Viscous damage model for timoshenko beam structures

A complete method to predict the behavior of reinforced concrete structures with beams and columns controlled by flexure is proposed. The concrete is modelled with a damage mechanics approach. The parameters of the model are adjusted on material tests and various procedures that account for confinement and cyclic response. Steel is modelled with a simple cyclic model. A simplified finite element program allows the prediction of the global and the local behavior from the constitutive laws of the material. This program uses multilayer beam elements. Localization of damage for softening structures is taken into consideration by a meshing procedure. The methodology is used to predict the behavior of three different kinds of structures subjected to three different types of loading. Predictions are in very good agreement with experimental results.

Journal of the Mechanical Behavior of Materials, 2005

IRJET, 2020

The main objective of this study is, evaluation damage index of reinforced concrete moment resisting frames by" NONLINEAR STATIC PROCEDURE" nonlinear static analysis includes the capacity spectrum method (CSM) that uses the intersection of the capacity (pushover) curve and a reduced response spectrum to estimate maximum displacement in terms of damage of building. Nonlinear static procedure is simple and practical method for static damage index. For this purpose, first some functions are derived to estimate damage to the structure using pushover analysis and then designed procedure is proposed. In this study damage function is estimated by using correlation between park-Ang. damage index (NLDD) and nonlinear static damage index (NLSD) which is based on the pushover analysis. For this purpose dynamic and static damage analysis are performed on several concrete frames subjected to various earthquake acceleration records. So the detail explanation is found in this study.

Revista IBRACON de Estruturas e Materiais, 2012

This work presents one and two-dimensional numerical analyses using isotropic and anisotropic damage models for the concrete in order to discuss the advantages of these modeling. Initially, it is shortly described the damage model proposed by Mazars. This constitutive model assumes the concrete as isotropic and elastic material, where locally the damage is due to extensions. On the other hand, the damage model proposed by Pituba, the material is assumed as initial elastic isotropic medium presenting anisotropy, plastic strains and bimodular response (distinct elastic responses whether tension or compression stress states prevail) induced by the damage. To take into account for bimodularity two damage tensors governing the rigidity in tension and compression regimes, respectively, are introduced. Damage activation is expressed by two criteria indicating the initial and further evolution of damage. Soon after, the models are used in numerical analyses of the mechanical behavior of rei...

The main purpose of the presented article is an investigation of the Timoshenko beam equation sensitivity to the presence of crack in the rode-like structure. We describe the crack in the Timoshenko beam as a cutting in the form as a smoothed delta-function. The solutions of this equation and experimental data on the natural frequencies and vibration modes shape then are used at forming of discrepancy functional that further optimized in order to determine the position and depth of a crack. We compare here the solutions of the cracked Timoshenko beam equation with results of 3D finite element analysis performed on the notched elastic beams and also with experimental data. The advantage of the proposed Timoshenko beam – based approach comparing with the method of two beams connected by a torsion spring, is that the Timoshenko model requires no assumptions about the stiffness of the spring. Moreover, the developed approach allows to model a crack in a non-uniform beams that unallowabl...

