Compression Flange Research Articles

Local Buckling of Curved I-Girder Flanges

Two analytical approaches are used to investigate the effect of curvature on the elastic local buckling behavior of horizontally curved I-girder compression flanges. First, a governing differential equation for the isolated curved flange plate elements under various loading and boundary conditions is derived in polar coordinates and the equation is solved using the finite-difference technique. Numerical results for various curvatures and aspect ratios are generated. Second, the finite-element method using MSC/NASTRAN is used where the entire cross section of the curved I-girder is modeled. A comparison of the results from the two approaches is made and differences are explained. The effect of curvature on the elastic buckling of the flange plates is observed and a simple but conservative formulation representing this effect is derived for design use.

Buckling of elastic—plastic square tubes under bending

This paper addresses the response, buckling and collapse of long, thin-walled, seamless steel square tubes under pure bending using a combined experimental and analytical approach. All tubes tested had nominal cross-sections with height equal to 1 in. (25.4 mm) and ranged in height-to-thickness ratios ( h/t) from 15.4 to 28.6. The experiments were conducted under curvature control. It was found that the deformation of the cross-section that accompanied bending was uniform along the tubes for low values of curvature. At higher values, periodic ripples with wavelengths approximately equal to the width of the cross-section appeared on the compression flange. These ripples increased in amplitude with further bending. For tubes with higher h∼ the increase was more pronounced. Tubes with lower h/t showed more moderate increases in ripple amplitude but developed regions spanning several ripples in which the cross-section deformation was more pronounced. In all cases, collapse occurred when a kink formed on the compression flange of the tube. Rayleigh—Ritz type formulations based on the principle of virtual work were developed to predict the response and buckling of the tubes. Results include predictions of the response considering the effect of uniform cross-section deformation and predictions of the critical curvature at which the ripples appear. The numerical results are in good agreement with experimental observations.

Time-Dependent Bending Properties of Lumber

Abstract Research related to structural stressed-skin panels (SSP) and their component parts has been ongoing at Chalmers University of Technology. In recent years, attention has been focused on SSP with lumber webs and sheet metal and chipboard panels as tension and compression flanges, respectively. In this study, certain mechanical and rheological properties of structural lumber were evaluated as part of a larger project designed to predict the long-term behavior of SSP under load. In this study, several test series were conducted to evaluate short- and long-term properties of European redwood (called Scotch pine in North America) (Pinus sylvestris). From 22 pieces of lumber measuring 25 by 125 by 4000 mm, specimens were cut for use in several test series to determine solid wood properties. Wood modulus of elasticity (MOE), accounting for the shear effects, was evaluated from initial deflections of long-term tests. Mean MOE values of about 14 500 MPa were obtained. Four series of long-term tests were conducted under different combinations of stress level and distribution, as well as loading history. The results suggested that the magnitude of relative creep was greatest under lower stress levels. Different stress distribution (resulting from center- and third-point loading) proved to have little effect on creep behavior. Two mathematical models, i.e., power functions (Clouser function without exponential terms and power function with exponential terms) [1] were evaluated as predictors of the deformation-time relationship for lumber under constant loading. Differences in accuracy of predicting creep behavior between the two models studied were very modest.

Local Buckling of Pultruded FRP Beams-Analysis and Design

An investigation of the local compression flange buckling and failure of pultruded fiber-reinforced plastic (FRP) beams is described in this paper. Results of tests on commercially produced pultruded E-glass/polyester and E-glass/vinylester composite material wide-flange I-beams are described. The beams were tested in a four-point bending configuration in a specially designed fixture which was designed to cause local buckling and ultimate failure of the compression flange of the beams and to avoid global lateraltorsional buckling and local web failure. All beams were monitored with strain gages and LVDTs. Buckling loads, failure loads, buckling stresses, deflections and failure modes are reported. Standard and "customized" pultruded beams in the 8 inch (203 mm) series were tested. Based on an analysis of the performance of the standard 8 x 8 x 3/8 in. (203 x 203 x 9.5 mm) beams, two 8 x 8 x 3/8 in. (203 x 203 x 9.5 mm) beams were "customized." In these "customized" beams the fillet region at the flange and web intersection was altered in order to increase its strength and the rotational stiffness. Analysis of the test results of the customized beams indicated that significant increases in load carrying capacity of pultruded beams can be achieved with minor geometry and fiber architecture modifications to the standard beams. A discussion of the differences in buckling and failure characteristics of the beams based on their resins, sizes, and custom modifications is provided.

