Corrugated Web Girders Research Articles

Sub-modelling based fatigue evaluation of welded details in composite trapezoidal corrugated web girders under coupled thermal-structural loading

Exploring the long-term performance of welded details in composite trapezoidal corrugated web (TCW) girders is a significant focus for the service life of these structures exposed to atmospheric environment and traffic flow. The majority of the present studies have been conducted without accounting for thermal stresses induced by temperature differences and accurately reflecting internal force transfers for the composite girders in flexural bending. The fatigue behaviour of the welded details in these girders under coupled thermal-structural loading is investigated herein through experimental and numerical methods. The results indicated three stages for the structural degradation from the test performance and justified a proper allowance of the cross-sectional stress in coordination with the flexural curvature in the derivation of S-N relations comparable to similar details in related design codes. A sub-modelling procedure is implemented to capture the thermal gradient, the local stress concentration, and the crack distribution in global modelling while replicate the semi-elliptical surface crack at the external side of the fillet weld toe in local modelling. The fatigue lives predicted from the proposed analytical model match reasonably well with experimental and numerical results, indicating its good applicability incorporating characteristic geometric correction factors into classical theoretical calculation for fatigue evaluation.

Shear buckling behaviour of sinusoidal corrugated web girders with stiffened circular openings

The mechanical properties and failure behaviours of three different specimens of sinusoidal corrugated web girders with stiffened circular openings were investigated experimentally and numerically. The experimental outcomes showed similarities in the mechanical properties and failure model of the specimens, despite differences in the geometric dimensions. The numerical simulations further confirmed the buckling as well as post-buckling behaviours of the experimental results. The influence of initial geometric imperfections on the shear buckling load of the corrugated web girders was quantified and neglecting geometric imperfections led to an overestimation of the actual shear load capacity, emphasizing the importance of considering imperfections in the design of structural components. The investigation results showed that the shear load capacities of the girders were significantly affected by the thickness of the opening stiffeners, and that the presence of openings reduced the load carrying capacity and the overall stiffness of the beams, whereas the existence of opening stiffeners increased both the ultimate load bearing capacity and the global stiffness. However, the strengthening effect of the opening stiffener becomes less pronounced beyond a specific thickness. Besides, a comparison between hand calculations and numerical simulations show that the recently developed calculation method provided a more reliable prediction of the shear buckling resistance of corrugated web with stiffened openings. This investigation provides valuable guidance on the shear buckling behaviour of sinusoidal corrugated web girders with circular opening stiffeners, thus benefiting the design and analysis of steel structural components with sinusoidal corrugated web.

Optimizing Gene Expression Programming to Predict Shear Capacity in Corrugated Web Steel Beams

Corrugated web steel systems, such as corrugated web girders (CWG) and beams (CWSB), have the potential to influence the modern construction industry due to their unique properties, including enhanced shear strength and reduced necessity for transverse stiffeners. Nevertheless, the lack of a rapid and accurate design approach still limits its wide applications. Recently, gene expression programming (GEP) has been employed to predict the shear capacity of cold-formed steel channels, demonstrating superior predictive accuracy and compliance with established standards. This study applies GEP to predict the shear capacity of sinusoidal CWSBs and optimizes its predictive performance by employing a systematic grid search to explore combinations of chromosomes, head sizes, gene counts, and linking functions. The process involved testing 19 different parameter combinations and more than 60 developed models. The findings include the sensitivity of the model's performance to gene count and the critical role of the linking function. The optimal model in the study, GEP13, achieved R² of 0.95, an RMSE of 100.5, and an MAE of 86.6 in the testing dataset with 150 chromosomes, a head size of 12, and four genes using a multiplication linking function. Doi: 10.28991/CEJ-2024-010-05-02 Full Text: PDF

Shear Test of Corrugated Web Girders with Concrete-Filled Compression Tubular Flanges Used in Buildings

Corrugated web girders with plate flanges have been widely applied in buildings and bridges due to the large shear capacity of the corrugated web (CW). However, experiments on corrugated web girders with tubular flanges are limited. Accordingly, this paper explores, through four full-scale small-size experimental tests used on buildings, the shear behavior of a type of girder formed with a CW, concrete-filled tubular flange, and bottom flat plate flange (CWGCFTF) with different CW thicknesses, wavelengths, and concrete strengths. Based on the imprecise results of one current test, a novel simple support device is proposed to improve the accuracy of the shear test of the CWGCFTF. The test results also show that the shear ratios of the tubular flange to the entire cross-section range from 15–18% when the loading reaches that of the corresponding shear stress to 80% of the shear yield strength of the CWs. Moreover, local buckling appears at the top surface of the steel tube with the CW shear buckling failure of the CWGCFTF under the shear tests. At the end, a theoretical equation of the shear ratio of the CW to the whole cross-section is derived, and a shear yield strength equation of the CWGCFTF is proposed and verified by comparisons with the test results.

