%. • Shear analogy method is accurate and easier to use for predicting CLT buckling load. • 5-layer CLT loses 16% load capacity vs. 3-layer panels of same thickness. • Non-bonded longitudinal strips significantly impact CLT buckling load capacity. [ABSTRACT FROM AUTHOR]

Highlights • The GB column with size and volume of material equivalent to B column is proposed. • The behavior of GB and B columns under constant axial and cyclic lateral loading is investigated. • The GB column is proved to have significant improvements in strength, ductility, and post-buckling behavior. • Proposed formulae for strength and ductility of the B and GB columns are given. Abstract Thin-walled steel stiffened square box columns are becoming an increasingly attractive choice as cantilever bridge piers due to their architectural, structural and constructional advantages. This paper investigates the behavior of thin-walled steel columns with uniform square box sections (B) and newly proposed graded-thickness square box sections (GB) under constant axial and cyclic lateral loading. The analysis is carried out using a finite-element model (FEM) which takes into account the effect of both material and geometric nonlinearities. First, the accuracy of the employed FEM is verified based on the experimental results. Then, a GB column with size and volume of material equivalent to a B column is introduced. The proposed GB column is proved to have significant improvements in strength, ductility, and post-buckling behavior as compared to its counterpart B column. As a part of this research, a comprehensive parametric study is carried out to investigate the effects of main key parameters including: the width-to-thickness ratio parameter (R f), the column slenderness ratio parameter (λ), the magnitude of axial load (P/P y), and the number of loading cycles (N) on the strength and ductility of the B and GB columns. Finally, a series of proposed formulae for strength and ductility evaluation of the B and GB columns is given. [ABSTRACT FROM AUTHOR]

Highlights • The dynamic responses of inclined beam with a constant moving load are investigated. • A new method for solving the moving load problem with a more general formulation is proposed. • The natural frequency of the inclined beam is changing as the moving load moves up the inclined beam. • The structural stability issues may surfaces when the angle of inclination is large. Abstract This paper is concerned with the dynamic response and stability of an inclined beam under a moving vertical concentrated load. The governing equation for transverse motion of the beam is presented and it contains the effect of the compressive axial component of the vertical load on the bending stiffness capacity of the beam. This moving load problem on inclined beam is no longer simply a dynamic problem, but it involves a structural stability problem when the load is large and the speed of the moving load is low. Furthermore, with the presence of the axial load component, this problem is no longer symmetrical. In other words, the ascending moving load and descending moving load produce different beam responses. For solving this time-dependent problem, we decouple the formulation and adopt the semi-discrete finite element method in the space domain. The equation of motion is then solved by using the Newmark method. The present numerical approach and the assumptions adopted were verified by considering a zero angle of inclination (i.e. the horizontal beam case). Based on this developed formulation, numerical solutions on the moving load problem were obtained for various angles of beam inclination. The natural frequencies of the beam become lower as the moving load moves up the inclined beam due to the compressive axial force component that degrades the elastic bending stiffness capacity. When the compressive axial force component is large enough and the speed of the moving load is low, a structural stability problem may surface. [ABSTRACT FROM AUTHOR]

Highlights • Applied the Hencky bar-chain model (HBM) for frame buckling analysis considering different configurations. • Used easy-to-code stiffness matrices with patterns to simplify the expression of HBM formulations. • Demonstrated the advantage of localized model modification of HBM in considering a local damage/stiffening. Abstract This paper presents the development of the Hencky bar-chain model (HBM) for the buckling analysis of non-symmetric portal frames under vertical compressive axial loads on the columns. Generic stiffness and geometric matrices are derived for the frame buckling analysis. Based on these matrices, a simple computer code is developed to determine the buckling loads. Illustrative frame buckling problems are solved to demonstrate the ease and simplicity of the HBM for analysis of different and complex design conditions imposed on the frames. The advantages of consistent formulation, localized model modifications, and convenience in obtaining the buckling modes are further noted for the HBM. [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]

