Web Slenderness Research Articles

Estimation of Collapse Load for Thin-Walled Rectangular Tubes Under Bending

In two recent papers, the authors investigated the bending collapse load of rectangular tubes consisting of a perfectly elastoplastic material. From these investigations, it is found that the collapse may also occur due to the buckling of web in a rectangular tube under bending, when the tube has a cross section with a large aspect ratio of web to flange b/a. In order to evaluate the collapse load of such tubes under bending, the effective width concept given by Rusch and Lindner for a plate compressed with stress gradient was used to calculate the postbuckling strength of the tube web. However, in the solution of Rusch and Lindner, the plate is supported at only one longitudinal edge with the other longitudinal edge being free. This boundary condition is obviously different from that of the tube web. This paper complements the previous work by addressing the postbuckling strength of the web under stress gradients. The postbuckling strength of the web under stress gradients is also calculated using the effective width concept given in AS/NZS 4600 standard and North American specification (NAS) for a plate compressed with stress gradient and supported at both two longitudinal edges. Moreover, the web slenderness also affects the condition for reaching cross-sectional fully plastic yielding when the web is wider. A new method is proposed to predict the maximum moment considering the effect of web slenderness on the cross-sectional fully plastic yielding. The validity of the collapse load estimation is checked by the results of FEM (finite element method) numerical analysis.

The origin of in-plane stresses in axially moving orthotropic continua

• In-plane motion of an axially travelling orthotropic sheet was modelled. • Velocity difference between supports generates strain due to mass conservation. • In a travelling viscoelastic material the axial strain varies along the length. • Small deformations of free edges due to the Poisson effect affect the velocity. • Inertial effects lead to additional cross-directional contraction. In this paper, we address the problem of the origin of in-plane stresses in continuous, two-dimensional high-speed webs. In the case of thin, slender webs, a typical modelling approach is the application of a stationary in-plane model, without considering the effects of the in-plane velocity field. However, for high-speed webs this approach is insufficient, because it neglects the coupling between the total material velocity and the deformation experienced by the material. By using a mixed Lagrange–Euler approach in model derivation, the solid continuum problem can be transformed into a solid continuum flow problem. Mass conservation in the flow problem and the behaviour of free edges in the two-dimensional case are both seen to influence the velocity field. We concentrate on solutions of a steady-state type, and study briefly the coupled nature of material viscoelasticity and transport velocity in one dimension. Analytical solutions of the one-dimensional equation are presented with both elastic and viscoelastic material models. The two-dimensional elastic problem is solved numerically using a nonlinear finite element procedure. An important new fundamental feature of the model is the coupling of the driving velocity field to the deformation of the material, while accounting for small deformations of the free edges. The results indicate that inertial effects produce an additional contribution to elastic contraction in unsupported, free webs.

Tests and behavior of hot-rolled channel steel sections subjected to web crippling

Web crippling failure of hot-rolled channel steel sections could be found due to localized concentrated loads or brace reactions. This paper reports the results of an investigation into web crippling behavior of channel sections subjected to end-one-flange (EOF), interior-one-flange (IOF), end-two-flange (ETF) and interior-two-flange (ITF) loading conditions. A total of 48 channel section tests subjected to web crippling were conducted. The investigation was mainly focused on the effects of bearing length and web slenderness ratio of channel sections on ultimate capacity against web crippling. The tests were performed on four different sizes of channel sections. The results obtained from these tests show that as the bearing length increases, the web crippling ultimate capacity increases significantly. When the bearing length was 50 and 100mm, the web crippling ultimate capacity of channel sections with web slenderness ratio (ht/t)=18 reached its peak. When the bearing length was 150mm, the web crippling ultimate capacity of channel sections with web slenderness ratio (ht/t)=12.55 reached its peak. The web crippling ultimate capacity of channel sections with web slenderness ratio (ht/t)=24.67 reached the minimum value. Plastic deformation developed near the mid-height of the web, and that a plastic hinge zone formed in the ultimate limit state. Finite element models have been developed and verified against the test results. The calculation equations of web crippling ultimate capacity put forward in the paper can accurately predict experimental value.

Review and Assessment of Design Methodologies for Perforated Steel Beams

AbstractDesigning perforated steel beams is always a practical challenge in steel construction. There are a number of design methods available in the literature for design of these structural members. However, the range of applicability and accuracy of these methods in estimating the resistance of perforated beams is not known precisely. In this paper, an extensive statistical analysis is performed on numerical and laboratory test results to evaluate different formulas used to estimate the ultimate strength of perforated beams. Considered specimens include noncomposite steel beams with unreinforced openings of rectangular, circular, and elongated circular shape. The effect of different parameters including opening size, opening shape, moment to shear ratio, web slenderness ratio, and dimensional limits are discussed. Based on the results, all of the proposed relations are somehow conservative. However, one of the studied equations is found to give more reliable predictions for most of the cases. Finally, ...

