Frequency-domain buffeting analysis of a long-span twin-box-deck bridge with distributed buffeting loads

Abstract

Excessive buffeting responses can cause fatigue damage in the structural components and connections of long-span steel bridges. Thus, buffeting analyses that can accurately predict fatigue-related stress responses are important for modern cable-supported bridges. Structure health monitoring systems (SHM) have been installed in a number of long-span cable-supported bridges to monitor and assess bridge performance and safety. The number of sensors in an SHM system is always limited, such that not all of the key structural components can be directly monitored. Therefore, to facilitate the effective assessment of stress-related bridge performance and safety, stress-level buffeting analysis is required so that the responses in all of the important structural components can be directly computed and compared with measured values for verification. Frequency-domain and time-domain methods have been developed to predict the buffeting-induced responses of bridges. These methods are based on integrated sectional aerodynamic and aeroelastic forces rather than distributed forces on the bridge deck. Disregarding the cross-sectional distribution of buffeting forces may affect the accuracy of computed buffeting-induced stress responses, which will in turn affect comparisons with the measured stresses from SHM systems. Thus, to accurately predict the buffeting-induced fatigue of bridges, it is imperative to take into account the cross-sectional distribution of aerodynamic and aeroelastic forces. Traditional finite element (FE) models that reduce bridge decks to beam elements with equivalent sectional properties are insufficient for such dynamic analyses. For a stress-level buffeting analysis, accurate FE models need to be built with detailed geometry using plate/shell/solid elements. Multi-scale modeling methods should be used to reduce the number of degrees-of-freedom (DOF) caused by such detailed modeling. Moreover, due to the uncertainties in models of large civil structures, updating processes are usually needed after the initial establishment of the FE models to improve modeling accuracy. The model updating process of multi-scale FE models requires both global and local measured data to ensure multi-scale accuracy. For long-span bridges, research in this area is limited. In view of the problems outlined, a practical framework that includes the acquisition of distributed aerodynamic and aeroelastic forces, buffeting analysis with distributed loads, and multi-scale FE modelling and model updating techniques are needed for the accurate prediction of the buffeting responses of a long-span bridge. In this study, the formulation for distributed aerodynamic forces on the surfaces of a bridge deck is first presented. Wind tunnel pressure tests are conducted to obtain the distributed aerodynamic forces on a sectional twin-box deck model. The cross-sectional distribution of signature-turbulence-induced pressure is investigated by separating the signature turbulence-induced pressure from the measured pressure time histories. The span-wise correlation of aerodynamic pressure on the sectional deck model is also studied. The results for the cross-sectional and span-wise distributions of aerodynamic pressure provide more detailed information and deeper insight into the fluid-motionless structure interaction in a twin-box bridge deck. Signature turbulence mainly affects the leeward box. For certain locations, the signature-turbulence-induced pressure may be significantly larger than the incident-turbulence-induced pressure. For the incident-turbulence-induced pressure, the span-wise correlation weakens stream-wisely on the windward box, and the span-wise correlation on the leeward box is generally weaker than that on the windward box. For the signature-turbulence-induced pressure, the span-wise correlation is negligible for most parts of the deck except for the windward edge of the leeward box and the leeward edge of the windward box. A new method to obtain distributed aeroelastic forces by distributing measured sectional aeroelastic forces is proposed. The distribution is based on the quasi-static expression of aeroelastic forces. A frequency-domain buffeting analysis framework with the obtained distributed aerodynamic and aeroelastic forces are developed. A case study is carried out on a segment of a twin-box bridge deck to demonstrate the feasibility of the proposed framework. The results show that the responses computed with distributed buffeting loads on a shell model are different from those computed with the traditional method on a beam model. The displacement responses computed with distributed buffeting loads are slightly smaller than those computed with the traditional method. The section-wise distribution of the stress responses yielded by the proposed method is more concentrated on the windward edge, resulting in a larger maximum stress value. The different boundary conditions on the beam and shell models can also cause significant differences in the computed stress response distribution. A 3D multi-scale FE model of Stonecutters Bridge in Hong Kong is established. The bridge deck is modelled in detail with shell elements, allowing an accurate stress analysis to be conducted. Each deck segment is condensed into a super-element by the sub-structuring method to reduce the computation time for the subsequent dynamic analysis. The established FE model is updated with the measured modal frequencies only. Validation with measured frequency data shows that the established model is generally consistent with the real bridge in terms of dynamic properties. The computed displacement and stress influence lines are also compared with measured data acquired from load tests. The results show that the established multi-scale model is capable of providing both global and local responses. As it is updated only with modal frequencies, however, the computed displacement and stress responses under a vertical load are not accurate. This indicates the need for multi-scale updating techniques that take into account both the dynamic properties and local responses of the multi-scale model. A new model updating method for the multi-scale FE model of Stonecutters Bridge is thus proposed. The objective functions of the proposed method include both the modal frequencies and multi-scale (displacement and stress) influence lines. The response surface method is adopted to simplify the optimisation problem in the model updating. The results show that the differences between the measured and computed modal frequencies and between the measured and computed multi-scale influence lines are all reduced with the proposed model updating method. A comparison of the additional measured modal frequencies and influence lines with the corresponding computed results further confirms the high quality of the proposed model updating method. The proposed buffeting analysis framework is then applied to the updated multi-scale model of Stonecutters Bridge. The buffeting responses of the bridge for two wind directions associated with two terrains and three attack angles are investigated. The displacement, acceleration and stress responses of the bridge under distributed buffeting loads are presented. The mean wind from the S-W direction with larger mean wind speed induces larger mean responses of the bridge deck. The mean wind-induced stresses are concentrated on the windward edge of the bridge deck. In terms of the total buffeting responses, turbulent wind from the N-E direction with larger turbulence intensity induces larger responses. The total wind-induced stresses are smaller in the mid-span than in the quarter-span, and the largest longitudinal stress occurs on the windward edge of the bridge deck. For different attack angles, the initial attack angle of -3{493} leads to the largest lateral and vertical buffeting responses among the three given angles of attack. To further evaluate the effects of the proposed framework, a traditional buffeting analysis is performed on a spine-beam model of Stonecutters Bridge. The results of the buffeting analysis for the multi-scale model with distributed buffeting loads are compared with those from the analysis of the spine-beam model with sectional forces. The responses at different wind speeds are also investigated to reflect the influence of signature turbulence. The results show that the responses computed with distributed buffeting loads are different from those computed with the traditional method on a beam model. The displacement responses computed with the proposed framework are smaller than those computed with the traditional method. The sectional distribution of the stress responses yielded by the proposed method is more concentrated on the two edges of each box, resulting in a larger maximum stress value. The signature turbulence mainly affects the buffeting responses at low wind speeds.