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A simplified column-buckling model is developed to understand the buckling mechanism of thin-walled strips restrained by uniform lateral pressure in the milling process. The strip is simplified as two rigid columns connected by a rotation spring, resting on a smooth surface, restrained by a uniform pressure and loaded by an axial force. Two loading cases are considered, i.e., the dead load and the follower load. Analytical solutions for the post-buckling responses of the two cases are derived based on the energy method. The minimum buckling force, Maxwell force and stability conditions for the two cases are established. It is demonstrated that the application of higher uniform pressure increases the minimum buckling force for the column and thus makes the column less likely to buckle. For the same pressure level, the dead load is found to be more effective than the follower load in suppressing the buckling of the system. The effect of initial geometric imperfection is also investigated, and the imperfection amplitude and critical restraining pressure that prevent buckling are found to be linearly related. The analytical results are validated by finite element simulations. This analytical model reveals the buckling mechanism of strips under lateral pressure restraint, which cannot be explained by the conventional bifurcation buckling theory, and provides a theoretical foundation for buckling-prevention strategies during the milling process of thin-walled strips, plates and shells commonly encountered in aerospace or automotive industries. [ABSTRACT FROM AUTHOR]

The study investigated how simulated notches within concrete-filled steel tube (CFST) columns affect their mechanical performance. It aimed to understand the impact of notch length, orientation, and location within the steel tubes on the behavior of these circular columns. Study conducted compressive tests on a total of 32 CFST specimens, varying in thickness (3 mm and 6 mm) and filled with High-Strength Concrete (HSC) or Normal-Strength Concrete (NSC). Four control specimens without notches served as reference points. Results indicated that CFST columns with notches exhibited reduced mechanical performance compared to those without notches. Notch parameters played a crucial role in this reduced performance. Notch length and orientation had a more significant influence than notch location. It also highlighted that the thickness of the steel tube was a paramount factor, surpassing the importance of concrete type. In summary, the study emphasized that presence of notches in CFST columns significantly impacted their load-bearing capacity, buckling behavior, and failure modes. Length and orientation of notches were identified as critical factors, with steel tube thickness being a dominant factor in determining overall mechanical performance of these columns. These findings provide valuable insights for structural engineers and designers working with CFST columns in various construction applications. [ABSTRACT FROM AUTHOR]

A simplified column-buckling model is developed to understand the buckling mechanism of thin-walled strips restrained by uniform lateral pressure in the milling process. The strip is simplified as two rigid columns connected by a rotation spring, resting on a smooth surface, restrained by a uniform pressure and loaded by an axial force. Two loading cases are considered, i.e., the dead load and the follower load. Analytical solutions for the post-buckling responses of the two cases are derived based on the energy method. The minimum buckling force, Maxwell force and stability conditions for the two cases are established. It is demonstrated that the application of higher uniform pressure increases the minimum buckling force for the column and thus makes the column less likely to buckle. For the same pressure level, the dead load is found to be more effective than the follower load in suppressing the buckling of the system. The effect of initial geometric imperfection is also investigated, and the imperfection amplitude and critical restraining pressure that prevent buckling are found to be linearly related. The analytical results are validated by finite element simulations. This analytical model reveals the buckling mechanism of strips under lateral pressure restraint, which cannot be explained by the conventional bifurcation buckling theory, and provides a theoretical foundation for buckling-prevention strategies during the milling process of thin-walled strips, plates and shells commonly encountered in aerospace or automotive industries.

In a box girder cross‐section with inclined web panel, transverse compression may be introduced into the bottom panel from both sides in addition to constant longitudinal compressive stresses. In EN 1993‐1‐5, the only analytical method for determining the resistance of panels to biaxial compression is the Reduced Stress Method (RSM). However, the current rules were mainly derived for longitudinal stresses. Due to missing rules, in practice the longitudinal stiffeners need being verified according to flexural member buckling considering the transverse updrift forces. Therefore, in order to assess the real behaviour, a large parametric study of stiffened panels with closed longitudinal stiffeners under transverse compressive stresses was carried out using a verified numerical model. LBA and GMNIA are performed for each case. To apply the RSM, all critical buckling stresses were determined considering the torsional stiffness of stiffeners. According to EN 1993‐1‐5, the support of the edges of the panels parallel to the load direction should be set free when determining the critical stress for column‐like behaviour. In the case of a longitudinally stiffened panel under transverse stresses, it is not clear whether the support of the plate and the stiffeners or only the plate should be released. In this paper, these interpretations are discussed and results are compared. Finally, a simplified procedure to determine the global reduction factor of plate buckling for transverse stresses in a single step is proposed. [ABSTRACT FROM AUTHOR]