Highlights • The mathematical model of corrugated shells with special shapes is presented. • Effect of corrugation parameters on critical load is investigated. • Linear and nonlinear buckling analyses are conducted. • Critical load of corrugated shells is compared to smooth ones. • Specific range of corrugation parameters significantly increase the value of relative critical load. Abstract The problem of elastic stability of the shells with special shapes with corrugated middle surfaces under external pressure is debated in the presented paper. Solution of the problem is based on FEM study. Corrugated barrelled, pseudo-barrelled, and cylindrical shells of constant mass are considered. Geometrical modification of the middle surface geometry is based on sine wave along principal directions. Middle surface of the corrugated shells are described referring to differential geometry of surfaces by parametric functions in three-dimensional Euclidean space. Linear and nonlinear buckling analyses are conducted. Examples of buckling modes are presented, which differ significantly from those typical for shells of revolution with positive or zero Gaussian curvature. It is proven that corrugation may lead to serious increase or decrease of critical load for all types of presented shells. [ABSTRACT FROM AUTHOR]

Highlights • Nonlinear finite element model of built-up section were developed and verified. • A proposed design approach is presented using direct strength method (DSM) • The proposed approach is evaluated by comparing with the current existing method and FEA data. • A parametric study showing the influence of D1/B ratio on the stability and strength of the built-up columns. Abstract This paper, based on new proposed approaches, is a numerical investigation of the behavior of thin-walled cold-formed steel built-up columns under a uniform compression. Two types of cross sections have been studied, built-up closed and open sections formed by two channels connected by battens plates. First, a nonlinear finite element model has been developed and the results obtained show a good agreement against experimental results, such as the ultimate strength, the type of deformed shapes at failure and the lateral displacement. Second, a new proposed approach based on the DSM approach where the local, distortional or global buckling has been obtained numerically, using finite element method software, the thickness at the contact area in the web is taken as 1.0 times the thickness of the plate "t", instead of 1.5 or 2.0 times "t". In this case, the compound section is acting as one rigidly connected section. Comparisons with experimental data give a satisfactory degree of accuracy in the proposed design method (DSM-t) and the results are more conservative than those found by the DSM-1.5 and DSM-2. The results, for either closed or open sections, are also slightly conservative for columns failing in global modes than in local ones, if compared with the AISI and EC3 specifications. Some parameters, such as the spacing channels-web length ratio (B1/D) influence the stability and strength of the built-up columns. [ABSTRACT FROM AUTHOR]

Highlights • A practical, educational augmentation for teaching elastic buckling. • Innovative use of 3D printing. • Measurement of critical loads. • Justification for various theoretical approximations. • Parameter variations and how geometry influences buckling. Abstract This is the third part in a trilogy of papers examining ways in which additive manufacturing can be used to facilitate the introduction of basic principles in structural analysis. Each paper uses 3D-printing and simple, but non-trivial, slender geometric forms, to provide a hands-on aspect to structural behavior in which flexure plays a dominant role. The first part dealt with linear structural analysis (Virgin, 2017), extended to dynamics and vibration in the second part (Virgin, 2017). The current paper focuses on slender structures in which compressive axial loading is the new ingredient and hence buckling becomes a central issue. This has similarities and differences with the two previous papers, but in all instances the role played by relatively high-precision 3D-printing opens the door to versatile and effective illustration, and the development of a deeper appreciation of structural phenomena. [ABSTRACT FROM AUTHOR]

Highlights • Both buckling and shear failure limit states are studied through tests on 24 rubber bearings. • A rare parametric study is performed on the influence of slenderness, shape factor and size on the limit states. • Novel aspects, comparisons and discussions about previous observations found in the literature are provided. • Usual estimations of the buckling load are not always conservative depending on the geometry of the bearing. • Rubber bearings experience internal damage before their ultimate limit even though no visual degradation is noticed. Abstract This paper aims to increase the existing experimental knowledge base concerning the limit states of performance of natural rubber elements that are typically used as bearing pads and seismic isolators for bridges. A large experimental study is performed on 13 reduced-scale and 11 full-scale natural rubber specimens subjected to different types of shear-compression tests. Both lateral stability and shear failure under realistic axial compression forces are addressed in the study, together with an investigation of different isolator sizes, shape factors and slenderness ratios. Stability curves are obtained from tests using the constant displacement method, and shear failure data from tests using the direct method are presented. Predictions of the critical buckling loads from different versions of the reduced area method are compared to the experimental stability curves, indicating that these commonly used estimates are not always conservative depending on the geometry of the bearing. Several buckling and shear failure test results obtained in this study specifically highlight the fact that the slenderness ratio is the most critical parameter when determining the ultimate limit states of rubber bearings, although this parameter is often neglected. The intermediate limit states before buckling or shear failure are also investigated. It is shown that such limit states of performance are nearly impossible to define experimentally because most bearings do not exhibit any visual damage before failure, although experimental data indicate that slight to moderate damage obviously occurs in bearings under large displacements. [ABSTRACT FROM AUTHOR]

