Compression Flange Research Articles

Refined nonlinear finite element modelling towards ultimate bending moment calculation for concrete composite beams under negative moment

In this study, a refined nonlinear finite-element (FE) model of steel-concrete composite beam (SCCB) capable of accommodating various effects such as the initial geometric imperfection, residual stress, interface slip, geometric nonlinearity, and material nonlinearity is developed to study the distortional instability of SCCBs under negative bending moment. The accuracy of the model is validated by publicly available results previously observed by experiments. On the basis of the refined nonlinear FE model, the ultimate bending moment of 54 groups of SCCBs with varying cross-section parameters is calculated. Also, the effects of the force ratio of the SCCB, width–thickness ratio of the compression flange, shear connection degree, and height–thickness ratio of the web on the ultimate bending moment stability coefficient of SCCB in negative bending moment area are investigated in detail. Results show that the effect of the degree of shear connection on the stability coefficient of the SCCB is insignificant, while the stability coefficient decreases with the increase of the remaining parameters, among which the effect of the height–thickness ratio of the web is proven to be the most significant. Finally, considering various effects aforementioned properly, practical formulas are proposed to compute slenderness ratio and ultimate bending moment stability coefficient of SCCB in a concise form, which are shown to be consistent with the FE modelling and experimental results, and thus are suitable for engineering design.

Influence of flanges on the shear‐carrying capacity of reinforced concrete beams without web reinforcement

T‐beams are acknowledged as economic and efficient structural members widely used for floor slab construction systems. In many cases, according to practice in some countries, the beams do not present transverse reinforcement, and their shear strength is governing for dimensioning the width of the web. Although experimental investigations have shown that the presence of the compression flange enhances the shear capacity with respect to equivalent rectangular cross sections, most current design codes neglect this phenomenon, which leads to the overdesign of these members. In this paper, the role of the compression flange of slender T‐beams with concentrated loads is investigated with reference to its influence on the shape of the critical shear crack and to the associated shear transfer actions (STA) of the beam. The flanges are considered elements that allow the smearing of applied loads over a certain length of the web. This consideration, in combination with the mechanical model of the Critical Shear Crack Theory (CSCT), allows a consistent treatment of the phenomenon and leads to simple design expressions accounting for the role of flanges. The results of the proposed model are compared together with design codes (Model Code 2010, Eurocode 2, and ACI 318‐11) and other shear design approaches to a database of 239 beams on T‐shaped members. The comparison shows that the role of flanges is finely accounted with the proposal based on the CSCT, leading to consistent agreement and to strength predictions that are more suitable for design purposes than the other investigated design models.

Flexural strength of steel plate girders with a tubular compression flange

This paper reports on a finite-element investigation conducted to study lateral torsional buckling of steel plate girders with a tubular compression flange. A parametric study was carried out on simply supported girders subjected to uniform bending by considering the radius of gyration of the hollow compression flange and the section modulus as key parameters. The results showed that using beams with less slender webs for medium-to-long spans optimised the girders by reducing their weight. Also, increasing the tubular compression flange depth resulted in lower fabrication costs by reducing the weld lengths. The flexural strengths of the girders were compared with the results predicted using a design method specified by the American Institute of Steel Construction. It was found that the design method provided highly conservative predictions in terms of limits between the behavioural stages of lateral torsional buckling and the design strength. A modified design method was developed to predict the flexural strength of tubular compression flange girders and the results agreed well with the finite-element results.