Yield-Interaction Relationships for Curved I-Girders

Yield-interaction relationships are developed for compact, compact-flange, and noncompact sections of curved girders under combined vertical and lateral (warping torsion) moments. These relationships define the bending strength of such compact, compact-flange, and noncompact sections if suitable web-slenderness, compression-flange slenderness, and compression-flange bracing limits are satisfied. The most convenient form of these relationships are equations defining reduced flange widths as a function of lateral moment. The correct vertical-bending strength can be calculated from a reduced steel section consisting of the actual web and reduced widths of flanges. Compact-flange sections have a compact compression flange and a noncompact web. For straight girders, there is no advantage in using a compact compression flange with a noncompact web. For curved girders, however, the compact flange permits a larger lateral moment to be carried in combination with a given vertical moment.

Mechanical performance of carbon-fibre- and glass-fibre-reinforced epoxy I-beams: I. Mechanical behaviour

This paper is the first in a series which detail the mechanical behaviour, finite element predictions and fractographic observations of the failure of composite I-beams. Experimental investigations into the behaviour under static load of both unnotched and web- and flange-notched continuously reinforced carbon-fibre/epoxy and glass-fibre/epoxy I-beams are discussed. A four-point flexural configuration is used. The global static response and ultimate failure are described in terms of strains, compliance, buckling and final fracture. A mode of buckling that is antisymmetric across the width of the compressive flange is observed prior to failure in all cases. Failure of the unnotched I-beams is concentrated around a buckle on the compressive flange whilst failure of the notched I-beams initiates from a shear-loaded circular cutout within the web. Buckling of the unnotched beams occurs at loads that are approximately 50% of the failure loads. Failure of the notched beams occurs at loads that are approximately 75% of the failure loads of the unnotched beams. Buckling and failure of the glass/epoxy beams occur at loads that are approximately 75% of the corresponding loads in the carbon/epoxy beams.

Mechanical performance of carbon-fibre and glass-fibre-reinforced epoxy I-beams: II. Fractographic failure observations

This present paper is the second in a series which together detail the static behaviour, fractographic observations, fatigue behaviour and finite element predictions of composite I-beams subjected to mechanical loads. Fractographic observations associated with the mechanical behaviour under static load of both unnotched and web- and flange-notched continuously reinforced carbon-fibre/epoxy and E-glass-fibre/epoxy I-beams are discussed. Ultrasonic scanning, X-radiography and both optical and scanning electron microscopy have been used to elucidate the presence of different damage mechanisms and the directions of delamination growth in different regions of the beams. The principal damage mechanisms which have been identified as causing failure are delamination, matrix cracking, splitting and fibre fracture. As discussed in detail in the previous paper, a four-point flexural configuration was used. A mode of buckling that was antisymmetric across the width of the compressive flange was observed prior to failure in all cases. Failure of the unnotched I-beams initiated from a buckle on the compressive flange and the subsequent damage was predominantly in the form of delamination. The main delaminations were along the interfaces between the separate sub-components which comprise the I-beams: namely, the flange caps and C-sections and the backs of the two C-sections. These are all −45 ° + 45 ° interfaces i.e. the relative fibre angle between the adjacent plies is 90 °. Failure of the notched I-beams initiated from a shear-loaded circular cutout within the web. The critical damage mechanism was matrix cracking in local 90 ° 90 ° plies which were subject to local tensile stresses. Fibre fracture and component failure resulted from this matrix cracking.

