SEISMIC RESPONSE CONTROL OF A CABLE-STAYED BRIDGE BY VARIABLE DAMPERS

Cable-stayed bridges exhibit unique responses under a strong motion. It is partly due to the complexity in their damping mechanism. Recently, the benchmark problem of a cable-stayed bridge was developed to clarify the effectiveness of various seismic control strategies. Due to the new development of magnetorheological dampers, the application of variable dampers in bridges becomes possible. In this study, the effectiveness of the nonlinear viscous damping force scheme and the two-step friction damping force scheme are investigated. It is found that the nonlinear viscous damping force scheme is effective to control the response of the cable-stayed bridge with less demand for the damping force capacity of a damper. In addition, the two-step friction damping force scheme shows the improvement over conventional friction damping because the energy dissipation of a damper can be increased.     

Optimum Design of Passive Control Devices for Reducing the Seismic Response of Twin-Tower-Connected Structures

Based on the 3-single-degree-of-freedom (SDOF) model of twin-tower structures linked by the sky-bridge and passive control devices, the frequency functions and the vibration energy expressions of the structures are derived by using the stationary white noise as the seismic excitation. The analytical formulas for determining the connecting optimum parameters of viscoelastic damper (VED) represented by the Kelvin model and the viscous fluid damper (VFD) represented by Maxwell model are proposed using the principle of minimizing the average vibration energy of either the single tower or the twin tower. Three pairs of representative numerical examples of twin-tower-connected structures are used to verify the correctness of the theoretical approach. The optimum parametric analysis demonstrates that the control performance is not sensitive to damper damping ratio of VED and relaxation time of VFD. The effectiveness of the proposed control strategies based on the 3-SDOF models is also proved to be applicable to multi-degree-of-freedom systems. The theoretical analysis and numerical results indicate that the seismic response and vibration energy of the twin-tower-connected structures are mitigated greatly under the two types of dampers. The presented control strategies of VED and VFD can help engineers in application of coupled structures.     

INTEGRATED PASSIVE-ACTIVE SYSTEM FOR SEISMIC PROTECTION OF A CABLE-STAYED BRIDGE

This paper presents an integrated passive-active (i.e. hybrid) system for seismic response control of a cable-stayed bridge. Since multiple control devices are operating, a hybrid control system could alleviate some of the restrictions and limitations that exist when each system is acting alone. Lead rubber bearings are used as passive control devices to reduce the earthquake-induced forces in the bridge and hydraulic actuators are used as active control devices to further reduce the bridge responses, especially deck displacements. In the proposed hybrid control system, a linear quadratic Gaussian control algorithm is adopted as a primary controller. In addition, a secondary bang-bang type (i.e. on-off type) controller according to the responses of lead rubber bearings is considered to increase the controller robustness. Numerical simulation results show that control performances of the integrated passive-active control system are superior to those of the passive control system and are slightly better than those of the fully active control system. Furthermore, it is verified that the hybrid control system with a bang-bang type controller is more robust for stiffness perturbation than the active controller with a μ-synthesis method, and there are no signs of instability in the over-all system whereas the active control system with linear quadratic Gaussian algorithm shows instabilities in the perturbed system. Therefore, the proposed hybrid protective system could effectively be used for seismically excited cable-stayed bridges.     

Optimal Control of Accelerations in a Base-Isolated Building using Magneto-Rheological Dampers and Genetic Algorithms

This article presents a numerical study aimed at improving effectiveness of the isolation system of an actual building by adding magneto-rheological (MR) dampers that act in parallel to the existing rubber bearings (RB). The building itself is modeled with uniaxial elastic elements. Additional elements that include the RBs and the MR dampers are added at the base of the building and two different genetic algorithms are used to optimize operation of the MR dampers. Maximum acceleration and relative displacement at the top of the building are taken as the variables to be minimized. Records of destructive earthquakes are used as input. A comparison is made between the building responses with RB and the one with the additional control system.     

Transverse Seismic Behavior Studies of a Medium Span Cable-Stayed Bridge Model with Two Concrete Towers

Due to lack of investigation on nonlinear seismic behavior of cable-stayed bridges under strong earthquake excitation, the concrete towers, as the main gravity-carrying component, are usually required to remain nearly elastic. However, in order to achieve this high seismic performance objective, the reinforcement ratio of the tower legs and the tower struts need to be greatly increased in addition to its static loading requirement. To study the potential plastic region and possible failure mode of the cable-stayed bridge, a 1/20-scale full bridge model from a typical medium span concrete cable-stayed bridge was designed, constructed and tested on 4 linear shake tables using a site specific artificial wave in the transverse direction. Test results showed that the damage characteristics of the bridge model were as follows: (1) the severe damage was observed at the upper strut, with several steel bars fractured at both ends; (2) the repairable damage was observed at tower legs at the bottom and the middle part, with concrete cover spalling and exposure of steel bars; (3) the minimal damage was observed at the lower strut and the both sides of the side bents, with only slightly concrete spalling; and (4) no damage was observed at the auxiliary bents, the superstructure and the cables. Numerical results and test results were further compared and showed good agreement in low amplitudes of excitations. The test also proved that the bridge system was stable in flexural failure of upper struts, and had the negligible residual displacement subjected to high amplitudes of excitations.     

