Current Design Specifications Research Articles

Lateral-Torsional Buckling Modification Factors in Steel I-Shaped Members: Recommendations Using Energy-Based Formulations

Lateral torsional buckling (LTB) is of concern in long-span flexural members, particularly in the negative flexure regions of continuous-span, steel I-shaped members and during construction. While the elastic critical LTB capacity of a simply supported I-shaped member subjected to uniform moment has a closed-form solution, most LTB modification factors for beams subjected to moment gradients in the literature are empirical and work well only for specific loading and boundary conditions. This paper investigates the suitability of the different LTB modification factors in literature and design specifications for various loading and boundary conditions, accomplished via comparisons with analytical solutions using the Rayleigh-Ritz method and numerical solutions from finite element analyses. The analytical LTB modification factors are derived for doubly symmetric I-shaped members with different combinations of ideal flexural and torsional boundary conditions (simply supported and fixed) and subjected to different loading scenarios. The validity of the LTB modification factors determined using the Rayleigh-Ritz method and other formulae in the literature are also assessed for realistic intermediate restraint conditions, which are neither fully pinned nor fixed, by examining laterally continuous beams. Demonstrating that current design specifications for elastic critical LTB modifications are overly conservative

Member capacity of cold-rolled aluminium alloy channel columns – Part II: Numerical investigation and design

The paper first presents the development of detailed finite element (FE) models for investigating the member capacity of cold-rolled aluminium alloy 5052-36 channel columns. The numerical non-linear FE models are developed using the commercial FE software package ABAQUS to simulate laboratory experiments and calibrated against the test results. The experimental program was performed by the authors at the University of Sydney and the detailed test results are fully described in a companion paper. The calibrated numerical FE models with actual mechanical properties and measured geometric imperfections in analyses accurately predict the experimental results and behaviours, including flexural and flexural-torsional buckling as well as local-global interaction buckling failure modes. A parametric study is subsequently performed to extend the data range by varying cross-section dimensions and member lengths. The effects of loading eccentricity positions and initial geometric imperfections are also considered in the parametric study. The experimental and numerical results are compared with design strength predictions from current Australian/New Zealand, American and European specifications for aluminium structures in the companion paper. In this paper, the Direct Strength Method (DSM) for the design of compression members as per the Australian/New Zealand standard AS/NZS 4600 for cold-formed steel structures is adopted for comparison. The DSM design rules for cold-formed steel compression members are found to provide more accurate predictions than those of current specifications for aluminium structures and therefore used to propose improved design equations for cold-rolled aluminium alloy columns. Finally, a reliability analysis is performed to evaluate the safety level of current design specifications and the proposed design rules.

Correction of Plane Strain Analyses for Corrugated Metal Culverts Subjected to Patch Loads

Today, culverts are often analyzed and designed using plane strain finite element analyses in which a transverse slice of the structure is simulated and assumed equal to any other slice. Although this works well for soil loads, in reality live loads are discrete pressure loads from tires, and the out-of-plane effects can be significant, especially when cover depths are relatively low. While current design specifications define minimum cover that precludes significant localized pressure effects on culverts, many culverts are currently in service that were constructed under very shallow cover depths. In this study, analyses of corrugated metal culverts under truck load were carried out using two-dimensional (2D) (plane strain) and three-dimensional (3D) finite element analyses to assess the difference between structural responses predicted by these two approaches. Thirty-six culvert models with different shapes, spans, and cover depths were created using both 2D and 3D meshes. A significant difference was found between the results of these two analysis methods. Specifically, the thrust from the 3D models under shallow cover can be as much as three times the thrust results from the 2D model, which is unconservative from a safety standpoint. An innovative explanation was provided to explicate the differences. Finally, to address the issue, a reduction ratio method was developed to correct the 2D results to match the corresponding 3D results so that the relatively simple plane strain approach can be used.