勾配曲げモーメントと圧縮軸力を受ける上フランジ連続補剛H形鋼梁の横座屈荷重と連続補剛材の水平・回転拘束効果

When steel moment frames are subjected to seismic forces, H-shaped beams carry the gradient flexural moment. Large cross-section beams are used as main beams to design structural members effectively in real large space structures. Long span beams may not possess the plastic strength due to lateral buckling, so that many lateral braces along the beams should be set up to prevent the lateral bucking deformation (AIJ 1998). Most oy beams in frames are connected by continuous braces such as folded-roof plates, which are effective to prevent the lateral buckling oy beams. However, in the Japanese design code, non-structural members are not considered as the braces. On the other hands, there have been many moment resisting frames with dampers to prevent damages oy main frames recently, and then H-shaped beams connected with dampers are subjected to compressive axial forces in addition to gradient flexural moment. If the beam carries the large axial force induced by the damper during earthquake, the lateral-torsional buckling behavior oy H-shaped beam becomes more unstable than that under flexural moment only. The axial force which the beams carry is possible to exceed 30% oy yield load oy the beam. Therefore, in this paper, the lateral buckling behavior for H-shaped beams with continuous braces under gradient flexural moment and compressive axial force is clarified and elasto-plastic lateral buckling stress oy the beams or lateral stiffing force and rotational stiffing moment oy continuous braces are evaluated by the energy method and numerical analyses. In this study, for H-shaped beams with continuous braces subjected to gradient flexural moment and compressive axial force, two types oy loading conditions and two types oy bracing rigidities are considered. One oy the loading conditions, which is called as Type A, is the case that the upper flange's compressive load is larger than the lower flange's one in the left side oy beam as shown in Fig. 3(a), and another, which is called as Type B, is that the upper flange's compressive load is smaller than the lower flange's one in the left side oy beam as shown in Fig. 3(b). Furthermore, the ratio oy the compressive axial force, P2 to P1 is represented as an axial force ratio ‘p’ in equation oy elastic lateral buckling load. The continuous braces are divided into the lateral braces, ku, and rotational braces, kβ, as shown in Fig. 1. In the case oy TypeA, ku is effective for preventing lateral deformation oy compressive upper flange, whereas in the case oy TypeB, kβ, is effective for preventing torsional deformation. This study is conducted by the following procedures: 1. The equations oy lateral buckling loads oy H-shaped beams with continuous braces under gradient flexural moment and compressive axial force are derived by energy method. To simplify the equations by energy method, the new equations oy lateral buckling loads are suggested with reference to the terms oy the flexural and torsional rigidities oy beams, the rigidities oy braces, and condition oy the loads. 2. The elasto-plastic buckling behaviors oy the beams are simulated by elasto-plastic large deformation analysis. The lower bound oy the elasto-plastic buckling stress oy the beams can be evaluated with the interpolated buckling curve between those oy bending member and compression member, which are provided by Recommendation for Limit State Design oy Steel Structure (AIJ), depending on the axial force ratio. 3. The upper bound oy moment and lateral force which continuous braces carry at the lateral buckling oy beams is evaluated based on the ratio oy the flexural and torsional rigidities oy beams, the rigidities oy braces, the axial force ratio, and the gradient oy flexural moment.

FEM simulations and rotation capacity evaluation for RHS temper T4 aluminium alloy beams

The aim of this work is the development of an empirical relationship for evaluating the rotation capacity of RHS temper T4 aluminium alloy beams subjected to non-uniform bending. The proposed relationships are based on the numerical results coming from an extensive parametric analysis performed by means of FE code ABAQUS, which gains insight into the influence of all the geometrical and mechanical parameters affecting the ultimate behaviour of aluminium alloy beams. In particular, the influence of the flange slenderness, the influence of the web restraining effect related to the flange-to-web slenderness ratio and the influence of the moment gradient are investigated. The modelling of the material is carried out by adopting the constitutive law proposed by Eurocode 9, based on the Ramberg-Osgood model whose shape factor characterises the hardening behaviour of the material. The investigations concern these factors considered separately as well as their interaction. The results are herein reported with reference to temper T4, i.e. an alloy characterised by a significant hardening behaviour, and show the importance of some of the investigated parameters on the maximum flexural resistance, corresponding to the complete development of local buckling of compressed flange, and on the rotation capacity of aluminium alloy beams. Successively, by means of monovariate and multivariate non linear regression analyses, empirical relationships are provided in order to predict both the ultimate bending resistance and the rotation capacity of RHS temper T4 aluminium alloy beams starting from their geometrical and mechanical properties.

Flexural Resistance of Longitudinally Stiffened I-Girders. II: LTB and FLB Limit States

AbstractThe current AASHTO specifications impose a penalty on the strengths corresponding to the compression flange in slender-web cross sections due to bend-buckling of the web in flexural compression. This web bend-buckling factor (Rb) does not account for any potential benefits from the influence of web longitudinal stiffening. In a companion paper, the authors developed a cross-section model that can be used to estimate the flexural capacity of I-girders at the yield limit state. In this paper, an improved handling of combined web bend-buckling and lateral torsional buckling (LTB) of longitudinally stiffened I-girders is proposed based on finite-element test simulations. Results from the proposed prediction model are compared to available experimental tests. In addition, the Rb calculated from the proposed model, used in conjunction with the current specification flange local buckling (FLB) equations, is shown to provide an improved characterization of the FLB capacity of these types of members.

