This paper examines the seismic behavior of steel tubular rocking bridge piers and proposes preliminary design recommendations to improve seismic stability. A two-span single-column prototype bridge is selected and designed. A continuum finite element model of the base rocking steel tubular bridge pier is developed, and the seismic performance is evaluated under multi-axis loading conditions. Post-tensioned rocking steel tubular bridge piers covering different cross-sectional classes are subjected to unidirectional and bidirectional lateral loading with different initial axial load ratios (ALR). The results obtained from the parametric continuum finite element simulations suggest that the column diameter-to-thickness ratio and the initial ALR are the two key parameters that significantly influence the stability of rocking columns. Seismic performance is found to be less sensitive to the base plate dimension of the bridge piers considered in the parametric study. Parametric continuum finite element simulation results demonstrate that rocking steel piers lose self-centering response and experience bulging in the tube wall under high initial ALRs when subjected to bidirectional cyclic loading. Axial shortening of steel tubes is also observed due to local bulging close to the rocking interface. The residual drift ratio of the proposed rocking steel tubular bridge pier remains below 0.5% for Class 1 and Class 2 steel sections under bidirectional cyclic loading, and is found to be reversible if the steel tube buckling can be avoided. This study suggests that the current slenderness limit in CSA S6 design provision needs to be revised when the ALR exceeds 15% to achieve a robust and stable self-centering response under multi-axis loading. Finally, the rocking steel tubular bridge pier designed in this study exhibits enhanced seismic performance, mitigating residual deformations while confining most of the hysteretic energy to the energy dissipaters.

This paper provides a detailed overview of an extensive parametric analysis involving more than 26,000 3D continuum finite element (FE) simulations of posttensioned base rocking steel bridge pier subjected to lateral cyclic loading. The FE model components included a circular tube, tendon, and foundation and base plates. Parameters such as the diameter-to-thickness ratio of tube, height-to-diameter ratio of tube, tendon-to-tube area ratio, prestressing ratio, axial force ratio due to dead load, and base plate thickness and extension were varied. The study measured response quantities such as residual drift, column shortening, and accumulated energy dissipation. It also assessed the impact of successive earthquakes through additional metrics of stiffness and strength degradations. The study was conducted in two primary phases, employing a displacement-based lateral cyclic loading protocol developed to simulate different types of earthquakes. Phase I comprised more than 18,000 static cyclic analyses of the 3D continuum FE model, whereas Phase II combined a 2D macro model (to establish rocking-induced axial force amplification) with a further 8,748 static continuum simulations that incorporated this variable axial load. Findings revealed that the residual drift, ratio of column shortening to height, and response degradations are closely associated with the occurrence of local buckling. The height-to-diameter ratio of tube and base plate dimensions had minimal impacts on these measures. The study confirmed that local buckling could be effectively curtailed by controlling the diameter-to-thickness and axial force ratios. Moreover, it was found that rocking steel piers with initial axial force ratios exceeding 20% had a higher susceptibility for local buckling.

To account for the possible interaction between local and global buckling in hot-rolled channel section members under compression, current design standards employ the effective width method embedded within the member buckling curves. This approach requires complex calculations, lacks consistency as effective widths calculations have been shown to be unconservative in many cases. Therefore, this paper aims to provide a simple and consistent design solution to assess the local/global buckling interaction using the Overall Interaction Concept (O.I.C.). This method introduces a local/global interaction factor derived from numerical results obtained through experimentally validated finite element models. Compared to the Design Standard for steel structures in Canada, the Specification for steel structures in the U.S. and the Eurocode 3 Design of steel structures in European union, the O.I.C.-based design proposal provides more accurate resistance predictions for hot-rolled channel sections members. Additionally, statistical analyses based on EN 1990 guidelines confirm that the method satisfies reliability requirements for structural design.

Frames with Intentionally Eccentric Braces (FIEBs) are steel frames that employ Braces with Intentional Eccentricity (BIEs): bracing members which, although connected at their ends to the beam-column joints, have their longitudinal axis offset to the frame diagonal. The ability to adjust the elastic and post-elastic stiffness of BIEs provides the designer with improved control over the response of the structure to different levels of seismic demand and contributes to reducing incidental overstrength and, thus, the capacity-based design forces for the non-dissipative components. Moreover, while the maximum height of CBFs in high-seismic hazard regions is limited by most design codes because of their susceptibility to global instability, the post-elastic stiffness and partial self-centring capacity of BIEs could presumably be harnessed to counteract P-Delta effects and guarantee stability of FIEBs under earthquake loading in high-rise buildings. In this study, the response to design-and service-level earthquake loading of FIEBs up to 40 storeys tall with different arrangements of square Hollow Structural Section (HSS) BIEs and W shape beams and columns is analyzed numerically through Non-Linear Response-History Analysis (NLRHA). The model buildings were designed following a procedure derived from the Direct Displacement-Based Design (DDBD) method, tailored to accommodate the particularities of BIEs, to prevent damage from frequent earthquakes and wind, and to ensure global stability at the displacements associated with design-level earthquake demands. In addition to evaluating the suitability of FIEBs as the Seismic Force-Resisting System (SFRS) of high-rise buildings, the study focuses on the demands on columns to determine whether the proposed design procedure succeeds in producing an adequate response of these members considering their involvement in distributing the drift demands over the height of the building.

