Web Slenderness Research Articles

Shear performance of horizontally curved steel box bridge girders under hydrocarbon fire exposure conditions: Numerical investigation and design implications

Recent fire incidents indicated that fire-induced bridge collapse is commonly associated with local shear failures occurred in web plates. However, current studies provided failure modes only related to deflection arose from steel bridge girders, irrespective of the underlying shear mechanism. To bridge the knowledge gap, this study presents an investigation on structural behavior of horizontally curved steel box bridge girders (HCSBBGs) under the combined effects of hydrocarbon fire exposure and shear-dominant loadings. The numerical models are developed utilizing the ANSYS program, incorporating a validated thermal-structural analysis model and a shear limit analysis model that accounts for web initial imperfections. These models are further employed to examine effects of fire-shear load scenarios, curvature radius, web slenderness ratio, and aspect ratio on shear performance of HCSBBGs. Herein, deflections, degradation of shear capacity, and web out-of-plane displacement (WOPD) of the steel box bridge girders are discussed in detail. Failure modes of steel box bridge girders can be determined via moment-shear interaction diagrams as specified by Eurocode 3 (EC3). The findings indicate that decreasing web slenderness ratio and web aspect ratio can enhance shear capacity of steel box girders. Further, shear failure modes are predominant when fire occurs near side support of HCSBBGs. Current fire-resistant design practices relying on deflection or flexural limit based failure criteria, cannot be applicable in predicting fire resistance of steel box bridge girders under shear failure mode. Therefore, a failure criterion based on the ultimate web out-of-plane displacement ratio (UWOPDR), related to the web shear limit state, can be more suitable for predicting fire resistance of HCSBBGs.

High strength steel unlipped channel sections subjected to ETF loading: Laboratory testing, numerical simulations and web crippling design

This paper presents web crippling and structural design of high strength steel unlipped channel sections under end-two-flange (ETF) loading based on experimental and finite element investigations. The experimental programme was composed of six grade S690 and four grade S960 test specimens, and the corresponding test set-up, procedures and results were reported in detail. The web crippling test results were used in the numerical modelling programme to validate the developed FE models, which were then adopted to perform parametric studies to enlarge parameter ranges of the bearing length, web slenderness and inside bend radius. Given that codified design rules for S690 and S960 high strength steel unlipped channel sections undergoing web crippling are absent, the corresponding normal strength steel design provisions, as stipulated in the European code EN 1993-1-3 and American specification AISI S100, were evaluated for their suitability to high strength steel unlipped channel sections. It is shown that the ultimate strength of high strength steel unlipped channel sections nonlinearly increases with increasing bearing length but with decreasing web slenderness and inside bend radius. The design methods of current EN 1993-1-3 and AISI S100 provide inaccurate and scattered resistance predictions for high strength steel unlipped channel sections. Finally, a modified AISI S100 design method and a slenderness-based design method were proposed, which can outperform the codified design methods.

Tests, simulations and web crippling design of S690 and S960 high strength steel unlipped channel sections under end-one-flange loading

This paper presents experimental and numerical investigations into the web crippling behaviour and structural design of high strength steel unlipped channel sections under end-one-flange loading. An experimental programme including six grade S690 and four grade S960 steel test specimens was firstly carried out, and the corresponding test set-up, procedures and results were reported. The web crippling test results were subsequently used in a finite element programme to validate developed finite element models, which were then adopted to perform parametric studies to cover wider parameter ranges of the bearing length, web slenderness and inside bend radius. It is found that the ultimate web crippling strength of high strength steel unlipped channel sections increases with increasing bearing length but decreasing web slenderness and inside bend radius. Considering that relevant codified design provisions are absent, the design rules of normal strength steel unlipped channel sections, as prescribed in EN 1993-1-3, EN 1993-1-5 and AISI S100, were assessed for their suitability to high strength steel unlipped channel sections. The codified design methods provide inaccurate and scattered resistance predictions for high strength steel unlipped channel sections under end-one-flange loading. Thus, an improved AISI S100 design method and a novel slenderness-based design method were proposed, which can outperform the codified design methods.

