A Nonlinear Static Procedure for the Seismic Design of Symmetrical Irregular Bridges

Displacement-based seismic design methods support the performance-based seismic design philosophy known to be the most advanced seismic design theory. This paper explores one common type of irregular-continuous bridges and studies the prediction of their elastoplastic displacement demand, based on a new nonlinear static procedure. This benefits to achieve the operation of displacement-based seismic design. Three irregular-continuous bridges are analyzed to advance the equivalent SDOF system, build the capacity spectrum and the inelastic spectrum, and generate the new nonlinear static analysis. The proposed approach is used to simplify the prediction of elastoplastic displacement demand and is validated by parametric analysis. The new nonlinear static procedure is also used to achieve the displacement-based seismic design procedure. It is tested by an example to obtain results which show that after several combinations of the capacity spectrum (obtained by a pushover analysis) and the inelastic demand spectrum, the simplified displacement-based seismic design of the common irregular-continuous bridges can be achieved. By this design, the seismic damage on structures is effectively controlled.

Displacement mitigation–oriented design and mechanism for inerter-based isolation system

The inerter-based isolation system, which comprises an inerter, a dashpot, and a spring, has been shown to be effective for improving the dynamic performance of isolated structures. However, the underlying theoretical basis of its vibration control mechanism has not been studied for superstructures with inerter-based isolation system; in particular, the functionality of the inerter has not been explicitly demonstrated. In this study, the displacement mitigation mechanism is established by deriving a fundamental equation, designated as the displacement demand equation. The mechanism is explained by clarifying the functionality of the inerter-based isolation system to determine the theoretical relationship between the displacements of the superstructure and isolation layer. A nominal displacement demand ratio is defined to evaluate the overall displacement demand of the structure–inerter-based isolation system, by considering the contribution of the inerter-based isolation system. Following the displacement mitigation mechanism, design strategies are developed for inerter-based isolation system, where the isolation frequency ratio can be directly determined once the target displacement performance of the entire structure–inerter-based isolation system is prespecified. In addition, the inertance-mass ratio and damping ratio of the inerter-based isolation system can be obtained according to the target demand of the superstructure displacement. Finally, a series of examples are used to verify the derived displacement demand equation and proposed design strategy. In this study, the displacement mitigation mechanism yields an effective design method that is suitable for the inerter-based isolation system and has a clear physical basis. Through the proposed displacement mitigation–oriented optimal strategy, a target displacement demand for a structure can be satisfied directly, which also provides an optimized displacement performance for the isolation layer. The displacement mitigation mechanism and equation are practical for the simplification of the design procedure and help to reveal the advantageous features of the inerter-based isolation system.

Accuracy Assessment of Nonlinear Seismic Displacement Demand Predicted by Simplified Methods for the Plateau Range of Design Response Spectra

The nonlinear seismic displacement demand prediction for low-period structures, i.e., with an initial fundamental period situated in the plateau of design response spectra, is studied. In Eurocode 8, the computation of seismic displacement demands is essentially based on a simplified method called the N2 method. Alternative approaches using linear computation with increased damping ratio are common in other parts of the world. The accuracy of three methods for seismic displacement demand prediction is carefully examined for the plateau range of Type-1 soil class response spectra of Eurocode 8. The accuracy is assessed through comparing the displacement demand computed using nonlinear time-history analysis (NLTHA) with predictions using simplified methods. The N2 method, a recently proposed optimization of the N2 method, and the Lin and Miranda method are compared. Nonlinear single-degree-of-freedom systems are subjected to several sets of recorded earthquakes that are modified to match design response spectra prescribed by Eurocode 8. The shape of Eurocode 8 response spectra after the plateau is defined by a constant pseudovelocity range (1/T). However, the slope of this declining branch may be specified using precise spectral microzonation investigation. However, the N2 method has been found to be particularly inaccurate with certain microzonation response spectra that are characterized by a gently decreasing branch after the plateau. The present study investigates the impact of the slope of the decreasing branch after the plateau of response spectra on the accuracy of displacement demand predictions. The results show that the accuracy domain of the N2 method is restricted to strength reduction factor values around 3.5. Using the N2 method to predict displacement demands leads to significant overestimations for strength reduction factors smaller than 2.5 and to significant underestimations for strength reduction factors larger than 4. Fortunately, the optimized N2 method leads to accurate results for the whole range of strength reduction factors. For small values of strength reduction factors, up to 2.5, the optimized N2 method and the Lin and Miranda method both provide accurate displacement demand predictions. However, the accuracy of displacement demand prediction strongly depends on the shape of the response spectrum after the plateau. A gently decreasing branch after the plateau affects the accuracy of displacement demand predictions. A threshold value of 0.75 for the exponent of the decreasing branch (1/Tα) after the plateau is proposed. This issue should be considered for the ongoing developments of Eurocode 8.

Inelastic displacement spectra for Chinese highway bridges characterized by single-degree-of-freedom bilinear systems

As for the inelastic displacement demand of a single-degree-of-freedom system, previous studies usually focus on the strength reduction factor, R, or the inelastic displacement ratio, C. Only a little literature reports the direct statistical results of the mean inelastic displacement spectra, Sd. Based on 308 earthquake records selected from three types of site soil, differences between the direct mean Sd and the indirect ones that respectively derived from mean R and mean Cμ are investigated, in which Cμ refers to the constant ductility inelastic displacement ratio. It is found the indirect Sd will introduce errors for using mean R and mean Cμ, while the dispersion of the direct spectra need to be reduced before putting into practice. Two methods, the period normalized method and the spectra-matching method, are employed to address the dispersion problem, and the latter one that modified a record to make its acceleration response spectra compatible with the specified standard, Chinese highway bridge seismic design guidelines in this study, works with more acceptable performance. Finally, a comprehensive equation is proposed to characterize the spectra-matching mean Sd, the practicality and efficiency of the identified parameters in the equation are verified. It is advisable to use the proposed equation to assess the inelastic displacement demand of Chinese highway bridges characterized by single-degree-of-freedom bilinear system, and the procedures to obtain the displacement spectra can also be utilized for other corresponding researches.