George D. Hatzigeorgiou

Static, seismic and stability analyses of a prototype wind turbine steel tower

Selected results of a study concerning the load bearing capacity and the seismic behavior of a prototype steel tower for a 450 kW wind turbine with a horizontal power transmission axle are presented. The main load bearing structure of the steel tower rises to almost 38 m high and consists of thin-wall cylindrical and conical parts, of varying diameters and wall thicknesses, which are linked together by bolted circular rings. The behavior and the load capacity of the structure have been studied with the aid of a refined finite element and other simplified models recommended by appropriate building codes. The structure is analyzed for static and seismic loads representing the effects of gravity, the operational and survival aerodynamic conditions, and possible site-dependent seismic motions. Comparative studies have been performed on the results of the above analyses and some useful conclusions are drawn pertaining to the effectiveness and accuracy of the various models used in this work.

A SIMPLE CONCRETE DAMAGE MODEL FOR DYNAMIC FEM APPLICATIONS

A simple damage model for concrete is presented. The basic version of the model is a combination between the elastic-damage part of the elastoplastic-damage model of Faria & Oliver and the damage theory of Mazars. This basic version of the model takes into account most of the basic traits of concrete under monotonic static and dynamic loading, like the different response under compression and tension, the stiffness reduction with the increase of external loading and the appearance of softening behavior. This model is further enhanced with a sensitivity to the rate of loading and the ability to simulate cycling behavior, characteristics which are necessary for general cases of dynamic loading. The main advantages of this model are the employment of only one damage parameter and the investigation of the damage state in concrete under static or dynamic loading. The model is implemented into a general three-dimensional finite element program capable of treating static and general dynamic problems. The validation and performance of the proposed model is demonstrated by characteristic numerical examples.

Static analysis of 3D damaged solids and structures by BEM

The boundary element method is employed for the analysis of three-dimensional (3D) brittle solids and structures, such as those composed of concrete, rock, ceramics or masonry, under static (monotonic or cycling) loading. The mechanical behavior of these solids can be successfully described by continuum damage mechanical theories. The integral formulation of the problem contains not only boundary, but also volume integrals as well, accounting for damage effects. Thus, in addition to the boundary one, an interior discretization is necessary, which can be restricted to those parts of the structure expected to behave inelastically. Isoparametric linear quadrilateral elements are used for the surface discretization and isoparametric linear hexahedra for the interior discretization. Advanced numerical integration techniques for singular and nearly singular integrals are employed. Numerical examples involving 3D concrete type structures under static loads are presented to illustrate the method and demonstrate its advantages.

Maximum seismic displacements evaluation of steel frames from their post-earthquake residual deformation

The maximum seismic displacements of a structure can be used for the assessment of its post-earthquake performance. In this paper, a simple and efficient procedure is proposed for determining maximum seismic displacements of planar steel frames from their residual deformation. More specifically, the inelastic behaviour of 36 moment resisting steel frames and 36 concentrically X-braced steel frames under one hundred strong ground motions is investigated. Thus, on the basis of extensive parametric studies for these structures and seismic records, empirical equations are constructed for simple and effective prediction of maximum seismic displacements from residual deformation, which can be measured in-situ after strong seismic events. It is found that the usage of residual deformation can be effectively utilized to evaluate the post-earthquake performance level of steel structures.

Seismic behavior of composite steel/concrete MRFs: deformation assessment and behavior factors

Abstract The seismic inelastic behavior of regular planar composite steel/concrete MRFs consisting of I steel beams and concrete filled steel tube (CFT) columns is investigated. For this purpose, a family of 96 regular plane CFT-MRFs are subject to an ensemble of 100 ordinary (far-field type) ground motions scaled to different intensities in order to accommodate different performance levels and their response to these motions is recorded to form a response databank. On the basis of this databank nonlinear regression analysis is employed in order to derive simple formulae which offer a direct estimation of seismic displacements, drift and ductility demands, and the strength reduction (or behavior) factor q, which describes the seismic strength requirements in order to restrict maximum roof ductility demand to a predefined value. The influence of specific parameters on the maximum structural response, such as the number of stories, the beam-to-column stiffness ratio, the column-to-beam strength ratio, the level of inelastic deformation induced by the seismic excitation and the material strengths, is studied in detail. Furthermore, emphasis is given to the ability of the proposed formulae to be employed in the framework of seismic design methods which utilize response spectrum analysis. This essential aspect makes possible both the simple and direct seismic assessment of existing structures and the straightforward deformation-controlled seismic design of new ones because the q factor is a function of deformation.