Effect of Nonlinear Seismic Torsion on the Performance of Skewed Bridge Piers

This article presents an analytical investigation on the effect of seismic torsion on the performance of a skewed bridge. A nonlinear torsional hysteretic model developed by the authors is applied to idealize the torsional behavior of bridge piers. Deterioration of the torsional strength of piers due to combined flexure is considered and deterioration of flexural strength due to torsion is not taken into account. The effects of pounding between deck and abutments, cable restrainers, and damage of bearing supports are also included in analysis. It is found that the eccentric impact force due to lock of bearing movement results in extensive torsion in piers.     

Tuned Mass Damper Positioning Effects on the Seismic Response of a Soil-MDOF-Structure System

Tuned mass dampers (TMDs) are effective structural vibration control devices. However, very little research is available on the experimental investigation of TMDs and their performance in systems undergoing dynamic soil-structure interaction. Geotechnical centrifuge tests are conducted to investigate story positioning effects of single and multiple TMDs in a soil-MDOF-structure system. The criteria for optimal story positioning will be established, and it is shown that story positioning influences TMD performance more than the number of TMDs used. Non-optimal story positioning was found to have the potential of reducing damping efficiency, amplifying peak structural response, and inducing lengthier high-intensity motion.     

DYNAMIC RESPONSE OF SKEW HIGHWAY BRIDGES

A simplified bridge model suitable for use in a parametric study of short-span skew highway bridges and bridges with stiffness eccentricity is presented. The proposed model is simple, yet it captures all essential features that affect the dynamic response of these bridges. Using this simplified model, formulas for computing earthquake response of the bridges are developed and parameters that significantly influence the dynamic response of the bridges are identified. The study indicates that the response of a given skew bridge depends not only on its deck aspect ratio, the stiffness eccentricity ratio, the skew angles, its natural frequencies, but also on the frequency ratio. In particular, the rotational to translational frequency ratio has a pronounced influence on the dynamic response of the bridge. It is found that skew bridges with high rotational to translational frequency ratios often exhibit less dependence on such parameters as deck aspect ratios, stiffness eccentricity ratios and skew angles.     

Seismic Demand on Shear Panel Dampers Installed in Steel-Framed Bridge Pier Structures

This study is aimed at investigating the demand on shear panel dampers (SPDs) installed in steel structures under strong earthquake motions to serve as guidance for the recommended capacity of SPDs in seismic design. For this purpose, an extensive dynamic analysis is carried out on steel bridge pier structures with SPD devices. To describe the restoring force characteristics of SPDs, the analysis uses a newly developed combined hardening model based on experimental data. The seismic demands made on SPD devices are examined and then summarized to give recommended values for determining the necessary deformation capacity of SPDs.     

Seismic Displacement Demands on Skewed Bridge Decks Supported on Elastomeric Bearings

The unseating of decks is one of the most prevalent failure modes of bridges after earthquake events, as observed in the 2010 Chile Earthquake. Damaged bridges in Chile often had skew angles and were supported on elastomeric bearings. Similar bridge construction practices with decks supported on elastomeric bearings are also common in the central and eastern U.S. (CEUS). The seismic displacement demands on skewed bridges are more complicated than those on bridges without skew angles due to the coupling of translational modes with the rotational mode of vibration. The study presented in this article seeks to understand the seismic response of skewed bridge decks supported on elastomeric bearings. The scope of the study is limited to one- and two-span bridges, which constitute a large portion of bridge inventory in the CEUS. The vibration modes of skewed bridge decks are derived in closed form and the modes are compared when the gaps between the bridge deck and the abutment are open and when one of the gaps is closed due to seismic excitation. Nonlinear response history analyses are carried out to understand the effects of vertical ground motion, skew angles, aspect ratios, and different ground motion types on the seismic displacement demand in these cases. Amplification factors that approximate the increase in the displacement demand due to the skew angle are proposed.     