Investigation of the buckling behaviour of thin‐walled hollow concrete piers

AbstractTall hollow concrete piers with high width‐to‐thickness ratios are commonly used in long‐span box girder bridges. Such thin‐walled structures present the possibility of failure due to local buckling. So, in common practice, diaphragms are usually included in hollow piers to improve the local stability; however, is that necessary? Although experimental research on the buckling behaviour of hollow piers has been conducted extensively, few analytical attempts have been performed to reveal the effects of the width‐to‐thickness ratio on local buckling behaviour. To this end, an analytical model has been proposed to investigate the local buckling behaviour of hollow piers. Following the Ritz‐Timoshenko method, an analytical formula for critical local buckling stress has been developed and verified to have good accuracy compared with finite element analyses. Based on the buckling failure mode of a hollow pier with a slenderness ratio > 6, it can be reasonably postulated that the strength of the hollow pier will be unaffected by local compression flange buckling when the wall width‐to‐thickness ratio is < 24, and it is entirely unnecessary to include diaphragms in hollow piers for stability. Additionally, it is equally interesting that the critical width‐to‐thickness ratio of a hollow pier with a slenderness ratio > 4 derived using the proposed model is the same as the value given by the current AASHTO‐LRFD Bridge Design Specifications.

Effects of Carbon Fiber Reinforced Polymer Strips on the Flexural Strength and Deflection of Steel I-Beam

This study investigates the use of carbon fiber reinforced polymer (CFRP) strips as an alternative way of retrofitting steel I-beams. The flexural strength and maximum deflection of unstrengthened and CFRP-strengthened steel I-beams were compared. Three groups of samples were studied: the first group has CFRP strip installed on the tension flange of the steel I-beam; the second group has CFRP strips installed on the compression and tension flanges of the steel I-beam; and the third group comprises unstrengthened steel I-beams which serve as control specimens. All specimens were tested as simply supported beams under third-point loading. A reaction frame machine was used to apply the load while a dial indicator was used to measure deflections.

A stiffened plate buckling model for calculating critical stress of distortional buckling of CFS beams

This paper presents a novel stiffened plate buckling model for describing the distortional buckling of cold-formed steel zed- and channel-section beams when they are bent about their major axis. In the model the compression flange and lip together with the web are treated as a plate with an angle stiffener. By using the classical principle of total potential energy, an analytical expression for the critical buckling stress of the stiffened plate is obtained. In order to validate the present model, finite strip analysis is also carried out for 59 CFS channel-section beams used in the UK market. The comparison of the critical stresses calculated from the present stiffened plate buckling model and those obtained from the finite strip analysis demonstrates that the present model provides an excellent prediction for the critical stress of distortional buckling of CFS section beams.

End-Warping Bracings during the Construction of Steel Bridges

AbstractSlight bracing of steel bridges to control end warping of the compression flanges near the end supports can be very effective in enhancing the load-carrying capacity of the main girders that are involved. Relatively little information is available, however, regarding the stiffness and strength requirements of end-warping bracings. The results of seven large-scale laboratory tests of different configurations of bracings, including plan bracing and corrugated metal sheets, used in a twin I-girder bridge to resist end warping at support points are presented here. Bracing forces generated in the plan bracings of the test bridge were also compared with those obtained through an approximate analysis for the preliminary analysis of such bracings. Moreover, the bracing forces present in the cross beam of the test bridge were obtained for the different end-warping brace configurations that were investigated. The bracings, the plan bracing type and corrugated metal sheets, were found to effectively enhance ...

Modified slenderness limits for bending resistance of longitudinally stiffened plate girders

In this study, the slenderness limits for flanges and webs were examined to rationally evaluate the flange local buckling (FLB) strength of longitudinally stiffened I-girders. It is known that the bending resistance of a plate girder greatly increases when the web is longitudinally stiffened. This additional strength can be attributed to the fact that the stiffened web provides improved restraint to the rotation of the compression flanges as well as web bend-buckling strength. This study conducted a series of numerical analyses and it was found that the American Association of State Highway and Transportation Officials' (AASHTO's) load and resistance factor design (LRFD) requirements provide highly conservative estimates of the FLB strength of longitudinally stiffened plate girders, especially in noncompact sections. The reason is that the buckling coefficient and corresponding slenderness limit for a noncompact flange is determined based on the bending resistance of an unstiffened girder. Therefore, this study conducted a series of eigenvalue analyses in which the slenderness ratios of flanges and webs were considered. As a result, a buckling coefficient equation that reasonably reflects the interaction of the stiffened web and flange was derived. Based on the results of the analyses, this study proposed modified slenderness limits for the noncompact web and noncompact flange of a stiffened girder. It was verified that the bending resistance of longitudinally stiffened girders could be rationally estimated on the basis of the AASHTO LRFD specifications only by replacing the slenderness limits with the proposed formulas.