Load and resistance factor design (LRFD) approach for reinforced-plastic channel beam buckling

Pultruded fiber reinforced plastic (PFRP) structural sections are rapidly gaining impetus in civil engineering applications. Thin-walled open beams with channel, I-shaped, and other types of sections are of practical importance to designers. In this paper, a load and resistance factor design (LRFD) approach for lateraltorsional buckling is presented based on an experimental and theoretical study of the behavior of PFRP channel section beams under the influence of gradually increasing static loads. Some experimental results for combined bending and torsion are also presented. Single span members with unrestrained end warping are considered with concentrated vertical loads passing through (a) the shear center, (b) the geometric centroid, and (c) a location which is neither at the shear center nor at the centroid. A pair of concentrated loads are applied symmetrically about the beam midspan, through a system of loading plates and tie rods in order to allow an unrestrained deformation of the beam. The loads are increased gradually and the resulting midspan vertical, lateral, and torsional deflections are recorded. The loads are generated with hydraulic jacks and recorded by means of calibrated load cells. Strains are also recorded at key locations using electrical resistance gages. Relationships between the applied load and the resulting deflections and strains are plotted and compared for the three load cases. The magnitude and significance of the warping stresses in comparison to the flexural stresses are identified. For the case of shear center loading, the deflections are monitored for various clear spans of the beam. This information is then utilized to generate the relationship between the lateral torsional instability load versus the minor axis slenderness ratio. An approximate theoretical formula is also developed to predict the lateral-torsional buckling load as possible prelude to the evolution of a formal construction specification formula for use by design engineers. The predicted buckling loads found using the formula are in excellent agreement with the experimental results. A comparison of the results from the formula applied to the case of compression flange loading is also made to those using the current AISC-LRFD specification. Lastly, the use of a proposed LRFD approach is demonstrated by means of analysis and design examples. The effect of the applied load height on the buckling load capacity is explained using the buckling formula.

構成板要素の局部座屈と延性破壊の相互効果を考慮した高張力鋼梁の塑性変形能力評価

The purpose of this study is to evaluate the plastic deformation capacity of high strength steel beams. It is evaluated by two categories, which are the local buckling of the compression flange and the ductile fracture of the tension flange. The effect of width-thickness ratio and length of specimens on the collapse form are investigated by experiments and numerical analysis. The plastic deformation capacity of considering the collapse form high strength steel beams is shown by the flange width-thickness ratio. Finally, the line of demarcation between local buckling and ductile fracture are shown by width-thickness ratio.

押出角管の回転引曲げ加工における積層弾性心材の効果

Extruded aluminum alloy sections are advanced materials in use as lightweight structural members. A secondly forming process such as bending is required when these materials are used for structural members of automobiles. It is known that undesirable deformations as wrinkling and split tend to occur easily when some sections having light gauge are formed by the bending process. This report shows the working limit for the draw bending process of square tubes with a laminated elastic mandrel. A6063S and A6061S square tubes having various thickness are applied to this experiment. It is shown that applying laminated elastic mandrels to this draw bending process is very effective in preventing either primary distortion or wrinkling of compression flange and compressive region of webs. In consequence, higher working limit is obtained by this method. On the working conditions of the thickness ratio t0/H0=0.075 or 0.05 of A6063S–O and A6061S–O, the working degree R0/H0 reaches to 2.4 or 4.3 without any defects, where t0 and H0 mean thickness and the height of the tube respectively.

