Compression Flange Research Articles

The Warping Constant for the W-Section with a Channel Cap

It is common practice in crane runway beams to place a channel, open-side down, over the top flange of a W-section to increase its lateral stability. This is done because it is not always convenient to brace the compression flange between columns. The lateral-torsional buckling capacity of a singly symmetric section may be determined by the formulas without knowing the warping section constant. However, these formulas were developed from research on three-plate mono-symmetric sections. If one is to develop a similar equation for the case of the W-section with a channel cap, it is necessary to return to the basic theory of lateral-torsional buckling and that means that one must calculate the warping constant (Cwc) for the cross-section. It is not a difficult matter to do this with a computer, but since the program may not be available to everyone, it would be useful to develop a simple empirical equation for preliminary design, making use of the section properties already given in the AISC steel manual.

Design of steel beams with end copes

Abstract In steel beams with end copes, the strength and torsional stiffness at the coped section are reduced and a high stress concentration in the web at the cope corner is introduced. Therefore, besides yielding, coped beams can fail in three distinct failure modes: lateral-torsional buckling, local web buckling and fatigue cracking. Based on the behavior and analytical studies of coped beams, design methods are proposed for these three failure modes. Simple interaction equations, which utilize the individual lateral buckling capacities of the coped region and the uncoped length, are developed for design of the lateral buckling of coped beams. Inelastic lateral buckling caused by the residual stresses and design of short span coped beams are also considered. As for local buckling strength at the coped region, a plate buckling model is developed for compression flange coped beams, and a lateral buckling model is adopted for double flange coped beams. Yielding at the coped corner caused by the high local stress concentration is considered in the design. For the fatigue strength of coped beams, the actual stress range, which is the nominal stress range multiplied by the stress concentration factor, could be used along with the category C from the existing S-N curves when one is designing coped beams subjected to fatigue loading.

Short‐Term Behavior of Pultruded Fiber‐Reinforced Plastic Frame

Results of an experimental and analytical investigation of the behavior of a pultruded fiber‐reinforced plastic (FRF) portal frame subjected to short‐term static loads are presented. A 6 ft high by 9 ft wide (1.83m×2.74m) plane portal frame was designed and constructed of glass/vinylester pultruded FRP thin‐walled sections. Data obtained from short‐term load tests on the frame are presented. Failure of the beam‐to‐column connections and compression flange buckling of the girder are discussed. An analytical investigation was performed to predict the nonlinear response of the frame. The numerical model includes the effects of axial, shear, and flexural deformation of the pultruded numbers, flexibility of the beam‐to‐column connections, and the postbuckling of the frame girder. An expression for the nonlinear rotational stiffness of the pultruded beam‐to‐column connection is presented. The experimental data, obtained from the full‐size test, are compared with the analytical model.

The Significance and Application of Cb in Beam Design

The basic provisions related to design and evaluation of bending members in the structural steel specifications, either according to Load and Resistance Factor Design (LRFD) or Allowable Stress Design (ASD), typically are first presented from the point of view that the magnitude of bending moment is constant throughout the entire distance between points of lateral support for the compression flange. Then, to account for variations in moment, one multiplies the expression associated with constant moment by a correction factor Cb to arrive at a result which predicts the actual bending strength (or allowable stress) for a specific moment gradient. What one accomplishes is to account for changes that occur in the force within the compression flange of the beam throughout the unbraced length. A procedure for selecting beams in situations involving non-uniform moment is suggested within the prelude to the charts of design moments in the LRFD manual, but only in extremely brief fashion. The purpose of this paper is to review the principles associated with the application of Cb, and to elaborate on the procedure briefly suggested in the LRFD manual for selecting beams which experience non-uniform moment.

Lateral-torsional buckling of a pultruded I-beam

Measured short-term critical loading for linear elastic lateral-torsional buckling of a pultruded I-beam has been compared with theoretical predictions. In the buckling experiment, an E-glass reinforced polymer I-beam was simply supported about the major axis, and supported at both ends such that lateral deflection, warping and twist were restrained. It was subjected to a central point load applied to the top compression flange. The experimental evidence for critical loading is shown to compare favourably with the predictions using a finite difference method. The finite difference approach is used to solve the governing differential equation derived using thin-walled theory. Through the finite difference and other analytical models, it is shown that the classical one-dimensional isotropic theories can be adapted, by suitable substitution for the moduli parameters, to predict the buckling load for composite beams made from orthotropic panels. For the case where the load is applied at the centroid of the I-section, the design procedure given in an American design manual is shown to be conservative, providing the assumed boundary conditions at the supports are met.

