Combined Bending Research Articles

New distortional buckling design rules for slotted perforated cold-formed steel beams

Cold-Formed Steel (CFS) members with slotted perforations in webs are used in civil construction to amplify the thermal and energy performance of structures. However, the slotted webs reduce the structural performance of the element, prominently their shear, bending and combined bending and shear strengths. Many research studies have been undertaken to examine the behaviour of CFS channel sections subject to bending. Yet, no research has been performed to investigate the distortional buckling behaviour of slotted perforated CFS flexural members. Finite Element (FE) models of CFS channels with staggered slotted perforations were developed herein to investigate their distortional buckling under bending stress. A parametric study was conducted in detail by developing 432 slotted perforated CFS FE models based on the validation process with available experimental results. In particular, this paper presents the FE analysis details of CFS flexural members with slotted perforations subject to distortional buckling and results. The reliability of the current Direct Strength Method (DSM) for CFS flexural members with web holes subject to distortional buckling in accordance with the North American Specification (AISI S100) (2016) and the Australian/New Zealand Standards (AS/NZ 4600) (2018) was investigated. Modified DSM formulae for slotted perforated CFS flexural members subject to distortional buckling were also proposed.

Fire-induced progressive collapse mechanisms of steel frames with partial infill walls

This paper presents a numerical investigation on progressive collapse mechanisms of steel frames with partial infill walls under fire scenarios using ABAQUS platform. The load redistributions and collapse mechanisms of steel frames subjected to different fire scenarios (edge bay and central bay fires) are studied. The influences of strength, opening percentage and layout of partial infill walls are also analyzed. The results of the numerical analysis indicate that the presence of partial infill walls causes combined tensile force and bending moment at the ends of surrounding beams. The strut action of partial infill walls and the overturning moment imposed by the frame in the collapse bay are identified as load redistribution mechanisms of the steel frame. The steel frame using higher strength steel, more number and lower opening percentage of partial infill walls collapses at higher temperatures. Furthermore, the analyses identify three deformation modes of beams depended on the layout of partial infill walls. Finally, a preliminary design method based on equivalent compressive strut model is proposed with good accuracy, in order to prevent the steel frame with partial infill walls from fire-induced collapse in engineering practice.

Numerical analysis of low cycle fatigue for welded joints considering welding residual stress and plastic damage under combined bending and local compressive loads

AbstractThe numerical analysis of low cycle fatigue of HTS‐A steel welded joints under combined bending and local compressive loads are implemented using the damage mechanics approach. First, a finite element numerical simulation of the welding process is employed to extract the welding residual stresses, which are then imported as initial stresses in the subsequent fatigue analysis. Second, a multiaxial fatigue damage model including damage coupled elasto‐plastic constitutive equations and plastic damage evolution formulation is applied to evaluate the mechanical degradation of the material under biaxial fatigue loads. Further, the fatigue lives of the HTS‐A steel welded joints are computed and compared with the experimental results from literature. A series of predicted load‐life curves clearly illustrates the variation of fatigue lives along with the combined loadings. Finally, the effects of local compression on accumulated plastic strain and fatigue damage are studied in detail. It is revealed that the local compression induces a damage competition between two critical zones.

Stiffness analysis of leaf spring system under large deformation

The paper proposes a semi-analytical model to analyze large deformation elastic behavior of leaf spring under static load. The model treats leaf spring system as a curved beam with one end directly hinged to a fixed support and the other end being attached to another fixed support through a rigid link (shackle). Constrained motion of the shackle with large deformation of curved beam is modeled using a rotational spring at fixed hinge point of the shackle. Two more physically plausible models for the restraint motion are also proposed, which are derived from the main model through post processing. In the first derived model, the constrained motion is captured by defining a longitudinal spring in a virtual rod connecting the curved beam ends, whereas in the second derived model, the restrained motion is modeled through vertical stiffness of the system. Due to combined complications coming from non-conventional boundary condition, asymmetric geometry, non-uniform curvature, and nonlinear kinematics, the problem is analyzed through successive geometry updation. Governing equation for the curved beam is derived in body fitted curvilinear frame considering combined bending–stretching effects. Global solution for the total system is then obtained by incorporating the elastically restrained shackle motion through satisfaction of kinematic and kinetic constraint relations. As the governing equation and the constraint conditions involve geometric nonlinearity, a numerical iterative scheme is developed and implemented in MATLAB®. For the purpose of validation, the theoretical model is simulated in commercial finite element package ABAQUS®. Comparison of deflection profiles with the finite element model validates the proposed leaf spring model. After the validation study, observations on effects of system parameters and curved leaf profile shape on system stiffnesses are furnished. Effects of the parametric study are presented through true and total system stiffnesses. The parametric study may lead toward optimized design of the system.