In some configuration cases for concrete pavements, such as at the intersection of two road pavements or the connection of a road pavement to a bridge abutment, the pavement can be considered to be semi-infinite with one end adjoining a rigid structure. In addition, continuously reinforced concrete pavements may weaken over time as a result of corrosion, erosion, shrinkage, fatigue cracking or the like, and in these instances the weakened pavement can also be considered as being semi-infinite with a joint. This rotational joint constrains the end of the pavement, which has an effect on the potential upheaval buckling of the pavement when subjected to heatwaves. This paper presents an analytical solution for thermal-induced upheaval buckling of such a semiinfinite continuously reinforced concrete pavement when constrained by a rigid medium with a quantifiable rotational stiffness. The method of minimum total potential energy is invoked to derive the differential equations for the post-buckling response, and the equilibrium equations with variable parameters that govern the behaviour are solved analytically by considering both the deformation of the pavement and the rotational and translational restraints. Parametric investigations are conducted on the buckling response of the pavement when constrained at one end; the parameters considered being the rotational stiffness of the joint, the thickness of the pavement, the properties of the pavement subgrade base and the effective weight of the pavement. It is found that the constraint affects the buckling temperature considerably, and the so-called safe temperature increases with the rotational stiffness of the constraint the end of the pavement. [ABSTRACT FROM AUTHOR]

In this paper, a calculation model to simulate the compressive behavior of R.C. columns with square cross-sections externally wrapped with FRP, including buckling effects of the longitudinal bars and reduction of the confinement pressure induced by the buckled compressed bars, is presented and discussed. The model distinguishes the cases of corner and side bars, calculating the different critical lengths and the critical loads. The Teng et al. (2009) model was adopted to predict the compressive behavior of FRP-confined concrete, and the Dhakal and Maekawa (2002) model was taken into account to predict the compressive behavior of longitudinal bars. The critical length and critical stress of compressed bars including interaction effects between concrete cover, stirrups and FRP wraps were calculated, distinguishing between corner and side bars. Based on the model mentioned, analytical expressions were derived to calculate the critical strain at the onset of bar buckling and the minimum thickness of FRP to prevent instability of the compressed bars. Finally, a theoretical–experimental comparison was made to validate the model. [ABSTRACT FROM AUTHOR]

Due to mainly thermal and energy potentials, Insulated Glass Units (IGUs) are largely used in modern buildings to realize curtain walls and enclosures. The typical IGU consists of two glass layers, either monolithic and/or laminated, joined together by enclosing an hermetically-sealed air (or gas) cavity between them. There, maximum stresses and deformations derive from external pressures (wind loads, etc.) or environmental/climatic loads (temperature variations, etc.). While the common IGU application involves 4-side continuous supports, novel restraint configurations are increasingly used in practice (i.e. 2-side supports, point-fixings, etc.), hence resulting in additional loading scenarios that could compromise the integrity of these systems. In this paper, following earlier research contributions, a standardized buckling approach in use for structural glass elements mainly compressed or under combined compression/bending is assessed, for the specific case of IGUs with 2-side continuous supports. Analytical and Finite Element (FE) numerical studies are reported, giving evidence of their actual performance and buckling resistance, including parametric analyses and comparisons towards simplified design formulations for both external and internal pressures. [ABSTRACT FROM AUTHOR]

