Elastic Shear Buckling Research Articles

Modified Easley formula for elastic critical global shear buckling stress of corrugated steel webs considering real boundary conditions

The real juncture between corrugated steel webs (CSWs) and flanges follows a multi-segmented line, distinct from that of flat steel webs. Classic methods may yield significant deviations in predicting the elastic global shear buckling capacity of CSWs of various scales due to their failure to consider real boundary constraints. Therefore, a universally applicable formula for calculating the elastic critical global shear buckling stress of CSWs, which accounts for real boundary conditions, is proposed. This formula is pertinent to both large-scale engineering CSWs and small-scale testing CSWs. This study commenced with a comprehensive reassessment of the elastic global shear buckling calculation method. Subsequently, the influence of geometric parameter ratios on the elastic critical global buckling stress was examined. The primary parameter was identified and employed to improve the global buckling coefficient. The proposed calculation method was validated using different corrugation configurations, including 1000-type, 1200-type, 1600-type, 1800-type, and 2000-type CSWs, as well as other CSWs used in experimental settings. These results were compared with those obtained from other reference methods. Findings indicate that the accuracy of the classic theoretical method is affected by variations in both boundary conditions and geometric dimensions due to the constraint effect of real boundary conditions. Under the real boundary conditions, the elastic critical global shear buckling stress of CSWs with simply supported boundary conditions is close to that of CSWs with consolidated boundary conditions. The ratio of web height to corrugation depth primarily affects the elastic global shear buckling capacity, which decreases as the ratio increases. The Easley formula can be modified based on the web height to corrugation depth ratio. Comparisons of numerous numerical and theoretical results reveal that the proposed calculation method exhibits commendable computational precision. In comparison to alternative formulas, the proposed method demonstrates enhanced consistency for calculating CSWs with varying geometric dimensions and boundary conditions, thereby demonstrating its favorable applicability. These conclusions provide valuable reference for the shear design of CSWs.

Elastic buckling formulas of multi-stiffened corrugated steel plate shear walls

Multi-stiffened corrugated steel plate shear walls (MCSPSWs) have desirable seismic behavior involving shear-resistant, ductile, and energy-dissipating capacities. The elastic buckling load of the MCSPSW is a major influencing factor on its seismic behavior and it lays a foundation for the further study and design of the elastoplastic shear bearing capacity of the MCSPSW. Current research on the elastic buckling load of the MCSPSW is limited. For the MCSPSW with corrugations laid horizontally, the number of pairs of stiffeners in engineering practice is usually larger than that of existing research. This study focused on the elastic buckling formulas of the MCSPSW with more than one pair of vertical stiffeners. Firstly, based on the orthotropic plate theory, the theoretical model of elastic shear buckling was established for the energy method derivation of the elastic buckling load of the MCSPSW. Then, for the stiffeners with transition rigidities, the effect of the stiffener layout on the elastic buckling load was investigated through theoretical analyses and numerical solutions. Accordingly, the optimal layout corresponding to the maximum elastic buckling load was determined. Considering the optimal layout of stiffeners, the elastic buckling load of the MCSPSW was solved using MATLAB. The uniform formulas for the elastic buckling coefficient of the MCSPSW involving more than one pair of vertical stiffeners were proposed by fitting the MATLAB results. Finally, eigenvalue buckling analyses based on finite element models were conducted to verify the accuracy of the optimal layout theory of stiffeners and proposed formulas.