Man‐made hazards, such as fire, explosions, or impacts, may induce the progressive collapse of structures, in which the localised failure spreads from the single affected structural component to other parts of the structure. A typical approach to model progressive collapse consists in performing static column removal analyses considering a Dynamic Increase Factor (DIF), whose determination becomes paramount to account for the dynamic effects related to a sudden column loss scenario. Current recommendations on the definition of such factor mainly consider a beam‐type collapse in non‐linear analyses, though different mechanisms, e.g., column buckling, may govern progressive collapse events. This paper presents the determination of the DIFs through a numerical procedure for five steel structures with an increasing number of storeys. Both global and local imperfections are modeled to account for the geometric non‐linearities of the structure and column buckling. DIF values are obtained considering two different Engineering Demand Parameters (EDPs), suited for describing beam‐type and column‐type mechanisms respectively. The evaluated DIFs are compared with the values recommended in the current UFC design prescriptions for progressive collapse, and considerations on the choice of the appropriate DIF values are provided. [ABSTRACT FROM AUTHOR]

Glass-reinforced composite columns (GRCCs) may provide an economical alternative to conventional construction materials due to the superior cost to strength provided by bulk glass. Prior to this study, no GRCCs had been physically tested, having previously relied on simulation to predict the behavior of the columns. This study utilizes polyurethane resin bonds in place of sizing agents for adherence between materials, a key requirement for the development of the structural system of the columns. The unreinforced control column failed at a load of 11.2 kN while the maximum GRCC load was 30.8 kN. This indicates that glass can be loaded to 123 MPa before the onset of delamination failure of the GRCCs. Maximum shear stress of 53 MPa was reached, exceeding the 11 MPa required for practical GRCCs. Buckling of the columns occurred at 30.8 kN, below the theoretical maximum of 64.4 kN. Through gradual delamination, the column slowly transferred to an unbonded condition, causing buckling failure. Delamination is unlikely to occur in practical GRCCs due to the lower required shear strengths. [ABSTRACT FROM AUTHOR]

When a fire develops within the fire compartment of a building, the columns in the compartment are heated, whereas the beams and columns outside the compartment remain cold. Hence, the relative stiffness ratio between the cold members and heated column increases. Consequently, the end-rotational restraint on the heated column is increased, and the effective buckling length of the heated column becomes shorter compared with the ambient temperature condition. However, studies regarding the effect of increased end rotational restraint on heated columns are rare. Although some recommendations to consider this effect are available in representative design standards, they are suggested under limited or ideal conditions and hence not applicable under general conditions. In this study, a procedure for calculating the effective length factor of non-sway steel columns with general end restraints at elevated temperatures is proposed based on the classical Euler column theory and tangent modulus concept. The proposed procedure is validated based on a test-backed nonlinear finite element analysis. It is shown that the proposed equations can be combined with the existing column buckling curve to predict the column buckling strength with significantly increased accuracy compared with the methods suggested by representative design standards. [ABSTRACT FROM AUTHOR]

A tree may receive compression and flexure combination, and the structural analysis governed by the building code may be capable of estimating the tree's safety in the built environment. This study proposed to refer to the building code to check the tree dimension adequacy resisting the load. This study simplified the case by focusing only on the self-weight and ignoring the external loads; therefore, the buckling analysis of a slender tapered round column subjected to compression is advocated. Buckling occurs when the tree's structure can no longer maintain its original shape. Euler and Ylinen's buckling stress analysis (Method 1) calculated tree safety with a 95% confidence level. This study also applied the Greenhill formula (Method 2) to determine the critical height of a tree receiving the stem weight, then modified it to include the crown weight (Method 3). The three methods calculated the critical height to determine the safety factor (Sf), that is, the ratio of the actual tree height (H) to the 95% confidence level estimated critical height (Hcr). The safety factors were then categorized as unsafe (Sf < 1.00), safe (1.00 < Sf < 1.645), and very safe (1.645 < Sf). This study demonstrated that Method 1 is the most reliable and applicable among other methods. Method 1 resulted in no unsafe trees, 10 safe trees, and 13 very safe trees among the observed excurrent agathis (Agathis dammara). Meanwhile, among the decurrent rain trees (Samanea saman (Jacq.) Merr), 5, 31, and 14 were unsafe, safe, and very safe, respectively. [ABSTRACT FROM AUTHOR]

This paper presents a dual approach to the conventional averaging (CA) in order to construct a weighted averaging. A one-parameter weighting function for the novel weighted local averaging (WLA) is presented and analyzed in detail. The advantage of the proposed WLA is demonstrated by its application to the Galerkin method, which leads to a so-called the Galerkin method with weighted local averaging (GWLA). Application of the GWLA to the problem of elastic buckling of columns shows that the new idea can improve significantly the accuracy of the first order approximate solution of the Galerkin method. In order to solve the problem of selecting a specific weighting function among the classes of one-parameter weighting functions, the global-local approach is implemented. Further approximations resulting in the simplified GWLA (SGWLA) have been made to reduce the computation cost while still maintaining the accuracy of the solutions obtained by the GWLA. In addition, the effectiveness of the WLA is demonstrated by its combination with the least squares method to transform column with variable cross-section into equivalent column with constant cross-section. Numerical calculations show that the approximate critical buckling loads obtained by the newly developed GWLA and SGWLA outperform those obtained by the Galerkin method with conventional averaging (GCA). These new numerical algorithms could provide a novel and potential effective alternative tool for engineering calculation in designing structures with varying cross-sections. [ABSTRACT FROM AUTHOR]