Numerical study of slender I-girders with one longitudinal stiffener under patch loading

Slender plate I-girders are steel members widely used in bridges, viaducts and heavy industrial buildings, which are subjected to combined bending and shear, making the web panel susceptible to stability problems. Therefore, longitudinal stiffeners are sometimes placed along the web. This paper aims at investigating the load carrying capacity of girders submitted to patch loading (common in bridge launching), using finite element models. A nonlinear stability analysis was carried out considering the initial geometric imperfection as the first buckling eigenmode, with amplitude defined according to EN 1993-1-5 recommendations. The performance of girders with different stiffener locations was evaluated, discussing the structural behavior and associated failure modes. If the stiffener is effective and properly placed, the failure mode is the local buckling of the two web subpanels (which increases the patch loading resistance), although it was verified that the optimal position for patch loading is mainly governed by the web crippling resistance of the upper subpanel. The numerical results are in accordance with the experimental results available in the literature. For the studied girder configurations, the optimal stiffener position for patch loading resistance is closer to the loaded flange when compared to girders under dominant bending. Depending on the cross-sectional shape of the buckling mode, the stiffener can be unfavorable to the patch loading resistance for certain range of positions. Furthermore, the definition of positive or negative cross-sectional imperfections, i.e., the inversion of the curvature of the buckling mode shape, has impact on the load capacity for larger patch loading lengths.

Flexural-torsional buckling and design recommendations of axially loaded concrete-infilled double steel corrugated-plate walls with T-section

This paper investigates the flexural-torsional buckling behaviour about the symmetric axis of axially loaded concrete-infilled double steel corrugated-plate walls with T-section (T-CDSCWs). The T-CDSCW is composed of steel corrugated-plates, infilled concrete and intermediate bolts, among which a positive composite effect further improves load-bearing capacities effectively and thus reduces the thickness of composite walls. The failure mode of the T-CDSCW with high height and small thickness is governed by global instability, and flexural and flexural-torsional buckling may occur for the T-CDSCW under axial compression. This paper focuses on numerical and theoretical analyses of the flexural-torsional buckling behaviour. Based on the refined finite element (FE) model validated by previous experimental researches, parameter analysis is carried out to investigate the elastic and inelastic flexural-torsional buckling behaviour. The formulas of the elastic flexural-torsional buckling load are derived and prove it feasible to design flexural-torsional buckling in accordance with torsional buckling. Numerical results show that the strength reduction factor of flexural-torsional instability can be delineated well by the height-to-thickness ratio of the web and the normalized torsional slenderness ratio of the T-CDSCW. Together with the design formulas of flexural instability, the design formulas of flexural-torsional instability proposed in this paper supplements the design method of axially loaded T-CDSCWs, and provides the foundation for further investigation into global instability of T-CDSCWs under combined compression and bending.

Behaviour and design of eccentrically loaded hot-rolled steel SHS and RHS stub columns at elevated temperatures

Abstract The structural fire response of hot-rolled steel square and rectangular hollow sections (SHS and RHS) under combined compression and bending is investigated in this study through finite element (FE) modelling. The developed FE models were firstly validated against available test results on hot-rolled steel SHS/RHS subjected to combined compression and bending at elevated temperatures. Upon validation, an extensive parametric study was then carried out to examine the resistance of hot-rolled steel SHS/RHS under combined loading at elevated temperatures, covering a wide range of cross-section slendernesses, cross-section aspect ratios, combinations of loading and temperatures up to 800 °C. The numerical data, together with the experimental results, were compared with the strength predictions according to the current structural fire design rules in the European Standard EN 1993-1-2 (2002) and American Specification AISC 360–16 (2016) for hot-rolled steel SHS/RHS under combined loading. The comparisons generally indicated significant disparities in the prediction of resistance of hot-rolled steel SHS/RHS under combined loading at elevated temperatures, owing principally to inaccurate predictions of the end points of the design interaction curves. The deformation-based continuous strength method (CSM) has been shown to provide accurate strength predictions for these end points i.e. the resistances of hot-rolled steel SHS/RHS stub columns and beams at elevated temperatures. In this study, proposals are presented to extend the scope of the CSM to the structural fire design of hot-rolled steel SHS/RHS under combined compression and bending. The CSM proposals are shown to offer improved accuracy and reliability over current design methods and are therefore recommended for incorporation into future revisions of international structural fire design codes.

CFRP strengthening of steel plate girders with web openings subjected to shear and bending.