Current Science, 2019

Different available analytical and experimental metho-dologies of local and global damage index (LDI and GDI) determination for bridges and buildings along with their mathematical expression are reviewed in this article. In the literature, impact of seismic loading and material deterioration due to ageing effects is the main focus to study the performance. Case studies for assessment of bridges and buildings are appended here to understand variation of damage index (DI) for various levels of seismicity. The utility of the proposed methods has been discussed in this case study. This article also includes progressive development, limitations and directions of future research on damage assessment of structures. Based on the extensive literature review, the authors have critically analysed the pros and cons of the available methods. However, time-dependent damage assessment, damage estimation for various structural and non-structural components using different materials, variation of damage for different configurations of structures, and deterioration of roads and bridges are the probable future scope for research. In future, damage-based design considering multiple response parameters along with uncertain load characteristics such as seismic load, wind load, blast load, floods and accidental load could be considered to select allowable damage of structures that would help to understand and ensure the time-dependent safety, progressive phases of collapse and serviceability with high reliability satisfying smart structural requirements. Keywords: Bridges and buildings, damage index, loss assessment, seismicity. DAMAGE to structures is mainly caused by different environmental factors and ageing. Over the years various methods have been used for damage assessment. In this article, an overview of damage assessment is provided. In 1921, Griffith 1 had introduced fracture mechanics for brittle materials, but practically it has been mostly applied to metallic materials. Kaplan 2 had implemented fracture mechanics for concrete. However, several researchers have shown interest in this approach and excavated this area with proficiency. Damage assessment of a building could be easily done with several damage indices (DIs). DI of the structure could be determined either by balancing, demand and capacity of the structure, or by degradation of some structural property 3. In Lee and Fenves plastic damage model, DI was estimated from nonlinear regression of experimental column test data, concentrating on local tensile damage variables such as drift ratio and moment 4. Another DI was proposed based on cumulative member ductility considering limiting rotation capacity for steel, reinforced concrete (RC) columns, composite beams and composite steel-concrete connection sub-assemblies 5. Damage probability matrices are useful for decisive criteria for strengthening strategies and repairing buildings; Monte Carlo simulation with building strength parameters and ground motions are the variables for it 6. DI has been determined from the pushover curve containing initial and final stiffness 7. Damage could be assessed from the relationship between modal parameters-based GDI and local stiffness degradation along with the ageing effect on structures 8. Further, seismic vulnerability of damaged and undamaged RC bare frames, RC buildings with infill wall considering in-plane behaviour, and combined in-plane and out-of-plane nonlinear behaviour examined under main seismic shock as well as aftershock events 9. A damage curve was derived with the decrease of bending stiffness at the fractured section and DI estimated by strain responses of steel beams for pre-and post-earthquakes 10. Structural damage was presented by flexibility matrices with changes of modal parameters (modal damping, frequency and mode shapes) 11. However, irrespective of structure type and material, the ratio between initial resistance and reduced resistance capacity was calculated as general DI 12. Plastic damage of concrete with thermodynamics laws depending on continuum damage mechanics theory was applied on fibre RC beam column simulated in ABAQUS 13. Global damage index (GDI) of RC structure was estimated considering pseudo plastic hinges 14. Seismic damage of RC members for shear-flexure interaction in inelastic range was analysed, which showed a sound relationship between finite element model and experimental results 15. A structural DI was calculated with curvature and stiffness 16. Inclusion of correlative term 'stiffness' in the Park-Ang DI in Bayesi-an framework was introduced 17. Influence of different durations of aftershock was measured in terms of degradation of strength and stiffness of a structure termed as damage ratio 18. Structural damage was accurately detected using modified Cornwell indicator with genetic algorithm 19. DI also depends on hysteretic energy dissipated by a structural member and a drift ratio of 76 RC

Bulletin of Earthquake Engineering, 2013

The city of Lorca (Spain) was hit on May 11th, 2011, by two consecutive earthquakes of magnitudes 4.6 and 5.2 M w , causing casualties and important damage in buildings. Many of the damaged structures were reinforced concrete frames with wide beams. This study quantifies the expected level of damage on this structural type in the case of the Lorca earthquake by means of a seismic index /" that compares the energy input by the earthquake with the energy absorption/dissipation capacity of the structure. The prototype frames investigated represent structures designed in two time periods (1994-2002 and 2003-2008), in which the applicable codes were different. The influence of the masonry infill walls and the proneness of the frames to concentrate damage in a given story were further investigated through nonlinear dynamic response analyses. It is found that (1) the seismic index method predicts levels of damage that range from moderate/severe to complete collapse; this prediction is consistent with the observed damage; (2) the presence of masonry infill walls makes the structure very prone to damage concentration and reduces the overall seismic capacity of the building; and (3) a proper hierarchy of strength between beams and columns that guarantees the formation of a strong column-weak beam mechanism (as prescribed by seismic codes), as well as the adoption of countermeasures to avoid the negative interaction between non-structural infill walls and the main frame, would have reduced the level of damage from I v = l (collapse) to about /" = 0.5 (moderate/severe damage).

Applied Mathematical Modelling, 2019

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Reinforced concrete structures are likely to experience some damage when subjected to earthquake loading. Damage index is a well accepted way of expressing the extent of damage and is widely used by researchers. Last few decades have seen many concepts for calibrating an appropriate damage index being proposed. This paper presents a detailed review of available concepts by classifying those into two broad categories: non-cumulative and cumulative. Non-cumulative indices do not include the effects of cyclic loading, whilst the cumulative indices are rather more rational. It is however observed that most of the existing damage indices are unable to accurately describe the state of damage of reinforced concrete structures. An ideally damage index should vary within a scale of 0 to 1 -0 being the state of elastic response whilst 1 should refer to collapse; most of the existing damage indices do not satisfy this criteria. A new damage index based on the hysteretic energy is proposed herein and its performance is compared against the widely accepted concept proposed by in the case of a column subjected to compulsive cyclic displacement at top. The proposal is still at preliminary stage but it meets the essential criteria for a damage index.

