Evaluation of stability and integrity of a steel truss bridge in a forensic investigation

The studies presented in this Thesis have been developed in the frame of the forensic investigation into the causes of the collapse of the I-35West Bridge (I-35W) in Minneapolis, Minnesota, USA that occurred on August 1 st, 2007. The failure of the I-35W represents a major case-study for the evaluation of stability and integrity of a steel truss bridge. The Thesis has been developed at Columbia University and at the engineering firm Thornton Tomasetti (TT) which was hired by a national law firm, Robins, Kaplan, Miller & Ciresi, to perform a forensic investigation into the cause of the catastrophic collapse. According to the findings of the forensic investigation, the collapse was triggered by the buckling of an element of the main truss bottom chord in the main span close to the pier. The Thesis focused on technical aspects and did not attempt to assign responsibility among the involved parties. In the first part of the thesis, the background and motivation for the forensic investigation are presented together with a description of the I-35W Bridge. The definition of bridge safety and related classifications are given. The concept of structural stability and integrity of steel structures are discussed. The nature of structures and their complexity are considered as well as the methodologies used to study them. An extensive description of the structural decomposition method is presented and detailed for the case study. In this work, using the framework of a multilevel approach, the structural system has been broken down in order to perform a detailed analysis and evaluate the system performances at macro (global) and micro (local) levels. The effect of boundary conditions, thermal loads on the global system and post buckling capacity of the main truss bottom chord built up member on a local level have been studied. First, a 3D finite element model has been developed in SAP2000 using frame elements. This global-level model reproduces the entire bridge based on original drawings, design and construction specifications. The model has been verified by comparing results with the available original design calculations. Member forces and reactions based on the asdesigned conditions with the specified design loads have been confirmed. The model served to investigate the elastic behavior of the bridge and its overall response to various loading and boundary conditions. In particular, from the global model it has been possible to evaluate the static stress condition on the bridge showing how some of the temperature changes and the possible deterioration of the designed supports could affect the demand on the load carrying members. A specific lower chord member was identified as a critical member for temperature loading in particular. Second, a 3D solid element model of the recognized critical load bearing member comprised of a welded built up section with perforated cover plates was built in Abaqus. This local-level model provided information on the post buckling behavior and capacity of the load bearing member. The effects of the perforations and boundary conditions have been outlined. Furthermore, the results have been compared against hand calculations following the provisions of the Code of Standard Practice for Structural Steel Buildings and Bridges (AISC, 2005) for built up members and the Timoshenko plate theory for columns with perforated cover plates

Reliability-Based Progressive Collapse And Redundancy Analysis Of Bridge Systems

Highway bridges like most structural systems are usually designed on a member by member basis and little consideration is provided to the effect of a local failure on system safety. There are concerns that some systems optimized to meet code-specified member design criteria may not provide sufficient levels of structural redundancy to withstand a possible local failure. In fact, a local failure of one structural element may result in the failure of another element creating a chain reaction that might progress throughout the whole structure or a major portion of it leading to a catastrophic collapse. Several recent catastrophic structural collapses have alerted the structural engineering community to the importance of designing structures with sufficient levels of structural redundancy and robustness to make them capable of withstanding local failures and retaining some level of limited functionality. This has led several agencies to develop criteria for evaluating the robustness of structural systems. However, in a departure from LRFD-based code developments, these recently proposed criteria, which are based on deterministic concepts, do not properly account for the random material properties, the variations in the strengths of the members, or the uncertainties associated with modeling the response of structural systems. Furthermore, it is not clear if the existing criteria which were developed for office buildings are applicable to highway bridges subjected to highly stochastic live loads or whether these criteria will lead to similar safety levels for different types of structures. The object of this Dissertation is to propose a methodology to evaluate the redundancy of highway bridge systems and verify their ability to withstand progressive collapse should a local failure take place. In keeping with current code development approaches, the proposed methodology must be calibrated to provide an acceptable and consistent level of reliability for different types of structures accounting for the uncertainties in estimating the bridge behavior and material properties. A first step for achieving the objectives of this study is to define non-subjective reliability-based criteria for evaluating the performance of originally intact bridge systems, those that have been subjected to local damage, and assessing the ability of the system to survive the sudden occurrence of local damage. The development of such reliability-based criteria requires the availability of probabilistic analysis algorithms capable of handling complex structural systems with low probability of failure. The review of existing structural system reliability methods shows that a Markov-Chain simulation known as the Subset Simulation method offers many advantages over other available methods for evaluating the reliability of complex structural systems with high numbers of failure modes and low probabilities of failure. To further improve the existing subset simulation algorithm, a hybrid Markov chain Monte Carlo method referred to as RASS is proposed. The proposed improvements include: a) a more efficient advanced Markov Chain sample generation algorithm; b) a Delayed Rejection process that allows partial local adaptation of the generated candidate samples at each time step of the Markov chain; c) an Adaptive Algorithm that uses the history of the chain to update the variances of the intermediate proposal probability distribution function; d) a Regeneration process to help in reducing the correlation between the generated samples; and e) a componentwise generation of samples is used to reduce the computational effort associated with multivariate input. This study demonstrates that the proposed simulation approach is robust to dimension size and is efficient in computing small probabilities of failure for complex structural systems. In addition, this approach can be used to obtain approximate expressions for the limit state equations for the pertinent failure modes. The applicability of the proposed reliability algorithm in analyzing the system performance of bridge structures and evaluating their levels of redundancy as well as their ability to resist dynamic progressive collapse is demonstrated through several examples for typical I-girder bridges, steel box-girder bridges, and truss systems. Since involved reliability analyses are beyond the day-to-day practice of bridge engineers, this study proposes an approach to develop a deterministic progressive collapse analysis method for bridges. Following current practice in the development of structural design codes, the deterministic analysis and associated criteria are calibrated to provide adequate and consistent levels of structural reliability for different bridge topologies. The validity of the proposed approach for calibrating progressive collapse analysis criteria is illustrated using two different bridge configurations subjected to different local damage scenarios