Numerical study of steel plate girders under shear loading at elevated temperatures

The ultimate shear capacity of steel plate girders may be influenced by shear buckling, an important and common instability phenomenon occurring in plate girders with slender webs. The transverse loads and consequent shear effort applied on such beams have a large impact on the webs, leading to the possible collapse by shear buckling. In a fire situation, the buckling phenomena in these structural elements are amplified due to the reduction of the steel mechanical properties caused by the elevated temperatures. Recently, there has been an increase in the use of those plate girders, arising from the search for more economical and competitive solutions. However, no specific rules for shear buckling verification in case of fire are given in Eurocode 3 (EC3).After the validation of the numerical models against experimental tests from the literature, an extended number of geometrically and materially nonlinear numerical analyses including imperfections (GMNIA) have been performed dealing with the evaluation of the effect of rigid and non-rigid end posts on the ultimate shear capacity of steel plate girders under fire. The obtained numerical results are compared with the specifications of EC3 for the design at normal temperature adapted to elevated temperatures. These specifications are non-conservative and, for this reason, a new design proposal harmonized with the EC3 principles is presented in order to evaluate the ultimate shear capacity of steel plate girders in fire situation.

Slender Compressed Plate in Component Based Finite Element Model

The paper presents an advance design model of a slender plate in the structural steel joint. Finite element methods and material models are described and design procedure for slender plates in numerical models of steel joints is proposed. The design procedure is demonstrated on examples. The results are verified with an analytical model according to European standards. A compressed beam with slender web and beam-to-column joint are studied by numerical analysis, buckling resistances are determined and results verified. The verification shows very good agreement.

Critical rigidity of stiffener for increasing shear stability of rectangular plate

In plate girder with slender web the big transverse forces lead to web buckling produced with shear. One of the ways to increase stability of web near supports is to install stiffeners. In work the task of finding of critical stresses of clamped rectangular plate with installed inclined stiffener is considering. Investigations were performed with the finite element method and were checked with the experiment. Recommendations were given on choice of optimal size of stiffener.DOI: http://dx.doi.org/10.5755/j01.mech.21.3.9045

Built-Up Cold-Formed Steel Beams with Corrugated Webs Connected with Spot Welding

Corrugated web girders emerged in the past two decades. Their main advantages consists in the possibility to use slender webs avoiding the risk of premature local buckling. Consequently, higher moment capacity might be obtained increasing the beam depth with really thin webs, which are stiffened by the corrugations. Increased interest for this solution was observed for the main frames of single-storey steel buildings and steel bridges. A new solution was proposed at the Politehnica University of Timisoara, in which the beam is composed by a web of trapezoidal steel sheet and flanges of back-to-back lipped channel steel sections. This solution uses self-drilling screws for connecting flanges to the web and to ensure the continuity of the web as seam fasteners. Starting from this new technological solution the paper extends and investigates the use of spot welding as seam fastening to build the web, in order to increase the degree of automation of fabrication. Experimental work of specimens in shear having two or three layers of steel sheets connected by spot welding will be presented. The results will be implemented on a numerical model in order to study the behaviour of the beams presented above.

Experimental and numerical parametric study on the capacity of coped beam ends

Here, the reaction force capacity of I-section steel beam ends with top flange copes was investigated experimentally and numerically, with a focus on local web buckling. An experimental test series was carried out on unstiffened top coped beam ends that were subjected to reaction forces under the bottom flange. Experimental results are given for beam ends with five sizes of cope and for a reference beam without a cope. The investigated beam section was a standard IPE 300 in steel grade S355. The test results were compared with existing design models for coped beams and with models primarily developed for triangular stiffener brackets. A new design formula is proposed for top coped beams supported at the bottom flange, which allows the capacity to be determined as a function of capacity of uncoped beam end with a reduction based on the size of the cope. Finite element models were verified against the experiments and used to extend the experimental data and investigate parameters affecting the web buckling resistance, such as web slenderness and the restraints provided by connection devices.

