Effective Flange Width Research Articles

Discussion of “Effective Flange Width Definition for Steel–Concrete Composite Bridge Girder” by Methee Chiewanichakorn, Amjad J. Aref, Stuart S. Chen, and II-Sang Ahn

This discussion article comments on recent research (Chiewanichakorn et al, 2004) that investigated composite sections (made up of a concrete slab attached to a steel girder by means of shear connectors). The researchers contend that current formulae regarding the effective flange width (as used in national and international design specification) ignore the fact that stresses vary through the thickness. They verify a three dimensional finite-element model of the composite bridge and provide a numerical example illustrating the proposed effective flange width definition. The discussion author maintains that formulas like the one proposed by the researchers tend to produce increasing effective widths with decreasing interaction between beam and slab. It would have been more informative if the researchers had presented their results in the format that has become customary in discussions of effective width. The discusser also points out that the researchers' comparison of interior and exterior beam specimens can be slightly misleading, since all beams were T-shaped. The discusser concludes that the foremost reason for maintaining the present limitations on effective width is that concrete cracks. Composite beams have become notorious for developing longitudinal cracks in the concrete slabs over their steel beam sections.

Closure to “Effective Flange Width Definition for Steel–Concrete Composite Bridge Girder” by Methee Chiewanichakorn, Amjad J. Aref, Stuart S. Chen, and Il-Sang Ahn

This closure article was written in response to a commentary on recent research (Chiewanichakorn et al, 2004) that investigated composite sections (made up of a concrete slab attached to a steel girder by means of shear connectors). The commentary author maintained that formulas like the one proposed by the researchers tend to produce increasing effective widths with decreasing interaction between beam and slab. The discusser also pointed out that the researchers' comparison of interior and exterior beam specimens can be slightly misleading, since all beams were T-shaped. The discusser concludes that the foremost reason for maintaining the present limitations on effective width is that concrete cracks. Composite beams have become notorious for developing longitudinal cracks in the concrete slabs over their steel beam sections. In their response, the original researchers contend that the discusser's argument is not valid and they stand strongly behind their findings. The researchers point out several major problems with using the girder deflection approach, versus using compressive bending stress. They conclude that the consequence of imposing the discusser's suggested limitations on effective flange width would be underestimation of the section resistance, especially after concrete cracking.

Effective Flange Width of Composite Girders in Negative Moment Region

In the analysis and design of steel-concrete composite bridges, stresses and displacements are typically computed on the basis of elementary beam theory by using the effective flange width concept. Currently, the AASHTO load and resistance factor design (LRFD) code specifies the same effective flange width design criteria for both positive moment sections and negative moment sections. The effective flange width concept for the positive moment has been well established by many researchers. However, the classical effective flange width definition does not take into account the strain variation through the slab thickness or the stress transfer mechanism from concrete to steel reinforcements after cracking. A more appropriate effective flange width definition for the negative moment section is introduced to account for these factors. This definition was developed on the basis of the effective flange width definition for positive moment sections proposed previously. The proposed definition for the negative mom...

Effective Flange Width Definition for Steel–Concrete Composite Bridge Girder

A composite section is made up of a concrete slab attached to a steel girder by means of shear connectors. Under positive bending moment, part of the slab will act as the flange of the girder resis...

Effective flange width provisions for composite steel bridges

In the analysis and design of steel–concrete composite girders of a bridge, deflections, stresses, and strengths are typically obtained from elementary beam bending theory by utilizing the effective flange width concept. Shear lag effects are accounted for indirectly, by replacing the actual slab width by an appropriate reduced “effective” width. Besides the exact numerical values that can be given by numerical analysis of a bridge, it is necessary that code provisions should provide simplified practical method of evaluation of effective flange width without significant loss of accuracy. So each code implements different ideas and approaches for specifying effective flange width. Comparing them highlights distinct philosophies underlying the various effective width code formulations, which is the main objective of this paper. In this paper, the effective flange width provisions in the US, Britain, Canada, Japan, and European Committee are presented and compared. Characteristics of each provision are briefly described and summarized. Numerical comparisons for simply-supported spans and negative moment regions of continuous spans follow. The paper concludes with a summary outlining the commonalities and main differences among all these provisions.