Lateral-torsional buckling of thin-walled composite I-beams by the finite difference method

The finite difference method has been used to solve the differential equation for the critical loading associated with a specific lateral-torsional buckling test configuration. The linear elastic analysis is valid for thin-walled composite doubly symmetric I-beams made from mid-plane symmetric, fibre-reinforced laminated panels. Here, the test configuration has an I-beam with specially orthotropic panels. It is subjected to three-point bending, and supported at each end such that the only degree of freedom is rotation about the major axis of the beam. For the modelling case where the central load is applied at the shear centre (centroid) of the cross-section there is a favourable comparison between the finite difference results and those results presented by Timoshenko and Gere (1961, Theory of Elastic Stability 2nd edn, McGraw-Hill, New York), which were originally generated for isotropic beams. A favourable comparison has also been found between the finite difference analysis and experimental evidence using an E-glass fibre-reinforced polymeric pultruded I-beam, where the central load is now applied to the top compression flange. The various theoretical models presented in the paper are used to show that the critical loading for buckling in real composite I-beams will be strongly dependent on both the support boundary conditions and the height of the loading relative to the centroid (shear centre).

Further stability problems of prestressed steel structures

In connection with the revision of the Czechoslovak national standard for designing prestressed steel structures (ON 73 1405, 1989), there were proposed, and in the present paper are presented, new formulae for checking the stability and/or strength of (i) a centrally compressed strut prestressed by concentric tendon, (ii) a compressed flange of a loaded plate girder prestressed by a straight tendon, and (iii) an anchor zone of a prestressed plate girder.

Nonlinear analysis of buckling behaviour of steel box girder components

Results of a large deflection nonlinear analysis of stiffened compression plates used in design of box girder bridges are presented. Both geometric and material nonlinearities were considered in the formulation. The soundness of the finite element model used in prediction of the buckling behaviour and ultimate strength of stiffened compression flanges is shown by comparison with experimental data.

Torsional rigidities of open stiffeners to compression flanges

A critical review of code provisions and other proposals concerning the requirements for torsional rigidities of flat stiffeners to compression flanges is made. The relevant rules are investigated by means of 65 tests on compressed, stiffened plates with various loading and supporting conditions. A new design rule for the determination of the dimensions of flat stiffeners, based on their ultimate stress and the ultimate stress of the stiffened plate, is proposed and relevant design charts are given.

Constrained Lateral Buckling of I‐Beam Gable Frames

An important failure mode of I‐beam gable frames is lateral buckling of the compressed inside flange near the corner of the frame. The magnitude of the buckling load depends on the support provided by the joint at the corner. The outside flange is restrained from translation out of the plane of the frame, whereby the buckling mode is described solely in terms of the angle of rotation of the beams. For the common joint type with a corner plate connecting the flanges a kinematic condition relating the angle of rotation and its derivative for the two beams is derived. A simple beam‐type finite element formulation suitable for design computations is given, and some numerical examples are presented. The support provided by the corner depends on the relative buckling stiffness of the two members. Examples indicate that reasonable approximations to the buckling load can be obtained by the present design procedures using two separate beam calculations. However, if the two beams have approximately the same bucklin...

Supermarket Roof Collapse in Burnaby, British Columbia, Canada

Part of the roof of the newly completed supermarket at the Station Square development in Burnaby, British Columbia, Canada, collapsed during the opening day. Framing was steel bar joists and Gerber system beams, and the roof was used as a parking deck. The government of British Columbia established a commissioner inquiry to ascertain the causes and to make recommendations that could prevent similar occurrences. The principal causes of collapse were an undersized beam and inadequate buckling resistance of both the compression flange of the cantilevered beam and the beam column assembly. The procedures that led to the design error are examined in detail. The inquiry made recommendations designed to strengthen the qualifications of engineers offering consulting services to the public, to clarify the lines of responsibility in the construction industry, and to tighten the practices used in design. Technical recommendations are also made with respect to the design of roof systems of the type involved, which were promptly acted upon by the Canadian Institute of Steel Construction.

Longitudinal shear strength of wide compression flanges

This work summarizes a test programme carried out in order to further knowledge of the behaviour of beams with wide compression flanges. The influences of the transverse flange reinforcement and of the transverse bending moment in the flange on the strengths of the beams were studied. On the basis of the test results, commentaries on the ACI and CEB-FIP recommendations for the design of the transverse flange reinforcement are made. An alternative design method is also proposed.

Linear and non-linear response of a simple box girder

Abstract The non-linear response of a steel box girder, within the elastic range, is studied using a finite element technique. The analysis includes the study of a complete cross-section and an idealized cross-section where the compressive flange is assumed to be isolated from the effect of web buckling. The influence of a variable width/length ratio and width/depth ratio for a box with a width/thickness ratio ( b t ) of 100 of the flange plates is examined. The analysis of a complete cross-section enables the interaction between different phenomena associated with the failure of a box girder to be studied. These phenomena include shear lag, bending lag, buckling of the compressive flange, and buckling of the webs. The results of the study show that ignoring the effect of web buckling can lead to an underestimation of the longitudinal stresses in the compressive flange. The non-linear analysis reveals a reverse distribution of bending lag across the compressive flange.

Experimental research on the ultimate load behaviour of steel plated structures

Abstract The paper describes the main results of two experimental investigations into the ultimate load behaviour of steel plated structures. The first is concerned with the performance of the longitudinally stiffened compression flanges of steel box girder bridges and reports tests on 12 large-scale girders. On the basis of an analysis of the progression of plastification in the girder, two criteria for the definition of the ultimate limit state of longitudinally stiffened compression flanges are put forward. The other study focuses on the behaviour of longitudinally stiffened webs under the action of partial edge loading. The results of 152 tests are analysed, and the effect of (i) the position and (ii) the size of the longitudinal rib on the ultimate load behaviour of the webs is studied.