Shear strength of corrugated web girders with compression tubular flanges

The current paper focuses on the shear strength of corrugated web girders with compression tubular flanges (CWGCTFs) which considers the real web-flange juncture behaviour. Accordingly, the real juncture behaviour between the corrugated web (CW) and compression tubular flange in CWGCTFs used in conventional buildings is explored first. An elastic bifurcation buckling analysis is carried out using the finite element (FE) software ABAQUS for isolated CWs with different boundary conditions at their juncture with the flanges. ِAssuming that the dimensions of the generated CWs depend on those of conventional buildings, it is found that the corresponding embedment of the CW by the flanges of the CWGCTFs acts as a fixed connection. Having identified the real web-flange juncture behaviour, a large number of nonlinear FE models are generated to obtain the shear strength of the CWGCTFs taking into account the geometrical imperfection and material nonlinearities. This has been done based on a validation recently presented by the authors. The FE strengths are then compared with available shear strength predictions for CWGs with plate flanges (those of Driver et al. (2006), Moon et al. (2009), Sause and Braxtan (2011), Nie et al. (2013), Leblouba et al. (2017)) as well as on the derived shear force distribution relation for tubular flange and CW of CWGCTFs of the current authors (2022). Finally, the shear strength of CWGCTFs proposed by Leblouba et al. (2017) is modified to design the shear strength of CWGCTFs.

Stainless steel corrugated web girders for composite road bridges: Optimization and parametric studies

To achieve sustainability in bridge design, it is critical to ensure both economic viability and low environmental impact. While stainless steel has great mechanical properties and life cycle performance, the material is expensive, which has limited its use in bridges. This research aims at exploring the benefits of using stainless steel corrugated web girders as an alternative to carbon steel flat web girders in composite road bridges. This concept is expected to lower the investment cost, which enables a broader utilization of the good properties offered by stainless steel. A genetic algorithm optimization routine has been developed to produce bridge designs with minimum weight, investment cost, life cycle cost (LCC), or life cycle impact. Multiple parametric studies are conducted using a simply supported reference bridge. The optimal design solutions are compared for two main design alternatives: conventional S355 flat web girders and duplex (EN 1.4162) corrugated web girders. The parametric studies consider the effects of different design parameters, including the span length, available girder depth, average daily traffic (ADT) with the corresponding indicated number of heavy vehicles in the slow lane (Nobs), and the paint maintenance schedule, on the optimal solutions. Furthermore, a sensitivity analysis is carried out to analyse the impact of inflation and discount rates on the obtained results. The results show that the concept of stainless steel corrugated web girders offers significant potential LCC and environmental impact saving for the examined span lengths, particularly in the case of deeper girders, high ADTs, and more intensive maintenance activities. Also, despite the influence of inflation and discount rates on LCC results, the studied concept consistently demonstrated favorable results.

Closed-form approach for the elastic critical moment of I-girders with corrugated web

Using corrugated web girders offers several advantages, including increased resistance to lateral-torsional buckling. Researchers have proposed various methods for determining the critical moment value as a function of the cross-sectional geometry. Previous studies have suggested that the enhanced critical moment is attributable to a larger warping constant. In this paper, we present the results of a systematic numerical study using finite element analysis on girders with various corrugated web shapes. Bending along the weak axis demonstrates that corrugated web girders possess a higher moment of inertia. Furthermore, our torsion linear analysis indicates that the increase in the critical moment is primarily due to a larger torsional constant. We compare the elastic critical moment values obtained using finite element linear buckling analysis to those derived from theoretical expressions that introduce equivalent section properties. Our results illustrate that the equivalent section properties method provides values that closely resemble those obtained using finite elements. Finally, we provide closed-form expressions that can be used to estimate equivalent section properties for any girder with a corrugated web. Our findings suggest that employing these expressions to calculate the critical moment yields results that are satisfactory when compared to those obtained through finite element linear buckling analysis.