Lifetime seismic fragility analysis of long-span spatial structures considering the wind-induced fatigue effect

Long-span spatial structures are susceptible to cumulative fatigue damage over their lifespan due to prolonged exposure to wind loads. The degradation in material properties resulting from fatigue can impact the structure's performance to resist earthquakes. However, previous studies and current design specifications do not address the issue of wind-induced fatigue in long-span spatial structures, making it difficult to evaluate the multihazard risk of the facilities under the combined action of fatigue and earthquakes. In this study, an assessment framework for the lifetime multihazard fragility of long-span spatial structures subjected to fatigue and earthquakes is developed to address this issue. The innovation of the proposed wind-induced fatigue analysis is that the influence of wind direction can be considered. Multihazard fragility surfaces are established with a mixed exponential model to assess the seismic fragility of the structure with different service times. The proposed method is applied to the seismic analysis of a typical single-layer Kiewitt-8 reticulated dome (SK8RD) to verify its feasibility. The results demonstrate that after 47 years of service, the ultimate bearing capacity of SK8RD decreases by 45.5% due to the wind-induced fatigue, while its collapse probability increases by 25.3% under the seismic action. Neglecting wind direction randomness and focusing solely on a single direction can lead to an overestimation of wind fatigue damage by more than twofold. Utilizing the probabilistic multihazard demand model based on the mixed exponential function enhances the regression accuracy by 12.9%, facilitating a more precise assessment of multihazard fragility for the SK8RD subjected to seismic and long-term wind fatigue. The proposed framework offers a valuable tool for evaluating multihazard risk considering the wind-induced fatigue for in-service long-span spatial structures.

Shear force distribution mechanism of perfobond leiste connectors in joint between corrugated steel web and concrete top slab

Compared to composite bridges with flat steel webs (FSWs), the corrugation shape and significant shear deformation of the steel web in composite bridges with corrugated steel webs (CSWs) will influence the distribution and magnitude of the shear force of connectors in the joint between the steel web and concrete slab. However, these effects have not been considered in current design specifications, which may lead to unsafe designs. This paper investigates the shear force distribution mechanism of perfobond leiste (PBL) connectors in the joint between the CSW and concrete top slab in composite bridges with CSWs. The theoretical solution for the shear force of the joint per unit length is firstly derived based on the elastic bending theory considering the shear deformation of the CSW. Then, finite element simulations using hybrid models of solid and spring elements are conducted to further investigate the shear force distribution of PBL connectors and influencing parameters. The results show that the shear deformation of the CSW has a negligible effect on the shear force of the joint per unit length. In contrast to composite bridges with FSWs, the CSW induces sinusoidal variations in the shear force of PBL connectors, which leads to an increase in the shear force of partial PBL connectors. The amplification factor for the shear force increases with the wavelength of the CSW and the shear stiffness of the PBL connector, while it decreases with the increasing dimensions of the steel upper flange, perforated ribs, and hole spacing. Finally, a calculation formula and corresponding procedure are proposed for predicting the shear force of PBL connectors in the joint between the CSW and concrete top slab for composite bridges with CSWs.

Evaluation of minimum flexural reinforcement for precast prestressed concrete NEXT beam bridges

The minimum flexural reinforcement requirement has been used in the current bridge design specifications to protect the member from brittle failure after the formation of the first flexural cracks. Several variables have been reported to affect this requirement, such as concrete strength, amount of prestressing in the member, and type of cross section. Recently, the Precast/Prestressed Concrete Institute (PCI) developed a new type of beam section (NEXT beam) to accelerate bridge construction and enhance the sustainability of bridges. As a newly developed beam section, no research on the minimum flexural reinforcement has been reported for NEXT beam bridges. This paper aimed to examine the minimum flexural reinforcement requirements in the current AASHTO LRFD Bridge Design Specifications for NEXT beam bridges. A comprehensive parametric study was analytically conducted with various parameters, including bridge section, beam section, concrete strength, and span length. The results from this study showed that the current minimum flexural reinforcement requirements were met for all bridges examined herein; the concrete strength, beam cross section, and span length could affect the levels of safety against brittle failure after first flexural cracks for NEXT beam bridges.

Experimental Study on Field Shrinkage of Deck Panel of Composite Girder Cable-stayed Bridge

In order to study the shrinkage performance of the deck panel of the composite girder cable-stayed bridge, the shrinkage test of the deck panel members of the real bridge was carried out in the field with the background of the Malukou Great Bridge, comparing the difference between the shrinkage values measured in the test and the theoretically calculated values of shrinkage in the various specifications, and finally the shrinkage equations and curves of the deck panel in 180d were fitted based on the test data. The results show that: on 180d, the shrinkage strain calculated by JTG D62-2018, the current design specification used for highway bridges in China, is only 66.30% of the test shrinkage, and the small prediction of bridge deck shrinkage may cause problems in terms of structural cracking; based on the large differences between various specifications for the shrinkage strain of bridge decks, It is recommended to use the actual shrinkage strain measured by the bridge deck shrinkage test as the real shrinkage curve as the data source to accurately assess the deformation and stress state of the bridge deck.