To address the various failure modes of built-up members, current design standards typically impose limitations on the slenderness ratios of the individual components. This approach avoids direct assessment of interaction between failure modes, but it primarily aims to prevent buckling of the individual components. As a result, it often leads to overly conservative and non-economical designs. More efficient solutions can be achieved by relaxing these limitations and instead evaluating the ultimate resistance of built-up members through the interaction of their failure modes. This paper presents a numerical investigation into the compressive resistance of battened built-up members using interaction factors derived from the Overall Interaction Concept (OIC). Detailed shell finite element models were developed in Abaqus, accounting for material, geometric, and contact non-linearities. These models were validated against experimental data on battened built-up members under compression, including both face-toface ([]) and back-to-back (] [) hot-rolled channel sections. Numerical parametric studies were then conducted to examine the influence of key parameters, such as built-up member slenderness, component slenderness, separation ratio, and member configuration. The proposed OIC-based design approach was evaluated against results from the validated finite element models and subsequently compared with existing provisions in CSA S16 (Canada), AISC 360 & AASHTO (U.S.), and Eurocode 3 (European Union). The comparisons showed that the OICbased method provides more accurate, continuous and consistent predictions of the ultimate resistance of hot-rolled channel built-up members. These findings were further supported by statistical analyses performed in accordance with EN 1990 guidelines.

This paper investigates the flexural buckling resistance of laced built-up steel columns subjected to compressive loading. These columns are quite sensitive to flexural buckling out of the plane of the lacing system, owing to a significant distance between the main chords, introduced by the built-up configuration. A companion study [1] focused on the in-plane buckling of laced built-up columns, where global buckling of the chords between lacing connectors was shown to significantly reduce the load-carrying capacity. In contrast, this paper focuses on members that buckle out of the plane of the lacing systems. Two critical phenomena, often overlooked in current design codes, are examined: (i) the influence of shear deformations resulting from the global buckling of chords between connectors, and (ii) the effect of local buckling on the overall member behaviour. A finite element model was developed to accurately predict the resistance of laced built-up columns, and its accuracy was validated through comparison with 23 available experimental data. Extensive parametric studies were conducted to evaluate the impact of geometric variations, sectional arrangements and member slenderness on the resistance. The numerical results were used to assess the merits of a design method for laced built-up columns that exhibit out-of-plane buckling of the lacing system, based on the Overall Interaction Concept (O.I.C.). This O.I.C.-based approach provides more accurate, consistent, and conservative strength predictions compared to the Canadian, Eurocode 3, and American standards. Its reliability is further supported by statistical analyses in accordance with EN 1990 and AISC-LRFD design provisions.

This paper investigates the ultimate strength of laced built-up columns that buckle in the plane of the lacing system, where shear deformations significantly reduce the load-carrying capacity. These members are influenced by Local/Global/Built-up (L/G/B) buckling phenomena and their interactions. The built-up section consists of two C-shaped chords connected by double "X" flat lacing bars. Three main buckling modes are examined through detailed numerical analyses: (i) Local buckling of the cross-section, (ii) Global buckling of individual chords between connectors, (iii) Built-up buckling of the overall member and (iv) coupling/interactions between these modes. For members with slender elements, local buckling and its interaction with other modes are not adequately captured by current design codes, resulting in unconservative strength predictions. Similar issues are observed for global buckling of the chord. To address these limitations, this study extends the existing Overall Interaction Concept (O.I.C.), which was originally developed for Local/Global interactions, to include more complex Local/Global/Built-up interaction behavior. The extended O.I.C.-based approach demonstrates a strong ability to capture these complex interaction effects. Its accuracy and consistency are confirmed through comparisons with numerical results from validated shell finite element models. The proposed method provides more accurate, consistent, and safer strength predictions than the recommendations provided by Eurocode 3 and the American Standards for both tip-to-tip and back-to-back built-up sections. Its reliability is also supported by statistical analyses in accordance with EN 1990 guidelines.