Elastic local shear buckling of beams with sinusoidal corrugated webs

Steel beams with corrugated webs are used in the construction industry to increase the shear capacity of the web without the need to weld stiffeners to the web. Most research in the past has focused on beams with trapezoidal corrugated webs with little research available for beams with sinusoidal corrugated webs. The Eurocode is the only standard with shear design rules for beams with trapezoidal and sinusoidal corrugated webs. However, the equation for the elastic local shear buckling stress for beams with sinusoidal corrugated webs shown in the Eurocode was derived for a specific girder geometry and it is uncertain whether this equation can be used for any general beam with sinusoidal corrugated webs. In this paper, a finite element analysis is described to compute the elastic local shear buckling stress for beams with sinusoidal corrugated webs. The finite element analysis was done by modelling the beam as a cantilever acted upon by an edge shear stress at the free end. The aim is to compare the elastic local shear buckling stress with that predicted by the Eurocode. Over 600 beams with different geometric parameters of the sinusoidal web were analysed to investigate the elastic local shear buckling behaviour. The results show that the Eurocode is unconservative for some beams with sinusoidal corrugated webs.

Lateral behavior and PFI model of sinusoidal corrugated steel plate shear walls

This study focused on the lateral behavior of sinusoidal corrugated steel plate shear walls (CoSPSWs), which consist of a steel boundary frame and sinusoidal corrugated infill wall plates. Firstly, eigenvalue buckling analyses were conducted on sinusoidal corrugated wall plates under pure shear, and local as well as global shear buckling stress formulas were proposed. Nonlinear pushover analyses were then conducted on sinusoidal corrugated steel plate shear walls with different corrugation configuration, corrugation direction as well as influences from gravity loads. The results show that the lateral behavior of sinusoidal corrugated wall plates is obviously affected by the corrugation configuration and gravity load effects, but not much by the corrugation direction. Based on the shear slenderness ratio, sinusoidal corrugated wall plates could be classified into stocky, moderate and slender walls, with lateral load-resisting mechanism corresponding to shear yielding, inelastic shear buckling, and elastic shear buckling followed by incomplete tension field action, respectively. CoSPSWs with stocky wall plates tend to have both good lateral capacity and ductility, CoSPSWs with moderate wall plates would still have good lateral capacity but lower ductility, and CoSPSWs with slender wall plates would have good ductility but lower lateral capacity. Shear strength formulas were proposed for horizontal corrugated wall plates, not affected by gravity loads due to accordion effects, as well as vertical corrugated wall plates considering the gravity load effects. Plate-frame interaction (PFI) models were also proposed for horizontal and vertical CoSPSWs considering the gravity load effects.

Elastic shear buckling of cold-formed steel channels with edge stiffened web holes

Cold-formed steel (CFS) beams are commonly deployed in construction with web holes to accommodate service conduits. The web holes are subjected to stiffening methods aiming to restore the load-carrying strength reduction. In the shear design of CFS channels with stiffened web holes, the elastic shear buckling strength is the basis for the design irrespective of the available post-buckling strength. Therefore, this paper investigates the elastic shear buckling characteristics of CFS channels with stiffened circular web holes, which is still unresearched. Numerical simulations were conducted using the Abaqus finite element analysis software to study the elastic shear buckling response. Parametric studies were then performed, where a data pool was generated for CFS channels with no web holes, unstiffened web holes, and stiffened web holes, covering a range of parameters including web slenderness, web hole size, corner radius and edge stiffening element length. It was shown that edge stiffening of the web hole improves the shear buckling capacity compared to the CFS channels with no web holes and unstiffened web holes. New unified design proposals to estimate the elastic shear buckling strength of CFS channels with no web holes, unstiffened web holes, and edge stiffened web holes were developed based on the generated data. The new unified design proposals of modified shear buckling coefficient and equivalent thickness method offer accurate elastic shear buckling strength predictions.

GEP-based models for estimating the elastic shear buckling and ultimate loads of cold-formed steel channels with staggered slotted web perforations in shear

Thermal bridging through cold-formed steel (CFS) channels can be substantially reduced by introducing staggered slots in the channels’ webs. The perforation size and pattern significantly affect the elastic shear buckling and ultimate loads of the channels in shear, which must be considered in the design. This paper proposes new models for accurate estimations of the shear buckling and ultimate loads derived from an extensive database by employing gene expression programming (GEP). The model constructions involve various dimensional parameters, types of boundary conditions, and the yield strength of the channels. The proposed GEP models, in the form of transparent mathematical expressions, provide reasonable prediction accuracy comparable to published descriptive equations. However, the GEP models are simpler than the existing equations and do not require additional advanced computations, as the existing equations do, to obtain the elastic shear buckling and ultimate shear loads. LRFD resistance and ASD safety factors for the proposed GEP model were determined in accordance with AISI S100-16 w/S2-20. Based on the presented information, the GEP models are recommended for estimating the elastic shear buckling and ultimate loads of CFS channels with staggered slotted web perforations in shear.