Shear behavior of square ultra-high performance concrete-filled high-strength steel tube members

High-strength steel and ultra-high-performance concrete (UHPC) can increase structural resistance and reduce material consumption efficiently. However, current design specifications do not permit the use of them in concrete-filled steel tube members due to the lack of research. To address it, this paper experimentally investigates the shear behavior of square ultra-high performance concrete-filled high-strength steel tube (referred to as CuFTh hereafter) members. A total of 20 CuFTh specimens were tested, considering the effects of the span-to-depth ratio, width-to-thickness ratio of the steel tube, yield stress of steel, and fiber volume content of UHPC. The test results showed that: (i) the failure mode was governed by the shear span-to-depth ratio (a/H), including shear failure (a/H = 0.2 or 0.5) and combined shear-flexural failure (a/H = 0.8 or 1.0); (ii) the shear strength increased with decreasing shear span-to-depth ratio and the width-to-thickness ratio of the steel tube; (iii) increasing the yield stress of steel and fiber volume content of UHPC improved the shear strength. The applicability of current specifications for estimating the shear strength of square CuFTh members was evaluated. It was shown that CECS 28 (CECS 2012) had the most reasonable estimation.

Overall flexural-shear buckling strength design of built-up radially battened columns

The built-up radially battened columns (RBCs) have a promising prospect in public building engineering due to their aesthetical form and good load-bearing capacity. However, their design methods are not covered in the current design specifications because of their distinctive appearance. This paper aims to present the flexural-shear buckling behavior of built-up RBCs and propose its corresponding strength design recommendations. At first, the finite element model (FEM) of the RBC is established, and a lot of examples are calculated in eigenvalue buckling analysis and elastoplastic analysis by using this FEM. Three kinds of possible first-order buckling modes are observed in the elastic buckling analysis, which are flexural-shear buckling, torsional buckling, and local buckling respectively. Only flexural-shear buckling is involved in this study, and torsional buckling will be investigated in a companion paper. Local buckling (of the chord tube wall) can be prevented by a radius-to-thickness ratio limit. It has been proven that shear deformation plays an essential role in determining the flexural-shear buckling of built-up members, thereby a unit shear angle model is established to study the shear stiffness of RBCs when they buckle overall. Then, the prediction equations for elastic flexural-shear buckling load and its corresponding normalized slenderness ratio are derived. The design curves for the ultimate load-bearing capacity of built-up RBCs are also proposed based on the numerous results from elastoplastic FEMs by changing normalized slenderness ratios. Furthermore, the compound buckling of RBCs is considered by employing a FEM that exerted the individual chord initial imperfection (FEM-c), and accordingly, a strength reduction factor caused by compound buckling is proposed. Finally, the design methods for the individual chords and radial-shaped battens are studied. The internal forces in chords and batten plates are derived and the analysis of the local buckling of batten plates is conducted. It is recommended that chords should be regarded as a member under combined compression and bending, and batten plates can be guaranteed to not lose their stability before the RBC reaches their ultimate load-bearing capacity by adopting the ‘isostable criterion’. In conclusion, these results provide a method for accurately and conservatively predicting the strength of RBCs when overall flexural or compound buckling occurs, which will expand the application of RBCs in engineering and make our public buildings more pleasing.