The present study illustrates the effect of applying combined shear and bending loading on steel plate girders having web openings strengthened with CFRP wrap. Five steel plate girders have been tested under the above-mentioned action; one of these plate girders which can be considered as a control specimen has no web opening whereas the other four girders have openings of circular or square cut-outs. Strengthening by attaching CFRP sheets using a type of adhesives has been applied to two of the plate girders, one with square opening and the other with circular web opening. Web opening size is chosen to have a depth equal to 40% of the web depth. In comparison with the reference girders with openings, results have shown that the ultimate load of the strengthened plate girder containing square and circular web openings increased 63.6% and 52.6%, respectively.

Analytical approach to elastic stability problems of plates with different boundary conditions subjected to combined bending, shear and patch loading

The elastic stability of plates with simply supported edges (SSSS) and with two edges clamped and two simply supported (CSCS) under combination of bending, shear and patch load is investigated.General analytical approach for elastic buckling analysis of plates with different boundary conditions, subjected to any combination of in-plane loads, is presented. Exact solutions for pre-buckling stress distributions and double Fourier series for deflection functions within Ritz energy method guarantees accuracy of results and enabled very complex stability analysis.Combined in-plane loads action is very common during incremental bridge lunching and different stress conditions can occur in web girders. All analyses conducted so far regarding such problems are related to simply supported plate (SSSS). However, web girder is elastically restrained to the certain point depending on flanges rigidity and authors considered interesting to investigate behavior of plate with two opposite edges restrained and other two simply supported (CSCS) under same load conditions as simply supported plate.First part of the paper deals with patch load problem for plates with two different boundary conditions and evaluation of input data for bending-patch load (M-F), shear-patch load (V-F) and bending-shear-patch load (M-V-F) interaction curves and surfaces definition. Second part is dedicated to presentation, analysis and comparison of the interaction curves and surfaces for the cases of simply supported plate (SSSS) and plate with two clamped and two simply supported edges (CSCS), in order to obtain realistic bucking load ratios in accordance with boundary conditions.

Longitudinally stiffened web purlins under shear and bending moment

Abstract This paper aims to better understand the influence of longitudinal web stiffeners in the structural behavior of cold-formed steel purlins. A set of specimens with stiffened web and plain web cross-sections were tested on predominantly shear, combined bending and shear, and bending only. Numerical analyses carried out in CUFSM and ANSYS investigated the buckling behavior of the sections, allowing the determination of elastic critical stresses and the calculation of the resistance for the tested specimens by Direct Strength Method (DSM). Numerical results showed that the intermediate web stiffeners improve the buckling strength in loading cases of pure bending and pure shear. Experimental and numerical data were used to evaluate the interaction between bending moment and shear force, and showed that the circular interaction diagram was conservative and the results were closer to the trilinear interaction diagram. The comparison between experimental data and DSM predictions demonstrated that DSM provides accurate estimates for shear and flexural strengths of purlins with stiffened web cross-section.

Experimental study on CFNRST members under combined compression and bending

The concrete filled narrow rectangular steel tube (CFNRST) member is being increasingly used in the apartment buildings in China. Experimental study is conducted on the behavior of CFNRST members subjected to combined compression and uniaxial bending about the weak axis. Eleven specimens were fabricated considering the variation of key parameters including the slenderness, the width/height ratio of cross-section and eccentricity of compression. Comparisons are made between the predictions of representative solutions of design codes and the test results to examine their capacity for predicting the ultimate load of CFNRST members. New solutions with modifications on two existing solutions are proposed for the ultimate load of CFNRST members subjected to combined compression and uniaxial bending. Good agreements are achieved between the predictions of the proposed solutions and test results.

A catchment scale assessment of patterns and controls of historic 2D river planform adjustment

The supply, transfer and deposition of sediment from channel headwaters to lowland sinks, is a fundamental process governing upland catchment geomorphology, and can begin to be understood by quantifying 2D river planform adjustments over time. This paper presents a catchment scale methodology to quantify historic patterns of 2D channel planform adjustment and considers geomorphic controls on 2D river stability. The methodology is applied to 18 rivers (total length = 24 km) in the upland headwaters of the previously glaciated Wasdale catchment (45 km2), Lake District, northwest England. Planform adjustments were mapped from historic maps and air photographs over six contiguous time windows covering the last 150 yr. A total of 1048 adjustment and stable reaches were mapped. Over the full period of analysis (1860–2010) 32% (8 km) of the channels studied were adjusting. Contrasts were identified between the geomorphic characteristics (slope, catchment area, unit specific stream power, channel width and valley bottom width) of adjusting and stable reaches. The majority of adjustments mapped were observed in third and fourth order channels in the floodplain valley transfer zone, where the channels were laterally unconfined (mean valley bottom widths of 230 ± 180 m), with low sediment continuity. In contrast, lower order channels were typically confined (mean valley bottom widths of 31 ± 43 m) and showed relative 2D lateral stability. Hence, valley bottom width was found to be important in determining the available space for rivers to adjust. Over the full period of analysis 38% of planform adjustments involved combined processes, for example, as bar and bend adjustments. The study demonstrates the importance of stream network hierarchy in determining spatial patterns of historic planform adjustments at the catchment scale. The methodology developed provides a quantitative assessment of planform adjustment patterns and geomorphic controls, which is needed to support the prioritisation of future river management and restoration.