Interpretable soft computing predictions of elastic shear buckling in tapered steel plate girders

The complexity of the shear buckling in tapered plate girders has motivated researchers to conduct experimental and numerical investigations to understand the underlying mechanisms controlling such phenomenon, and subsequently develop related design-oriented expressions. However, existing predictive models have been developed and validated using limited datasets and/or traditional regression techniques—restricting both the model utility, when considering a wider range of design parameters, and the model generalizability, due to associated uncertainties. To address these issues, the present study employed a powerful soft computing technique—multi-gene genetic programming (MGGP), to develop design expressions to predict the elastic shear buckling strength of tapered end plate girder web panels. A dataset of 427 experimental and experimentally validated numerical results was used in training, validating, and testing the developed MGGP models. Guided by mechanics and findings from previous studies, the key parameters controlling the strength were identified, and MGGP were employed to reveal the interdependence between such parameters and subsequently develop interpretable predictive models. The prediction accuracy of the developed models was evaluated against that of other existing models using various statistical measures. Several filter and embedded variable importance techniques were used to rank the model input parameters according to their significance in predicting the elastic shear buckling strength. These techniques include the variable importance random forest and the relative influence gradient boosting techniques. Moreover, partial dependence plots were employed to explore the effect of the input variables on the strength. The results obtained from this study demonstrated the robustness of the developed MGGP expression for predicting the elastic shear buckling strength of tapered plate girder end web panel. The developed model also exhibited a superior prediction accuracy and generalizability compared to currently existing ones. Furthermore, the developed partial dependence plots facilitated interpreting the influence of all input variables on the predicted elastic shear buckling strength.

Experimental investigation into NiTi shape memory alloy panels under cyclic shear loading

Shape memory alloys (SMAs) are widely employed in buildings and bridges as energy dissipation devices because of their superelasticity, shape memory, fatigue resistance, and high damping performance. In this study, SMA plates were fabricated into a shear device as a seismic structure. To understand the seismic performance of the SMA plate, an experimental study was conducted on the tension and shear behaviours of SMA plates under cyclic loading. Monotonic and cyclic tensile tests were carried out on 12 SMA plate coupons, and the important influencing factors, including the annealing temperature, annealing duration, and loading protocol, were evaluated. Based on the principle of maximum elastic modulus of austenite, maximum energy dissipation, and minimum residual strain, an optimal heat treatment scheme for a Ti–55.8 wt%Ni SMA plate with a thickness of 1.6 mm was suggested: annealing at 500 °C for 5 min. Further, the optimised SMA plate was installed in a shear device to conduct cyclic shear loading tests. Three pure shear tests with the SMA plate, structural steel, and stainless steel were designed and performed. The test results showed that the elastic modulus of the SMA plate is the lowest, which facilitates elastic shear buckling, and the tension field effect could significantly enhance the ultimate bearing capacity after buckling. In particular, when the applied shear is unloaded to zero, the SMA plate does not produce any residual deformation. Compared with the structural and stainless steel, the SMA plate exhibits more ideal self-centring behaviours, perfect fatigue fracture resistance, slow stiffness degradation, and greater yield deformation capacity; however, the initial stiffness, displacement ductility ratio, and energy dissipation capacity are slightly lower than those of the other test specimens. Although the SMA plate develops a large deformation, it produces a fracture failure mode without any evident sign.