An experimental investigation of the effects of imperfections on the strength of steel box girders

As part of a major study, an experimental box girder having nominally identical cantilever sections was constructed to model the geometry of a pier girder of the Hunt Club–Rideau Bridge structure in Ottawa. The one-fourth scale model did not, however, replicate the varying depth of the prototype. The objective was to determine whether a deliberate reduction in the gross heat input for welds attaching longitudinal stiffeners to the flange plates for one end of the girder (and hence would incur reduced plate distortions and residual stresses) could augment the carrying capacity of a statically loaded box girder. In fact, the results from the two tests are such as to suggest that inward bent transverse stiffeners may account for a greater reduction in strength than do the imperfections of local plate panels of compression flanges. Key words: box girders, bridges, experiments, geometric imperfections, residual stresses, strength, structural steel.

Buckling of multi‐lamellae compression flanges of welded I‐beams: A unilateral elasto‐plastic plate‐stability problem

AbstractBuckling of compression flanges of welded I‐beams consisting of more than one lamella is characterized by partial loss of contact between the lamella welded to the web and the neighbouring lamella. The boundaries of the contact regions of the buckling modes of the two lamellae are originally unknown. Thus, the present elasto‐plastic plate‐stability problem is coupled with a contact problem. It represents a unilateral problem because eigenforms with penetrations of lamellae are physically impossible. This problem is solved first for the elastic material domain. The Rayleigh‐Ritz method is used for determining symmetric eigenforms. A finite‐strip technique is employed for determining unsymmetric eigenforms. The solution of the unilateral elastic plate‐buckling problems serves as the starting point for the iterative solution of the corresponding elasto‐plastic plate‐stability problem. The buckling pressures obtained are compared with corresponding buckling stresses resulting from a classical design procedure disregarding the interaction of the lamellae at buckling.

COUPLED TESTS OF LATERAL-TORSIONAL BUCKLING AND WEB BUCKLING OF PLATE GIRDERS UNDER BENDING

This paper presents the experimental researches on the coupled behavior of lateral-torsional buckling and web buckling of transversely stiffened plate girders. The cross-sectional dimensions of all the six specimens were proportioned to prevent from local torsional buckling of compression flange, and the web width-thickness ratio was kept constant being equal to 200 for mild steel which is over the current JRA upper limit, 152. Then the effect of preceded web buckling on the ultimate strength of girders failed by lateral-torsional buckling is investigated. In-plane bending strength was also examined. The test results are also compared with those for girders with the web width-thickness ratio smaller than the JRA limit.

Sag Rods as Lateral Supports for Girts and Purlins

Although cold‐formed sections provide substantial savings, because of their high strength‐to‐weight ratio, their cross‐sectional configuration gives rise to behavioral phenomena not encountered in the more familiar hotrolled sections. Of great concern to structural engineers is the tendency of these members to deform under most conditions of loading and to fail by yielding or local buckling as a result of the stresses developed. Channels and Z‐sections are commonly used as girts and purlins. In many installations, sag rods are used to provide alignment for these members for the attachment of the steel panels and to reduce their tendency to bend laterally and twist. Test results indicate that the presence of sag rods may not always be beneficial to the girts or purlins and, in fact, may cause premature distortional buckling of the compression flange.

OPTIMUM DEPTH OF A PLATE GIRDER DESIGNED BY ALLOWABLE STRESS METHOD

It seems there are too many formulations about optimum depth of a plate girder and one may wonder which is most preferable for his case. The authors studied the problem by theoretical but rather classical way taking into account every factors having effect to the depth.The result shows the effect of specified allowable compressive stress formulation and the number of sectional changes in a girder must be considered and these factors lower the optimum depth of it. In case of rather short span, the practical limit on the compressive flange area has large effect, even that is not explicitly specified in a code.

Full-scale load test of three-span concrete highway bridge

A full-scale load test to failure of a 34-year-old three-span continuous reinforced concrete highway bridge located in southern Alberta is described. The opportunity to load test the structure to failure occurred as a result of the scheduled demolition of the bridge.Load was applied to the structure in two phases. In the first phase, precast concrete sections were placed at the centre of the middle span until a load of approximately 1900 kN was reached. At this load level a mid-span deflection of 28 mm was measured for the interior span. Additional load was applied by jacking the ends of the bridge at the abutment supports. Loading continued until a maximum deflection of 157 mm was reached at mid-span. Significant cracking as well as crushing of the compression flange at mid-span were evident. On removal of load at mid-span, a residual deflection of 118 mm was observed indicating that the bridge had been loaded well into the postyield range without collapsing.Results of the test are presented in the form of plots of load vs. deflection, reactions vs. deflection, mid-span moment vs. deflection, and deflection profiles at various loading stages. In addition the calculated flexural capacity is compared with measured values. Key words: highway bridge, load test, reinforced concrete.