Experiment and Analysis of a Hybrid Composite Post-tension Plate Girder

Steel plate girders have been employed as structural bridge parts since the 19th century. They are typically made up of built-up sections in the shape of I-beams. Web and flange plates withstand shear force and bending moment, respectively. However, plate girders are vulnerable to shear buckling. Shear buckling resistance is increased by adding reinforced vertical stiffeners and, in some cases, longitudinal stiffeners. Nevertheless, these stiffeners are sometimes not enough to prevent extreme shear buckling and only delay the shear buckling of slender web panels. This study investigated a hybrid composite post-tension (HCPt) plate girder by experiment and finite element (FE) analysis. The structural performance of the HCPt plate girder was tested using three specimens: a double-web plate girder, an in-fill concrete double-web plate girder and an in-fill concrete double-web plate girder with prestress. Results showed that the steel web filled with concrete presented preferable strength and behaviour to the hollow steel web because of the concrete in-fill. It had high load capacity, strength and ductility. The concrete in-fill prevented the steel web plate from buckling, and beams generally failed in a ductile manner. Applying prestressing techniques reduced deflection under external loads, increased the load-carrying capacity and enhanced its flexural behaviour by 126% compared to the double web plate girder. The failure mode was changed from web shear buckling in a double web girder to bending in a hybrid composite plate girder, with an improvement of web shear buckling by 88%. The FE analysis result showed excellent consistency with the experimental result.

Effects of shear on the lateral torsional buckling of singly-symmetric I-beams

This paper presents an investigation on the negative effects of shear on the lateral torsional buckling (LTB) of singly-symmetric I-shaped beams due to web distortion associated with shear. Results from a parametric FEA study including eigenvalue buckling analyses and large-displacement analyses were utilized considering both stiffened and unstiffened webs to consider the impact of shear on the LTB resistance. Moment gradients caused by constant shear and a shear gradient were considered. The FEA solutions demonstrate that shear can significantly reduce the lateral-torsional buckling resistance. The FEA results were used to develop design equations that account for the reduction in the LTB capacity from shear. The solutions were compared with conventional methods proposed by Winter to account for the effects of web distortion on girders with slender webs. Results from the study show that (i) the average flange area should be used to account for the effects of shear of singly-symmetric beams; (ii) post-buckling strength has limited impact on the shear effects with regards to the LTB resistance; and, (iii) compared to Winter's approach, the proposed method can capture the variation of the moment reduction factor with the shear force in the unbraced length, and is able to predict moment resistances with reasonable accuracy compared to refined FEA solutions using both eigenvalue analysis and large-displacement analysis. Design examples are provided to demonstrate the calculation procedure.

Experimental and numerical characterization of column webs/faces loaded out-of-plane in steel joints

This paper presents a comprehensive investigation into the behavior of column webs/faces under out-of-plane loading within steel joints. The experimental component of the study involves testing five profiles, encompassing both open and closed sections with varying web slenderness and steel grade, subjected to direct out-of-plane tensile loads through bolted connections, utilizing both single and double rows of bolts. Concurrently, numerical simulations are conducted using finite element models, thoroughly calibrated with the experimental results. Drawing upon the calibrated numerical models, the paper systematically explores the influence of key parameters, including web slenderness, bolt arrangement, and analysis methods, through a parametric study involving 167 cases. A careful comparison of the observed behavior of the component from experimental tests, numerical models, and analytical models for initial stiffness is presented. Finally, the initial stiffness formulation derived from a recent model developed by the authors is improved to align with the observations from the experimental and numerical results.