On local buckling of cold-formed channel members

The paper deals with local buckling of the compressed flanges of cold-formed thin-walled channel beams subjected to pure bending or axially compressed columns. Arbitrarily shaped flanges of open cross-sections and the web-flange interactions are taken into account. Buckling deformation of a beam flange is described by displacement related to torsion of the flange about the line of its connection with the web. Total potential energy of the flange is a base for the fundamental differential equation of the critical stress of local buckling. The differential equation is derived by means of the stationary total energy principle. The critical buckling stress corresponding to a number of the buckling half-wave matches to the minimum eigenvalue of equation. Numerical examples dealing with single, double bend and lipped flanges are included. The analytical results are compared with the finite element stability analysis carried out by means of the computer systems ABAQUS and CUFSM.The aim of the paper is to find a closed-form analytical solution of the buckling problem, considering web-flange interaction. The results are compared with the finite element method outcomes. Some conclusions are formulated, too.

A closed-form equation for the local buckling moment of pultruded FRP I-beams in major-axis bending

Abstract A new closed-form equation for the local instability of pultruded fiber-reinforced plastic beams in bending is derived by substituting suitable buckling approximating functions for compression flange and web into the total potential energy functional. Being obtained from a full-section approach, the equation does not require independent calculations for web and compression flange, which are typical of discrete plate analysis. Moreover, the contribution of the elastic restraint stiffness commonly used to reproduce the web–flange junction behavior naturally arises in the proposed formulation because of the assumed buckling shape. From comparisons with available experiments on 10 beams and FE solutions for 55 beams, the proposed equation appears to be accurate and reliable.

Effect of stiffened element and edge stiffener in strength and behaviour of cold formed steel built-up beams

The aim of this study is to investigate the effect of stiffened element and edge stiffener in the behaviour and flexural strength of built-up cold-formed steel beams. An experimental and analytical analysis of CFS channel sections in four different geometries is conducted, including simple channel sections, a stiffened channel section with or without edge stiffeners. Nonlinear finite element models are developed using finite element analysis software package ANSYS. The FEA results are verified with the experimental results. Further, the finite element model is used for parametric studies by varying the depth, thickness, and the effect of stiffened element, edge stiffener and their interaction with compression flanges on stiffened built-up cold-formed steel beams with upright edge stiffeners. In addition, the flexural strength predicted by the finite element analysis is compared with the design flexural strength calculated by using the North American Iron and Steel Institute Specifications for cold-formed steel structures (AISI: S100-2007) and suitable suggestion is made.

Abolladura de estructuras de barras de sección tipo doble-T

A stepped methodology for the evaluation, with limited computational effort critical buckling load factor which produces the instability of the walls of double-T sections is proposed in this work. For this purpose, each wall of the cross-section studied in a local level as a thin plate. It is ratified that it is enough to check the most compressed flange and the web of the most loaded beams of the structure.

Elastic lateral-torsional buckling strength and torsional bracing stiffness requirement for monosymmetric I-beams

Elastic lateral-torsional buckling (LTB) is a common failure mode of large span beams. In this phenomenon the beam becomes unstable along the unbraced length. This instability of beams can be identified by out-of-plane deflection and twisting. Using discrete torsional braces is one of the ways to prevent LTB. In this paper the LTB strength and bracing stiffness requirements of monosymmetric I-beams with discrete torsional braces, under pure bending condition is investigated. First, an analytical solution for an unlimited number of braces is presented by using an energy approach. Then the results of the proposed equations are compared with the results of a 1-D finite element analysis and the equivalent continuous brace stiffness concept. The comparison shows that the proposed equations are in good agreement with the finite element analysis. A parametric study is carried out for various dimensions and geometrical properties of cross sections. The results show that using the monosymmetric I-sections with larger compression flange is the more economical solution. Finally, the effects of linear moment gradient conditions and the cross sectional distortion on the LTB strength and bracing stiffness requirement are investigated.