Point-to-Surface Pounding of Highway Bridges with Deck Rotation Subjected to Bi-Directional Earthquake Excitations

Post-earthquake survey of several strong earthquakes demonstrated that pounding between the neighboring civil infrastructures, such as building and highway bridge, would induce significant structural damage, even collapse, of the structures. This article presents a pounding experiment of highway bridge, especially focused on the point-to-surface pounding of bridge decks due to torsional rotation, when subjected to extreme bi-directional earthquake excitations. To experimentally investigate the point-to-surface pounding between the neighboring bridge segments, a base-isolated highway bridge model, in which the mass centers of the bridge decks do not strictly coincide with the corresponding stiffness centers, is manufactured. A series of shaking table tests of the highway bridge model are carried out for the structural model with large and small separations of the expansion joint to investigate the dynamic responses of the bridge model with and without including the pounding effects, respectively. An analytical model of the highway bridge, in which the point-to-surface pounding is represented by using a modified contact-friction element, is also established based on the lump mass model with three degrees of freedom for each segment. Based on the test results, the model parameters of the modified contact-friction element are identified, and the analytical responses of the highway bridge model with pounding effects are compared with the experimental data. The results show that the highway bridge is vulnerable to the deck rotation, and point-to-surface pounding should be considered in the structural design to lighten the pounding damage of the highway bridge under strong earthquake excitations.     

A Five-Step Procedure for the Dimensioning of Viscous Dampers to Be Inserted in Building Structures

Viscous dampers have widely proved their effectiveness in mitigating the effects of the seismic action upon building structures. In view of the large impact that use of such dissipative devices is already having and would most likely have soon in earthquake engineering applications, this article presents a practical procedure for the seismic design of building structures equipped with viscous dampers, which aims at providing practical tools for an easy identification of the mechanical characteristics of the manufactured viscous dampers which allow to achieve target levels of performances. Selected numerical applications are developed with reference to simple, but yet relevant, cases.     

Reduction Factors for Seismic Design Spectra for Structures with Viscous Energy Dampers

A simple mathematical expression is proposed to estimate spectra reduction damping factors for seismic design of systems with viscous dampers. The expression is obtained from the ratios between ordinates of uniform hazard spectra associated with two different return intervals (50 and 125 years), corresponding to sites with different types of soil within the Valley of Mexico. The expression proposed depends on the dominant period of the soil, and on both the vibration period and damping ratio of the structural system. Values of the damping factors proposed here are comparable to those recommended by different authors and seismic design building codes.     

Physical and Numerical Approaches for the Optimal Insertion of Seismic Viscous Dampers in Shear-Type Structures

This article presents the results of an exhaustive parametric analysis which compares the performances offered by various systems (which lead to both classical and non classical damping matrices) of added viscous dampers in shear-type structures. The aim of the research work here presented is the identification of the system of added viscous dampers which maximizes the dissipative properties under an equal “total size” constraint. The choice of the systems of added viscous dampers considered in the comparison is carried out both using a numerical approach (based upon the use of genetic algorithms) and a physically based approach (based upon the properties of classically damped systems). The comparison is carried out through the numerical evaluation of the dynamic response of representative shear-type structures to both stochastic and recorded earthquake inputs. The results obtained using both approaches indicate that a damping system based upon the mass proportional damping component of the Rayleigh viscous damping matrix (referred to as MPD system) is capable of optimizing simultaneously a number of different performance indexes, providing the best “overall” damping performances. The MPD system is characterised by viscous dampers (a) which connect each floor to a fixed point and (b) which are sized proportionally to the corresponding floor mass.     

Cyclic Performance of an Elliptical-Shaped Damper with Shear Diaphragms in Chevron Braced Steel Frames

Several advantages of yielding dampers in controlling seismic energy have attracted the attention of many researchers in designing new buildings and retrofitting existing structures. In recent decades, various shapes and substances of such dampers have been used in engineering structures and their behavioral features, including the energy dissipating capacities, have been assessed. In this article, a novel method is presented to obtain the design relationship of two types of yielding elliptical dampers in terms of their selected geometric properties, i.e. distance between the shear diaphragms or virtual diameter and thickness. In addition, two different elliptical-shaped steel dampers equipped with the shear diaphragms are proposed and modeled using the finite element software ABAQUS and their performances are investigated. Then, 30 and 25 models, respectively, of the first and second types are studied using pushover analysis. The designed dampers considering the proposed relationships are used in two chevron braced steel frames placed between the bracing and the beam. Due to their desirable efficiency in energy dissipation and increase in the equivalent viscous damping of the frame, better efficiency is achieved in the modified damper with easier fabrication.     