Improving the behavior of the CBF system using an innovative box section damper: Experimental and numerical study

In this study, an innovative shear damper made of a box section with an easily constructed method, lower cost, and higher energy dissipation capacity compared to existing dampers was introduced to address the low energy dissipation capacity of Concentrically Braced Frames (CBFs) resulting from the buckling of their diagonal compression members under earthquake loading. In this regard, firstly, an experimental test was conducted to evaluate the cyclic performance of the proposed damper. Subsequently, a comprehensive parametric study, based on robust finite element analysis validated by experimental results, was carried out to examine the effects of the proposed passive metallic energy damper on the cyclic performance of CBFs. Experimental and numerical results indicated that the proposed damper exhibits suitable performance with stable hysteresis curves and no degradation in stiffness, strength, and energy dissipation. The results also revealed that the proposed damper demonstrates an overstrength exceeding 1.5 (as recommended by AISC341), and therefore, an overstrength of 2.0 was proposed for the damper. Furthermore, limitations of ρ > 0.55 and ψ > 10 must be applied in the damper design, where…. For optimal performance, it is suggested to design the damper in a way that its web slenderness varies between 67 and 113. Additionally, the proposed equation was in good agreement with finite element results in predicting the ultimate strength of the damper.

Strengthening of slender webs of steel plate girders using FRP composites

Web buckling of steel plate girders creates an undesirable failure mode as it can limit the ultimate load capacity of plate girders. This paper presents details of an experimental investigation aimed at strengthening slender end panels of steel plate girders using three different types of fibre-reinforced polymer (FRP) composite materials (glass-fibre-reinforced polymer (GFRP) pultruded section stiffeners and woven carbon-fibre-reinforced polymer (CFRP) and GFRP fabrics). The plate girders were fabricated using non-rigid end posts and were tested in three-point bending. The test results showed an increase of up to 54% in the ultimate strength of the FRP-strengthened end panels compared with the non-strengthened control panel, which was the result of increased out-of-plane stiffness of the web. A breakdown of the bond between the steel and the FRP fabric occurred in the end panels strengthened with CFRP and GFRP fabrics, while no bond breakdown of the pultruded sections was observed at the ultimate load. Analytical methods proposed by some of the design codes underestimated the critical buckling load and overestimated the ultimate load of the non-strengthened end panel.

Four-Bolt Unstiffened End-Plate Moment Connections with 36-in.-Deep Beams for Intermediate Moment Frames

Previous testing has shown that four-bolt extended, unstiffened end-plate moment connections can be used with beams up to 24 in. deep and develop sufficiently ductile performance to satisfy seismic qualification. It is desirable to extend this depth limit to allow deeper beams for intermediate moment frames. Three moment connection specimens using built-up 36-in.-deep beams with a four-bolt extended, unstiffened end-plate moment connection were tested to determine if they satisfy the intermediate moment frame qualification criteria given in AISC 341-16 (2016a). The web of the specimens satisfied the moderately ductile section criteria for web slenderness, which is required for intermediate moment frames, but not highly ductile section criteria required for special moment frames.
 All three specimens passed qualification criteria for intermediate moment frames (IMFs) as given in AISC 341-16 by retaining at least 80% of the nominal plastic moment strength through 2% story drift. The observed failure modes included lateral torsional buckling of the specimen, flange local buckling, net section fracture of the beam flange, and failure of the beam flange-to-beam web fillet weld. The results of these tests support current moderately ductile limits associated with lateral bracing and cross-section slenderness, given that the associated specimens reached IMF qualification criteria but not special moment frame (SMF) criteria. It was concluded that four-bolt extended, unstiffened end-plate moment connections satisfy intermediate moment frame requirements with a beam depth of 36 in. and that a modification is needed for beam web to flange welds in built-up sections near the moment connection.

Study on stability of H-type section aluminum alloy perforated members under axial compression and eccentric compression around weak axis

Aluminum alloy components have the advantages of light weight, high strength, favorable machinability, and good acid corrosion resistance, which can greatly reduce maintenance costs and easy to make the structures with beautiful appearance. Based on the shortcomings of existing research fields, the stability of H-type section 6082-T6 aluminum alloy perforated members under axial compression and eccentric compression around weak axis is studied by combining experimental and numerical simulation methods in this paper. The test results of aluminum alloy members under axial compression and aluminum alloy members under eccentric compression around weak axis with different web opening numbers, opening diameters, slenderness ratios and eccentric distances are analyzed. The verified finite element model is used to carry out the extensive parameter analysis focusing on the key variables. Based on the test and numerical simulation results of the stability bearing capacity of 134 members, the design methods for H-type section aluminum alloy perforated members under axial compression and eccentric compression are proposed and evaluated by reference to the existing specification.

