Dynamic amplification factors of girder and cables of extradosed bridges during sudden cable failure

The rupture of a cable in cable-supported bridges is an accidental condition that should be considered during the design phase due the impact that this situation could have on the structural safety of the bridge and users. For that reason, design guidelines suggest carrying out a pseudo-static analysis where the failing cable is replaced by a load of the same magnitude as the pre-rupture tension but applied in the opposite direction and multiplied by a dynamic amplification factor (DAF) between 1.5 and 2.0. Previous studies in cable-stayed bridges have shown that the pseudo-static approach may not be suitable. Due to the wide use of extradosed bridges in infrastructure projects around the world, a computational analysis was performed in this investigation to estimate the dynamic amplification factors of extradosed bridge girders and cables when sudden failure of an extradosed cable occurs. The main goal of the study is to determine whether the pseudo-static approach suggested in the guidelines is acceptable. Linear response history analyses were performed by using computational models of extradosed bridges in which the girder stiffness and the suspension (lateral or central) and cable layout (fan or harp) of the cables were modified. From the analysis, the DAFs were calculated and compared to those recommended in the design guidelines. The calculated DAFs for the axial forces and bending moment in the girder of the bridges and for the axial forces in the extradosed cables were smaller than 2.0. However, in some cases the DAF for shear forces were higher than 2.0, especially when the girder stiffness was relatively low. The results indicate that the recommendations of the design guidelines are adequate for extradosed bridges, which is a result of the relatively high stiffness of the girder and low inclination of extradosed cables. Despite this, response history analyses like the one performed in this study are recommended to assess the response of the bridge under cable breakage.

Structural Vibration Control with the Implementation of a Tuned Mass Rocking Wall System

A tuned mass rocking wall (TMRW)-frame structure system is proposed to improve the energy dissipation ability of the traditional rocking wall-frame system. Based on the energy dissipation principle of the traditional tuned mass damper (TMD), a TMRW is designed with proper mass and stiffness according to the dynamic characteristic of the host structure. Firstly, considering the presence of inherent structural damping, the dynamic amplification factor of the main mass was derived from the dynamic equations of the TMRW mechanism. A practical design table was then obtained after parameter study. Secondly, by taking a six-story frame structure as an example, the dynamic time-history analysis was conducted to study TMRW’s seismic performance. The inter-story drift ratios of the TMRW-frame, the traditional rocking wall-frame, and the frame structures were compared, and the seismic responses of the controlled and uncontrolled structures were also compared. The results demonstrate that the TMRW can effectively reduce the inter-story displacement of the host structure, and the lateral deformation mode of the host structure tends to be more uniform. However, compared with the traditional rocking wall-frame system, the proposed TMRW has less ability on coordinating deformation.

Kustīgās slodzes dinamiskās iedarbes uz autoceļu tiltiem eksperimentāla izpēte un novērtējums

Using data obtained from the dynamic load testing of bridges a method was developed to evaluate level of the dynamic performance without performing a dynamic load test. In this method a dynamic index of the bridge is calculated. Dynamic index allows to evaluate the dynamic performance level of existing and new structures taking into account such bridge parameters as span length / height ratio, natural frequency, vibration damping coefficient, relative deflection and international roughness index IRI. Dynamic index method can be used by bridge owners and maintainers to determine the dynamic potential of a particular bridge. The maximum allowable values of the dynamic amplification factor for standard prestressed concrete beam bridges were determined. These values were calculated for maximum allowed traffic load in Latvia. The obtained results can be used for the safety assessment of existing and reconstructed reinforced concrete beam bridges.

Optimization of Multiple Tuned Mass Dampers for Road Bridges Taking into Account Bridge-Vehicle Interaction, Random Pavement Roughness, and Uncertainties

Road bridge designs are based on technical standards, which, to date, consider dynamic loading as equivalent static loads. Additionally, the few engineers who perform a dynamic analysis typically do not consider the effects of bridge-vehicle interaction and also simplify the road’s irregularity profile. Moreover, often, even when a simplified dynamic analysis is carried out and shows that there will be a high dynamic amplification factor (DAF), designers prefer to solve this problem by adopting high safety factors and thereby oversizing the bridge, rather than using energy dissipation devices that would allow reducing the amplitude of vibration. In this context, the present work proposes a complete methodology to minimize the dynamic response of road bridges by optimizing multiple tuned mass dampers (MTMD), taking into account the bridge-vehicle interaction, the random profile of pavement irregularities, and the uncertainties present in the coupled system and in the excitation. For illustrative purposes, the coupled vibration problem of a regular truck traveling on a random road profile over a typical Brazilian bridge is analyzed. Three different scenarios for the MTMD are considered. The proposed optimization problem is solved by employing the Whale Optimization Algorithm (WOA). The results showed the excellent ability of the proposed methodology, reducing the bridge’s DAF to acceptable values for all analyzed cases, considering or not the uncertainties present in the system. Furthermore, the results obtained by the proposed methodology are compared with results obtained using classical tuned mass damper (TMD) design methods, showing the best performance of the proposed optimization method. Thus, the proposed method can be employed to optimize MTMD, improving bridge design.

Dynamic Response and Robustness Evaluation of Cable-Supported Arch Bridges Subjected to Cable Breaking

Cable-supported arch bridges have had many cable break accidents, which led to dramatic deck damage and even progressive collapse. To investigate the dynamic response and robustness of cable-supported arch bridges subjected to cable breaking, numerical simulation methods were developed, compared, and analyzed, and an effective and accurate simulation method was presented. Then, the cable fracture of a prototype bridge was simulated, and the dynamic response of the cable system, deck, and arch rib was illustrated. Finally, the robustness evaluation indexes of the cable system, deck, and arch rib were constructed, and their robustness was evaluated. The results show that the dynamic response of the adjacent cables is proportional to the length of the broken cable, while the dynamic response of the deck is inversely proportional to the length of the broken cable. The dynamic amplification factor of the cable tension and deck displacement is within 2.0, while that of the arch rib bending moment exceeds 2.0. The break of a single cable will not trigger progressive collapse. When subjected to cable breaking, the deck system has the least robustness. The proposed cable break simulation procedure and the robustness evaluation method are applicable to both existing and new cable-supported bridges.