Direct damage controlled seismic design of plane steel degrading frames

A new method for seismic design of plane steel moment resisting framed structures is developed. This method is able to control damage at all levels of performance in a direct manner. More specifically, the method: (a) can determine damage in any member or the whole of a designed structure under any given seismic load, (b) can dimension a structure for a given seismic load and desired level of damage and (c) can determine the maximum seismic load a designed structure can sustain in order to exhibit a desired level of damage. In order to accomplish these things, an appropriate seismic damage index is used that takes into account the interaction between axial force and bending moment at a section, strength and stiffness degradation as well as low cycle fatigue. Then, damage scales are constructed on the basis of extensive parametric studies involving a large number of frames exhibiting cyclic strength and stiffness degradation and a large number of seismic motions and using the above damage index for damage determination. Some numerical examples are presented to illustrate the proposed method and demonstrate its advantages against other methods of seismic design.

A NUMERICAL APPROACH FOR ESTIMATING THE EFFECTS OF MULTIPLE EARTHQUAKES TO SEISMIC RESPONSE OF STRUCTURES STRENGTHENED BY CABLE-ELEMENTS ∗

Abstract The behaviour of reinforced concrete (RC) frames, which have been strengthened by cable elements and are subjected to multi- ple earthquakes, is numerically investigated. The purpose is to estimate damage indices in order to compare the seismic response of the structures before and after the retrofit by cable element strengthening and to select the optimum strengthening version

Damage detection of framed structures subjected to earthquake excitation using discrete wavelet analysis

This paper describes an application of discrete wavelet analysis for damage detection of a framed structure subjected to strong earthquake excitation. The response simulation data on each floor were obtained by non-linear dynamic analysis. Damage to the frame was introduced due to the non-linear behaviour of the columns and beams. In order for the structural members to reach the yield point or go slightly beyond yielding, the earthquake excitation was scaled up with the appropriate factor. Since the dynamic behaviour of an inelastic structure during an earthquake is a non-stationary process, discrete wavelet analysis was performed in order to analyze the simulation response data for each floor. It was shown that structural damage on a floor, and the time when this occurred can be clearly detected by spikes in the wavelet details of the response, acquired from the corresponding floor. Damage can be detected by observing the spikes directly from the wavelet details or following a statistical procedure. An automatic numerical procedure that can clearly distinguish between the spikes associated with damage and the spikes due to non-stationary excitation is proposed. The effects of noise were taken into account by adding a white Gaussian noise to the simulation response data. Damage to the element can also be detected again from the noised signal, if the level of details and the order of wavelets in the wavelet analysis of the response signal are increased. Numerical results show the effectiveness of the discrete wavelet approach to damage detection of framed structures.

Seismic Design of Steel Frames Equipped by Control Devices

The design philosophy of EC8 is to ensure that in the event of the design earthquake, human lives are protected and no collapse will occur, while extended damages will be observed. This is achieved by ductility and capacity design. This design philosophy drives to an additional cost for repairing damage of structures. On the other hand, it is costly and uneconomic to design structures behaving in elastic range, especially under high level of earthquake excitation. An alter- native direction to this strategy, which is examined in this paper, is to design a controlled structure capable to resist a de- sign earthquake loads, remaining in elastic range and thus without damage. The idea behind this philosophy is that one portion of earthquake loading will be resisted by a control system while the rest will be resisted by the structure. The structure, initially, is analyzed and designed according to the current codes. The elastic and design earthquake forces are first calculated according to the elastic and the design spectrum. The required control forces are calculated as the differ- ence between elastic and design forces. The maximum value of capacity of control devices is then compared with the re- quired control force. If the capacity of the controlled devices is higher than the required control force then the control de- vices are accepted and installed to the structure. Then, the structure is designed according to the design forces. In the case where the maximum available control device capacity is lower than the demanded control force then an additional portion of control forces should be resisted by the building. In that case, an iterative procedure is proposed and a scale factor, � , that reduces the elastic response spectrum to a new design spectrum, is calculated. The structure is redesigned based on the new design spectrum and then the devices are installed to the structure. The proposed procedure imposes that the con- trolled structure will behave elastically for the design earthquake and no damage will occur, consequently no additional repair cost will be needed. An initial cost of buying and installing the control devices is required. In order to ensure that the controlled structure behaves elastically, a dynamic control analysis with saturation and time delay control is per- formed. Following the proposed procedure the numerical results show that the structure remains in elastic and no damage occurs.

Pounding Effects on the Earthquake Response of Adjacent Reinforced Concrete Structures Strengthened by Cable Elements

Abstract A numerical approach for estimating the effects of pounding (seismic interaction) on the response of adjacent Civil Engineering structures is presented. Emphasis is given to reinforced concrete (RC) frames of existing buildings which are seismically strengthened by cable-elements. A double discretization, in space by the Finite Element Method and in time by a direct incremental approach is used. The unilateral behaviours of both, the cable-elements and the interfaces contact-constraints, are taken strictly into account and result to inequality constitutive conditions. So, in each time-step, a non-convex linear complementarity problem is solved. It is found that pounding and cable strengthening have significant effects on the earthquake response and, hence, on the seismic upgrading of existing adjacent RC structures.