Round bamboo culms offer excellent sustainable materials for a green building construction. Round bamboo culms are tied or fastened into a multi-culm composite member to resist the heavier load. Circles externally touching each other can well model a multi-culm bamboo composite's section. This study aimed to obtain formulas for drawing a cross-section of a multi-culm bamboo composite, calculating its section properties, and then embedding them into a graphing calculator and spreadsheet. As many as nine full-sized single and multi-culm bamboo composite columns were tested in the laboratory to resist the buckling load until the failure occurred. The column acting as the sum of some individual culms capacity was considered. In addition, the embedded equations analyzed the multi-culm column working in unity as a composite. This study found that the multi-culm columns tend to inhibit the combination (pseudo-composite) behavior rather than acting as a perfect composite column or the sum of individual culm's capacities. A perfect composite columns approach resulted overestimated value of the multi-culm column's critical buckling load; on the other hand, the sum of individual culm's capacity approach approximated underestimated value. The weighted average approach with a weight coefficient of k = 1 explains the empirical critical buckling load-bearing capacity's variance very well.

Modular structural systems have been used increasingly for low- and mid-rise structures such as schools and apartment buildings, and applications are extending to high-rise buildings. To provide sufficient resistance and economical construction of the high-rise modular structural system, the steel-concrete composite unit modular structure was proposed. The proposed composite unit modular system consists of the composite beam and the partially encased nonsymmetrical composite column. The outside steel member of the composite column has an open section, and is manufactured using a pressed forming procedure so that easy joining connecting work and manufacturing cost reductions are possible. However, the design methods are complicated due to the inherent nonsymmetrical properties of the section. Therefore, in this study, the focus was made on the strength evaluation and development of design methods for the partially encased nonsymmetrical steel-concrete composite column. Four full-scale specimens were constructed and tested. The experimental study focused on the effect of the slenderness ratio of the column, eccentricity, and the through bars on the strength of such columns. Additionally, the P–M interaction curve to estimate the strength of the proposed composite column under general combined loading was developed based on the plastic stress distribution method. The results indicate that the through bars are needed to delay the local buckling and distribute the loading uniformly throughout the composite column. Finally, the proposed design methods provide a conservative strength prediction of the proposed composite column. [ABSTRACT FROM AUTHOR]

The mechanical properties of biological nanofibers such as collagen fibrils are important in many applications, ranging from tissue-engineering to cancer treatment. However, mechanical testing is not straightforward at the nanometer scale. Here, we use the theory of column-buckling to determine the bending properties of individual collagen fibrils. To achieve this, fibrils were deposited on a manually pre-stretched foil, which was then released with the fibrils attached. Atomic Force Microscopy (AFM) imaging was used to determine the tensile modulus by measuring the buckling-wavelength and the radius for each fibril. Comparison with data obtained by AFM nanoindentation and other, more sophisticated methods, shows that our results are in very good agreement. The great advantage of this simple approach is that it can be used to quickly determine mechanical properties without force or stress-strain measurements, which are challenging to obtain accurately and at high throughput at the nanoscale. The method could be applied to any nanofibers, not just collagen fibrils. Collagen fibrils are the main constituent of the extracellular matrix, and alterations of their mechanical properties can have significant effects on cell adhesion and motility. This has, ultimately, implications in age-related diseases and cancer. Furthermore, tuning the mechanical properties of collagen fibrils could be an important tool in the design of artificial cell scaffolds in tissue-engineering. For these reasons, it is important to have methods that can be used to determine the mechanical properties of fibrils at the single-fibril level and, therefore, at the nanometer scale. The method presented here has the advantage of being easy to use and avoids some of the fundamental issues of more established methods. [Display omitted] [ABSTRACT FROM AUTHOR]

The wire arc additive manufacturing (WAAM) technology in combination with computational design shows a big potential for realising novel force‐flow optimised and material‐efficient connections. This contribution deals with point‐by‐point WAAM, a material deposition strategy that allows to place material precisely where structurally needed or aesthetically desired. This could be applied, among others, for realising a novel optimised type of steel nodes between custom‐oriented profiles, as they occur in freeform steel‐glass grid‐shells. In this paper, the structural behaviour of robotically fabricated straight WAAM steel bars under uniaxial tensile and compressive loading is discussed. The focus is set on the ductility exhibited by such components as well as on the buckling behaviour observed under compressive loading. Experimental tests were conducted, both under tensile and under compressive loading to assess the influence of the irregular geometry on the structural performance. Furthermore, it was studied to what extent a prediction of the ductile structural behaviour, of the compressive load‐bearing capacity and of the post‐buckling behaviour is possible by finite element simulations. This contribution presents and discusses highlights of the obtained results. [ABSTRACT FROM AUTHOR]