Normalized shear strength of trapezoidal corrugated steel web dominated by local buckling

The elastic local shear buckling of trapezoidal corrugated steel web (TCSW) with clamped edges is investigated using finite element methods. An improved method is proposed to calculate the local buckling stress of TCSW with unequal widths of longitudinal fold panel and inclined fold panel. The simpler calculation method proposed by this study agrees well with the numerical analysis results and the previous calculation methods when the buckling is controlled by local buckling. The interactive shear buckling stress and buckling slenderness ratio are suggested for the local buckling-dominated TCSW. Test results also demonstrate that the suggested buckling slenderness ratio has a strong correlation with the normalized shear strength. Finally, the normalized shear strength equation is proposed for the local buckling-dominated TCSWs, which is accompanied with the approximate condition.

Numerical investigation of cold-formed stainless steel lipped channels with longitudinal stiffeners subjected to shear

The shear response of the cold-formed stainless steel lipped channel sections with longitudinal stiffeners has not been investigated adequately in the past. Therefore, this paper presents the details of numerical investigations conducted to study the shear behaviour of longitudinally stiffened cold-formed stainless steel lipped channel sections. Following a validation study of the finite element models of lipped channel sections, the effect of return lips and web stiffeners on the shear response of lipped channel sections was examined through comprehensive numerical parametric studies. In addition, numerical investigations were conducted to study the elastic shear buckling response of the sections and the shear buckling coefficients were back-calculated. It was found that the longitudinal web stiffeners enhance the shear buckling resistance of lipped channel sections considerably with increased stiffener depth. However, the shear capacity increment is not significant compared to plain lipped channel sections. The presence of the web stiffeners is found to be not preventing the out-of-plane buckling of the sections. The evaluation of Eurocode 3 and the direct strength method shear provisions for stainless steel channel sections with longitudinal stiffeners illustrates inaccurate capacity predictions. Therefore, modifications were proposed and comparisons reveal that the proposed provisions enhance the shear resistance predictions with good accuracy over the codified provisions.

A Generalized Formula for Elastic Shear Buckling of Trapezoidal Corrugated Web Girder

Trapezoidal corrugated web girder is widely used. The elastic shear buckling stress is an important parameter in the design and calculation of trapezoidal corrugated web girder. Accordingly, much research has been devoted on the analysis of typical elastic global shear buckling, elastic local buckling and elastic interactive shear buckling, and the corresponding formulae existing in a variety of literature. The results of finite element analysis suggest that there is a certain deviation in the calculated values based on classical elastic shear buckling formulae. The boundary conditions of corrugated web play an important role in the calculation of elastic shear buckling. And it is found that the shear buckling modes of the actual trapezoidal corrugated web may be called the atypical buckling, which is different from typical local buckling, global buckling and interactive buckling. The existence of the atypical buckling may result in some calculation deviations for the existing formulae of elastic shear buckling. Based on the classical elastic shear buckling formulae, a generalized formula for elastic shear buckling of trapezoidal corrugated web girder is obtained by numerical simulation. It intuitively reflects the relationships among various buckling modes. The formula has high calculation reference value and will promote the research of elastic shear buckling of trapezoidal corrugated web girder.

Parametric study for shear design of cold-formed channels with elongated web openings

Cold-formed steel members are commonly perforated with elongated web openings in practice to allow more access for the building service systems. The presence of such extended web holes in the members, when subjected to high shear forces, influences the shear buckling characteristics, the shear failure modes and generally leads to a reduction of shear capacity as well. In order to provide a better insight into the shear behaviour of cold-formed members with elongated web cut-outs, this paper presents a numerical study using finite element method (FEM) models employing ABAQUS/Standard to investigate the elastic shear buckling and post-buckling behaviour of cold-formed members in the form of thin channel sections. A full non-linear FEM model is developed and calibrated against previous shear tests with elongated web holes carried out using a dual actuator test rig. Based on the successful calibration against the tests, a parametric investigation is conducted to extend the resulting database. Further, a new proposal for the Direct Strength Method (DSM) of design of perforated channels in shear with both non-elongated and elongated web holes is further validated by using the results from the parametric study. A comparison between the empirical approach (“qs” method) and the new DSM of design derived from the Vierendeel mechanism approach is also provided to enhance the applicability of the new proposal to different cases of perforated channel members in shear with a wider range of sectional dimension and thicknesses.