This paper investigates the compressive resistance of hot-rolled built-up steel columns, including battened and laced configurations composed of tip-to-tip “[]” or back-to-back “] [” C-shaped channels connected by batten plates or lacing systems. These members are commonly used in largescale structures, such as truss bridges, where standard rolled sections provide insufficient strength and built-up solutions are required. In optimized configurations, the spacing between channels is often selected so that the minor-axis flexural rigidity approaches that of the major axis. As a result, flexural buckling about both axes may occur with similar resistance levels, leading to a reduction in the critical load due to coupled instabilities. Major design standards such as Eurocode 3 and AISC specifications neglect this interaction by requiring only the minimum of the major- and minor-axis flexural resistances, which leads to unconservative predictions. To address this limitation, advanced non-linear shell finite element (FE) models were developed; the models capture material yielding, local cross-sectional buckling, global buckling of individual chords, overall built-up member instability (both in-plane and out-of-plane flexural buckling modes), including their interactions. Model accuracy was verified against 23 experimental tests from five independent test programs, showing excellent agreement across a wide range of geometries. The validated FE models were used to conduct extensive parametric studies varying the channel dimensions, material properties, built-up spacing, overall configuration and member length. The results demonstrate that (i) flexural resistance erosion due to biaxial interaction can exceed 10

Existing design provisions for hot-rolled built-up steel members typically impose limits on the slenderness of individual components to avoid local and global buckling. Although conservative, this simplified approach does not fully account for the coupled interaction between local, global, and built-up buckling modes, which can lead to uneconomical designs or, in some slender cases, unsafe predictions. This paper presents an extensive numerical study on the ultimate resistance of battened and laced built-up members made of hot-rolled C-shaped channels arranged in face-to-face or back-to-back configurations and connected using batten plates or lacing systems. Nonlinear shell finite element models developed in Abaqus, incorporating both material and geometric nonlinearities, were validated against experimental results. These models successfully reproduce key failure mechanisms, including local cross-sectional buckling, global chord buckling, overall built-up buckling, in-plane flexural instability, and their mutual interactions. A parametric investigation was conducted to evaluate the effects of member slenderness, component slenderness, spacing ratio, section arrangement, and configuration on the ultimate strength. The extended Overall Interaction Concept (O.I.C.) was applied to capture interaction effects through locally calibrated interaction factors derived from numerical analyses. The proposed O.I.C.-based formulation provides smooth, consistent, and safe resistance predictions, addressing the limitations of current design standards (AISC 360, AASHTO, and Eurocode 3). The results confirm that the extended O.I.C. framework effectively represents complex interaction phenomena in slender built-up members, including both in-plane and out-of-plane buckling behavior, offering a more reliable and economical design approach for hot-rolled channel built-up sections.

Current design standards for built-up steel members often overlook buckling effects, particularly when 2nd order shear forces in the lacing are substantial. This oversight can lead to overestimated member capacities and inaccurate force predictions. This study explores various nonlinear finite element (FE) models of laced built-up members fabricated from pairs of hot rolled C shaped sections connected by either double (X) or single (diagonal) flat lacing bars. It further investigates the influence of member properties and lacing configurations on the overall stability of the lacing system, explicitly considering axial forces both in compression and tension acting on the lacing elements. The developed FE models were carefully developed and rigorously validated against existing experimental data. A series of parametric studies was performed, and the numerical results were used to evaluate a newly proposed shear force design formula for laced built-up members with both double and single lacing systems. The assessment demonstrates that the proposed formulas provide more adaptable, accurate, and reliable predictions compared to those specified in Eurocode 3, Australian, and American design standards, and are also simpler than the current design rules.

This paper presents full-scale quasi-static testing of four two-tiered steel special concentrically braced frames performed to examine the seismic response of steel multitiered concentrically braced frames and improve their design requirements. Three of these specimens are designed in accordance with the 2010 AISC Seismic Provisions and the fourth specimen using the 2022 AISC Seismic Provisions. The loading protocols were obtained from numerical nonlinear dynamic analysis using a high-fidelity structural model of the specimens. The experimental results confirm nonuniform distribution of lateral deformation in braced frames designed in accordance with the 2010 provisions, which led to brace low-cycle fatigue fracture and flexure yielding in the columns. The seismic performance of the frame designed to 2022 provisions is significantly improved by more evenly distributed lateral frame deformation between tiers. Additionally, the seismic stability of columns was found to be heavily influenced by the column base condition. The results of the tests were finally used to propose improvements to the seismic design of steel multitiered special concentrically braced frames, with emphasis on column in-plane and out-of-plane bending demands taking into account column base conditions.