Square and rectangular cold‐formed hollow sections are generally produced by either direct forming or indirect forming. These methods allow manufacturing nominally similar geometries of the cross‐sections, but leading to some different mechanical characteristics. The present paper addresses cold‐formed structural hollow sections produced by indirect forming that are characterized by the greater residual stresses, focusing on (i) the ductility of the cold‐formed material in the corners and flat parts of the section; (ii) the reliability of the buckling curves given by EN1993‐1‐1 for this type of columns. The reliability assessment is performed using first order reliability method on a detailed and validated numerical model developed in OpenSees. The results show that the current curve "c" in EN1993‐1‐1 underestimates the buckling capacity of stocky members. [ABSTRACT FROM AUTHOR]

Steel buildings are generally susceptible to the risk of progressive collapse in case one or a few load-carrying members are lost in an extreme event such as blast, impact, or fire. Thus, to avoid the catastrophic collapse of steel structures, it is imperative to investigate and learn from the performance of existing steel buildings for progressive collapse potential. The Ohio Union building, a multi-story steel-framed building that existed on the campus of Ohio State University, was tested earlier before its demolition by one of the co-authors for progressive collapse assessment under the successive removal of four columns located at the first-story level. The aim of this study is to conduct NLD (nonlinear dynamic) analysis for the building considering buckling of columns to numerically assess its potential for progressive collapse and then compare it with test observations. The calibrated finite element (FE) model was then extended to incorporate more hypothetical sequential and simultaneous column-loss scenarios. As one of the most widely accepted documents used among practicing engineers for numerical assessment of progressive collapse potential of buildings, the 2003 GSA (General Services Administration) guidelines were also applied. The simplified LS (linear static) analysis approach of the GSA guidelines was used for assessing the progressive collapse risk of the building, and the results were then compared with both test observations and NLD analysis. New dynamic increase factors (DIFs) are recommended for both force- and deformation-controlled actions to be used with the LS analysis.

Glass-reinforced composite columns (GRCCs) may provide an economical alternative to conventional construction materials due to the superior cost to strength provided by bulk glass. Prior to this study, no GRCCs had been physically tested, having previously relied on simulation to predict the behavior of the columns. This study utilizes polyurethane resin bonds in place of sizing agents for adherence between materials, a key requirement for the development of the structural system of the columns. The unreinforced control column failed at a load of 11.2 kN while the maximum GRCC load was 30.8 kN. This indicates that glass can be loaded to 123 MPa before the onset of delamination failure of the GRCCs. Maximum shear stress of 53 MPa was reached, exceeding the 11 MPa required for practical GRCCs. Buckling of the columns occurred at 30.8 kN, below the theoretical maximum of 64.4 kN. Through gradual delamination, the column slowly transferred to an unbonded condition, causing buckling failure. Delamination is unlikely to occur in practical GRCCs due to the lower required shear strengths.

In general, the insertion of Stone-Wales (SW) defects into single-walled carbon nanotubes (SWNTs) reduces the buckling resistance of SWNTs under axial compression. The magnitude of reduction is more noticeable in zigzag-type SWNTs than armchair- or chiral-type SWNTs; however, the relation between the magnitude of reduction and aspect ratio of the zigzag SWNTs remains unclear. This study conducted molecular dynamics (MD) simulation to unveil the buckling performance of zigzag SWNTs exhibiting SW defects with various tube diameter. The dependencies of energetically favorable buckling modes and the SW-defect induced reduction in the critical buckling point on the tube diameter were investigated in a systematic manner. In particular, an approximate expression for the critical buckling force as a function of the tube diameter was formulated based on the MD simulation data. [ABSTRACT FROM AUTHOR]

• Dynamic Increase Factors derived for beam and column failure mechanisms with non-linear static/dynamic analyses procedure. • Numerical models validated for axial force-bending moment interaction in the beams andcolumn buckling. • Procedure for factors that apply only on the spans above the removal, consistently with UFC guidelines. • Most suited dynamic increase factor based on the actual collapse mode, but both mechanisms should be checked separately. • Dynamic effects vary with demand, stories, collapsing mechanism, column loss, and damping in structures. • UFC is not accurate in accounting for dynamic effects, especially on axial forces and in MRFs prone to column buckling. Progressive or disproportionate collapse of structures may have severe socio-economic consequences. Aiming at buildings that can withstand such events, one solution is to prevent or minimize the propagation of damage that may lead to progressive collapse by means of robust design strategies. As a typical approach to model progressive collapse and assess robustness, the Alternate Path Method (APM) allows for static analyses, in which the dynamic effects induced by a sudden column loss are taken into account by amplifying loads through a Dynamic Increase Factor. Current recommendations for Dynamic Increase Factors to be used within non-linear static analyses have mainly considered beam-type collapse, overlooking other failure mechanisms, e.g. , column buckling. The present paper investigates the dynamic effects of steel structures subjected to progressive collapse when buckling of columns is relevant. Five low- to high-rise case study building structures are considered together with three different column loss scenarios. A numerical procedure is introduced to evaluate the Dynamic Increase Factors considering two different Engineering Demand Parameters (EDPs), suited for describing beam- and column-type mechanisms, respectively. As Dynamic Increase Factors are typically assessed by increasing the loads on all the spans (DIF), a procedure was proposed for deriving factors that apply only on the spans above the removal (DIF*), consistently with UFC guidelines. The obtained DIF and DIF* are compared with the current literature and with values recommended in the UFC guidelines, highlighting the limits of current recommendations. Relevant considerations on the derived Dynamic Increase Factors and failure mechanisms involved are provided. [ABSTRACT FROM AUTHOR]

