Tomaso Trombetti

Linear dynamic modeling of a uni‐axial servo‐hydraulic shaking table system

This paper focuses on the development of a linear analytical model (even though servo-hydraulic actuation systems are inherently non-linear, especially for large amplitude simulations — near the performance capacity of the system — linearized models proved experimentally to be quite effective overall in capturing the salient features of shaking table dynamics) of a uni-axial, servo-hydraulic, stroke controlled shaking table system by using jointly structural dynamics and linear control theory. This model incorporates the proportional, integral, derivative, feed-forward, and differential pressure gains of the control system. Furthermore, it accounts for the following physical characteristics of the system: time delay in the servovalve response, compressibility of the actuator fluid, oil leakage through the actuator seals and the dynamic properties of both the actuator reaction mass and test structure or payload. The proposed model, in the form of the total shaking table transfer function (i.e. between commanded and actual table motions), is developed to account for the specific characteristics of the Rice University shaking table. An in-depth sensitivity study is then performed to determine the effects of the table control parameters, payload characteristics, and servovalve time delay upon the total shaking table transfer function. The sensitivity results reveal: (a) a potential strong dynamic interaction between the oil column in the actuator and the payload, and (b) the very important effect of the servovalve time delay upon the total shaking table transfer function. Copyright

ADDED VISCOUS DAMPERS IN SHEAR-TYPE STRUCTURES: THE EFFECTIVENESS OF MASS PROPORTIONAL DAMPING

In this paper the authors investigate the dynamic performances of multi-degree-of-freedom shear-type structures equipped with manufactured viscous dampers. The system of added viscous dampers that leads to a mass proportional damping (MPD) matrix is identified as the one providing the best overall performance in terms of minimum top-storey response variance to a Gaussian band limited white noise input within the class of classically damped systems. A performance index developed by the authors and based upon modal damping ratios confirms that, within the class of Rayleigh damping systems, the MPD limiting case provides the largest damping effect. For a 6-d.o.f. system, a comparison with results available in literature also shows that the MPD system provides better performance than optimised (as suggested by other research works) non-classical damping schemes. A physical explanation for the optimum damping performance offered by MPD systems is also provided herein, together with clear indications about how to implement MPD systems in real building structures. A check on the applicability of MPD systems to real structures and its effectiveness is also carried out successfully through the development and study of a realistic finite element model of an actual 18-storey building.

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.

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.

On the evaluation of the horizontal forces produced by grain-like material inside silos during earthquakes

This paper presents analytical developments devoted to the evaluation of the effective behaviour of grain in flat-bottom silos during an earthquake. This research work starts from all the same basic assumptions of Eurocode 8 except for the one regarding the horizontal shear forces among consecutive grains. Only this difference leads to a new physically-based evaluation of the effective mass of the grain which horizontally pushes on the silo walls. The analyses are developed by simulating the earthquake ground motion with time constant vertical and horizontal accelerations and are carried out by means of simple dynamic equilibrium equations that take into consideration the specific mutual actions developing in the ensiled grain. The findings indicate that, in case of squat silos (characterized by low, but usual, height/diameter slenderness ratios), the portion of the grain mass that interacts with the silo walls turns out to be noticeably smaller than the total mass of the grain in the silo and the effective mass adopted by Eurocode 8.

On the dimensioning of viscous dampers for the mitigation of the earthquake-induced effects in moment-resisting frame structures

The effectiveness of viscous dampers in mitigating the seismic excitation impacts upon building structures has been widely proved. Recently, with reference to the specific case of equal mass, equal stiffness, shear-type structures, the authors developed a direct practical procedure which gives the mechanical characteristics of the manufactured viscous dampers capable of providing the frame structure with a prescribed value of the first damping ratio. In this paper, a comprehensive rational framework is presented, which allows to formally extend the validity of the proposed procedure to the more realistic case of a generic moment-resisting frame structure. Also the influence of various lateral stiffness distributions is investigated.