• Tests were conducted to study deck bracing effects on continuous stringer LTB resistance. • Finite element analyses were performed to simulate behavior of the tested grillage. • Continuous stringer LTB resistance can be tripled considering noncomposite deck bracing effects. Louisiana's bridges used two-girder or truss systems in the 1950 s and 1960 s, in which floorbeams are carried by main members and continuous stringers are supported by the floorbeams. The main members are either two edge (fascia) girders or trusses. Continuous span stringer bottom flanges are in compression in their negative moment regions, which could result in lateral torsional buckling (LTB). When these stringers are load rated using AASHTOWare Bridge RatingTM analysis software, lateral torsional buckling (LTB) resistance is calculated in accordance with the AASHTO LRFD Bridge Design Specifications, which the authors have determined may not adequately account for bracing effects provided by a noncomposite deck, and therefore could underestimate the flexural strength. Resulting ratings may be low enough to require restrictive, and possibly unnecessary, load postings or even bridge closures. This issue affects more than 20 significant bridges that are key parts of Louisiana's highway system. To address the challenge of underestimated stringer LTB resistance and assess bracing effects provided by a concrete deck, experimental and analytical studies were performed on a two-span, continuous, steel stringers in a grillage system, which included three stringer lines, an interior transverse support (floorbeam), and transverse diaphragms at the end supports. The tests encompassed a variety of configurations, with and without a concrete deck. This paper describes laboratory testing setups and discusses experimental results, focusing on bracing effects on LTB resistance due to the presence of a noncomposite concrete deck. Finite element models using ANSYS were calibrated, validated using test results and used to simulate stringer behavior in Louisiana's representative bridges. Finite element analyses of various tests showed generally comparable results to test data, and provided a feasible approach to load rate continuous stringers if a refined analysis is deemed necessary. The studies showed that stringer LTB resistance could possibly be tripled when noncomposite deck bracing effects are considered. [ABSTRACT FROM AUTHOR]

• 10 specimens composed of 20 press-braked stainless steel lipped channel beams were investigated in the bearing capacity test. • An in-depth exploration of deformation process of local – distortional interaction was conducted. • All test specimens were subjected to local buckling first, then distortional buckling, and finally interaction buckling. • Existing design methods based on Direct Strength Method underestimate the ultimate bearing capacity of stainless steel lipped channel beams. Stainless steel lipped channel beams are prone to complex buckling modes due to the large width-thickness ratio. An in-depth experimental study of local – distortional interaction of press-braked stainless steel lipped channel beams was conducted. The chemical composition was proved to meet the requirements of European and Chinese standards. A tensile test of four coupons extracted from the press-braked lipped channel beams was carried out to investigate the material properties. A total of 10 specimens composed of 20 press-braked stainless steel lipped channel beams were investigated in the bearing capacity test. The relationship of the vertical displacement of mid-span, vertical displacement of loading points, support rotation, flange deformation and web deformation with the load was obtained, as well as the bearing capacity of each specimen. According to the measured displacement and strain, the development and failure mechanism of local – distortional interaction of stainless steel lipped channel beams were revealed. All test specimens were subjected to local buckling first, then distortional buckling, and finally interaction buckling. Each specimen had a certain post buckling strength. Near the failure load, each specimen experienced a long loading process and showed good ductility. The test results were utilized to assess the existing design methods which were all based on Direct Strength Method for the guidance of engineers. The existing design methods for local – distortional interaction underestimated the bearing capacity of press-braked stainless steel lipped channel beams. The existing design methods for local buckling or distortional buckling of stainless steel beams overestimated the bearing capacity of local – distortional interaction. [ABSTRACT FROM AUTHOR]

Buckling instability is one of the factors that limit the ultimate load-carrying capacity of I-section beams, and the coupling of global buckling and local buckling makes it difficult to predict the mechanical behavior of I-section beams. Hierarchical one-dimensional finite elements for the global/local buckling analysis of I-section beams are presented in this paper. Within the framework of Carrera's Unified Formulation (CUF), a model is built by using Lagrange polynomials to describe the three-dimensional displacement field as an arbitrary order approximation by displacement variables over the beam cross-section. One-dimensional finite elements are obtained by discretizing the governing equation along the beam length. Due to its high efficiency and step length adaptability, the Asymptotic Numerical Method (ANM) is adopted to solve the nonlinear governing equations. Several typical buckling problems in I-section beams, including global buckling, local buckling and global–local coupled buckling, are investigated. The numerical results demonstrate the validity and efficiency of the proposed model. The critical buckling load and displacement field can be precisely predicted, and a good agreement is found in comparison with results obtained via three-dimensional finite element solutions. • A model for the global/local buckling analysis of I-section beams is established. • Carrera's Unified Formulation and Asymptotic Numerical Method are used in this model. • The degrees of freedom and Gauss points are reduced comparing with 3D FEM model. [ABSTRACT FROM AUTHOR]