Modular structural systems have been used increasingly for low- and mid-rise structures such as schools and apartment buildings, and applications are extending to high-rise buildings. To provide sufficient resistance and economical construction of the high-rise modular structural system, the steel-concrete composite unit modular structure was proposed. The proposed composite unit modular system consists of the composite beam and the partially encased nonsymmetrical composite column. The outside steel member of the composite column has an open section, and is manufactured using a pressed forming procedure so that easy joining connecting work and manufacturing cost reductions are possible. However, the design methods are complicated due to the inherent nonsymmetrical properties of the section. Therefore, in this study, the focus was made on the strength evaluation and development of design methods for the partially encased nonsymmetrical steel-concrete composite column. Four full-scale specimens were constructed and tested. The experimental study focused on the effect of the slenderness ratio of the column, eccentricity, and the through bars on the strength of such columns. Additionally, the P–M interaction curve to estimate the strength of the proposed composite column under general combined loading was developed based on the plastic stress distribution method. The results indicate that the through bars are needed to delay the local buckling and distribute the loading uniformly throughout the composite column. Finally, the proposed design methods provide a conservative strength prediction of the proposed composite column.

Buckling of a column under pre-load restraint has been found to differ from the conventional bifurcation problems and thus requires better understanding. To this end, a simple model consisting of two collinear rigid bars connected by a rotational spring, resting on a smooth surface, loaded by an axial force and restrained by a constant force at the common joint is investigated. The energy method is adopted to establish the equilibrium and stability conditions. The post-buckling response of the simple system indicates that the load-restrained buckling problem is a snap-through problem. The minimum possible buckling force and the buckling force based on the Maxwell construction are found to increase with the restraining force, and can be approximated by power-law functions. It is further shown that an energy barrier exists for the snap-through to occur and the buckling force depends on the perturbation energy. Sensitivity of this system to initial geometric imperfections is also investigated, and an energy barrier is also found to exist for the buckling of systems with imperfection amplitudes smaller than a certain critical value. The characteristic imperfection amplitude depends on the restraining force and, interestingly, transforms the snap-through problem into an eigenvalue problem identical to the conventional one, i.e., the one without imperfection and restraining force. [ABSTRACT FROM AUTHOR]

In general, the insertion of Stone-Wales (SW) defects into single-walled carbon nanotubes (SWNTs) reduces the buckling resistance of SWNTs under axial compression. The magnitude of reduction is more noticeable in zigzag-type SWNTs than armchair- or chiral-type SWNTs; however, the relation between the magnitude of reduction and aspect ratio of the zigzag SWNTs remains unclear. This study conducted molecular dynamics (MD) simulation to unveil the buckling performance of zigzag SWNTs exhibiting SW defects with various tube diameter. The dependencies of energetically favorable buckling modes and the SW-defect induced reduction in the critical buckling point on the tube diameter were investigated in a systematic manner. In particular, an approximate expression for the critical buckling force as a function of the tube diameter was formulated based on the MD simulation data.

During the preliminary design of stiffened panels, the stability behaviour is critical and both buckling modes, global and local, have to be considered in order to avoid panel configurations in which the minimum stiffness of the stringers is not achieved. In the present work, a new simple computational model is presented that computes the critical column buckling load of an omega-stringer-stiffened panel with periodic boundary conditions. This is achieved by obtaining the effective stiffness properties for an equivalent composite column. The model is able to predict column buckling conservatively as numerical studies show and can easily be used, e.g. as a constraint for optimization studies.

Contractility of cells in wound site is important to understand pathological wound healing and develop therapeutic strategies. In particular, contractile force generated by cells is a basic element for designing artificial three-dimensional cell culture scaffolds. Direct assessment of deformation of three-dimensional structured materials has been used to calculate contractile forces by averaging total forces with respect to the cell population number. However, macroscopic methods have offered only lower bounds of contractility due to experimental assumptions and the large variance of the spatial and temporal cell response. In the present study, cell contractility was examined microscopically in order to measure contractile forces generated by individual cells on self-standing fiber scaffolds that were fabricated via femtosecond laser-induced two-photon polymerization. Experimental assumptions and calculation errors that arose in previous studies of macroscopic and microscopic contractile force measurements could be reduced by adopting a columnar buckling model on individual, standing fiber scaffolds. Via quantifying eccentric critical loads for the buckling of fibers with various diameters, contractile forces of single cells were calculated in the range between 30-116 nN. In the present study, a force magnitude of approximately 200 nN is suggested as upper bound of the contractile force exerted by single cells. In addition, contractile forces by multiple cells on a single fiber were calculated in the range between 241-709 nN.