Stiffening of I-section MRF beams against degradation due to local buckling

Moment resisting frame (MRF) beams under cyclic loading are vulnerable to local flange and web buckling. The Seismic Provisions for Structural Steel Buildings (AISC341) prescribe width-to-thickness ratio limits, which are contingent on target rotations during predefined cyclic loadings. Some rolled I-sections available in the market cannot be employed in special MRFs since they fall short of satisfying the AISC341 flange slenderness limit. Moreover, local buckling leads to a decrease in both strength and stiffness in cyclically loaded MRF beams, ultimately increasing the risk of frame side-sway collapse. This paper introduces a stiffening method aimed at improving the behavior of I-section MRF beams. The proposed method involves placing a pair of stiffeners at the plastic hinge regions. A two-phase numerical study was conducted to assess the effectiveness of this approach. In the first phase, nine unstiffened beam cross-sections with varying flange and web slenderness were considered. The slenderness limits specified by AISC341 were evaluated based on cyclic analyses of these beams. In the second phase, a parametric study was conducted on the same cross-sections, with the flange width and the placement of the pair of stiffeners considered as variables. The results revealed a substantial improvement in behavior with the addition of a pair of stiffeners. Cross-sections that failed to meet the flange slenderness limit could be used in MRFs when stiffened. The optimal location for the stiffeners was found to be significantly influenced by the flange width. Design recommendations for the ideal stiffener placement are presented in this paper.

Elastic Buckling of Prismatic Web Plate under Shear with Simply-Supported Boundary Conditions

This study aims to investigate the local elastic buckling behavior of simply-supported prismatic web plates under pure shear loading. Comprehensive finite element analysis is conducted to analyze the effects of various geometric parameters, such as tapering ratio, aspect ratio, and web slenderness, on the local elastic buckling behavior with simply-supported boundary conditions. An eigenvalue analysis is conducted to determine web plates’ natural frequencies and corresponding shape modes with varying geometric parameters. Particular attention is given to the effect of the slenderness ratio, since current formulas do not consider the impact of the slenderness ratio on the elastic shear buckling coefficient. A sensitivity analysis is conducted to examine the importance of the web slenderness ratio for estimating the critical buckling coefficient of a prismatic plate under pure shear loading. Finally, a formula of the elastic local critical buckling coefficient for a simply-supported prismatic web considering the web slenderness effect is proposed, which can be used in international codes.

Analysis of the Effect of Slenderness Ratio on Nominal Moment in T Section

T-section is similar to the single-symmetry plane. Mostly used in railway engineering, temporary work stands and machinery equipment. In the AISC1999 specification, due to the unfamiliarity with the T-section. Therefore, a conservative definition of a tee fracture is a noncompact section. With the evolution of the times, there are more and more researches on T-section. The T-section is defined as the flange slenderness and the web slenderness. The calculation formula of the nominal moment (Mn) is mainly limited by the slenderness ratio. In recent years, the AISC2017 has added limiting laterally unbraced length for the limit state of yielding (Lp) and limiting laterally unbraced length for the limit state of inelastic lateral-torsional buckling (Lr) to the calculation formula of the nominal flexural strength (Mn) of the T-section. The nominal flexural strength (Mn) shall be the lowest value obtained according to the limit states of yielding moment (Mp), lateral-torsional buckling (LTB). Therefore, this study will analyze and compare the changes in the AISC2017 with the previous norm. Largest laterally unbraced length along either flange at the point of load has 3% difference between AISC2017 and other specifications in plastic moment.