It is well-established that beams of relatively narrow cross-section have a tendency to buckle laterally when loaded. This type of lateral–torsional instability, which has considerable practical importance in a variety of thin-walled structures, is a classical buckling situation in which the critical load is related, among other things, to characteristic features of the cross-section. In this short paper, 3D-printing is exploited to provide a parametric study based on a fixed cantilever geometry in which a number of standard cross-sectional forms are compared in terms of their effect on this kind of buckling behavior. • Innovative use of 3D printing. • Lateral–torsional buckling (LTB). • Experimental testing. • A practical enhancement of teaching LTB. [ABSTRACT FROM AUTHOR]

This paper is concerned with the effects of distortion on the lateral buckling of steel beams which have rectangular or square hollow flanges and folded plate webs. The hollow flanges potentially make very large contributions to the torsional stiffness, but flange distortion (in a shear mode) causes a significant reduction in the effective torsional stiffness and in the lateral buckling resistance. In this paper, the shear distortion of the hollow flanges is analysed, and the strain energy stored in a distorted flange is compared with the strain energy stored during uniform torsion of the flange. This comparison allows the development of a suitable parameter for use in the evaluation of the effect of flange distortion on the torsional stiffness of a hollow flange beam. Uniform torsion test results are used to confirm the significance of this parameter. Finite strip analyses of simply supported hollow flange beams in uniform bending show that there is a significant interaction between distortion and uniform torsion during lateral buckling, which may be approximated by combining their flexibilities. More accurate finite element analyses show that the finite strip predictions are conservative. An approximate method of predicting the effects of flange distortion on elastic lateral buckling is presented which shows good agreement with the finite element predictions. [ABSTRACT FROM AUTHOR]

Analytical investigation of collapse of a pinned non-uniform shallow circular arch under uniform radial pressure is presented in this paper. The non-uniformity is introduced by dividing the arch into three regions of constant stiffness. The equilibrium equations are obtained by using least potential energy principle. By proper nondimensionalization, the presented solution is independent of total length of the arch. And two modified slenderness parameters are identified which enables the result to be valid for any symmetric cross-section shape. Parametric study on different geometric parameters has been carried out on the snap-through buckling load and anti-symmetric bifurcation load. The validity of the analytical result is verified by comparison with FEA results. Criteria concerning four deformation modes are identified. We show there is an equal potential energy load for some non-uniform shallow arches by a straightforward deduction, the existence of which load is a necessary condition for the buckle propagation of a corresponding long shallow panel. Finally two limiting cases (rigid center case and rigid end case) with extreme non-uniformity are analytically studied by using augmented potential energy with Lagrangian multipliers. For rigid center case, closed-form condition for the possible occurrence of symmetric snap-through is presented. For rigid end case, an asymptotical analysis leads to a somewhat surprising critical value of slenderness which makes the snap-through buckling just possible. This paper intends to improve the understanding of the effect of non-uniformity on collapse of shallow arch under radial uniform pressure. [ABSTRACT FROM AUTHOR]

In the present paper a Probability Density Evolution formulation is proposed for the limit analysis of stochastic systems, which can accurately and efficiently evaluate the effect the system’s random parameters have on its nonlinear and limit response. The proposed formulation of the classic Probability Density Evolution Method reduces the corresponding Generalized Density Evolution equations, which are partial differential equations, to a system of ordinary differential equations, that can be efficiently solved with the method of characteristics. With this reformulation, the cumulative distribution function of the critical load of the structure can be accurately and efficiently evaluated. The estimation of stochastic limit buckling loads of imperfection sensitive structures is a natural extension of this method. In addition, a methodology is put forward for the estimation of the probabilistic characteristics of the full load-displacement curve for a stochastic nonlinear system in the context of Newton-Raphson incremental-iterative schemes. The main advantage of the proposed approaches is that they allow for a quantification of the effect of uncertainties on the structural capacity, with only a small number of deterministic analyses compared to Monte Carlo simulation. The applicability and validity of the proposed methodology for limit and nonlinear structural analysis is verified through extensive numerical investigations. [ABSTRACT FROM AUTHOR]