Numerical simulation of damage evolution of Daikai station during the 1995 Kobe earthquake

Abstract Three-dimensional (3D) finite element (FE) analyses are performed to identify the collapse mechanism of the Daikai station, which suffered major structural damage during the 1995 Kobe earthquake. To investigate the damage evolution in the reinforced concrete structure, concrete and steel rebars are modeled separately and assembled in a soil–tunnel model. Bilinear models are used for both the concrete and steel rebars, whereas a nonlinear hysteretic model is used for the soil. Simulation results illustrate that the 3D FE model is capable of accurately reproducing the structural collapse and surface settlement. The cracks are observed to form initially at the outer walls of the tunnels and subsequently in the center column. As the ground motion intensity increases, longitudinal and shear cracks form in the center column, inducing a significant loss of axial capacity and eventually leading to a structural collapse. Irrecoverable damage initiates in the center column under the combined shear force (V) and bending moment (M). Therefore, it is recommended to utilize the V-M failure surface to estimate the onset of structural damage. The damage evolution of the Daikai station is also correlated with the drift ratio of the center column. Additional analyses show that when the equivalent linear soil model is used, the calculated peak drift ratio is similar to that obtained using the nonlinear model. However, it results in unrealistic gapping at the tunnel–soil interface and lower surface settlement. The no-slip condition for the tunnel–soil contact interface produces a pronounced lower response of the tunnel and therefore should not be used in a damage analysis.

Total life approach analysis of ductile cast iron smooth specimens

Ductile cast irons (DCIs) offer an interesting combination of good castability and high mechanical properties, with acceptable costs. DCI structural components are widely used in important applications like automotive components (e.g. crankshafts and truck axles), wind turbines components and pipelines components (e.g., valves, fit-tings and pipes). In this paper, several sets of fatigue tests, available in the literature, are simulated by using a total life approach, and the fatigue lifetime is computed. The examined ductile cast iron EN-GJS-400-18 specimens were alternatively subjected to tensile and torsional loading, and to in-phase and out-of-phase combined bending and torsion. The obtained results are compared with experimental ones, and a quite good accuracy of the criterion used is observed for the simulated tests.

Experimental and numerical study on large-curvature curved composite box girder under hogging moment

Curved steel-concrete composite box girder has been widely adopted in urban overpasses and ramp bridges. In order to investigate its mechanical behavior under complicated and combined bending, shear and torsion load, two large-curvature composite box girders with interior angles of 25 and 45 were tested under static hogging moment. Based on the strain and deflection measurement on critical cross-sections during the static loading test, the failure mode, cracking behavior, load-displacement relationship, and strain distribution in the steel plate and rebar were investigated in detail. The test result showed the large-curvature composite box girders exhibited notable shear lag in the concrete slab and steel girder. Also, the constraint torsion and distortion effect caused the stress measured at the inner side of the composite beam to be notably higher than that of the outer side. The strain distribution in the steel web was approximately linear; therefore, the assumption that the plane section remains plane was approximately validated based on strain measurement at steel web. Furthermore, the full-process non-linear elaborate finite element (FE) models of the two specimens were developed based on commercial FE software MSC.MARC. The modeling scheme and constitutive model were illustrated in detail. Based on the comparison between the FE model and test results, the FE model effectively simulated the failure mode, the load-displacement curve, and the strain development of longitudinal rebar and steel girder with sufficient accuracy. The comparison between the FE model and the test result validated the accuracy of the developed FE model.