Physically-based prediction of the maximum corner displacement magnification of one-storey eccentric systems

This paper gives a new insight into the linear dynamic behavior of one-storey eccentric systems, with particular attention devoted to provide a comprehensive physically-based formulation of the maximum corner displacement magnification, which involves three contributions (translational response, torsional response and their combination). It is shown that the largest magnifications, which mainly occur for the class of torsionally-flexible systems, are due to the translational contribution which is caused by the shift of the fundamental period of the eccentric system with respect to that of the equivalent not-eccentric system. A simplified method for the estimation of the maximum corner displacement under seismic excitation, based on the physical properties of the eccentric system, is finally proposed.

Numerical Verification of the Effectiveness of the “Alpha” Method for the Estimation of the Maximum Rotational Elastic Response of Eccentric Systems

In previous research works, the authors have identified a key system parameter which controls the maximum rotational response under free and forced vibrations of one-story linear-elastic systems representative of asymmetric seismic base-isolated building structures. This parameter (called “ALPHA”) has also led to the identification of a simplified procedure (called “ALPHA method”) for the estimation of the maximum rotational response of such systems. The main goal of this article is to verify the properties of the ALPHA parameter and the predictive capabilities of the ALPHA method, when applied to one-story systems representative of generic asymmetric building structures. The verification is carried out through a comprehensive set of 11,600 numerical simulations developed with reference to different representative structures subjected to historically recorded ground motions, with special attention devoted to the identification of the sensitivity of the ALPHA parameter and the ALPHA method upon the fundamental period of vibration of the structure (not yet considered in previous research works). The results obtained: (a) confirm the effectiveness of the ALPHA parameter to capture the intrinsic propensity of an eccentric system to develop a torsional response; (b) confirm the capacity of the ALPHA method to effectively estimate the maximum rotational response of a given eccentric system under seismic excitation; and (c) indicate that the ALPHA method is only weakly sensitive upon the period of vibration of the structure. The article also introduces a simple code-like provision for conservative estimations of the maximum rotation developed under seismic input by asymmetric structures based upon the confidence interval concepts.

Peak velocities estimation for a direct five-step design procedure of inter-storey viscous dampers

In the last decades, the use of added viscous dampers for the mitigation of the effects due to the seismic action upon the structural elements has been worldwide spread. In this respect, several design methods aimed at sizing the viscous dampers to be inserted in building structures have been proposed. Among others, some of the authors proposed a five-step procedure which guides the practical design from the choice of a target reduction in the seismic response of the structural system (with respect to the response of a structure without any additional damping device), to the identification of the corresponding damping ratio and the mechanical characteristics (i.e. the damping coefficient values for chosen damping exponent, the oil stiffnes, the maximum damper forces) of the commercially available viscous dampers. The procedure requires the development of numerical simulations for the evaluation of the peak inter-storey velocity profiles, necessary for the evaluation of the damper forces. In the present paper a comprehensive study on the inter-storey velocity profiles developed in shear-type building structures under seismic excitation is conducted with the purpose of deriving analytical formulae for their estimation. The analytical estimations of the peak inter-storey velocities are then used to simplify the original five-step procedure leading to a direct (i.e. fully analytical) procedure. The direct procedure is suitable for the preliminary design of the added viscous dampers, in particular for practitioners not dealing everyday with the design of added viscous dampers.

A Structural Analysis of the Modena Cathedral

ABSTRACT Historical monuments, by their own features and evolution over time, represent a unicum characterized by large uncertainties. With the aim of preserving cultural heritage for future generations, the assessment of the static conditions of the monuments is a crucial point. In order to perform a robust and reliable evaluation of the structural behavior and to eventually forecast possible evolution of the safety level, it is of fundamental importance to carry out a comprehensive study by taking into account contributions coming from different fields. The aim of this article is to present a preliminary assessment of the structural “health” of the Cathedral of Modena (Italy) making use of a multi-disciplinary multi-analysis approach, capable of providing an integrated knowledge of the monument. Different analyses (simple, but more reliable limit schematizations, and more complex, but too much sensitive to uncertainties, computer-based models) have been conducted on the global structure of the masonry fabric as well as on the local response of the single masonry walls and other significant structural elements, in order to identify the main static vulnerabilities.