Experimental study on fatigue behavior of trapezoidal corrugated-web girders based on T-section members

Fatigue of steel corrugated-web girders (CWGs) is a new research topic. This study uses trapezoidal corrugated-web T-section members (CWTs) to lower the cost of fatigue tests when investigating the fatigue behavior of a trapezoidal CWG. First, static tests were conducted, and the CWG under a bending moment and CWT under an axial force were compared, which verified that the flanges had the same stress distribution characteristics under equivalent loads. This demonstrates that it is suitable to investigate the fatigue behavior of a CWG using a CWT. Second, fatigue tests were performed on trapezoidal CWT specimens with two different waveform radii, R30 and R60, and their hot spot stress concentration factors at the fatigue critical location of CWG (the intersection between a parallel fold and an inclined fold of a web) were obtained, which reached 1.63 and 1.54, respectively. Of the 18 CWT specimens that experienced fatigue failure, 72 % of the initial cracks occurred at point S, indicating that this location was the most susceptible to fatigue cracking. The same S-N curve (log10N = 12.928-3log10Δσhs) could be applied in calculating the fatigue strengths of CWTs with different wave radii (R30 and R60) when the hot spot stress range that considered the stress concentration factor (SCF) was used.

Lateral-torsional buckling resistance of corrugated web girders

AbstractThere is currently no accurate calculation procedure for determining the lateral-torsional buckling resistance of trapezoidally corrugated web girders. Therefore, a detailed investigation is performed in the frame of an experimental and numerical research program at the Department of Structural Engineering of the Budapest University of Technology and Economics. Based on the previous experimental results, a numerical model is developed to be used to determine the lateral-torsional buckling resistance by using deterministic method. The effect of flange size, corrugation geometry and boundary conditions are investigated. An improved design method is developed for the determination of the lateral-torsional buckling resistance of trapezoidally corrugated web girders.

Stability behaviour of sinusoidal corrugated web girders under fire conditions

AbstractSinusoidal corrugated web girders, which are in the focus of the current paper, have been increasingly used in the past years in civil engineering applications due to economical design. Recently, a number of experiments dealing with the particular behaviour of this girder type have been carried out at room temperature, while the structural behaviour at elevated temperature has not been widely analysed and requires further investigation and clarification. The current paper deals with the improved geometrically and materially nonlinear analysis with imperfections (GMNIA) of sinusoidal corrugated web girders under fire conditions. The developed finite element model, which is validated based on previous measurements during fire tests found in the international literature, is capable of modelling the specialties, e.g., the so‐called ‘accordion effect’, of corrugated web girders. The applicability of design formulae is also illustrated in the paper while an extensive numerical parametric study is also carried out to demonstrate the impact of different parameters on the stability behaviour and failure mode of corrugated web girders at elevated temperature.

Life Cycle Cost and Life Cycle Assessment of Composite Bridge with Flat and Corrugated Webs

AbstractTo satisfy the sustainability criteria, a bridge design must be economically viable during its entire service life with a minimal impact on the environment. While stainless steel is known for its excellent life cycle performance, its high cost prevents it from being used in bridges to a larger extent. This study evaluates a new design solution that takes advantage of using corrugated web in bridge girders to overcome this issue. Three design concepts are evaluated for a three‐span case‐study bridge. These include a bridge with carbon steel flat web, stainless steel flat web, and stainless‐steel corrugated web girders. Each design is optimized using a genetic algorithm. The three optimal solutions are then evaluated in terms of investment costs, life cycle costs (LCC) and life cycle impact. The results show that the investment costs in a flat web girder bridge increase by 27% when stainless steel is used instead of C‐Mn (carbon) steel. However, this increase is only 10% when corrugated web girders are used. On the other hand, the LCC savings increase from 6% to 18% for corrugated web girders. Finally, the use of corrugated web in stainless steel leads to a reduction in the climate impacts of up to 32% compared to carbon steel for the studied bridge.

Lateral torsional buckling analysis of corrugated steel web girders using homogenization approach

Corrugated web beams have become popular in recent years due to their high strength-to-weight ratio, ductility and high shear resistance without stiffeners. The developments in the automated production of corrugated steel plates have further amplified their use as structural elements in bridges and buildings. In this paper, we develop a strain energy-based homogenization scheme to convert corrugated sections into equivalent flat sheets with modified elastic properties. The thin-walled theory is implemented in a one-dimensional (1D) finite element (FE) framework along with a modified analytical expression to study the lateral torsional buckling of corrugated web girders. The homogenization-based FE modelling reduces the computational requirement of finer mesh sizes on the corrugation profile. The present thin-walled FE model is implemented to different corrugation profiles and lengths, and their responses are compared with methodologies available in the literature. The effects of the geometrical parameters and loading on the lateral torsional buckling behaviour are investigated and important observations are made for structural designs.