Experimental response of headed stud connections subjected to combined shear and bending actions

Experimental response of headed stud connections subjected to combined shear and bending actions

Static performance of a new GFRP–metal string truss bridge subjected to unsymmetrical loads

A unique lightweight string truss deployable bridge assembled by thin-walled fiber reinforced polymer (FRP) and metal profiles was designed for emergency applications. As a new structure, investigations into the static structural performance under the serviceability limit state are desired for examining the structural integrity of the developed bridge when subjected to unsymmetrical loadings characterized by combined torsion and bending. In this study, a full-scale experimental inspection was conducted on a fabricated bridge, and the combined flexural–torsional behavior was examined in terms of displacement and strains. The experimental structure showed favorable strength and rigidity performances to function as deployable bridge under unsymmetrical loading conditions and should be designed in accordance with the stiffness criterion, the same as that under symmetrical loads. In addition, a finite element model (FEM) with a simple modeling process, which considered the multi segments of the FRP members and realistic nodal stiffness of the complex unique hybrid nodal joints, was constructed and compared against experiments, demonstrating good agreement. A FEM-based numerical analysis was thereafter performed to explore the effect of the change in elastic modulus of different FRP elements on the static deformation of the bridge. The results confirmed that the change in elastic modulus of different types of FRP element members caused remarkable differences on the bending and torsional stiffness of the hybrid bridge. The global stiffness of such a unique bridge can be significantly enhanced by redesigning the critical lower string pull bars using designable FRP profiles with high elastic modulus.

Experimental and numerical investigations onremaining strengths of damaged parabolic steel tubular arches

This paper presents experimental and numerical studies on effects of local damages on the in-plane elastic-plastic buckling and strength of a fixed parabolic steel tubular arch under a vertical load distributed uniformly over its span, which have not been reported in the literature hitherto. The in-plane structural behaviour and strength of ten specimens with different local damages are investigated experimentally. A finite element (FE) model for damaged steel tubular arches is established and is validated by the test results. The FE model is then used to conduct parametric studies on effects of the damage location, depth and length on the strength of steel arches. The experimental results and FE parametric studies show that effects of damages at the arch end on the strength of the arch are more significant than those of damages at other locations of the arch, and that effects of the damage depth on the strength of arches are most significant among those of the damage length. It is also found that the failure modes of a damaged steel tubular arch are much related to its initial geometric imperfections. The experimental results and extensive FE results show that when the effective cross-section considering local damages is used in calculating the modified slenderness of arches, the column bucking curve b in GB50017 or Eurocode3 can be used for assessing the remaining in-plane strength of locally damaged parabolic steel tubular arches under uniform compression. Furthermore, a useful interaction equation for assessing the remaining in-plane strength of damaged steel tubular arches that are subjected to the combined bending and axial compression is also proposed based on the validated FE models. It is shown that the proposed interaction equation can provide lower bound assessments for the remaining strength of damaged arches under in-plane general loading.

Influence of the cracking consideration in the displacements of a shallow tunnel lined in steel-reinforced concrete: numerical model

abstract: The study of shallow tunnels introduces different aspects when compared to deep tunnels analysis. Among these characteristics can be emphasized the non-uniform shape of the deformed cross-section and the impossibility of some simplifications such as the consideration of homogeneous stresses around the excavation. Since the tunnel lining is subject to combined bending and compression, shallow tunnels are more susceptible to the development of final tensile stresses (not founded in deep tunnels) and the consequent concrete cracking. This paper presents a numerical simulation in finite elements with the ANSYS software. The purpose of the study is to analyze the cracking influence in the displacements of shallow tunnels, treating the concrete behavior by three different models: elastic, viscoelastic and viscoelastic with cracking effects.

Experimental behaviour of stainless steel plate girders under combined bending and shear

The behaviour of stainless steel plate girders subjected to combined bending and shear was experimentally studied in this paper. Both tensile and compressive material properties of the two adopted stainless steel alloys, including austenitic grade EN 1.4301 and duplex grade EN 1.4462, were determined by standard coupon tests. The three-dimensional (3D) optical scanning technology was introduced to acquire an accurate distribution of initial geometric imperfections for each plate girder specimen. A total of six plate girders were fabricated by hot-rolled stainless steel plates, and were tested to failure under combined bending and shear. In-depth analyses of the critical buckling characteristics, the ultimate resistances and the collapse behaviour of the tested specimens were all presented. The obtained ultimate resistances were further employed to assess the existing moment and shear (M-V) interaction design methods in EN 1993-1-5, GB 50017-2017, ANSI/AISC 360-16 and SEI/ASCE 8-02, and the design proposal presented by Jáger et al. It has been found that most of the existing codified M-V interaction formulae can be applicable for both carbon steel and stainless steel plate girders, yet they lead to relatively conservative predictions for stainless steel plate girders, except that the design method in ANSI/AISC 360-16 provides apparently unsafe strength predictions.