Prediction of Creep Properties of Chipboard Used in Stressed-Skin Panels

Abstract In recent years, attention has been focused on structural stressed-skin panels (SSP) with lumber webs and sheet metal and chipboard panels as tension and compression flanges, respectively, at Chalmers University of Technology. In this study, certain mechanical and rheological properties of structural chipboard were evaluated as part of a larger project designed to predict the long-term behavior of SSP under load. Several series of tests were conducted to evaluate short- and longterm properties of urea-formaldehyde bonded chipboard. From eight full-sized panels, specimens were fabricated for use in the determination of chipboard properties. Compressive strength and modulus of elasticity (MOE) were evaluated from short-term tests. Average strength and MOE values of 20 and 4100 MPa, respectively, were obtained. The MOE value was virtually identical to that obtained from initial deformations found in subsequent creep tests, indicating that test method had no effect on MOE. Three series of long-term (11 000-h) tests were conducted under constant and similar environmental conditions and different combinations of stress-level and loading history. The results suggested that the magnitude of relative creep was greatest under lower stress levels. Two empirical models, a Clouser function without exponential terms and a power function with exponential terms (Clouser, W. S. “Creep of small wood beams under constant bending load,” FPL Report 2150, U.S. Forest Products Laboratory. Madison, WI., 1959), were evaluated as predictors of the deformation-time relationship for chipboard under constant loading. The power function with the exponential terms proved to be superior at extrapolating short-term results to long-term predictions. However, both functions were relatively similar with respect to describing the long-term behavior of chipboard as the compression flange in a SSP. Measuring methods and definition of the initial deformation were found to be important, especially for predicting the relative creep factor for chipboards under different load histories.

Distortional Buckling of Thin-Walled Beams/Panels. I: Theory

The introduction of the standing seam panel for roof systems provided the building industry with an efficient solution to watertightness problems. These panels have two major advantages over the conventional trapezoidal through-fastened panel: an elevated seam and concealed “hold-down” clips. The relatively small depth-to-width ratio of the panel guarantees that overall, the panel is laterally stable under gravity load. The capacity of laterally stable standing-seam panels may, however, be reduced due to lateral instability of the unsupported compression flange. This mode of instability has been referred to in the literature as distortional buckling—a form of instability for unsupported lengths between those for local and lateral buckling. In the present paper, an analytical expression, based on a beam on elastic foundation model, is presented for estimating the elastic distortional buckling stress in sections with laterally unsupported compression flanges. The beam is assumed to comprise the outstanding leg, and the elastic foundation is provided by the rotational restraint of the tension flange and the web. A comparison of the analytical results with the results from elastic finite-strip buckling analyses shows good agreement between the two methods of analysis.

Distortional Buckling of Thin-Walled Beams/Panels. II: Design Methods

The design of standing seam roof panels must necessarily consider two loading conditions; construction and in use (occupancy) loading, in addition to the effects of ponding if sufficient drainage or specific drainage mechanisms are not provided to avoid accumulation of water. In the present paper, the results of tests on single panels with laterally unsupported compression flanges are presented along with two design methods for the interaction between local and distortional buckling. The design method is based in the analytical expression presented in the first paper and is conceptually consistent with the design procedures currently used for flexural, torsional, and lateral-torsional buckling. Overall, the new design methods give better approximations of the maximum capacity of wide-flange standing-seam panels than previous design methods. More research is still needed to demonstrate the applicability of the methods presented here to full-scale panel systems in which the outstanding legs are crimped together.

A simple formulation for predicting the ultimate strength of ships

The aim of this study is to derive a simple analytical formula for predicting the ultimate collapse strength of a single- and double-hull ship under a vertical bending moment, and also to characterize the accuracy and applicability for earlier approximate formulations. It is known that a ship hull will reach the overall collapse state if both collapse of the compression flange and yielding of the tension flange occur. Side shells in the vicinity of the compression and the tension flanges will often fail also, but the material around the final neutral axis will remain in the elastic state. Based on this observation, a credible distribution of longitudinal stresses around the hull section at the overall collapse state is assumed, and an explicit analytical equation for calculating the hull ultimate strength is obtained. A comparison between the derived formula and existing expressions is made for largescale box girder models, a one-third-scale frigate hull model, and full-scale ship hulls.