This paper presents a method for improving the buckling capacity of slender columns by employing functionally graded materials (FGMs) instead of isotropic materials in constructing these members. The volume fractions of FGM constituents are varied along the column length by a trigonometric function thereby causing variations in material properties such as stiffness and density. The effective material properties are evaluated based on Mori-Tanaka scheme. The buckling problem has been solved using the finite element method (FEM) whereas optimal solution was obtained through a genetic algorithm. The present design problem considered identification of the optimal volume fraction distribution of the FGM that maximizes the critical buckling load-to-weight ratio for columnar members with different boundary conditions. The different design examples presented in this paper illustrate the effectiveness of using FGMs in constructing axially compressed columns. The present results can be successfully applied in designing FGM-columns for optimal buckling capacities.

The analytical approach of Leonhard Euler to the solution of an elastic column under compression is seen today as a landmark in buckling studies. However, this work was not well received in Great Britain during the late XVIII and XIX centuries. This paper considers the reaction of John Robison, Professor at the University of Edinburgh, published as an article in Encyclopedia Britannica, who attempted to disqualify Euler at scientific, methodological, and personal levels. The article was reproduced from edition three to eight, thus covering a period of some 90 years. The technical arguments made by Robison, together with the context in which he lived, are taken into account in order to explore the reasons behind the aggressive campaign of Robison against one of the most famous mathematicians of the XVIII century. [ABSTRACT FROM AUTHOR]

Based on a number of numerical investigations into welding simulations, highly non-linear welding-induced residual stresses within high strength S690 welded H-sections have been evaluated successfully, and surface residual stresses along their flange / web junctions have been carefully calibrated against measured data. This modelling technique has been extended to cover residual stresses of cold-formed circular hollow sections recently, and also of cold-formed square hollow sections as described in this paper. Hence, a full presentation on the proposed approach of integrated and coordinated numerical simulations on various mechanical, heat transfer and thermomechanical, and stresses analyses on these cold-formed square hollow sections is described. Subsequent structural analyses of these models on both stocky and slender columns of these cold-formed square hollow sections are then carried out. Structural adequacy of the proposed approach is thoroughly demonstrated through a systematic calibration against various measured data – both temperatures and residual stresses of these sections induced during fabrication, and load-deformation curves of these sections under compression. It should be noted that the proposed approach provides a scientific mechanism to determine directly residual stresses due to transverse bending and longitudinal welding as initial materials imperfections in these high strength S690 cold-formed square hollow sections. With an adoption of the lowest eigenmodes of these columns as their initial geometric imperfections after adjusted with measured or design values of the member out-of-straightness, both the effects of initial materials and of initial geometric imperfections onto the structural performance of these columns are readily quantified separately. [Display omitted] • An integrated and coordinated numerical simulation approach is developed. • Fabrication-induced effects of cold-formed square hollow sections are considered. • Both residual stresses and strains are incorporated into the structural models. • All of the models have been calibrated with measured results of stocky and slender columns. [ABSTRACT FROM AUTHOR]

Abstract The seismic provisions of the Canadian CSA S16-14 standard for steel structures for heavy industrial steel structures are reviewed and applied for a 65.4 m tall concentrically braced frames (CBFs) for an industrial application in Vancouver, BC. Two approaches are examined: a capacity design method in accordance with CSA S16 Annex M and a simpler, non-capacity design approach for the structures of the Conventional Construction (Type CC) category. Nonlinear response history analyses are performed to examine and compare the seismic response of the structures. Modifications are proposed to mobilize higher brace inelastic response, mitigate storey drift concentrations, and ensure that the columns can safely resist the seismic induced axial and flexural demands. The modified provisions are validated for additional structures having heights varying from 43 to 80 m and two different vertical distribution of the seismic weights. The robustness of the structures against excessive storey drifts and column buckling limit states is verified through incremental dynamic analysis. Both Annex M and Type CC design approaches, as modified in this study, represent two practical options to achieve cost-effective designs resulting in satisfactory seismic response. Three-dimensional nonlinear response history analysis is used to compare the 100%–100% and 100%–30% combination rules to predict the axial load demand on columns part of two orthogonal CBFs. For the structure studied, the results showed that the latter would give more realistic force estimates. Highlights • CSA S16 seismic provisions for tall industrial steel braced frames are reviewed. • Capacity and non-capacity design methods are applied and compared for sample frames. • Nonlinear response history analyses are performed to assess the seismic responses. • Modifications to design provisions are proposed to improve the frame responses. • Seismic axial loads in columns part of two orthogonal braced frames are evaluated. [ABSTRACT FROM AUTHOR]

This study deals with the generalized second moment of area (GSMA) of regular polygon cross-sections for the Ludwick type material and its application to cantilever column buckling. In the literature, the GSMA for the Ludwick type material has only been considered for rectangular, elliptical and superellipsoidal cross-sections. This study calculates the GSMAs of regular polygon cross-sections other than those mentioned above. The GSMAs calculated by varying the mechanical constant of the Ludwick type material for the equilateral triangle, square, regular pentagon, regular hexagon and circular cross-sections are reported in tables and figures. The GSMAs obtained from this study are applied to cantilever column buckling, with results shown in tables and figures. [ABSTRACT FROM AUTHOR]