Shear behavior of stainless steel girders with corrugated webs

In this paper, the shear strength of corrugated web girders made of EN 1.4162/LDX 2101 stainless steel is investigated. Four full-scale trapezoidal corrugated web girders were tested under shear. Before conducting the tests, DIC was used to measure the real geometric imperfections in the web panels. Complementary finite element analysis studies were conducted to assess the sensitivity of the shear strength to initial imperfections. The experimental results indicated that all the tested girders with a local slenderness ratio of λ = 0.7 attained the shear yield strength, which was then followed by strain hardening in the material at a level that was 8–18% higher than the yield strength. This implies that the Eurocode's limit of λ = 0.25 to attain the plastic shear strength in corrugated webs can be quite conservative for stainless steel. According to the findings of the imperfection sensitivity studies, an initial geometric imperfection based on the first eigen buckling mode and with a maximum amplitude of amax/200, where amax is the maximum corrugation fold length, yielded ultimate strength within 3% of the test results. When the amplitude was increased to hw/200, where hw is the web height, the ultimate strength was estimated to be 25% lower on average than in the experiments. In three of the studied girders, initial imperfections with other forms than the first buckling mode were found to be more critical. Further, it was found that regardless of mode number, mode shapes that are more extended over the web panel result in a higher degradation of the ultimate shear strength.

Equivalent flat-web thicknesses and modified flange-based moment resistance for corrugated-web steel I-girders

This study proposed analytical formulations for equivalent flat-web thicknesses at horizontal and inclined fold sections and modified flange-based moment resistance for corrugated-web girders (CWGs), accounting for the accordion effect due to corrugations. The finite element (FE) analysis approach was used for examining the nonlinear flexural behavior of CWGs. Numerical models were first validated against flexural tests from two documented CWG studies. For additional verification, nonlinear theoretical analysis of flat-web girders was compared and verified against detailed FE-based analysis results. A detailed parametric study was performed to examine the effect of corrugated-web trapezoidal profiles and girder geometry on the moment resistance of CWGs using the validated nonlinear FE modeling. Then, the parametric study results were used in the theoretical nonlinear moment-curvature analysis on equivalent flat-web girders to derive the proposed formulations for flat-web thicknesses at horizontal and inclined fold sections of a CWG. Alternatively, a modified flange-based moment resistance formulation was proposed for CWGs by accounting for the accordion effect of their trapezoidal corrugated webs. Both the proposed formulations simplified the accordion effect analysis in CWGs and can result in potentially economical girder designs and further development of design specifications for CWGs.

Comparison of the Efficiencies of Web Cutouts for Steel Plate Girders with Corrugated Webs Versus Flat Webs Under Pure Shear

Abstract Corrugated steel-plate girders are used as structural elements in many applications because of their properties, cutouts are always provided in these plate elements to enable inspection and servicing. This study presents an experimental and analytical study to investigate the efficiency of a steel-plate girder with corrugated webs (GCWs) and flat webs (GFWs) having cutouts under shear loading. In this study, we investigated the influence of some important parameters on the girders’ load-bearing capacity. The experimental program was conducted on six full-scale plate girders, which have been tested under central load at mid-span. The analysis was conducted using ANSYS V20 to perform a nonlinear technique for the determination of the ultimate load of the tested girders. Finally, experimental and finite element model were used to define the ratio of increasing carrying capacity in plate girder with flat and corrugated web, having cutout under shear loading. The ultimate strength, failure mechanism, and load-deflection curves from the experimental and analytical study show that the shear capacity of the girder with corrugated web girders extends loads by 22 % compared with the flat web.

Analysis on the shear failure of HSS S690-CWGs via mathematical modelling

This paper aims to present a new and accurate design equation by employing the applications of deep learning and mathematical modeling techniques in calculating the shear strength and the failure mode of corrugated web girders (CWG) formed by S690 high-strength steel (HSS). HSS provides slenderer and weight-efficient structures than those would be possible if ordinary-strength steels were used, while the corrugated web (CW) increases the shear stability of steel girders and eliminates the need of transverse stiffeners. Therefore, the CWGs and HSS can be combined into one structure for gaining more structural benefits for civil engineering applications. A finite element (FE) model is firstly established and verified by the available experimental data in the literature. Thereafter, 106 FE models of CWGs are generated and analyzed, then employed in deep learning and mathematical modeling techniques such as the neural network (NN) and Kriging model, respectively. This investigation helps to present a new mathematical model able to predict the shear strength of S690-CWG with almost zero mean square error. The predicted results via the new equation agree well with those via the experimental tests, FE analysis and NN predicted data. Moreover, the comparative results show that the currently proposed equation gives an accurate or even exact shear strength of S690-CWGs than thus via the existing equations in the literature. Finally, an extensive parametric study has been established to investigate the influence of the CWGs’ geometrical perimeters on the shear strength of S690-CWGs.