Behaviour and strength of hollow flange channel sections under torsion and bending

Hollow flange channel section is a cold-formed high-strength and thin-walled steel section with a unique shape including two rectangular hollow flanges and a slender web. Due to its mono-symmetric characteristics, it will also be subjected to torsion when subjected to transverse loads in practical applications. Past research on steel beams subject to torsion has concentrated on open sections while very few steel design standards give suitable design rules for torsion design. Since the hollow flange channel section is different from conventional open sections, its torsional behaviour remains unknown to researchers. Therefore the elastic behaviour of hollow flange channel sections subject to uniform and non-uniform torsion, and combined torsion and bending was investigated using the solutions of appropriate differential equilibrium equations. The section torsion shear flow, warping normal stress distribution, and section constants including torsion constant and warping constant were obtained. The results were compared with those from finite element analyses that verified the accuracy of analytical solutions. Parametric studies were undertaken for simply supported beams subject to a uniformly distributed torque and a uniformly distributed transverse load applied away from the shear centre. This paper presents the details of this research into the elastic behaviour and strength of hollow flange channel sections subject to torsion and bending and the results.

Investigation of Residual Stresses in Thin-Walled Structure and Slender Web

Presented paper offers simplified equations for evaluation of residual stresses. Residual stresses are very important for evaluation of properties of steel thin-walled structures. They play a crucial role in definition of ultimate load and stiffness properties. Generally the residual stresses must be in equilibrium. In the case of statically determinate beam structures residual stresses do not have influence for natural frequency. But in case of plate structures situation is different. Relationship between residual stresses and natural frequency can be used as the base for preparation of non-destructive method for the investigation of residual stresses in thin-walled structures.

Local seismic stability of flanged cruciform sections (FCSs)

Flanged cruciform sections (FCSs), as an appropriate alternative for column cross-section in orthogonal moment-resisting frames, need more cross-section specific code requirements in design specifications. To extend the specifications for FCSs, local buckling of webs, flexural ductility under axial compression and cyclic bending moments, and also P–MP interaction relationships have been studied. A validated material and geometric nonlinear finite element model in ABAQUS has been used to perform a comprehensive parametric study on FCSs. The modeling protocol includes a new residual stress distribution, as well as appropriate geometric imperfections. A wide range of web depth-to-thickness ratios is considered to evaluate the current AISC-341 seismically compact limit state. As the web slenderness and axial load have significant effects on the cyclic behavior and ductility of the FCS beam-columns, a new web seismically compact limiting ratio is proposed for FCSs as a function of the axial load to provide the desired ductility. It is shown that taking half of the depth in calculating web slenderness of FCSs and using the current I-section web compactness limitations for FCSs, can be non-conservative. The study shows that the AISC-341 and ASCE-41 P–MP interaction curves for beam columns made from wide flange sections are overly conservative when applied to FCSs. A modified interaction curve is proposed which more accurately represents beam column behavior of FCSs.

Web crippling tests of cold-formed steel channels under two flange load cases

Cold-formed steel members have many advantages over hot-rolled steel members. However, they are susceptible to various buckling modes at stresses below the yield stress of the member because of their relatively high width-to-thickness ratio. Web crippling is a form of localized failure mode that can occur when the members are subjected to transverse high concentrated loadings and/or reactions. The four common loading conditions are the end-one-flange (EOF), interior-one-flange (IOF), end-two-flange (ETF) and interior-two-flange (ITF) loadings. Recently a test method has been proposed by AISI to obtain the web crippling capacities under these four loading conditions. Using this test method 42 tests were conducted in this research to investigate the web crippling behavior and strengths of unlipped channels with stocky webs under ETF and ITF cases. DuraGal sections having a nominal yield stress of 450MPa were tested with different web slenderness and bearing lengths. The flanges of these channel sections were not fastened to the supports. In this research the suitability of the currently available design rules for unlipped channels subject to web crippling was investigated, and suitable modifications were proposed where necessary. In addition to this, a new design rule was proposed based on the direct strength method to predict the web crippling capacities of tested beams. This paper presents the details of this experimental study and the results.