1995

Local, modal and overall damage indicators for reinforced concrete shear frames subject to seismic excitation are defined and studied. Each storey of the shear frame is represented by a Clough and Johnston hysteretic oscillator with degrading elastic fraction of the restoring force. The local maximum softening damage indicators are defined in a closed form based on the variation of the eigenfrequency of the local oscillators due to the local stiffness and strength deterioration. The modal maximum softening damage indicators are calculated from the variation of the eigenfrequencies of the structure during the excitation. The linear and nonlinear parameters of the local oscillators are assumed to be known. Next, a statistical analysis is performed where a sample 5 storey shear frame is subject to sinusoidal and simulated earthquake excitations. The shear frame is subject to 30 independent simulations of the earthquake excitation which is modeled as a stationary Gaussian stochastic process with Kanai-Tajimi Spectrum, multiplied by an envelope function. Equations of motion of the storeys are solved by a Runge-Kutta fourth order scheme where the local softening value is recorded. The modal maximum softening indicators are calculated from the known instantaneous stiffness matrix which is a function of structural properties and local damage. Alternatively, a Fourier analysis is performed for consecutive time-windows to measure the same evolution using the top storey displacement. Finally, the relationship between local and modal damage indices are investigated statistically.

Acta Physica Polonica A, 2019

Performance of structures depends on the vulnerability of the structure and the seismic hazard of the region. As part of the Mediterranean-Transasian belt, the Croatian territory is located in an earthquake prone area. Implementation of earthquake-resistant building design rules is essential in order to mitigate the damages of earthquakes affecting settlement areas. Performance-based evaluation of buildings may be conducted through fragility curves developed for different levels of performance. In this paper, a reinforced concrete frame structure was designed as a moderately ductile building according to EN 1998-1:2004. Incremental dynamic analysis of the nonlinear numerical reinforced concrete model is implemented in the software package SeismoStruct, wherein the frame elements (column, beam) were defined as finite elements. The seismic risk of the model is estimated by probabilistic analysis that takes the randomness of seismic excitation into account and evaluates the probability of exceeding a certain critical condition. Seven real time histories selected from European Strong-motion Database were used. The structural behaviour is observed based on maximum interstorey drifts through the entire height of the building for each seismic excitation. The results obtained by incremental dynamic analysis of the nonlinear numerical model are also compared with an empirical seismic vulnerability method-macroseismic method.

Keywords: residual capacity, damaged building, pushover analysis, nonlinear time history analysis, post-earthquake assessment, reinforced concrete frame.

There are several methods to predict buildings' damage index using traditional non-destructive evaluation method, such as visual inspection and instrument evaluation method. However, these types of method are complex for large structures since it is difficult to assess some parts of them. The evaluation of damage index in Malaysia is limited especially when the building subjected to earthquake loading. Due to increased number of earthquake incidents in Malaysia, the development of damage detection method therefore become much more challenging. This paper presents the prediction of damage index of building using RUAUMOKO 2D program. The RUAUMOKO 2D program presents Park and Ang damage model to predict damage index of buildings. The study of the damage state of building on the reinforced concrete (RC) frame which subjected to four ground motions was conducted. The time history analysis method was applied using Acheh earthquake recorded at Ipoh, Malaysia which occurred on December 26, 2004 at Indian Ocean with magnitude 9.3 on Richter scale and the analyses were carried out using four intensities of seismic load; 0.05g, 0.10g, 0.15g, and 0.20g, respectively. The performance of the structure is shown by the damage index recorded from RUAUMOKO 2D analysis. Seismic performance of the RC frame structures indicates that high-rise buildings are much affected than low-rise when exposed to the ground acceleration up to 0.15g.

A simplified model is proposed to simulate the nonlinear behavior of a four-story full-scale reinforced concrete framed structure submitted to severe dynamic loading. The structure has been tested pseudodynamically in the European Laboratory for Structural Assessment (ELSA) at the Joint Research Center of the European Commission. The proposed model uses 2D multi layered Bernoulli beam elements and uniaxial constitutive laws based on damage mechanics and plasticity. Comparison with the experimental results shows the well funding of the approach.

Journal of Constructional Steel Research, 2010

In the last two decades, many studies have reported the effectiveness of Experimental Modal Analysis and Finite Element Model Updating in mechanical and aerospace engineering, where they represent useful tools for Structural Health recognition and can provide an information base for detection, assessment and quantification of structural damage due to exercise actions and exceptional events.