Elastic Lateral‐Torsional Buckling of Girders with Corrugated Web: Equivalent Section Properties Approach

AbstractOne of the benefits of using corrugated web girders is the increase of lateral‐torsional buckling resistance. Different approaches have been presented to obtain the value of the critical moment as a function of the cross‐section geometry. Previous research works consider that the increase in buckling resistance must be accredited to a higher warping constant. The paper presents a systematic finite element numerical analysis of girders with different corrugated web shapes. Bending with respect to the weak axis shows that corrugated web implies higher moment of inertia. Torsion analysis results clearly demonstrate that the increase of torsion resistance is mainly due to higher torsional constant. The paper compares the elastic critical moment values obtained by using finite element elastic buckling analysis with the values provided by theoretical expressions introducing equivalent section properties. Results show that the equivalent section properties approach provides values very close to those obtained using finite elements. Finally, the paper presents closed form expressions to directly compute approximate equivalent section properties of any girder with corrugated web, which compare very satisfactory with those values obtained with finite element buckling analysis.

Calculation of the Elastic Maximum Transverse Bending Moment of Trapezoidal Corrugated Web Girder

Trapezoidal corrugated web girder (TCWG) is widely used in many fields. The elastic transverse bending moment which exists in the flange influences the mechanical properties of TCWG. For the simply supported TCWG, the equivalent load method is proposed in this paper. And the transverse bending moment calculation model is established. The calculation formula of the elastic maximum transverse bending moment under the most unfavorable geometrical situation is deduced. The formula is consistent with the existing literature. ANSYS finite element method is used to calculate the elastic transverse bending moment of the flange. The calculation results of formula are in good agreement with the finite element analysis. The existence of transverse bending moment is verified by the experimental data. The physical significance of the transverse bending moment as the integral bearing performance index of the TCWG is revealed in this paper. This paper provides a reference for further analysis of transverse bending moment of simply supported TCWG.

Shear mechanism and design of small-scale tubular flange corrugated web girders

This paper explores numerically the shear behaviour and web strength of a new type of corrugated web girders (CWGs) consisting of an upper tubular flange, a corrugated web and a lower flat plate flange. The current finite element (FE) models, simulate by ABAQUS software, are validated using the results of three new small-scale experimentally tested girders that have been recently published by the authors. Three main points are studied in this paper, namely the propagation of the plastic shear hinges (PSHs), the effect of the corrugation wavelength and the development of a new elastic design model for the girders. First, the girders are simulated to unveil their shear failure mechanism, focusing on the propagation of the plastic shear hinges (PSHs) that characterise the shear failure of conventional flat-webbed girders. Through comparisons between the tubular flange CWG and the corresponding CWG with flat plate flanges (called hereafter as the conventional CWG), it is found that PSHs occur in the lower flange of former girder at the ultimate load whatever the type of the shear buckling is, while the later does not show PSHs for cases failing by local or interactive buckling. The effect of the wavelength of the corrugation of the tubular flange CWG is secondly analysed and the results show that as the corrugation wavelength decreases, the shear capacity increases with the local shear buckling or interactive shear buckling, but this rule is not suitable for the global shear buckling mode. Finally the shear ratio of the tube to that of the entire cross-section is derived and the shear strength equation of the tubular flange CWG is provided and verified through comparisons with test results.

A new shear strength model for steel corrugated web girders

Steel corrugated web girders have three shear failure modes: local, global, and interaction shear buckling. Despite several research studies, only EN1993-1-5 provisions have a design manual for such beams. However, this code does not consider the interaction buckling mode in design equations, while many researchers have emphasized the importance of this instability aspect. In this paper, the EN design manual is improved by considering interaction shear buckling mode, and a new model for the shear strength design of these girders is developed. The accuracy of the proposed model is verified by comparing it with the previously published models and available experimental test data in the literature. An extensive statistical and finite element analysis (FEA) is conducted to evaluate the model for various geometry and material specifications. Results demonstrate that the proposed model is more reliable than those previously reported. The effects of corrugation geometry on the shear strength of these beams are discussed in detail, and a logical geometry range is specified. An equation is also presented for corrugation specifications to achieve the maximum shear capacity. Furthermore, some limitations are defined for the corrugation angle and longitudinal to inclined fold width ratio to reduce the beam weight and reach the optimum design. Based on the recommendations from this research, the corrugation geometry of some existing bridges is modified, and their shear capacity and weight per unit length are compared with the original corrugations using FEA. Results show the effectiveness of the proposed limitations and equation for corrugation geometry.