Service Load Effective Compression Flange Width in Fiber Reinforced Polymer Deck Systems Acting Compositely with Steel Stringers

This paper reports on the field study of a steel stringer-fiber reinforced polymer (FRP) deck composite bridge in Pennsylvania. The objective of the study is to assess the effective compression flange width in the FRP deck and floor systems when they act compositely with underlying steel girders at service conditions. The research results reported herein support the notion of employing a design approach, for both interior and exterior girders of a composite floor system, that is philosophically consistent with current practice related to steel girders acting compositely with concrete decking. It appears from the results presented herein that FRP decks and floors acting compositely with underlying steel girders exhibit an effective width that is close to the actual girder spacing for interior beams, and approximately one-half this value for exterior beams.

Determination of Slab Participation from Weigh-In-Motion Bridge Testing

The objective of this paper is to determine the locations of the neutral axis and the effective flange widths for steel girder bridges that may be used in bridge design or, at least, in the bridge rating process. A study using weigh-in-motion field test results was conducted to determine the various section properties for slab-and-beam bridge structures. From the field testing of four existing bridge structures under real truck loading, the girder neutral axis is determined using several alternatives developed by the study team. The results are studied, compared, and evaluated to find the most reliable alternative for the bridge testing. The research is also extended to the determination of the effective flange width from neutral axis results and other parameters. Comparisons are made against some of the previously developed methods and design codes. Results are given in tabulated form and conclusions are drawn from the tables.

Shear lag in orthotropic beam flanges and plates with stiffeners

An FEM parametric study of the stress distribution in orthotropic beam flanges was performed. Several beam boundary conditions and cross sections were considered explicitly. The practical variations of cross-sectional dimensions were extended in order to cover the case of thin cover plates with stiffeners. In the FE analyses a two-dimensional plane stress model was used. An empirical formula was established for the shear lag coefficient λ which is used for computing the effective flange width Be = λB for stress calculations. Longitudinal flange stiffeners can be accounted for by modifying the E/G ratio. The formula is accurate and gives good results even for small Tf/Tw and high E/G ratios, as is the case with fiber reinforced laminated composite plates with stiffeners. Several existing analytical solutions, discussed in the paper, are not reliable for this case.

Shaking Table Tests of Three-Dimensional Scale Models \ of Reinforced Concrete High-Rise Frame Structures with Wall Columns

The objectives of these tests were to understand the behavior of high-rise frame structures with wall columns (HFW system) during an earthquake, and to validate an analytical model with the test results. Two one-seventh-scale, 11-story HFW models were tested on a shaking table. One model was excited in the longitudinal direction only, and the other model was excited simultaneously in both the longitudinal and transverse directions. These tests indicate that under one-way excitation, the test model failed in flexure at the girders, and under two-way excitation, the test model failed in flexure at the walls and girders. Calculated values of maximum shear strength from the analytical model were close to the test values in the longitudinal direction when either one-half or the full width of the transverse bay length was assumed as the effective flange width.

Toward an accurate effective flange width of composite beams

Presented in this paper is the rigorous analysis for the determination of effective flange width for composite beams. To make the solution suitable for routine design, formulas and tables for determining effective flange width for varying load types and geometric shapes are suggested. A variety of effective flange width problems for simple and continuous T- and I-beams can be solved by these tables and formulas. Although they are derived for T- and I-beams with symmetrical shapes, flanges and loads, they can be applied for non-symmetrical cases. Typical numerical examples are given to show how to use the formulas and tables; and their validity and accuracy are assessed by comparison with other known results that are based on the American Codes AISC, AASHTO and ACI.