Lateral buckling of simply supported C- and Z-section purlins with top flange horizontally restrained

Lateral buckling is a main failure mode controlling the strength of C- and Z-section purlins under wind suction, as the compressive flange of cross-section is laterally free in this case. The lateral buckling of roof purlins is different from the normally considered simply supported beams, because the top flange of cross-section of these purlins is laterally restrained due to the bracing of the above roof sheeting. To reveal the lateral buckling of C- and Z-section purlins with their top flanges horizontally restrained, two representative buckling theories for the lateral buckling of thin-walled beams, the traditional buckling theory and a new theory recently proposed by the authors of this paper, are adopted in this study. Comparisons made in this study indicate that the total potentials derived from these two theories have different expressions for the considered purlins. Subsequently, the finite element (FE) analysis using the shell element modeling is adopted to examine the buckling loads of purlins based on these two buckling theories, which indicates that the buckling theory proposed by the authors of this paper is more reasonable for this problem. Simple solutions are also proposed for buckling loads of C- and Z-section purlins with their top flange horizontally restrained, and very good agreements are achieved in the comparisons between the predictions of the proposed solutions and FE results.

Neural Approximation of the Buckling Coefficient of Compression Flange of Box Girder Evenly Loaded Transversely

There are situations in the thin-walled steel girders with box intersection, in which the internal wall of compression flange is elastically restrained in the webs of section and along its length occurs the change of normal stresses. Such a wall was modelled, as a bilateral elastically restrained internal plate variably loaded at the length. Explicit formulation of neural formula on buckling coefficient of internal plate at non-linear distribution of longitudinal stress was discussed in this paper. A few structures of neural networks (NN) were envisaged in order to obtain the best of the numerical effectiveness of the final formula. The results noted from the literature were used for the evaluation of neural prediction of coefficient.

합리적 응력경도 산정을 위한 수평 곡선 I-형 거더의 플랜지 국부좌굴의 해석적 연구

Abstract Horizontally curved I-girders are subjected to not only bending moments but also torsional moments. The torsional moment of the plate girder is addition of St. Venant torsion and non-uniform torsion. In the flange of I-shaped plate girder, a kind of open-section, the normal stresses is not distributed uniformly due to the non-uniform torsion. Because of that, one of compression flange tip can be yielded faster than the flange of general straight girder.In other words, the flange local buckling strength is decreased when the girder has initial curvature. In this paper,the numerical analysis is conducted to investigate the average stresses in flange for curved girders. The subtended angle and slenderness ratio are taken as parameters. Keywords : Curved I-girder, Flange local buckling, Stress gradient 본 논문은 건설교통부가 출연하고 한국건설교통기술평가원에서 위탁시행한 건설교통기술촉진연구사업의 연구비 지원(12기술혁신B01-곡선 강교량의 합리적인 LRFD 설계기술 개발)에 의해 수행됨 * Corresponding Author : Young-Jong Kang(Korea Univ.)Tel: +82-2-927-7715 email: yjkang@korea.ac.krReceived August 18, 2015 Revised September 2, 2015 Accepted October 8, 2015 Published October 31, 2015

Experimental and Numerical Investigation on Bending Capacity of Steelconcrete Composite Truss Girder

This article presents an experimental investigation on the bending capacity of steel-concrete composite truss girder (SCCTG). Four full-scale specimens named CB1, CB2a, CB2b and CB3 respectively, are tested and numerical analyzed. Stress distribution, load-displacement relationship, load-slip relationship and ultimate bending capacity of SCCTGs are investigated. The results show that SCCTG follows plane section assumption on the whole. SCCTG has a higher ultimate bearing capacity and good performance of deformation. Concrete slab and the steel truss can work together better using denser studs. In elastic stage, the effective width of the SCCTG flange plate remains the same with negligible variation. While in plastic stage, the effective width increases. Tests also prove that there is obvious shear lag effect in the concrete compression flange. Three-dimensional numerical model by finite element package ABAQUS is established to examine the bending behaviour of SCCTG. Hopefully, an acceptable correlation has been observed between the analytical and experimental results. There is obvious shear lag effect in the concrete compression flange. Shear lag should be paid great attention when designing and calculating the bearing capacity and deformation of SCCTG.