Alternate Load Paths and Retrofits for Long-span Truss Bridges under Sudden Member Loss and Blast Loads

In current bridge design practices, due to the existence of alternate load paths (ALPs), continued stability and progressive collapse-resistance of long-span bridges following the initialed loss of a critical member can be attributed to “redundancy”. However, “redundancy”, also indicated as the post member failure behavior of long-span bridges is not well understood and is not explicitly considered, especially for long-span truss bridges. As one of the most famous collapse events that took place recently, collapse of the I-35W truss bridge has demonstrated the vulnerabilities of long-span truss bridges, and their societal and economic consequences under the abnormal events, such as sudden loss of a critical member or members and the explosive attacks. These long-span truss bridges that are designed under the provisions of past and current specifications, particularly those in the urban environments, may be incapable of maintaining their structural capacity and integrity under the influence of extreme loadings generated by sudden member loss and the blast loads. Current existing design specifications have none or limited provisions that are related to structural design against the extreme loadings, therefore, their automatic extension to the protective design of long-span truss bridges to the abnormal events may not be guaranteed. This dissertation proposes an integrated framework and performance-based criteria to quantify the load-path redundancy in the form of ALPs and proposes further three-dimensional (3-D) retrofit schemes to enhance the ALPs of long-span truss bridges subjected to sudden loss of a critical member. By taking the I-35W truss bridge as the case study, this dissertation investigates the redundancy or existing ALP capacity of long-span truss bridges before and after the abnormal events such as sudden member loss by two different indicators: demand to capacity ratio (DCR) for linear elastic analysis and strain ratio (SR) for nonlinear dynamic analysis. Based on the possible failure modes and failure scenarios after sudden critical member loss, performance-based retrofit criteria and recommendations for 3-D ALP retrofits are proposed in terms of both DCR and SR metrics. To investigate the complicated behavior of truss members under the coupled actions of axial forces and bending moments, this dissertation proposes a simplified modeling approach to simulate the structural behaviors of truss bridge systems by multiple Hughes-Liu (H-L) beam elements with material model *MAT_Simplified_Johnson_Cook (*MAT_98) in LS-DYNA for each truss member. The effectiveness and accuracy of this simplified modeling approach are validated by several numerical examples that are related to both elastic and nonlinear large-deformation problems. Then, based on a small truss bridge (Aby truss bridge) that is previously designed as fracture critical, an integrated framework to identify critical members by using nonlinear dynamic analysis in LS-DYNA is proposed and validated with the simulation results available in previous literature. Meanwhile, both the implicit model in SAP2000 and the explicit model in LS-DYNA of the I-35W truss bridge are developed and validated by the available shop drawings and FHWA reports. Subsequently, the ALP of long-span truss bridges is numerically studied through the numerical simulations of the I-35W truss bridge before and after sudden member removal (MR) analyses. Moreover, similar to the performance-based seismic retrofit philosophy that is widely utilized in earthquake engineering, a performance-based design (PBD) approach is considered to enhance the redundancy and ALPs of long-span truss bridges. Various ALP retrofit strategies, such as member strengthening and addition of extra members as diagonal or floor trusses are numerically investigated and evaluated. Analysis results indicate that the member strengthening approach only has limited effectiveness in enhancing the ALPs of the long-span truss bridges, whereas retrofitting strategies that help to improve the three-dimensionality of the truss bridge, such as adding diagonal members and floor truss members are more cost-effective in improving the ALP and redundancy of the truss bridge while minimizing the increase in the weight of steel (because of retrofit). Performing the nonlinear dynamic analysis using LS-DYNA in the development of ALP retrofit strategies for enhancing ALP and redundancy of long-span truss bridges is more cost-effective than the linear static analysis using SAP2000. Performance levels in terms of DCR and SR metrics are proposed for the practicing engineering community to use for the retrofits of long-span truss bridges to help them survive from the progressive collapse. Furthermore, to investigate the blast load effects on long-span truss bridges, the above-deck close-in explosions are numerically simulated for the I-35W truss bridge using the *Load_Blast_Enhanced (LBE) formulation in LS-DYNA. Based on several blast loadings simulation examples, the identification of finite element (FE) model-related parameters, i.e., mesh size, material models and properties (i.e., strain rate effect) both for concrete and steel are presented and validated. Then the effectiveness and capability of the modeling using the H-L beam formulation with the shell elements are numerically investigated and validated through several numerical examples. Afterward, by using the validated multiscale modeling method, high-fidelity FE models of the I-35W truss bridge are developed and several comprehensive studies regarding the blast load effects (i.e., the above-deck close-in denotations) on this truss bridge are investigated. Finally, by inputting the calibrated and validated material parameters for the material model *MAT_Concrete_Damage_REL3 (*MAT_72R3) for the UHPC that is available in previous studies, and the effectiveness and capability of UHPC strengthening in improving the blast resistance of the I-35W truss bridge under the blast loads are numerically investigated and validated, and UHPC can be utilized as the retrofit material to strengthen the RC deck system and helps in reducing the damage of truss members for long-span truss bridges

