Oren Lavan

OPTIMAL PERIPHERAL DRIFT CONTROL OF 3D IRREGULAR FRAMED STRUCTURES USING SUPPLEMENTAL VISCOUS DAMPERS

A methodology for the optimal seismic design of supplemental viscous dampers for 3D irregular framed structures is presented. Optimal design, for which the added damping is minimised and subjected to a constraint on inter-storey drifts at the floor edges, is achieved while considering an ensemble of realistic ground motion records for linear behaviour of the damped structure. A variational approach is adopted for the derivation of the gradient of the constraint, thus enabling the use of a gradient based optimisation algorithm for the solution of the optimisation problem. An optimal design is first attained for one “active” ground motion record. If it fails for other records apart from the original ensemble, additional ground motions (loading conditions) are added one at a time to the “active” set until the optimum is reached. Optimal designs of supplemental dampers are attained for two, 3-bay by 3-bay, 8-storey 3D framed structures. The first has an asymmetric plan whereas the second is a setback structure. The resulting optimal designs are characterised by added damping in the exterior frames only, and full drift utilisation occurs in those storeys with assigned damping.

Simple Iterative Use of Lyapunov's Solution for the Linear Optimal Seismic Design of Passive Devices in Framed Buildings

This article presents a Lyapunov-based analysis/redesign approach for the optimal seismic design of added viscous dampers in 3D framed structures. The optimal solution minimizes the total added damping while the mean squared drifts at the peripheral frames are constrained to allowable values under a white noise excitation. The proposed approach uses Lyapunov equation for analysis and an optimality criterion that dictates “fully stressedness” for redesign. Hence, the design process is actually comprised of an iterative solution of a set of algebraic equations. Three examples are solved so as to highlight the advantages of the proposed approach — a 3-story shear frame, an 8-story, 3-bay by 3-bay setback frame, and a 10-story industrial frame.

Seismic behavior of viscously damped yielding frames under structural and damping uncertainties

This paper examines the sensitivity of the response of optimally damped frames to uncertainty in structural and damping properties. Viscous dampers are first optimally designed for given nominal properties of the retrofitted structures and a given ensemble of records for each structure. The behavior of the retrofitted structures (in terms of the maximum envelope peak inter-story drift) considering uncertainty in their properties as well as in the dampers’ properties is then tested using Monte Carlo simulation. It is shown that the uncertainties lead to larger mean drifts than expected, and that some designs are more sensitive than others. The physical reasons for this behavior are discussed and some rules as to what designs are expected to be more sensitive are given.

Multiple-Tuned Mass Dampers for Multimodal Control of Pedestrian Bridges

AbstractThis paper deals with the allocation and sizing of multiple-tuned mass dampers (MTMDs) in an attempt to retrofit footbridges with multiple critical modes resulting from the excitation of pedestrian traffic. The simple and practical methodology proposed herein includes the use of an iterative analysis/redesign type procedure that converges to a given allowable level of accelerations. An example that uses this methodology to retrofit an existing footbridge is presented.

Dynamic Analysis of Gap Closing and Contact in the Mixed Lagrangian Framework: Toward Progressive Collapse Prediction

Previous research has shown many advantages of the mixed Lagrangian formulation (MLF) for the solution of dynamic problems. In particular, it has shown a very stable and robust behavior with respect to the time step size required for convergence, even in cases where plasticity and fracture were considered. This paper presents another step toward enabling the prediction of progressive collapse of structures using MLF. A new gap element is added to the framework by formulating an additional component in the Lagrangian function. It is shown that by carefully formulating the new component, the optimization problem to be solved in each time step of the MLF algorithm retains its form which is quadratic in the cases considered. Hence, a unified formulation is attained for all stages of the analysis whether contact forces are present or not. After presenting details of the formulation, the proposed method is used for the solution of two examples. These examples illustrate that relatively large time steps can be considered even for contact problems. Furthermore, the reasons for this capability of the algorithm are discussed in the paper.