Behavior of Thin-Walled Concrete Box Piers

The objectives of this study were to investigate experimentally and analytically the behavior of hollow, thin-walled concrete box bridge piers and pylons, and obtain methods for predicting their capacities. Twelve one-fifth-scale short concrete box pier specimens were loaded to failure under combined axial load and uniaxial bending about the weak axis. Both monolithically cast and segmentally constructed, post-tensioned specimens were tested. An analytical model was developed to predict the strength of a concrete box column subject to simultaneous oxial load and unioxial bending. This model includes the effects of local buckling of a thin compression flange. It was determined that concrete box columns with wall width-to-thickness ratios less than 15 are unaffected by local compression flange buckling. Members with wall width-to-thickness ratios of 15 or greater may exhibit reduced strengths due to local buckling. An empirical strength reduction factor is proposed to account for the effects of compression flange buckling. −

鋼道路橋の疲労設計のための垂直補剛材取付け部の変動荷重実験

A long-life variable amplitude fatigue test is performed using plate girder specimens with four types of transverse stiffener connections under highway traffic loading. Fatigue cracks are initiated from the fillet weld toe at the stiffener end on both the tension side and compression side, from blow holes contained in web-to-flange longitudinal fillet welds, and from the transverse fillet weld toe of the patch plate on the compression flange. The fatigue failure life of all four details of the transverse stiffener connections satisfies the condition of JSSC category D.

ウエブに鋼板を添接したH形鋼曲げ部材の塑性変形性状に関する研究

The deformation capacity of a H-shaped steel member is reduced by the coupled local buckling. It is, however, obvious that the tension flange and the web are stable at the beginning of the local buckling of the compression flange. In this paper, the new method which the steel cover plates are welded on both sides of the web is suggested. These plates restraint the coupled local buckling and contribute the bending strength after the local buckling. So that the deformation capacity of the H-shaped steel member increases. The effectiveness of these plates is shown by experiments and analysis.

Local Buckling and Failure of Pultruded Fiber-Reinforced Plastic Beams

An experimental investigation of the local compression flange buckling and failure of commercially produced pultruded fiber-reinforced plastic (FRP) I-shaped beams is described in this paper. Results of tests on pultruded E-glass/polyester and E-glass/vinylester composite material beams are described. The test configuration was designed to cause local buckling and ultimate failure of the compression flange of the beams and to prevent global lateral-torsional buckling. The beams were stiffened to prevent crippling and warping at the supports, and local tensile failure at the load points. All beams were monitored with strain gages and LVDT’s. Buckling loads, failure loads, buckling stresses, deflections, and failure modes are reported. Effective mechanical properties of the beams, obtained from overall flexural and shear strain data, are presented. A discussion of the different failure characteristics of the polyester and the vinylester beams is provided.

Coupled instability and negative shear lag phenomenon in box girders

The explanation of the negative shear lag phenomenon in linear analysis of box girders is reviewed. The extension of the analysis to include geometrical nonlinear effects in a compression flange, due to buckling in both classical and negative shear lag environments, is presented. It is shown that in interaction the buckling and the negative shear lag have opposite effects on longitudinal stress distribution across the flange and, depending on load level, both the effects are effectively damped out. However, the overwhelming significance of buckling near the peak load may be expected. The important influence of flange transverse stiffeners and the very unusual distribution of longitudinal stresses in box girder webs in the negative shear lag region are also mentioned.

Tests of Profiled Steel Decks with V‐Stiffeners

The size and position of intermediate stiffeners in the compression flanges of thin‐walled profiled steel decks exert a strong influence on the dominant buckling mode of the flange. The ability of the deck to provide both high load‐carrying capacity before the onset of elastic buckling and a high ultimate‐load capacity may therefore be affected. A program of tests to determine the effectiveness of intermediate stiffeners in controlling buckling modes is undertaken. A series of specimens are loaded in pure bending resulting in various buckling waveforms prior to ultimate failure through a plastic collapse mechanism. The experimentally determined buckling stresses are found to be comparable with studies performed using a finite‐strip numerical analysis in which both local, and distortional buckling modes are predicted. A simplified design procedure for distortional buckling is proposed. The existing design procedure for local buckling in the Australian Standard AS1538‐1988 is confirmed.