More efficient cold-formed steel elements and bolted connections

Modern society is challenged by economic and environmental issues, requiring engineers to develop more efficient structures. Using cold-formed steel (CFS) frame in construction industry can lead to more sustainable design, since it requires less material to carry the same load compared with other materials. However, the application of CFS structural systems is limited to low story buildings due to the inherent weaknesses of premature buckling behaviour of members and the low ductility of connections. Consequently, current design guidelines of CFS systems are very conservative especially in the case of seismic design. Furthermore, there is no generic optimisation framework for the CFS elements, capable of taking into account both manufacturing/construction constraints and post-buckling behaviour. This study aims to better understand, to predict, and to optimise CFS elements based on their strength and post-buckling behaviour. The optimised elements can be then included in full-structure modelling to develop more efficient CFS structural connections with high ductility and energy dissipation capacity, suitable for multi-story buildings in seismic regions. The geometrical dimensions of manufacturable CFS cross-sections were optimised regarding their maximum compressive and bending strength. All the sections were considered to have a fix coil width and thickness while the optimisation was performed based on effective width method suggested in EC3. The optimised solutions were achieved using Particle Swarm Optimisation (PSO) algorithm. The accuracy of the optimisation procedure was assessed using experimentally validated nonlinear Finite Element (FE) analyses accounting for the effect of imperfections To allow for the development of a new ‘folded-flange’ beam cross-section, the effective width method in EC3 was extended to deal with the presence of multiple distortional buckling modes. Improved strength were achieved for CFS elements by using the proposed optimisation framework. A non-linear shape optimisation method was presented for the optimum design of CFS beam sections based on their post-buckling behaviour. A developed PSO algorithm was linked to the ABAQUS finite element programme for inelastic post-buckling analysis and optimisation. The results also demonstrate that the optimised sections develop larger plastic area, which is particularly important in seismic design of moment-resisting frames. An experimental programme was carried out at the University of Sheffield to investigate the design and optimisation, considering interactive buckling in cold-formed steel channels under compression and bending. Both standard and optimised sections were tested. The specimen imperfections were measured using a specially designed set-up with laser displacement. Material tests were also carried out to determine the tensile properties of the flat plate and of the cold-worked corners. A total of 36 columns with three lengths and 6 back-to-back beams were completed. The column specimens were tested under a concentrically applied load and with pin-ended boundary conditions while the beams were tested in a four-point bending configuration. Based on the tests, numerical models were proposed and calibrated and the proposed optimisation framework was verified. A numerical study on the structural behaviour of CFS bolted beam-to-column connections under cyclic loading was presented. An innovative two node element which can take into account the slippage-bearing effects was proposed and implemented using an ABAQUS user defined subroutine. The connection performance in terms of strength, ductility, energy dissipation capacity and damping coefficient were investigated. The effects of bolt configuration, cross-sectional shapes and thicknesses on the connection performance were therefore examined. It is indicated that the proposed numerical model is robust and computationally efficient to simulate the failure modes and moment-rotation response of CFS bolted moment resisting connections