This paper presents a method to optimize the dimensions of z-stiffened panels under a compressive load. Buckling coefficient curves for local buckling and stiffener lateral buckling are developed. The effects of transverse shear, coupling of buckling modes, and stiffeners on one side of the skin are considered in the column buckling stress estimation. An optimization tool is developed using MS-Excel. Examples of the design charts are presented and a design guideline is derived. [ABSTRACT FROM AUTHOR]

This paper presents a method to optimize the dimensions of z-stiffened panels under a compressive load. Buckling coefficient curves for local buckling and stiffener lateral buckling are developed. The effects of transverse shear, coupling of buckling modes, and stiffeners on one side of the skin are considered in the column buckling stress estimation. An optimization tool is developed using MS-Excel. Examples of the design charts are presented and a design guideline is derived. [ABSTRACT FROM AUTHOR]

Most current structural fire codes focus on achieving prescribed fire ratings, which are based on standard fire tests with minor relevance to what is required for fire safety. These prescriptive design approaches do not provide sufficient information regarding the performance of structural members or systems under elevated temperatures. Furthermore, the limited structural design provisions provide no indication of the level of reliability of structures since comprehensive treatment of the uncertainties associated with the hazard is not considered. It is therefore imperative to move towards performance-based engineering not only to quantify structural reliability for given performance objectives but also to ensure more economic and safe design. This paper provides details on the development of a new analysis framework for probabilistic performance-based analysis of a fire following an earthquake. The framework is then utilized to develop fragilities of steel structural members and systems subjected to cascading hazards of earthquake and fire while considering buckling of columns as the damage limit state. Uncertainties associated with fire hazard, passive fire protection, gravity load, and earthquake intensity are accounted for in the framework. The proposed performance-based approach for the analysis of a fire following an earthquake can be considered an extension of the Pacific Earthquake Engineering Research (PEER) performance-based earthquake engineering framework and used by engineers to assess structural performance under the multiple hazards. [ABSTRACT FROM AUTHOR]

Our recent buckling experiments on superelastic shape memory alloy columns (initially straight rods and tubes) discovered that during axial shortening, certain specimens bent (buckled) at a critical compressive load and then, surprisingly, straightened (unbuckled) at a larger compressive load. This "buckling -- uunbuckling' phenomenon, defined here as the deviation from and then return to a straight configuration during monotonic loading, is not only an intriguing phenomenon (contrary to the post-buckling behavior of conventional materials) but also presents the possibility for novel applications. This work aims to provide a clearer understanding of when and why unbuckling occurs, presenting the experimental observations of this phenomenon and the stability analysis of a modified Shanley column model that captures the unbuckling behavior. Unbuckling behavior is shown to be a consequence of a secondary branch that deviates from the principal path at a low-load level (critical buckling load), but reattaches to the principal path at a higher load level (unbuckling load). The analysis shows that unbuckling behavior can only ocajr for certain combinations of column geometries and nonlinear (stiff-soft-stiff) material laws, that is, relatively stout columns with the right sequence of softening/stiffening to create the necessary restorative bending moment to reset the column to a straight configuration. The feasible space is defined by closed-form bounds on geometric and material parameters, along with a sensitivity analysis of these parameters on the amplitude of unbuckling. [ABSTRACT FROM AUTHOR]

Practical use of high-strength (HS) steel in contemporary construction has become one of the most important design solutions. Loading capacities of columns may benefit enormously from the HS steel, whilst their overall buckling behaves differently compared with conventional mild (CM) steel columns due to varying effects of initial imperfections and inelastic properties of the HS steel materials. Despite a number of investigations regarding the HS steel columns being undertaken, there is lack of research focused on variation of HS steel grades and their effects. To deepen understanding of overall buckling behaviour of the HS steel columns, a comprehensive review of an extensive body of column test data available in the literature is carried out in the present paper, based on which a three-dimensional finite element (FE) model developed herein is validated. Parametric analyses are subsequently undertaken with various HS steel grades, welded cross-sectional geometric parameters, slenderness values and initial imperfections being involved. The FE analysis results are also compared with calculation values in accordance with national standards. It has been demonstrated that with an increase of the grade of HS steel, effects of imperfections decrease whilst that of Y/T ratios are rather limited; reduction effects on the overall buckling strength become less severe, and therefore higher column curves available in current national standards may be selected and imperfection factors in the alternative column curve equations proposed herein descend accordingly. In addition, new theoretical column curves based on Perry-Robertson formula are developed by introducing imperfection parameters independent on the steel strength. [ABSTRACT FROM AUTHOR]