Numerical Modelling and Proposed Design Rules of 7075-T6 and AA-6086 High-Strength Aluminium Alloy Channels under Concentrated Loading

This study presents a detailed numerical investigation into the web buckling behaviour exhibited by high-strength aluminium alloy channels, namely 7075-T6 and AA-6086, when subjected to concentrated loading. A nonlinear finite element (FE) model was established and verified using the experimental data reported by other researchers, and the material properties of 7075-T6 and AA-6086 high-strength aluminium alloy were obtained through the literature. A parametric study comprising 1024 models was performed using the validated FE models. Variables examined in this work included web slenderness ratio, internal corner radii, bearing lengths, and aluminium alloy grades. The numerical results generated by the parametric investigation were used to evaluate the applicability and reliability of the most recent design specifications given in the Australian and New Zealand Standards (AS/NZ S4600) (2018) and Australian Standards (AS/NZS 1664.1) (1997). The comparison indicated that the calculated design strength using AS/NZ S4600 was over-conservative by 41% and 43% for 7075-T6 and AA-6086 aluminium alloy, correspondingly, while the design strength computed using AS/NZS 1664.1 was marginally unconservative, compared to numerical results. Finally, using bivariate linear regression analysis, new design formulas with new coefficients for determining the web buckling behaviour of 7075-T6 and AA-6086 high-strength aluminium alloy channels were proposed. A reliability analysis was then undertaken, indicating that the proposed design equations possess the capability of accurately predicting the web buckling behaviour of these members.

Investigation on shear buckling of steel welded I‐section beams with reinforced web openings

AbstractPlate girders with I‐section frequently require large web openings to accommodate ducts and pipes in buildings and bridges. It is known that the critical load equivalent to an unperforated plate can be achieved by an appropriate reinforcement of the web opening. The majority of the investigations on thin‐walled webs with web opening under shear loading has been focused on web slendernesses ranging between 200 to 360. Three tests on plate girders with a web slenderness of 416 are presented that contain web openings. The effect of an all‐around reinforcement (hollow section) of the web opening is studied in three‐point bending tests. The tests are calculated with finite elements accounting for imperfections that had been measured before testing. A parametric study is performed to evaluate different types of reinforcements for high web slendernesses.

Buckling analysis of steel members by extension of EC‐3 methods in bridge girders under Patch Loading

AbstractThe buckling “General Method” of EN 1993‐1‐1 and EN 1993‐1‐5 can be applied to solve problems characterized by non‐uniform geometries and complex stress fields. A typical example occurs during the incremental launching of bridge girders with slender web panel subjected to patch loading. However, this method does not explicitly provide the most critical verification point of a structural element and does not allow to consider the mechanical interaction between instability modes. The objective of the study is the development of a novel methodology that can solve these important special design issues, using a completely automatic process by linear static and linear buckling analyses only. The procedure provides the definition of a slenderness parameter for each point of the structure, in order to avoid the nonlinear analyses with imperfections permutation (as described in Annex C of EN 1993‐1‐5) that require a high computational effort. This pointwise slenderness parameter indicates not only where the slenderness is maximum in each buckling mode, but also the slenderness in other points of the structural elements. This would allow to consider the interaction between global and local buckling, with the definition of an equivalent slenderness parameter for buckling modes coupling.

Novel method for the prediction of load bearing capacity of compressed C channels considering interaction of buckling modes

AbstractThe proposed method focuses on the interaction of global and local buckling. A modified Ayrton‐Perry type buckling curve is proposed to calculate the ultimate compression force resistance of centrically compressed cold‐formed C channel. The new buckling curve incorporates both the effects of global imperfections and shift of the center of gravity caused by local buckling of slender web plate of the considered sections. Distortional buckling usually does not play any role for this configuration.The effective cross‐section properties for the use of the new buckling curve are determined using critical stresses obtained both by finite‐elements analysis and finite strip analysis. The shift of center of effective cross‐section will produce an additional second order bending moment amplified with the corresponding global buckling multiplier.The results are compared with the curve proposed by AISI Direct Strength Method for global‐local interaction and with simulation results, in agreement with the recommendations of the new prEN 1993‐1‐14.