Dynamic Factor of Suburban Railway Bridge Considering Random Vibration

The focus of this paper is to examine the dynamic factor of the suburban railway by utilizing the random vibration approach. Breaking through the previous methods of relying on huge amounts of measured data, herein, the dynamic factor essentially results from two major parts: the dynamic effect caused by moving train loads and that generated by track irregularity, which has clear physical significance. As the internal excitation of the vehicle–bridge system, track irregularity has strong randomness. Based on the dimension reduction method, the spatial domain power spectral density (PSD) of the track irregularity is transformed into the time-domain PSD. Therefore, the randomness of the random process is reduced by exploiting the constraint form of a random function, and then, the typical samples of the track irregularity considering randomness are constructed. Using the vehicle–bridge coupled vibration model, the standard deviation of the dynamic factor is evaluated accounting for the random track irregularity and 99.7% guarantee rate. Finally, the impact coefficient of the track irregularity on the bridge is methodically obtained. The sensitivity of the standard deviation of the dynamic factor to vehicle speed and bridge frequency is analyzed. The given solution methodology can fully take into account the randomness of the track irregularity. Thereby, it provides the dynamic factor formulas as a reference for the dynamic performance evaluation of suburban railway bridges and possible revision of current design specifications.

Fatigue strength of the joint of steel cantilevers in composite bridges

AbstractBox girders with steel cantilevers underneath the deck are frequently used in the design of composite steel bridges. Hereby, the welded joints between the main girder and the transverse system have to endure fatigue loads. Current design specifications for this joint, e.g., a tapering in thickness of the top flanges at the same position of a transition radius, are complex to manufacture and provide a higher fatigue resistance than necessary. This article addresses the optimization of this structural detail, which is realized hundreds of times per structure. Several laboratory tests and numerical simulations were carried out regarding the load‐bearing behavior and the fatigue safety of the cantilevers as double‐T‐sections and as box girders. Additionally, 60 fatigue tests were conducted on small‐scale specimen to classify the resulting simplified design variants in detail categories of the nominal stress concept. As a result, two design recommendations are proposed for the joint at the intersecting top flanges. Moreover, the effect of an unplanned axial misalignment on the fatigue strength of the joint at the bottom flange is quantified.

Human-Induced Vibration Analysis and Reduction Design for Super Long Span Pedestrian Arch Bridges with Tuned Mass Dampers

With the increasing demands on span length, aesthetics, and urban landscapes of pedestrian bridges, the fundamental frequency of pedestrian bridges is continuing to decrease, and their vibration and walking comfort issues are becoming increasingly prominent. The pedestrian load model of the pedestrian bridge was introduced here referencing current design specifications, and a spatial finite element model was established to study the dynamic characteristics of the case of a long-span pedestrian arch bridge. The comfort of the bridge under human-induced vibration was analyzed using the time history analysis method. According to the optimal damper parameter expression, the design parameters of the damper were obtained. In addition, the vibration reduction effects of different generalized mass ratios were analyzed, and the damping effects of setting the tuned mass damper (TMD) at different positions were compared. The results indicated that setting the TMD on the bridge can enhance the damping effect, and the transverse vibration can be suppressed by setting TMDs on both the arch ribs and the bridge deck. The research content could provide recommended parameters for the vibration reduction design of long-span pedestrian arch bridges.

Assessment of buckling strength curves in Direct Strength Method for estimating axial strengths of Cold-formed Steel members considering average yield stresses of cross-sections

The Direct Strength Method (DSM) is incorporated in current design specifications for designing Cold-formed Steel (CFS) members under compression. The North American design specification AISI S100 allows taking advantage of the increased material yield stress due to cold-forming in the application of the DSM only for members subjected to (i) local buckling and having slenderness ratios (λl) ≤ 0.776 or (ii) global buckling and having strengths not reduced by local buckling. This study aims to explore whether this limit could be released. First, Karren’s model for predicting the yield stresses of corners in CFS members was modified to improve the performance and extend the application limit. Second, Karren’s expression for estimating the average full-section yield stresses of CFS members was refined. Third, an extensive experimental database established previously by the authors was employed to assess the buckling strength curves in the DSM. Nominal axial strengths of the CFS members in the database were calculated using the average cross-section yield stresses as design parameters, which were then compared with the tested axial strengths. The modified Karren’s model and expression were used to estimate the average cross-section yield stresses of these members. Finally the LRFD resistance factors (ϕc) for the DSM buckling strength curves were calculated for a target reliability index of 2.5, and the results were compared with their counterparts obtained previously, considering the yield stress of virgin material as the design parameter. The results show that the design parameter of average cross-section yield stress was safe to be used with the DSM for estimating the axial strengths of solid CFS members subjected to local or global buckling.