The previously formulated model of the gravity-driven collapse of the twin towers of the World Trade Center (WTC) on September 11, 2011 was shown to match all the existing observations, including the video record of the crush-down motion of the top part of tower during the first few seconds, the seismically recorded duration of collapse, the size distribution of particles caused by impact comminution of concrete floor slabs, the loud booms due to near-sonic lateral ejection velocity of air and dust, and precedence of the crush-down collapse mode before the crush-up. Nevertheless, different degrees of ductility, fracturing and end support flexibility of WTC columns could lead to an equally good match of these observations and remained uncertain, due to lack of test data. Recently, Korol and Sivakumaran reported valuable experiments that allow clarifying this uncertainty. They revealed that, under the simplifying assumptions of rigid end supports and unlimited ductility (or no fracturing) of unheated columns, the energy dissipation of the WTC columns would have been at maximum 3.5-times as large as that calculated by the plastic hinge mechanism normally considered for small-deflection buckling. This increase would still allow close match of all the aforementioned observations except for the first two seconds of the video. The proper conclusion from Korol and Sivakumaran's tests, based on close matching of the video record, is that the fracturing of unheated columns and the flexibility of their end restraints must have significantly reduced the energy dissipation in columns calculated under the assumptions of no fracture and no end restraint flexibility. [ABSTRACT FROM AUTHOR]

NACA conducted extensive tests of z-stiffened panels under compressive load in the 1940s and 1950s in order to create direct-reading design charts. Because of the asymmetry of z-stiffened panels, the buckling behavior is complex and buckling analysis of the NACA data has not been conducted. In order to analyze the buckling of z-stiffened panels, a new tool for the buckling analysis of thin-walled structures is developed. This paper presents the results of the buckling analysis of the NACA data and investigates the buckling behavior of z-stiffened panels. It is found that the lateral buckling of the stiffener is critical in the short column region, while the torsional buckling of the stiffener is not critical. [ABSTRACT FROM AUTHOR]

This paper discusses aspects related to the determination of the buckling resistance of multi-span steel columns and beams in accordance with Eurocode 3 (EN 1993-1-1:2005, 2005). In particular, the paper reviews and extends the method previously proposed by the authors (Gonçalves and Camotim, 2005) for uniformly compressed members (columns) integrated in structural systems, which means that it is (i) system-based , i.e. relies on system parameters, and (ii) consistent with the Eurocode 3 buckling curves. It is shown that, besides making it possible to avoid individual member checks, the proposed approach provides relevant insight into the structural efficiency of the complete system. In order to illustrate the application of the proposed approach, several examples are presented and discussed throughout the paper. For comparison purposes, “exact” buckling (collapse) loads are provided, which are obtained from non-linear elastoplastic finite element analyses including member imperfections. [ABSTRACT FROM AUTHOR]

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Multitiered steel concentrically braced frames (CBFs) are commonly used to provide lateral resistance for tall single-story commercial, performing arts, sports, and industrial buildings. The seismic response of these frames is studied in this paper. A set of seven special concentrically braced frames (SCBFs), ranging from 9 to 30 m tall with two to six tiers, located in a high seismic area was designed according to the 2010 AISC Seismic Provisions. Fundamental behavior of the two- and four-tiered frames was investigated using three-dimensional (3D) finite element models with shell elements, with particular focus on the buckling response of the columns. The seismic frame response and column stability were then studied more broadly for all frames using more computationally efficient 3D finite element models with fiber-based beam-column elements, which were validated against the shell element models. Multitiered CBFs designed according to current multistory CBF procedures are shown to develop drift concentration in a single tier and high in-plane column bending demand, which in some cases leads to flexural yielding and column instability. As potential solutions to this problem, alternate design strategies were studied and their seismic performance is also presented. Designing for higher seismic forces did not appreciably improve column stability, but use of fixed column bases or buckling-restrained braces provided improved distribution of drift over multiple tiers and reduced the occurrence of column instability. Unlike multistory braced frame seismic design, column flexural demands are more important in multitiered braced frames and must be considered in seismic design. [ABSTRACT FROM AUTHOR]

This paper examines the possibility of mobilizing gravity columns in the resistance of in-plane bending moments imposed on the columns of multi-tiered steel braced frames subjected to seismic loading. This would be the case when horizontal struts are used to connect gravity columns to braced frames at every tier level, as is often seen along exterior walls. A seismic design strategy based on the AISC Seismic Provisions is presented for four-tiered prototype steel concentrically braced frames. Three different approaches are proposed for the design of the braced frame and gravity columns. A set of 12 four-tiered X-braced frames, ranging from 15 to 30 m in height and located in a high seismic area were designed based on the proposed design approaches. The seismic behavior of the frames is evaluated using nonlinear response history analysis. The results show that the seismic performance of the braced frames is improved as nonlinear seismic demand on the bracing members is reduced when mobilizing the gravity columns for lateral resistance. Furthermore, gravity columns bending moment demands are distributed between braced frame and gravity columns in proportion of their relative flexural stiffness. Adequate seismic performance and cost-effective design can be achieved when columns of both types are designed to resist their respective share of the flexural demand. Alternatively, satisfactory response was achieved when the gravity columns are verified for the seismic induced bending moments acting together with concomitant axial loads. [ABSTRACT FROM AUTHOR]