Dissertations and Theses

Date of Award


Document Type



Civil Engineering

First Advisor

Anil Kumar Agrawal


Progressive collapse, Truss bridges, Alternate load path, sudden member loss, blast


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.


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