A Simplified Approach for Dynamic Analysis of Suspension Bridges under Extreme Limit State

Abstract

The design of suspension bridges predominantly emphasizes wind and earthquake loads, frequently overlooking the consideration of extreme events in the design stage, thus posing a threat to bridge safety. The purpose of this research is to spread awareness among engineers for identifying weak zones in a bridge and to provide a new insight into how much damaging the blast loading could be for the long-span suspension bridges if not designed properly under the blast loads. The current dynamic analysis procedures for bridges under blast loads are complex and computationally expensive, making them unsuitable, especially for long-span bridges. To address this, a simplified dynamic analysis approach is proposed to assess the structural response and extreme limit state of suspension bridges exposed to blast loads. The method involves a bilayer solution: blast loading is modeled as nodal loads, and the structural aspect is represented by a three-dimensional (3D) fishbone skeleton finite-element (FE) model. Time-history simulations of blast loads are conducted for various bridge locations and explosive sizes. The parametric dynamic analysis reveals that the tower top node is the most vulnerable location in the suspension bridge under blast loads, which potentially exceeds the stress limits of nearby main cable elements and triggers the zipper-type progressive failure of the entire suspension bridge. Similarly, blasting at the deck nodes nearby tower on the main span side as well as on the side span side significantly amplifies axial stresses in nearby suspenders and the main cable, i.e., demand-to-capacity ratios of C18 and C19 surpass unity under BS4-6W and BS4-8W, respectively confirming that the failure state has reached for C18 and C19 under medium- to large-sized explosives. Therefore, it is recommended that the maximum demand-to-capacity ratio for all bridge components under medium- to large-sized explosives shall be kept below 0.8 to ensure the safety of the entire structure under extreme limit state. This paper provides a methodology to investigate the structural redundancy of suspension bridges under extreme limit state by providing a bilayer solution: the blast aspect, which is simulated as nodal loads on the bridge road surface and the structural aspect, is simulated as a 3D fishbone skeleton FE model. The implicit dynamic analysis approach is adopted parametrically by considering variable explosive weights and locations. For each blast scenario, the time-history of nodal loads is applied to various locations of the bridge considering small- to large-sized blasts. From a practical viewpoint, this study is relevant to develop comprehensive understanding of the dynamic behavior exhibited by long-span bridges when subjected to extreme loading scenarios. In essence, the aim is to explore the benefits and applicability of this research to the design of long-span bridges under blast loading conditions. The simplified approach presented in this paper, along with the corresponding bridge response results, allows a bridge design engineer to analyze a suspension bridge effortlessly. This method eliminates the need for intricate computations required to assess blast pressure over a solid bridge model, enabling a straightforward visualization of the anticipated behavior under blast loading. The research serves a crucial role in checking and verifying the extreme limit state, in addition to assessing the serviceability and ultimate limit states according to AASHTO’s requirements. For existing suspension bridges, the study proves beneficial in formulating a comprehensive blast-resistant plan through retrofitting and strengthening identified weak zones. Consequently, this research holds practical significance, serving as a foundation for further exploration and investigation into the effects of blast loading on various types of long-span bridges.