Hybrid cold-formed steel structural systems for buildings

Cold-formed steel (CFS) shear walls or strap-braced walls are the primary lateral load resisting components in light-weight steel framed (LSF) structures. Despite the increasing demand on the application of CFS systems in mid-rise construction, the relatively low lateral load resistance capacity of these systems has remained one of the major obstacles for further growth, as this low resistance becomes problematic in their use in cyclonic wind regions or highly seismic zones. In this thesis, in order to address this issue, a new Hybrid CFS wall composed of CFS open sections and square hollow sections (SHS) is developed and investigated. The proposed hybrid system is suitable for light-weight steel structures for mid- to high-rise construction, due to its satisfactory lateral load resistance. The thesis presented provides the results of the study which contains experimental and numerical investigation as outlined in the following. In the first stage of this study, a comprehensive literature review was conducted to reveal the existing gaps in the previous studies on CFS structures under lateral loads. In the second stage, a series of full-scale experimental tests were performed on seventeen hybrid CFS wall panels in order to investigate their lateral performance, shear resistance, failure modes and energy absorption. In the third stage of this thesis, a comprehensive study was performed on the theories and applications of the numerical models for analysis of the lateral behaviour of CFS wall systems during the past several decades, and all existing numerical methods for simulating the behaviour of CFS shear walls were accordingly classified. In stage four of this study, proposed hybrid wall panel was further developed, and twenty new wall configurations were evaluated using non-linear finite element analysis, aiming to further investigate the seismic performance of CFS hybrid walls. Finally, in the last stage, a sustainability analysis was performed which could be of interest to all stakeholders including owners, builders and investors, when assessing the potential use of hybrid CFS systems, in particular for mid-rise buildings

Experimental methods for evaluating strain rate dependency of shape memory alloy materials under quasistatic and impulsive loading

Shape memory alloys (SMAs) are innovative materials that have great potential in structural engineering because they can provide significant energy dissipation capacity and introduce considerable re-centering ability to structures. The stress-strain relations of SMAs are dependent on loading rates, and the responses of SMAs under intermediate strain rates are hard to obtain using conventional experimental techniques. This research developed an innovative high-loading-rate tensile testing system to test specimens under intermediate strain rates, bridging the gap between quasistatic strain rates from conventional servo-hydraulic techniques and high strain rates from typical Kolsky bar techniques. This testing system converted impacts from a high-speed actuator into high-loading-rate tensile forces and elongated specimens under relatively constant deformation rates. This testing system is capable of testing not only prismatic material specimens to evaluate stress-strain behavior but also non-prismatic structural components composed of different materials to evaluate force-deformation behavior. The testing system was verified and calibrated through a series of validation tests on aluminum tensile specimens. Experimental results were compared with theoretical estimations and finite element simulations to confirm this system obtained reliable force-deformation measurements in a repeatable and controllable manner. This research conducted two types of experimental tests on SMA specimens: a quasistatic cyclic loading test on a seismic bracing system based on an SMA ring and a series of high-loading-rate tensile tests on various SMA tensile specimens. The test results corroborated that this new testing system is capable of assessing the behavior of material specimens and structural components under intermediate strain rates.Ph.D