This work presents an analysis of upheaval buckling of pipelines triggered by internal pressure. It discusses the existing relationship between internal pressure and equivalent compressive axial force in the buckling context. The main focus is on the relative influence of prop imperfections and soil friction coefficients in critical load prediction and post-buckling configuration. To perform the analyses, numerical models are developed using geometrically-exact finite element of beams, undergoing large displacements and finite rotations. Contact between the pipeline and the soil is also included in the models. As a result, the work shows the equivalence of applying the internal pressure as a distributed load dependent on pipe curvature and as a follower compressive axial force, both in terms of critical load and post-buckling configuration. Varying prop imperfections and soil friction coefficients, it is concluded that the first parameter has more influence in critical load prediction than the last one. The same occurs in terms of post-buckling configuration: for the same increase of internal pressure from critical load, the imperfections have more influence in the post-buckling displacements than the friction between the pipeline and the soil. [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]

Lateral brace is an effective way to increase the out-of-plane stability of steel arches, and the certain bracing stiffness achieving full restraining effect is concerned. Unlike braced columns and beams, the buckling of steel arches with discrete lateral braces and the effect of bracing stiffness are not well explored. This paper deals with the bracing stiffness effect of equally-spaced lateral translational braces and rotational braces in steel circular arches pertaining to elastic out-of-plane flexural-torsional buckling. Firstly, for arches with discrete lateral translational braces in uniform compression, an analytical solution for the threshold bracing stiffness is derived by the Rayleigh–Ritz method, ensuring full restraint of the displacement at the bracing points. Then for arches with discrete rotational braces in uniform compression, the flexural-torsional buckling modes are explored using the finite element analysis (FEA), then improved predictions to the buckling load related to the bracing stiffness are obtained theoretically by assuming proper buckling shapes. Compared with the FEA results, it is found that the analytical solutions of threshold stiffness proposed for arches in uniform compression are reasonably accurate and can be used in other loading cases for arches under combined compression and bending moment conservatively. [ABSTRACT FROM AUTHOR]

Enhancing the load capacity of aged and deficient thin-walled steel structures can be accomplished by increasing member stiffness in buckling prone regions. The literature shows that composite materials have become a major player in retrofitting applications. A new strengthening concept, Strengthening-by-Stiffening ( SBS ) , is applied to buckling prone web panels in thin walled steel beams by bonding pultruded glass fiber reinforced polymer (GFRP) sections. The first part of present study is focused on the construction of a finite element (FE) model for accurate simulation of experimentally obtained results. Initial imperfections, material non-linearity, interlaminar fracture law to simulate adhesive debonding, and GFRP rupture or delamination are accounted for in the construction of the FE model. The second part of the study was focused on parametric studies using the validated FE model to investigate different GFRP sizes, contact areas, panel aspect ratio and slenderness of the web panels on steel beam with SBS retrofitting. Results from the parametric study were used to establish some limits to assist in SBS design. Finally, possible use of SBS strengthening method in new construction was investigated by substituting all steel stiffeners with bonded composite GFRP stiffeners for the improvement of fatigue related behavior that is known to start at the weld toes of steel stiffeners. [ABSTRACT FROM AUTHOR]