Seismic Design of Friction-Damped Braced Frames Based on Historical Records

This paper is concerned with the design of friction dampers designed to slip at a predetermined level and dissipate a substantial portion of the seismic energy, leaving the structure practically intact without its members having to yield or buckle. They are appropriate for use in seismic design of new buildings and in retrofitting existing structures. By choosing a practical design requirement rather than minimizing some energy criterion, a novel design procedure attains the stiffness of the individual braces and their displacements at the threshold of activation. The procedure is a two-phase process that uses in Phase 1 an equivalent single-degree-of-freedom (SDOF) system to obtain an optimal natural period of the structure by performing a full nonlinear dynamic analysis for a set of earthquake records. Phase 2 then enforces the same first mode on both the braced and unbraced frames, with the aim of ensuring simultaneous slippage. The procedure was applied to a 10-story steel frame. It yielded a rather technically attractive design of the braces since for close to mean plus standard deviation of the records, the resulting maximum roof displacements fell within the allowable design, as initially constrained to, and simultaneous slip of all braces occurred for most records. This procedure is rather simple in that the main computational effort, i.e., nonlinear analysis needed for Phase 1, is performed on an equivalent SDOF system only, whereas analysis of the multi-degree-of-freedom (MDOF) system is a linear eigenvalue analysis.

Towards realistic minimum-cost optimization of viscous fluid dampers for seismic retrofitting

This paper presents an effective approach for achieving minimum cost designs for seismic retrofitting using viscous fluid dampers. A new and realistic retrofitting cost function is formulated and minimized subject to constraints on inter-story drifts at the peripheries of frame structures. The components of the new cost function are related to both the topology and to the sizes of the dampers. This constitutes an important step forward towards a realistic definition of the optimal retrofitting problem. The optimization problem is first posed and solved as a mixed-integer problem. To improve the efficiency of the solution scheme, the problem is then re-formulated and solved by nonlinear programming using only continuous variables. Material interpolation techniques, that have been successfully applied in topology optimization and in multi-material optimization, play a key role in achieving practical final design solutions with a reasonable computational effort. Promising results attained for 3-D irregular frames are presented and compared with those achieved using genetic algorithms.

Earthquake engineering research needs in light of lessons learned from the 2011 Tohoku earthquake

Earthquake engineering research and development have received much attention since the first half of the twentieth century. This valuable research presented a huge step forward in understanding earthquake hazard mitigation, which resulted in appreciable reduction of the effects of past earthquakes. Nevertheless, the 2011 Tohoku earthquake and the subsequent tsunami resulted in major damage. This paper presents the timeline of earthquake mitigation and recovery, as seen by the authors. Possible research directions where the authors think that many open questions still remain are identified. These are primarily based on the important lessons learned from the 2011 Tohoku earthquake.

Elemental damping formulation: an alternative modelling of inherent damping in nonlinear dynamic analysis

To date, nonlinear dynamic analysis for seismic engineering predominantly employs the classical Rayleigh damping model and its variations. Though earlier studies have identified issues with the use of this model in nonlinear seismic analysis, it still remains the popular choice for engineers as well as for software providers. In this paper a new approach to modelling damping is initiated by formulating the damping matrix at an elemental level. To this regard, two new elemental level discrete damping models adapted from their global counterparts are proposed for its application in nonlinear dynamic analysis. Implementation schemes for these newly proposed models using Newmark incremental method and revised Newmark total equilibrium method is outlined. The performance of these proposed models, compared to existing models, is illustrated by conducting nonlinear dynamic analyses on a four story RC frame designed to Eurocodes. The incremental dynamic analysis study presented in the paper illustrates the fact that both the proposed models seem to produce more reliable results from an engineering perspective in comparison to the global models. It is also shown that the proposed elemental damping models lead to smaller and more realistic damping moments in the plastic hinges. Furthermore, these models could be easily included in existing software frameworks without adding noticeably to the computational effort. The computation time required for these models is approximately equivalent to the one required when using the tangent Rayleigh damping matrix with constant coefficients.

Seismic Behavior and Design of Wall–EDD–Frame Systems

Walls and frames have different deflection lines and, depending on the seismic mass they support, may often poses different natural periods. In many cases, wall-frame structures present an advantageous behavior. In these structures the walls and the frames are rigidly connected. Nevertheless, if the walls and the frames were not rigidly connected, an opportunity for an efficient passive control strategy would arise: Connecting the two systems by energy dissipation devices (EDDs) to result in wall-EDD-frame systems. This, depending on the parameters of the system, is expected to lead to an efficient energy dissipation mechanism. This paper studies the seismic behavior of wall-EDD-frame systems in the context of retrofitting existing frame structures. The controlling non-dimensional parameters of such systems are first identified. This is followed by a rigorous and extensive parametric study that reveals the pros and cons of the new system versus wall-frame systems. The effect of the controlling parameters on the behavior of the new system are analyzed and discussed. Finally, tools are given for initial design of such retrofitting schemes. These enable both choosing the most appropriate retrofitting alternative and selecting initial values for its parameters.