Numerical investigation on ultimate shear strength of long steel plate girder web panels at high temperatures

In this article, elastic shear buckling and ultimate shear strength of long steel plate girder web panels subjected to pure shear loading are investigated at both ambient and elevated temperatures by the finite element method (FEM). Ninety-six plate girders with compact, non-compact and slender long web panels are numerically analyzed and compared. From linear eigenvalue analysis, it is shown that AISC 360-16 predictions are more conservative than FEM results such that the difference is about 40% for all ranges of web panel slenderness. According to nonlinear analysis results at ambient temperature, there must be reduction factors applied to AISC 360-16 non-conservative predictions for considering the strength degradation caused by large slenderness values and effects due to initial geometrical imperfection. Furthermore, it is observed that the adopted equation of AISC 360-16 for fire situations yields values that are more non-conservative such that the difference reaches almost 18%. In this regard, the FEM results are used to develop a new equation for predicting the ultimate shear strength of long web panels by taking into account strength degradation caused by large slenderness values, high temperature and initial geometrical imperfections.

Investigation on the Collapse Behavior of Diagonal Stiffened Composite Plate Girders Subjected to Shear Loading

In this study, a new analytical method is presented to estimate the shear capacity of diagonally stiffened steel–concrete composite plate girders. This method is formulated based on tension field action in steel girder web and failure mechanism of concrete slab deck. To validate the accuracy of the proposed method, the obtained results are compared with three-dimensional finite element analysis of composite plate girders with different configuration of stiffeners. The results of analytical and numerical investigations indicate that the proposed method can accurately estimate the ultimate shear capacity of composite plate girders. In addition, it is shown that the diagonal stiffeners on one hand can reduce the buckling effects of shear panel of girders and on the other hand can increase the strength of elastic shear buckling and ultimate shear capacity of girders well in comparison with the unstiffened thin steel plate girders.

Mechanical behaviors of C/SiC pyramidal lattice core sandwich panel under in-plane compression

C/SiC composite lattice-core sandwich panels combined with thermal insulation and load-bearing capacities are considered as the most promising candidates for thermal protection system (TPS). In this study, C/SiC pyramidal lattice-core sandwich panel with different inclination angles were fabricated using a compression molding and precursor infiltration and pyrolysis (PIP) method. In-plane compressive experiments are conducted to study the failure behavior of these sandwich panels. The analytical failure modes including elastic buckling, face sheet wrinkling, face sheet crushing and interlayer delamination are established to construct the mechanism maps. The effect of geometrical parameters on failure modes are symmetrically and analytically studied. Due to the limits of the cost, virtual tests are supplemented by finite element method (FEM). Face sheet crushing is experimentally observed for almost all specimens with different inclination angles, which is in good agreement with analytical predictions. Numerical simulation results show that interlayer delamination occurs at the attachment between face sheet and lattice core after elastic buckling and core shear buckling. This paper gives us some fundamental understanding of the mechanical response and failure mechanism of C/SiC composite lattice-core sandwich panels.

Study on Elastic Global Shear Buckling of Curved Girders with Corrugated Steel Webs: Theoretical Analysis and FE Modelling