An approach to reliability-based design (RBDO) of beam reinforced composite structures with non-linear geometric behavior is proposed. A unified approach following both buckling and first-ply failure (FPF) is used to verify the integrity of beam reinforced shallow shell laminated structures. A new RBDO methodology using a genetic algorithm and a hierarchical decomposition searches the global most probable failure point (MPP). For the reliability analysis, the random parameters are the mechanical properties of laminates. Simultaneously the optimal design based on weight minimization under prescribed reliability and buckling constraints is searched through this hierarchical genetic algorithm (HGA). The design variables are the ply angle, the ply thickness, the height and the width of the cross sections of the stiffeners. Numerical results show the capabilities of the proposed approach using the MPP search inner loop integrated in a HGA scheme. Based on a sensitivity methodology the uncertainty for the optimal solution obtained from HGA is analyzed. In the neighborhood of critical buckling values of the structural response the asymptotic behavior of uncertainty propagation is observed. The influence of uncertainties from random parameters and design variables are studied on critical load factor and critical displacement. The variability of these structural response functions are measured by their coefficients of variation and Sobol indices. The most important influences for uncertainty propagation are obtained from ply angle of shell laminates and from longitudinal elastic modulus group. [ABSTRACT FROM AUTHOR]

In this paper, non-linear elastic pre-buckling and in-plane buckling analysis for a circular shallow concrete arch subjected to a uniformly distributed load and time-varying uniform temperature field is performed. Transient thermal strain and basic creep strain are considered, the latter modelled using a fractional derivative creep law, to investigate the coupling effects of time, temperature and geometric non-linearity on mechanical behaviour and stability boundaries. The first correspondence principle is invoked allowing the problem to be treated elastically and statically, with the non-linear equilibrium equations derived using the principle of virtual work. Numerical solutions to the variable order fractional derivatives are obtained through a finite-difference based discretisation scheme. Results show that the coupling effect between transient thermal strain and geometric non-linearity is significant as it influences pre-buckling behaviour and reduces buckling strength. Basic creep strain is less influential, causing a slight enhancement of the effects of transient thermal strain. [ABSTRACT FROM AUTHOR]

This paper presents the Hencky bar-net model (HBM) for elastic buckling analysis of rectangular plates with any combination of edge conditions. HBM comprises a grid (or net) of rigid bar segments joined by rotational springs as well as a torsional spring system in each grid panel. The HBM is developed from the finite difference plate model that allows researchers to perform plate buckling analysis via solving a set of algebraic equations instead of solving a fourth order partial differential equation. The elastic spring stiffnesses for the HBM that provides the flexibility for deformation are established for the first time for elastic rotationally restrained edges and free edges. Some plate buckling problems were solved by using the developed HBM and the solutions shown to converge to those of the continuum plate counterparts when the grid size becomes very small; thereby verifying the validity of the model. [ABSTRACT FROM AUTHOR]

Wide-flange members with sinusoidal corrugations in webs are recently developed and gradually accepted as alternatives to wide-flange members with flat webs and trapezoidally corrugated webs. However, limited knowledge is available regarding flexural behavior of such members. This research investigates flexural behavior of the cantilever wide-flange members with sinusoidal corrugations in webs. First, four cantilever specimens were constructed. Each specimen was tested using a monotonically increased point load applied at the free end. Test results show that the specimens overall exhibited the flexural torsional buckling behavior, which is similar to that of the conventional wide-flange members with the flat webs and subjected to the same loading and boundary conditions. Next, computer models were developed for the tested specimens. Both eigenvalue analyses and nonlinear static analyses were conducted to glean the buckling strength of each specimen. It was found that the nonlinear static analyses can provide reasonable predictions of the strengths of the tested specimens. Based on the validated computer models, parametric analyses were conducted to investigate the influence of initial geometrical imperfection on strength of the cantilever wide-flange members with corrugations in webs. In addition, the flexural performances of the cantilever wide-flange members with sinusoidally corrugated webs were compared with those of the corresponding wide-flange members with the flat webs based on the computer simulations. The computer models were further analyzed to assess adequacy of some existing models for calculating strength of the wide-flange members with sinusoidal corrugations in webs. [ABSTRACT FROM AUTHOR]

A new approach to the buckling analysis of non-prismatic columns is proposed. The method of rigid elements is used for this purpose. The general form of the characteristic equation is given by which it is possible to perform buckling analysis of columns with continuously varying cross-section and multiple-stepped columns under different boundary conditions. It is assumed that the column cross-section is doubly symmetric. The proposed method is verified through numerical examples. The influence of different geometric parameters, self-weight of the column, and stiffness of the introduced springs on the critical buckling load is analysed. [ABSTRACT FROM AUTHOR]