ACTIVE/PASSIVE SEISMIC CONTROL OF STRUCTURES

In civil engineering, structural integrity and safety are of utmost importance as the consequences of failure are devastating. Maintaining the structural integrity becomes particularly important when the structures are subjected to severe earthquakes and strong wind-loading. Various passive and active control means have been considered to avoid catastrophic failure due to seismic or wind excitations. In this paper, a new class of hybrid actuators is presented which consists of a piezoelectric stack actuator combined with a viscoelastic damper to form a passive/active brace system (PAB). The actuator is used for mitigating structural dynamic responses of a three-storey structure subjected to simulated earthquakes loading. The proposed hybrid actuator is selected because it combines the attractive attributes of active and passive systems as well as because it has high stiffness-weight ratio, high frequency bandwidth, and low power consumption. The theoretical and experimental performance characteristics of the three-storey structure with the hybrid PAB actuator are presented. Comparisons are also included when the structure is controlled with conventional viscoeiastic dampers or conventional active control braces that operate without any viscoelastic damping. These comparisons emphasize the effectiveness of the hybrid actuator in damping out simulated seismic vibrations.     

SIMULATION OF THE CYCLIC BEHAVIOUR OF R/C RECTANGULAR HOLLOW SECTION BRIDGE PIERS VIA A DETAILED NUMERICAL MODEL

In the search for robust constitutive models suitable for reproducing the performance of bridge piers during a seismic event, this paper details the simulation of the cyclic responses of four rectangular hollow section R/C bridge piers. These four R/C bridge piers were built at scale 1/2.5 and tested experimentally. Both tall and short piers are considered, covering situations where bending or shear are of relevance. Furthermore, the four piers were reinforced according to rather different design strategies: (I) the first is a 30-year-old bridge designed without allowance to the seismic action, and (ii) the second is a bridge fulfilling the EC8 provisions. The detailed constitutive model that provides the numerical predictions includes two submodels: one with two scalar damage variables, reproducing the tensile and compressive degradations of concrete, and the other is based on the Giuffre-Menegotto-Pinto formulation, simulating the cyclic behaviour of the re-inforcement. The Damage Mechanics submodel is implemented at the Gauss points of the finite elements that discretize the concrete, whereas the steel submodel is implemented on the 2-noded truss elements adopted for the rebars. A comparison between the numerical and the experimental results is discussed in detail in this paper.     

STRUCTURAL CONTROL ALGORITHMS IN EARTHQUAKE RESISTANT DESIGN

The dynamic finite element equations of a two-dimensional structure made of axial-flexural frame elements with tendon-driven actuators have been derived. A critical review of classical optimal control theory is made with respect to its application to the control of structure under seismic excitations. Seven control algorithms, including two newly proposed algorithms, have been described, investigated and discussed. The need of an optimal observer, Kalman filter, is discussed. The validity of separation theorem applicable to the optimal stochastic control of structure for earthquake resistance is shown. How the control system perform under the circumstances of actuator saturation is also shown. Several numerical examples are worked out to demonstrate and compare the efficiency and limitations of those control algorithms.     

Natural Frequency of Single Pier Bridges Considering Soil-Structure Interaction

Because of the crucial role of free vibration frequency of a structure (e.g., a bridge) in design procedure, more realistic estimation of the frequency ends up in safer and more optimized design. As obtaining the free vibration frequencies of a bridge, considering soil-pile group-structure interaction, provide more realistic values, development of an analytical model to obtain such free vibration frequencies is studied in this research work. Most researchers have studied models with a single pile foundation. The purpose of this study is to assess soil-structure interaction (SSI) effects on dynamic performance of pile group supported bridges. A new analytical model is proposed to predict seismic analysis of these bridges. Applying the dynamic equations of motion for the system, SSI effects have been estimated. Based on the suggested analytical model, a new approximate equation is proposed for calculating natural frequency of pile group supported bridges. Equation accuracy has been investigated by comparing the results with those achieved by previous studies. Most periods calculated by the approximate equation are similar to those given for other case studies, indicating that the model could be applicable to other projects. Since the proposed model is very similar to real soil-pile-pier systems, this approximate equation can be used in preliminary seismic design of bridges.     

INSTANTANEOUS OPTIMAL CONTROL FOR SEISMIC ANALYSIS OF NON-LINEAR STRUCTURES

In this paper, an effective active control algorithm is developed for the vibration control of non-linear structural systems subjected to earthquake excitation. It is an attempt to include the non-linear characteristics of the structural behaviour throughout the entire analysis (design and validation), accounting for the eventual cumulative structural damage and energy dissipation. This is a very important factor since, in current design practice, structures are assumed to behave nonlinearly when subjected to strong ground motion. The proposed algorithm focusses on the instantaneous optimal control approach for the development of the control algorithm where the nonlinearities are brought into the analysis through a non-linear state vector and a non-linear open loop term. A performance index that is quadratic in the control force and in the non-linear states and is subjected to a non-linear constraint equation, is minimised at every time step. The effectiveness of the proposed non-linear instantaneous optimal control (NIOC) strategy is critically evaluated in comparison with currently available active control techniques. Numerical simulation results indicate that the proposed approach provides a significant reduction of the peak response quantities, such as maximum response deformation, maximum response acceleration, ductility of the system, associated with a reduced maximum control force.