Numerical study on steel plate girders ‐ Intermediate transverse stiffeners axial force

AbstractTransverse stiffeners are used in steel plate girders with slender webs to provide lateral support to the web along the span and thus increase the plate girder shear resistance. Furthermore, transverse stiffeners anchor the tension field, resulting in axial compression in the stiffener. Despite this, it is widely assumed that the design axial force provided by the FprEN 1993‐1‐5 [1] for the transverse stiffeners is significantly greater than that observed in experimental testing and numerical simulations.The results of 550 nonlinear numerical simulations of plate girders loaded in shear up to failure are presented. Shear resistance and axial stiffener forces are evaluated while the effects of a wide parameter range as web aspect ratio and thickness, flange‐to‐web area ratio, and steel grade are investigated. The numerical results are compared to the European standard design values. Finally, a statistical analysis of the set of results is presented.The numerical analyses show that the axial forces installed in the intermediate transverse stiffeners are significantly lower than those specified by FprEN 1993‐1‐5 [1].

Assessment of the ultimate strength of stiffened panels of ships considering uncertainties in geometrical aspects: Finite element approach and simplified formula

The development of reliability-based assessments has improved the safety design of ship structures by considering the stochastic behaviour of structural components such as stiffened panels. However, previous studies generally considered the variation in the initial geometric imperfection of a stiffened panel as a single deterministic value. To enhance the analysis, in this study, a series of ultimate strength analyses of stiffened panels were carried out by varying and combining the stiffened panel parameters, including variations in the initial geometric imperfection (2.5%, 25%, 50%, 75%, and 100% of the maximum value), modes of the imperfection (column, local, and torsional imperfection modes), slenderness ratios (plate and web slenderness), and span-to-bay ratios (3 and 6). A total of 750 stiffened panel configurations were investigated through a nonlinear finite element method (FEM) analysis using ANSYS APDL incorporated with a code in MATLAB to model the imperfections based on idealised models. The obtained ultimate strength values were then formulated using a nonlinear correlation between the variables in the regression method to yield a new formula for predicting the ultimate strength of the stiffened panel. The results showed that combining the varied parameter values significantly affected the ultimate strength of the stiffened panel and collapse modes. The newly derived formula provided good accuracy with a standard error of only 2.08% when compared with the FEM results of stiffened panels having a significant disparity with the configuration of the idealised models. This confirms the validity of the formula as a reference for evaluating the ultimate strength value with the influence of an initial geometric imperfection.

Web crippling tests on cold-formed high strength steel channel sections having different stiffened flanges and stiffened web

This paper reports 59 tests on cold-formed high strength steel channel sections with different stiffened flanges and stiffened web. The test specimens were brake-pressed from high strength zinc-coated grades G450, G500 and G550 structural steel sheets. The test program consisted of 6 series of channel sections having different stiffened flanges, web slenderness, material strengths and loading conditions. The loading conditions were End-Two-Flange (ETF), and Interior-Two-Flange (ITF) loadings as specified in the North American Specification for cold-formed steel structures. The web crippling test strengths and load–displacement relationships of the channel section specimens were obtained from the tests. The channel sections having stiffened flanges as well as the channel sections having stiffened web enhanced the web crippling strengths of the specimens, especially for those specimens loaded under ETF loading condition. The web crippling test strengths were also compared with the design strengths calculated using the current North American Specification and European Code for cold-formed steel structures. In addition, reliability analysis was performed to assess the reliability of the design rules. Generally, it is found that the predictions obtained from the North American Specification are unconservative and unreliable for the cold-formed high strength steel channel section specimens, except for the specimens with unstiffened flanges under ITF loading condition, while the European Code was unreliable but conservative in predicting the web crippling strengths, except for the specimens with unstiffened flanges under ETF loading condition.