This work presents an effective approach to investigating the buckling and post-buckling behavior of porous FGM plates. The main objective of the present analysis is to use a High Order Continuation based on the Asymptotic Numerical Method with the Finite Element Method for nonlinear behaviors of a Porous Functionally Graded Material plate (PFGM) with different porosity distributions under various types of transverse loads. In our study, we will take into account the lack of uniform and non-uniform porosity using a Higher-order Shear Deformation Theory (HSDT). The adapted solver proves to be more effective for analyzing non-linear mechanical phenomena and more precisely the post-buckling analysis of the PFGM plates. Indeed, this numerical high order algorithm presents an adaptive step length to the local nonlinearity of the solution branch and to detect easily the bifurcation points and bifurcated branches. When compared to iterative techniques like Newton–Raphson, the proposed high-order algorithm has the benefit of speeding up the resolution of nonlinear problems. The mathematical formulation is based on the higher-order shear deformation plate theory taking into consideration geometrical nonlinearity and initial imperfections. Numerical results of a parametric study on the effect of various types of load, porosity distribution, grading index, porosity index and different span-to-thickness ratios will be investigated. • A High Order Continuation is applied to solve nonlinear buckling of porous FG plates. • Effects of various types of loads, porosity distribution, grading index, porosity index and different span-to-thickness on the critical buckling loads of a porous FG plates were examined. • A finite element model is used in the framework of Higher Order Shear Deformation Theory. [ABSTRACT FROM AUTHOR]

The aim of this work is to develop an efficient numerical model for bifurcation analysis within the Föppl–von-Kàrmàn plate theory. This model consists in adapting the High Order Continuation Method (HOCM) with a Hermit-type Weighted Least Square (WLS) method. The collocated Hermit-type technique allows to approximate the binding unknowns and their derivatives. Furthermore, a new implementation of boundary conditions is developed by using the normal boundary derivatives of the main field unknowns to overcome the edge vertex's nodes normal issues related to the strong formulation boundary value problem. The HOCM has an adaptative step length which is very efficient and performed especially for bifurcation problems. By this way, we are able to detect precisely the critical buckling and wrinkling loads for very thin membranes with fewer degrees of freedom and less CPU time. A comparison between the proposed approach with analytical solution, Finite Element Method (FEM), and Element-Free Galerkin (EFG) method is illustrated in some numerical results that demonstrate the accuracy and robustness of the proposed approach. • Development of a Hermit mesh-free model to solve boundary value problems in the strong formulation of von-Kàrmàn plates. • Coupling the Hermit model with a high order continuation method to evaluate the buckling and wrinkling critical loads. • Overcoming the normal edge vertex's nodes boundary condition issues encountered in the use of strong formulation. • Reducing the huge number of degrees of freedom and CPU time performed by the reference methods as the finite element. • Analyzing the influence of the tensile effort and the plate geometry on the wrinkling modes and critical load. [ABSTRACT FROM AUTHOR]

For a system consisting of multiple columns, horizontal discrete braces are often used to increase the system's strength by decreasing the effective length of columns. Since the bracing requirements for such systems in current design standards were developed based on the assumption of identical columns with pin-ends, an analytical method is proposed to evaluate the ideal brace stiffness and brace forces for multiple columns by accounting for the stiffness interaction among columns and braces. For systems with uniform column lateral stiffness, the explicit solution for the maximum brace force is derived, and a simple formula is subsequently proposed by fitting the analytical results. The proposed formula explicitly accounts for the influences of column initial curvature and semi-rigid end connections on the maximum brace force. The method is comprehensive and applicable to multi-column systems with nonuniform column lateral stiffness, which can result from differences in column sizes, end connections, or applied loads. The results obtained from the proposed formulae are verified against those of finite element analyses. The ideal brace stiffness and brace forces for a system containing a distinctive column with a greater moment of inertia than the other columns are investigated. The results show that the location of the distinctive column affects the magnitudes of the ideal brace stiffness and the maximum brace force, which is yet to be considered in current design standards. • Proposed a method to assess bracing requirements for multiple nonidentical columns. • Influences of column initial curvature and semi-rigid connections are considered. • Systems with nonuniform column stiffness are considered. [ABSTRACT FROM AUTHOR]