Capacity of piles subject to downdrag: a comparison of North American bridge design codes and observations from a full-scale test pile program

Negative skin friction caused by ground settlement is an important consideration for deep foundations in limit states design. However, there are inconsistencies in the methodology whereby negative skin friction and associated drag force are considered in assessing the geotechnical capacity or geotechnical ultimate limit state (ULS) in various design codes. This includes two current North American bridge design codes, the Canadian Highway Bridge Design Code, and AASHTO LRFD Bridge Design Specifications. A test pile program was developed to observe effects of ground settlement on pile settlement, capacity, and drag force. Two instrumented steel H-piles were driven through a compressible clay layer to a hard end-bearing stratum, subjected to ground settlement by constructing a 1.5 m high embankment, followed by static load testing. A load-transfer model was calibrated from the test pile program observations. Test results and the calibrated model were used to compare geotechnical ULS requirements of the two bridge design codes. It is demonstrated that drag force did not detrimentally impact pile capacity. The results showed that for conditions of the test pile program, assessing the geotechnical ULS can be more conservative when adhering to the current AASHTO LRFD Bridge Design Specifications than the Canadian Highway Bridge Design Code.

More accurate design equations for cold-formed steel members subjected to combined axial compressive load and bending

Cold-formed steel (CFS) load-bearing members in multi-storey frame systems are subjected to combined actions sourced from gravity and lateral loads. However, limited information is available on the complex interaction behaviour of such elements affected by different buckling modes. This study aims to provide a better understanding of the behaviour and design of CFS sections under various combinations of compression and bending about both major- and minor-axes. Experimentally validated finite element (FE) models of CFS elements were developed in ABAQUS software, accounting for material nonlinearity and geometric imperfections. The validated models were then used to conduct a parametric study to assess the structural performance and failure modes of over 500 CFS elements with various lengths, thicknesses and cross-sectional dimensions under 19 different load eccentricities. It was demonstrated that the element and web slenderness ratios and the magnitude and direction of eccentricity are the key factors affecting the behaviour of the CFS beam–column elements. The accuracy of current design specifications, including American Iron and Steel Institute (AISI-S100), Australian/New Zealand Standard (AS/NZS-4600) and European standard (Eurocode-3) was then investigated. Subsequently, the results were used to propose a new design interaction equation as a function of element and web slenderness ratios. It was shown that the proposed equation could considerably improve the accuracy of the code strength predictions, especially in the case of medium to high slenderness elements. Finally, a reliability analysis was conducted within the framework of the AISI-S100 to ensure that the proposed design equation provides the required level of safety.

Accuracy of Buckling Strength Curves Using Direct Strength Method in Estimating Axial Strengths of Cold-Formed Steel Members under Compression: Critical Review

Current design specifications for cold-formed steel incorporate the Direct Strength Method (DSM) to design cold-formed steel members under compression. Although the DSM has been used for quite some time, its buckling strength curves have not been experimentally assessed thoroughly. This study attempts to fulfill this objective. First, a thorough literature review was conducted to inspect the buckling strength curves in the DSM, and the issues are summarized in this paper. Second, experimental data associated with compression tests of 453 solid and 228 perforated cold-formed steel columns were collected from the literature. Design parameters (e.g., elastic critical buckling loads) of the columns were then determined and assembled with the experimental results in a database to be used as a source to assess the buckling strength curves in the DSM. Finally, the LRFD resistance factors (ϕc) of the DSM buckling strength curves were determined in accordance with the AISI S100. This paper highlights the level of accuracy of the buckling strength curves in the DSM.

Experimental study of DED-arc additively manufactured steel double-lap shear bolted connections

An experimental study into the structural behaviour of Directed Energy Deposition-arc or wire arc additively manufactured (DED-arc AM and WAAM, respectively) steel double-lap shear bolted connections is presented. The mechanical properties of the material, which had a nominal yield stress of 420 MPa, were first determined by means of tensile coupon tests. Sixty connection specimens of two different nominal thicknesses and two print layer orientations were then tested to failure. The geometry of the test specimens was determined by 3D laser scanning, while the deformation and strain fields were measured during testing using digital image correlation. The observed failure modes included shear-out, net section tension, bearing and end-splitting, while a new hybrid mode of shear-out and net section tension was identified for the first time. The test results were compared against the predictions of current design specifications, namely AISI S100 and AS/NZS 4600 for cold-formed steel and AISC 360 and Eurocode 3 for structural steel, to evaluate their applicability to WAAM elements. Overall, the structural behaviour of the tested specimens followed the anticipated trends, and the predicted resistances determined from the current design specifications were generally reasonable. There were, however, a number of exceptions to this, highlighting the need for new design provisions, together with appropriate safety factors, that are specific to this form of manufacture.