Aluminum tubular sections subjected to web crippling

This paper presents the details of experimental and numerical research study on web crippling property of aluminum tubular under concentrated web crippling loadings. A total of 48 aluminum square hollow sections with different boundary conditions, loading conditions, bearing lengths and section heights were tested. The experimental scheme, failure modes, load–displacement curves and strain intensity distribution curves were also presented. The investigation was focused on the effects of different boundary conditions, loading conditions, bearing lengths and web slenderness on web crippling ultimate capacity and ductility of aluminum square hollow sections. The results obtained from the experiments are shown that the effect of bearing length on the web crippling ultimate capacity under End-One-Flange (EOF) and End-Two-Flange (ETF) loading and boundary conditions is more obvious than those under Interior-One-Flange (IOF) and Interior-Two-Flange (ITF) boundary and loading conditions. The web crippling ultimate capacities under EOF and ETF loading conditions decreased as the slenderness ratio increased. As the bearing length was 150, the web crippling ultimate capacity under IOF and ITF loading conditions reached its peak when the value of the web slenderness was minimum. The web crippling ultimate capacities of aluminum tubular with bearing length=50mm and 100mm under IOF, ITF, EOF and ETF boundary and loading conditions decreased progressively. The web crippling ultimate capacity of aluminum tubular with bearing length=150mm was approximately equal. Finite element models were developed to numerically simulate the tests performed in the experimental investigations. Based on the results of the parametric study, a number of design formulas proposed in this paper can be successfully employed as a design rule for predicting web crippling ultimate capacity of aluminum tubular sections under four loading and boundary conditions.

Numerical study of unstiffened extended shear tab connections

This paper presents the results of a numerical study on the behavior and strength of unstiffened extended shear tab connections using finite element modeling. The model was verified with the experimental results reported in the literature. The parameters studied included the web slenderness ratio of supporting member, distance between the center bolt line and weld line, plate thickness, number of bolts, double-row of bolts, and beam lateral restraint. Results were analyzed to determine the effects of these parameters on the behavior and bolt shear strength and also used to assess the effectiveness of the AISC manual 2011 design procedure. It shows that the AISC design procedure for bolt shear fracture was overly conservative for extended shear tab connections with number of bolts less than 6 in a single row configuration. For connections with 6 bolts or higher or double-row bolts, the AISC design procedure provided reasonably good estimate. When the AISC design procedure was used but in combination with the finite element determined effective eccentricity, the estimate on bolt shear strength was markedly improved, especially for connections with less than 6 bolts in a single row configuration.

Experimental Study on Flexural Structural Performance of Sinusoidal Corrugated Girder

강구조물에서 장스팬의 경우, 일반적으로 스티프너로 보강된 플레이트거더를 많이 사용하는데, 보(girder)의 춤이 크고 웨브의 폭이 좁은 단면을 선택하는 경우는, 웨브가 세장해져서 면외좌굴이 문제가 된다. 이를 해결하기 위한 방안으로, 이 연구에서는 국내에서도 공장, 창고건물을 중심으로 많이 사용되고 있는, 춤이 큰 주름 웨브 보를 휨재로 사용했을 때, 그 적용가능성을 판단하기 위하여, 그 선행작업으로, 주름 웨브(파형, Sinusoidal)를 가진 H형 단면보의 재하실험을 실시하였다. 평판웨브 P-4.5실험체에 비해서 주름웨브 CP-2.3실험체는 최대 휨내력은 12% 부족했지만, CP-3.2 실험체는 약 24% 내력상승이 나타났다. 이는 주름웨브 보는 평판보보다 불리한 판폭두께비를 가진 경우에도 충분한 내력확보가 가능함을 의미한다. 그리고 유로코드(EN 1993-1-5)에 의하여 산정된 휨 내력 및 전단내력을, 재하실험에 의한 휨내력과 KBC2009에 의한 전단내력을 비교하였다. 유로코드에서는 주름웨브의 판두께 증가는 휨성능 향상에 도움이 안 되며, 전단성능은 웨브 판두께와 주름 웨브의 형상에 민감함을 알았다. In long span steel structure, the plate girder reinforced with stiffeners are commonly used. When choosing the cross section with deep depth of girder as well as narrow width, however, out of plane buckling can be a problem due to web slenderness. In an effort to solve this issue, current study determined the applicability of using corrugated web girder with deep depth as bending member, which is generally being utilized in both factory and warehouse nationwide. To accomplish this, we performed the loading test of H-shaped beam with sinusoidal corrugated web. Corrugated web CP-2.3 specimen exhibited 12% less maximal bending strength but CP-3.2 specimen exerted 24% increase in strength compared to plate web P-4.5. this result indicates that corrugated web provides enough strength even with unfavorable width-thickness ratio of plate. And bending as well as shear strength estimated by the Eurocode (EN 1993-1-5) were compared with both bending strength by loading test and shear strength estimated by KBC2009. In case of eurocode, increase in plate thickness did not help in bending performance improvement. moreover, shear performance was sensitive to the thickness of the web folds and the shape of the web plate.