This article assesses the novel seismic stability provisions proposed for the Commentary of the Canadian Steel Design Standard CSA S16:24 to enhance the seismic stability performance of steel buildings and replace the classic strength amplification approach. They mitigate inelastic drift concentrations over the building height and reduce residual drifts. They also allow for the relaxation of existing stringent height limitations. The provisions stipulate that the seismic force-resisting system is required to develop a specified minimum positive post-elastic lateral storey shear stiffness and maintain this stiffness for a storey drift of at least 2.5

An innovative steel braced frame system is introduced that is designed and detailed to exhibit an elastic self-centring hysteretic response and achieve damagefree seismic response for low-rise building structures. The system is implemented in the first storey of buildings so that all seismic-induced deformations intentionally develop in that storey to obtain a seismic response similar to that offered by base isolation systems. The proposed system is first described together with a design approach that is based on the single-mode analysis method widely adopted for the design of base isolation systems. The system is applied for two- to three-storey office buildings located in the high seismicity region of Vancouver, British Columbia, Canada, where the seismic hazard is contributed by shallow crustal, deep in-slab, and interface subduction earthquakes. Nonlinear response history analysis is performed under site representative ground motion records to verify the seismic performance of the proposed system. The study shows that the system can exhibit enhanced seismic performance in terms of peak lateral displacements and peak horizontal floor and roof accelerations, with no structural damage nor residual deformations. The results also suggest that peak lateral displacements can be reliably predicted using the simple single-mode method for base isolation systems.

Concrete-filled coupled composite plate shear walls (also known as as SpeedCore walls) are gaining acceptance for construction in seismic region throughout North America. Design provisions for this lateral load-resisting system have already been added to ASCE 7-22 and to the American Institute of Steel Construction Seismic Design Provisions. Adequacy of the seismic design parameters used for this structural purpose has been validated in the USA using the FEMA P695 methodology. An interest was expressed by the practicing engineering community to use these walls in Canada, which requires demonstration of satisfactory seismic performance within the Canadian context. As such, new analyses are needed using Canadian-specific sets of ground motions to confirm the adequacy of the seismic design parameters proposed for implementation of these composite walls in the National Building Code of Canada. This paper presents the results of these analyses, showing that the proposed seismic performance factors are appropriate for this structural system in Canada.

Recent decades have seen increased interest in using the controlled rocking concept in seismic resisting systems. Unlike conventional systems, where lateral deformation of a member is achieved through the formation of plastic hinges in critical regions, in the rocking systems this is achieved through a gap opening mechanism. Due to gravity load and/or post-tensioning forces, the rocking systems exhibit a self-centering behavior. Conducting a continuum finite element analysis to investigate the seismic response of such a system is quite expensive in terms of computational resources. On the other hand, a simplified macro model using two springs to simulate the gap opening/closing mechanism cannot accurately predict the dynamic response of the system. This study utilizes a multiple-spring model to simulate the nonlinear seismic response of circular tubular steel piers. An efficient optimization procedure based on a genetic algorithm is developed to calibrate the parameters of the springs. The results of continuum finite element analyses are compared with those obtained from the multi-spring model to verify the accuracy of the model. The proposed method is shown to be advantageous for accurately simulating the seismic response of a bridge model subjected to multi-directional ground motions, particularly the hysteretic force-displacement relationship, and dynamic response time history.

Controlled-rocking piers have gained popularity over the last few decades to achieve enhanced seismic performance for bridge structures. Past research on this system has focused on concrete rocking bridge piers. Recently, rocking bridge piers made from tubular steel sections have been proposed as a possible cost-effective alternative to concrete piers. A steel rocking bridge pier comprises a circular steel tube with welded circular plates at the top and bottom ends, post-tensioned tendons, and energy dissipaters at the rocking interface(s). During a seismic event, lateral displacement of the bridge superstructure is accommodated by means of gap opening and closing at the rocking interfaces located at the top and bottom ends of the columns. Upon column rocking, the gravity load is no longer evenly distributed over the column cross-section, which induces stress concentration and flexural demand on the column that can detrimentally affect its compressive resistance. This article presents a numerical investigation using three-dimensional continuum finite element analysis that was performed to evaluate the effect of column rocking on the compressive resistance of tubular steel bridge piers. The influence of key parameters is examined, including the column diameter-to-thickness ratio, the thickness and overhang dimension of the end plates, the axial load ratio, and the tilt angle of the column. For the range of values considered for those parameters, the study shows that the loss in compressive resistance compared to a vertical column can vary from 13 to 58