Estimates of Internal Forces in Torsionally Braced Steel I-Girder Bridges Using Deep Neural Networks

The bracing components in steel I-girder bridge systems are essential structural components for the bridges to restrain their rotation due to lateral torsional buckling (LTB). Current design specifications require bracing components to be installed to prevent I-girder sections from unexpectedly twisting due to instability. To estimate the bracing internal forces acting on the bracing elements, we can use approximate design equations that provide considerably conservative design values. Otherwise, it is necessary to conduct a thorough finite element analysis considering initial imperfections to obtain accurate bracing internal forces in the steel I-girder bracing systems. This study aims to provide estimation models based on deep neural network (DNN) algorithms to more accurately estimate the internal forces acting on the bracing element compared with the current design methodology when LTB occurs. This is conducted by constructing structural response data based on the geometrically nonlinear analysis with imperfections to provide accurate bracing internal forces, namely bracing moments (Mbr) and bracing forces (Fbr). To propose prediction models, 16 input and three output variables were selected for training the structural response data. Furthermore, a parametric study on the hyperparameters used in DNN models was analyzed for the number of hidden layers, neurons, and epochs. Based on statistical performance indices (i.e., RMSE, MSE, MAE, and R2), the estimated values using DNN models were evaluated to determine the best prediction models. Finally, DNN models that more accurately estimate internal forces (Mbr, Fbr) in bracing elements, and that provide the best prediction results depending on hyperparameters (numbers of hidden layers, neurons, and epochs), are proposed.

A Deterministic Method for Evaluating Safety Factor of Deep Excavation Stability against Groundwater Inrush Equivalently Considering Soil Uncertainty

In current design specifications for deep excavation, the determination of safety factors against groundwater inrush only considers the self-weight effect of soil mass at the bottom. However, the shear strength and its spatial variability in a cement-solidified bottom layer also plays an important role in safety factor estimation. Based on that, in this study, the strength reduction method was introduced into reliability analysis of deep excavation engineering, and the influence of shear strength and its spatial variability of cement-solidified soil on the stability of deep excavation is studied. Furthermore, a deterministic analysis method that can equivalently consider soil uncertainty is proposed and verified.

The strength design of deeply buried circular corrugated steel arches with considering only soil radial restraining

Buried circular corrugated steel arches (BCCSAs) are often adopted in underground engineering. However, the current design specifications cannot accurately estimate the BCCSA’s load-bearing capacity due to the complicated interaction between the soil and the arch. This paper presents the strength design recommendations for deeply buried circular corrugated steel arches with various rise–span ratios under axial compression and under combined axial compression and bending moment respectively, with meeting a proposed width–thickness ratio limit of the BCCSA for local buckling prevention. At first, a finite element model (FEM) of sinusoidally corrugated steel plate (S-CSP) for analyzing its local plate buckling under axial compression (FEM-l) is established, and this FEM can eliminate other possible buckling modes except the local buckling mode by constraining the out-of-plane displacement at the crest and valley lines in S-CSPs. Through FEM-l, the local buckling behaviors of S-CSPs are studied and the width–thickness ratio limit of S-CSPs under axial compression for local buckling prevention is determined in terms of a design principle that local buckling of plate elements does not occur before fully sectional yielding. Then, a global arch-spring model of BCCSA is established for analyzing its elastic global buckling, with considering the interaction between the soil and arches by simplifying the radial restraint of soil as radial unidirectional springs around the arch. The normalized slenderness of BCCSA in the arch-spring model is obtained from its elastic global buckling load calculated by theoretical derivation with bidirectional spring assumption. Finally, the ultimate load-bearing capacity of BCCSAs is calculated by employing elastoplastic finite element models under axial compression and under combined axial compression and bending moment respectively. Based on extensive numerical results obtained in this study, the conservative strength design methods for BCCSAs are proposed in practical engineering applications.