Effective Flange Width for Stress‐Laminated T‐System Timber Bridges

Stress-laminated T-system timber bridges consist of laminated deck sections combined with glued-laminated timber beams compressed transversely with high-strength steel bars. In the design of these structures, a deck-and-beam T-section is isolated and analysed as a T-beam. This paper presents a regression equation for the computation of effective flange width for stress-laminated T-system timber bridges; a width over which the normal stress can be assumed constant. Using actual dimensions, orthotropic material properties, and AASHTO truck loads, 125 bridge models were analyzed by a special finite element program for general anisotropic shell-and-beam-type structures. The results of the analysis were used to conduct a parametric study followed by a regression analysis to develop a prediction equation for the computation of effective flange width. Simplified equations for the computation of the effective width, which are within current upper and lower bound elasticity solutions, are proposed for use in design.

A simplified method for the determination of the effective width due to shear lag effects

Abstract While it is usually assumed in bending theory that plane sections remain plane after loading, this assumption does not hold for short span beams with wide flanges. Shear lag effects cause the stress distribution over the cross-section to be non-linear. This paper presents simplified formulae, which relate the effective flange widths to the significant parameters. The solution is restricted to the bending problem by assuming that twisting and warping effects can be neglected. The accuracy of the method presented is only slightly affected by the approximations introduced. Rules suitable for code applications are derived and proposed for the unification of the national and international code specifications.

Finite strip evaluation of effective flange width of bridge girders: Discussion

The authors are commended for doing a useful study on the effective widths of flanges in beam and slab and box-girder bridges. The fact that the effective flange widths increase with the level of load in the zone of nonlinear behaviour is confirmed by several research workers. Dowling et al. (1977), after testing models of steel box girders, concluded that shear lag has little weakening effect on the flange strength. Maisel et al. (1973) , made similar remarks about concrete box girders. Consideration of the shear-lag effects can be important for working loads but at ultimate loads the usefulness of such consideration tends to diminish. In Fig. 1 the authors have shown BE to be measured from the edges of the beam flange for beam-slab bridges, from the centre line of webs for multispine box-girder bridges and from the face of webs for multicell box-girder bridges. Considering that the actual flange width of AASHTO and steel wide-flange girders was not directly considered in the idealization, why do these differences in determining 2B and BE exist? It might be appropriate to measure BE and 2B from the centre line of the webs in all cases. Such a simplification would make the use of Fig. 7 a and b even simpler. For serviceability limit states the Ontario highway bridge design code requires one-lane loaded conditions to be considered for all bridges. The empirical effective-width charts appear to have been developed for all design lane loaded conditions. Will the charts be still applicable if only one of the design lanes is loaded ? The authors clearly state that the purpose of the exercise was to determine effective widths of com-

Finite strip evaluation of effective flange width of bridge girders: Reply

Finite strip evaluation of effective flange width of bridge girders: Reply

Finite strip evaluation of effective flange width of bridge girders

Concrete and steel–concrete composite beam-slab type and box-girder bridges are analyzed using the finite strip method, a variation of the powerful finite element method. The results obtained are used to determine the effective width of the compressive flange of the bridge girders. A study of a wide range of bridge models resulted in an empirical relationship that is in good agreement with the design criteria set down in the composite road bridge design code of the Federal Republic of Germany.The empirical relationship presented in this paper is intended to supplant the effective width specifications in current American and Canadian design codes, which in general lead to conservative designs.