This study describes a preliminary evaluation of the compressive resistance of built-up members used in steel trusses of an old long-span bridge. This study is part of the research and development programs on the deconstruction of the original Champlain bridge initiated by Jacques Cartier and Champlain Bridges Inc. (JCCBI). Finite element analysis was performed on 14 built-up truss member specimens to be extracted from the Champlain bridge to determine their compressive behaviour and ultimate strength under compression loading. The examined members are made of two face-to-face channels, or four angles connected by batten plates. The analyses accounted for material and geometric nonlinearities. Local and global geometric imperfections were also considered; however, residual stresses were not incorporated in this preliminary exploratory investigation. All members were assumed to be pinned at their ends to reflect the conditions that will be imposed in the planned experimental program. The compressive behaviour and ultimate capacities from the numerical simulations are compared with the predictions from the equations for built-up members that are provided in the 2020 AASHTO LRFD bridge Design Specifications in the U.S. The comparison shows a good correlation for most of the members examined. In the case of built-up members with slender elements, significant differences were observed between the numerical simulations and the code predictions, which is attributed to the fact that local buckling and its interaction with other buckling modes are not well addressed in current code provisions for this type of members.

A full-scale, two-tiered steel buckling-restrained braced frame (BRBF) was tested to evaluate experimentally the seismic behavior of steel multitiered BRBFs, namely, column stability response, column seismic demands, and tier deformations under a loading protocol representing earthquake ground motions. The test specimen consisted of diagonal braces oriented in opposing directions in the two adjacent tiers to create the most critical multitier response. The test frame was designed in accordance with the 2010 AISC Seismic Provisions as a lateral load-resisting system of a single-story building. The frame was subjected to a three-phase loading protocol consisting of lateral displacement time histories corresponding to a far-field ground motion record and a near-field ground motion record applied sequentially achieving total frame drifts in excess of 3.5%, followed by a final monotonic lateral displacement corresponding to 4.5% story drift. The test frame exhibited a stable response despite a non-uniform distribution of frame inelastic deformation between the tiers, which induced significant in-plane bending moments in the columns. Flexural bending, combined with a large axial compression force, led to partial yielding in the columns. Large deformation demands were also observed in the BRB yielding in tension and attracting the majority of frame lateral deformation. On the basis of test results, a displacement-based analysis approach was proposed to relate column in-plane bending and flexural stiffness to relative inelastic tier deformations.

Light rail transit (LRT) is a popular mode of transportation in modern metropolitan areas. In LRT systems, trains run on tracks over elevated guideways, streets, or combinations of both. The passengers inside the train feel vibrations due to the vibration of the train, tracks, and bridge while the train is running on the bridge/elevated guideway. In order to determine passenger comfort, vibration analysis is often required if a fundamental vertical flexural frequency of the bridge is less than 3.0–4.0 Hz (usually specified by the owner). Passenger comfort increases with decreasing vertical acceleration inside the train and vice versa. In accordance with Eurocode EN 1990:2002, Table A2.9, recommended levels of comfort (vertical accelerations) are usually followed. These levels of comfort and associated limiting values may be further defined by the owner for the individual project. Per Eurocode, vertical acceleration less than 1.0 m/s2 is very good, and more than 2.0 m/s2 is unacceptable. The vertical acceleration of the train is a function of vehicle speed, mass of the coach and bridge, and stiffness and damping of the primary and secondary springs of the coach, tracks, bridge, and soil. Therefore, train–track–bridge–soil interaction (TTBSI) analysis is required to determine the vertical acceleration of the train in other words passenger comfort. In this parametric study, a two-span LRT bridge supported on rocking pier and isolated abutments is chosen to demonstrate these interactions; however, the TTBSI analysis is applicable for any conventional bridges. This paper presents train–track–bridge–soil interaction analysis of a bridge. This study is intended to be a reference for bridge designers and owners to provide a step-by-step procedure for TTBSI analyses.

This brief technical note compares the adjusted collapsed margin ratios for concrete-filled coupled composite plate steel walls, as obtained from the FEMA P695 methodology, separately considering only subduction zone earthquakes and only shallow earthquakes. For shallow earthquakes, collapse margin ratios were similar to those obtained in prior studies, but they were substantially smaller for the set of subduction earthquakes. While both sets of collapse margin ratios were considered to provide satisfactory seismic performance, this study provides insights into the impact of considering subduction earthquakes in FEMA P695 studies and, by inference, on expected collapse margin ratio for subduction earthquakes.