Despite the construction of several curved prestressed concrete girder bridges with corrugated steel webs (CSWs) around the world; their shear behavior has seldom been investigated. Accordingly, this paper substitutes the lack of available information on the global elastic shear buckling of a plane curved corrugated steel web (PCCSW) in a curved girder. This is based on the equilibrium equations and geometric equations in the elastic theory of classical shells, combined with the constitutive relation of orthotropic shells. Currently, the global elastic shear buckling process of the PCCSW in a curved girder is studied, for the first time in literature, with an equivalent orthotropic open circular cylindrical shell (OOCCS) model. The governing differential equation of global elastic shear buckling of the PCCSW, as well as its buckling strength, is derived by considering the orthotropic characteristics of a corrugated steel web, the rational trigonometric displacement modes, Galerkin’s method and variational principles. Additionally, the accuracy of the proposed theoretical formula is verified by comparison with finite element (FE) results. Moreover, the expressions of the inner or outer folded angle and radius of curvature are given by the cosine theorem of the trigonometric function and inverse trigonometric function. Subsequently, parametric analysis of the shear buckling behavior of the PCCSW is carried out by considering the cases where the radius of curvature is constant or variable. This parametric analysis highlights the effects of web dimensions, height-to-thickness ratio, aspect ratios of longitudinal and inclined panels, corrugation height, curvature radius and folded angles on the elastic shear buckling strength. As a result, this study provides a theoretical reference for the design and application of composite curved girders with CSWs.

Numerical simulations on cold-formed steel channels with longitudinally stiffened slotted webs in shear

This paper presents results of a numerical finite element parametric study on elastic shear buckling and ultimate shear strength of cold-formed steel channels with longitudinally stiffened slotted webs. The following parameters were varied: channel height, thickness, flange width, flange lip length, longitudinal stiffener size, perforation pattern, aspect ratio, steel yield stress and boundary conditions. Channels with longitudinally stiffened solid webs subjected to shear load were also studied to provide reference data for comparison with the slotted channels. The parametric study described in this paper allowed us to develop equations for predicting the shear buckling coefficient of longitudinally web stiffened solid channels, as well as equations for predicting the elastic shear buckling load and the ultimate shear strength of channels with longitudinally stiffened slotted webs. The developed shear strength equations without and with tension field action are presented in the paper in the traditional and direct strength method formulations. The developed equations account for the studied parameters and showed good agreements with the finite element simulation results.

Shear strength of tapered end web panels

Hot rolled beams can show insufficient strength or inertia and result in the utilization of steel plate girders in the design. For cost-effective design, tapered plate girders are employed, where the depth of the end web panel is linearly varied with the panel length. In most of design codes, the shear capacity is well estimated for prismatic web panels, with reasonable accuracy. The tapered web panels, however, are lacking investigation. The objective of this numerical study is to examine the effect of different geometric parameters of tapered end web panel on the elastic shear buckling and the nominal shear strength. The geometric parameters in question are, namely: tapering angle; tapering direction; panel aspect ratio; web slenderness ratio; flange to web thickness ratio; and attachment of transversal vertical stiffeners to panel ends. The finite element method has been employed, where linear elastic buckling and nonlinear inelastic post-buckling analyses have been performed. The numerical results have been verified against classical web buckling theory, design codes, and experimental results published in the literature. Furthermore, regression analysis has been performed for the obtained results, where new design rules have been proposed for both elastic and nominal shear strength. It has been reported that tapered end web panels possess post-buckling strength that is highly dependent on the geometric parameters.

Numerical simulations on cold-formed steel channels with flat slotted webs in shear. Part I: Elastic shear buckling characteristics

This paper presents results of a numerical parametric study on elastic shear buckling of cold-formed steel channels with flat slotted webs. The study was performed on finite element models developed in ANSYS and validated against test data. The effects of perforation pattern, channel flange width, flange lip length, and aspect ratio on the elastic shear buckling load were investigated on the models with realistic and test setup boundary conditions. Equations for predicting the elastic shear buckling load of slotted channels were developed. The equations account for the effects of the studied parameters on the elastic shear buckling load of cold-formed steel channels with flat slotted webs and showed a good agreement with the finite element analysis results.

Compression Model for Ultimate Postbuckling Shear Strength at Elevated Temperatures

AbstractTension field theory assumes that after elastic shear buckling has occurred, compressive stresses in the web plate do not increase; therefore, postbuckling shear strength solely results fro...