Experimental and finite element analysis research on I-beam under web crippling

To research web crippling property of I-beam under concentrated load, 48 I-beam with different boundary conditions, loading conditions, bearing lengths and section heights were tested. The experimental scheme, failure modes, concentrated load–general vertical deformation and equivalent strain distribution curves were presented in the paper. The effects of boundary condition, loading condition, bearing length and section height on web crippling ultimate capacity and ductility of I-beam were also studied. Results of these tests show that as bearing length increases, web crippling ultimate capacity of I-beam increase significantly. When bearing length was 50 and 100 mm, web crippling ultimate capacity of I-beam with web slenderness = 17.5 reached its peak; when the bearing length was 150 mm, web crippling ultimate capacity of I-beam with web slenderness = 22.5 reached its peak. The middle web entered plasticity and formed plastic hinge zone in the ultimate limit state. The web crippling ultimate capacity of I-beam with bearing length = 50 mm in interior one flange condition, interior two flanges condition, end one flange and end two flanges condition decreased progressively. Finite element analysis could simulate experimental failure mode and web crippling ultimate capacity. The simple calculation method of web crippling ultimate capacity put forward in the paper can accurately predict experimental value.

Behavior of steel bridge girders under fire conditions

This paper presents results from experimental and numerical studies on the fire performance of typical steel girders used in bridges. As part of experimental studies three steel–concrete composite girders were tested under simultaneous loading and fire exposure. Test variables included: load level, web slenderness, and spacing of stiffeners. Results from fire tests indicate that typical steel girders can experience failure under standard fire conditions in about 30–35min. The time to failure and mode of failure in fire exposed steel girders is highly influenced by web slenderness, spacing of stiffeners, and type of fire exposure. Steel bridge girders fail through flexural yielding when web slenderness is around 50; however failure mode changes to web shear buckling when web slenderness in girders exceed 100. Data from fire tests is utilized to validate a finite element based numerical model for tracing the response of steel bridge girders exposed to fire. Results from numerical analysis show that the proposed finite element model is capable of tracing the response of steel bridge girders under simultaneous loading and fire conditions.

Buckling strength of tapered bridge girders under combined shear and bending

This paper represents the finite element results for the local buckling of tapered plate girders subjected to combine pure bending and shear stresses. An idealized model is developed representing the loading of the tapered panel that generates uniform normal stresses due to flexure, or uniform and constant shear stresses in the case of shear. Eigen-value analysis was performed for several tapered web plate girders that have different geometric parameters. A parametric study is made to reduce the FE model size showing the effect of decreasing the tapered panel adjacent straight panels, maintaining the same result accuracy as a complete girder model. The combined buckling capacity of bending and shear is determined by applying all possible load pattern combinations, together with different interaction ratios. An analysis study is presented to investigate the effect of the tapering angle on the combined bending–shear capacity of the girder. The study also includes the effect of the flange and web slenderness on the local buckling of the girder. Considering residual stresses as part of the loading stresses, the analysis procedure is repeated for some cases, and the effect of combining of the residual stresses together with the external loads is found. Empirical approximate formulae are given to estimate the combined flexure–shear buckling resistance of the tapered girder safely.

Bending and torsion of hollow flange channel beams

The LiteSteel beam (LSB) is a cold-formed high strength steel channel section made of two torsionally rigid closed flanges and a slender web. Due to its mono-symmetric characteristics, its centroid and shear centre do not coincide. The LSBs can be used in floor systems as joists or bearers and in these applications they are often subjected to transverse loads that are applied away from the shear centre. Hence they are often subjected to combined bending and torsion actions. Previous researches on LSBs have concentrated on their bending or shear behaviour and strengths, and only limited research has been undertaken on their combined bending and torsion behaviour. Therefore in this research a series of nine experiments was first conducted on LSBs subject to combined bending and torsion. Three LSB sections were tested to failure under eccentric loading at mid-span, and appropriate results were obtained from seven tests. A special test rig was used to simulate two different eccentricities and to provide accurate simple boundary conditions at the supports. Finite element models of tested LSBs were developed using ANSYS, and the ultimate strengths, failure modes, and load–displacement curves were obtained and compared with corresponding test results. Finite element analyses agreed well with test results and hence the developed models were used in a parametric study to investigate the effects of load locations, eccentricities, and spans on the combined bending and torsion behaviour of LSBs. The interaction between the ultimate bending and torsional moment capacities was studied and a simple design rule was proposed. This paper presents the details of the tests, finite element analyses, and parametric study of LSBs subject to combined bending and torsion, and the results.