中央集中荷重時単純支持鉄筋コンクリート T 梁の有効幅と破壊性状

The purposes of this paper are to investigate the influences of the span ratios of flanges a/l_x and the thickness of flange for effective widths in elastic and plastic ranges, ultimate strengths and failing behaviour of reinforced concrete T-beams, and to discuss the application of elastic theory and the Code Requirements to effective widths of T-beams and the application of plastic bending theory to the ultimate strengths of T-beams. For these purpose, six simply supported reinforced concrete T-beams classifled by two kinds of a/l_x and three kinds of flange thickness were tested under a concentrated load, and effective widths and flexural rigidity in elastic range, effective widths for ultimate strength in plastic range and the shear cracks due to membrane shear stress at the joints of flange and web were analyzed and discussed. 1) Effective overhanging flange widths λ on either side of the web obtained from the experiments in elastic range decreased from the supports to the center of span and the distribution of λ along the span agreed with the curve calculated by two dimentional elastic theory. 2) Average values of λ along the span obtained from the experiments in elastic range agreed with the values of the Eq. (5) proposed by HIGASHI as average λ of members for the calculation of the flexural rigidities of T-beams. λ=(0.5-0.3a/l_x)a, [when a<l_x]……(5) Average values of-λ along the span obtained from the experiments for three kinds of flange thickness t/D=0.067, 0.133, 0.200 were approximately same and the influence of flange thickness for λ was not observed. 3) Ultimate strengths calculated by using full flange width as the effective flange width agreed with the values obtained from experiments in both positive and negative moments. It would be considered as the results of enough anchorage for longitudinal reinforcements and enough transverse reinforcements in flanges. 4) The shear cracks due to membrane shear stress were observed on the top surface at the joints of flange and web in plastic range. However, after such cracks occured the load did not decrease, because enough transverse reinforcements were placed at the joints. Tensile principal stress on the top surface at the joints when such cracks occured (which were calculated with the experimental results) were 1/12〜1/20 of the compressive strength of concrete F_c.

APhA Academies and Sections

Floor systems composed of beams and slabs are critical structural elements of frame structures to resist progressive collapse. Previous experimental studies have focused mainly on beam–column or continuous-beam substructures and have ignored the influence of the slab. To study the progressive collapse-resisting mechanisms of reinforced concrete (RC) floor systems, seven 1/3-scaled one-way substructure specimens, including five beam–slab specimens and two continuous-beam specimens without slabs, were tested under a middle-column-removal scenario. The effects of various structural parameters, including sectional dimensions (beam height, slab width, and slab thickness) and seismic reinforcement, on the progressive collapse resistance were studied by analyzing material strains and load–displacement curves. Under small deformations, the progressive collapse resistance was largely affected by the beam height, slab width and seismic reinforcement in the beams. However, the effect of the slab width, upon exceeding the effective flange width, became insignificant. Note that increasing the slab thickness simultaneously increased the amount of slab reinforcement according to the minimum requirement of reinforcement ratio for slabs, such an increase will in turn enhanced the progressive collapse resistance. In addition, the existence of the slab led to an over-reinforced damage in the compressive zones of the beam ends, which accelerated the bending failure and the presence of the catenary action of the specimens. Under large deformations, the progressive collapse resistance was mainly influenced by the reinforcement area of the entire beam–slab section. The total reinforcement area of a beam–slab substructure designed to meet a higher seismic requirement was not significantly increased, and consequently, the progressive collapse resistance of the substructure under the catenary mechanism was not notably improved. This finding stands in stark contrast to those of previous tests of beam–column specimens without slabs.

Tests on a one-twelfth scale model of the Mancunian Way

A description is given of the building and testing of a 1:12 scale model, made of micro-concrete, of a typical interior span of the proposed Mancunian Way. Data have been obtained regarding the diffusion of prestress through the section, the behaviour of the structure under its design loading and under the action of point loads on the cantilevers, and the behaviour of the structure at ultimate load. It was found that the effective flange width to be used in calculating section properties varied along the span; the properties pertaining to the box section alone should be used at the support sections and those for the full section used at midspan. The behaviour of the structure under its design loading was satisfactory and could be predicted using simple elastic theory. The distribution of bending moment along the root of a cantilever, subjected to point loads, could best be predicted using the method due to Westergaard (1). At ultimate load, the structure was found to have a load factor of at least 3 on full live loading.