• Structural Engineering and Mechanics
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• v.84 no.2
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• pp.285-293
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• 2022

Lumped damage mechanics (LDM) is a recent nonlinear theory with several applications to civil engineering structures, such as reinforced concrete and steel buildings. LDM apply key concepts of classic fracture and damage mechanics on plastic hinges. Therefore, the lumped damage models are quite successful in reproduce actual structural behaviour using concepts well-known by engineers in practice, such as ultimate moment and first cracking moment of reinforced concrete elements. So far, lumped damage models are based in the strain energy equivalence hypothesis, which is one of the fictitious states where the intact material behaviour depends on a damage variable. However, there are other possibilities, such as the energy equivalence hypothesis. Such possibilities should be explored, in order to pursue unique advantages as well as extend the LDM framework. Therewith, a lumped damage model based on the energy equivalence hypothesis is proposed in this paper. The proposed model was idealised for reinforced concrete structures, where a damage variable accounts for concrete cracking and the plastic rotation represents reinforcement yielding. The obtained results show that the proposed model is quite accurate compared to experimental responses.

• Structural Engineering and Mechanics
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• v.26 no.5
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• pp.569-589
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• 2007

This paper presents an analytical model for RC beam-column connections that takes into account bond deterioration between reinforcing steel and concrete. The model is based on the Lumped Damage Mechanics (LDM) theory which allows for the characterization of cracking, degradation and yielding, and is extended in this paper by the inclusion of the slip effect as observed in those connections. Slip is assumed to be lumped at inelastic hinges. Thus, the concept of "slip hinge", based on the Coulomb friction plasticity theory, is formulated. The influence of cracking on the slip behavior is taken into account by using two concepts of LDM: the effective moment on an inelastic hinge and the strain equivalence hypothesis. The model is particularly suitable for wide beam-column connections for which bond deterioration dominates the hysteretic response. The model was evaluated by the numerical simulation of five tests reported in the literature. It is found that the model reproduces closely the observed behavior.

• Computers and Concrete
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• v.29 no.1
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• pp.1-14
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• 2022

Several aspects influence corrosive processes in reinforced concrete (RC) structures such as environmental conditions, structural geometry and mechanical properties. Since these aspects present large randomnesses, probabilistic models allow a more accurate description of the corrosive phenomena. Besides, the definition of limit states in the reliability assessment requires a proper mechanical model. In this context, this study proposes a straightforward methodology for the mechanical-probabilistic modelling of RC structures subjected to reinforcements' corrosion. An improved damage approach is proposed to define the limit states for the probabilistic modelling, considering three main degradation phenomena: concrete cracking, rebar yielding and rebar corrosion caused either by chloride or carbonation mechanisms. The stochastic analysis is evaluated by the Monte Carlo simulation method due to the computational efficiency of the Lumped Damage Model for Corrosion (LDMC). The proposed mechanical-probabilistic methodology is implemented in a computational framework and applied to the analysis of a simply supported RC beam and a 2D RC frame. Curves illustrate the probability of failure evolution over a service life of 50 years. Moreover, the proposed model allows drawing the probability of failure map and then identifying the critical failure path for progressive collapse analysis. Collapse path changes caused by the corrosion phenomena are observed.

• Steel and Composite Structures
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• v.1 no.3
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• pp.283-294
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• 2001

In the present work a constitutive model is developed which permits the assessment of the structural performance through a criterion based on cumulative damage. For it, a damage index is defined and is evaluated through the application of the Miner's rule in low-cycle fatigue. However, the damage index is not considered as a posteriori variable since is incorporated explicitly as an internal variable in the constitutive equations which produces a direct coupling between the damage and the structural mechanical behaviour allowing the possibility of considering as a whole different coupled phenomena. For the elaboration of this damage model, the concepts of the mechanics of continuum medium are applied on lumped dissipative models in order to obtain a coupled simplified model. As a result an elastoplastic model coupled with damage and fatigue damage is obtained.

• Earthquakes and Structures
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• v.7 no.3
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• pp.349-365
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• 2014

The dynamic response of structures under extremely short duration dynamic loads is of great concern nowadays. This paper investigates structures' response as well as the associated structural damage to explosive loads considering and ignoring the supporting soil flexibility effect. In the analysis, buildings are modeled by two alternate approaches namely, (1) building with fixed supports, (2) building with supports accounting for soil-flexibility. A lumped parameter model with spring-dashpot elements is incorporated at the base of the building model to simulate the horizontal and rotational movements of supporting soil. The soil flexibility for various shear wave velocities has been considered in the investigation. In addition, the influence of variation of lateral natural periods of building models on the obtained response and peak response time-histories besides damage indices has also been investigated under blast loads with different peak over static pressures. The Dynamic response is obtained by solving the governing equations of motion of the considered building model using a developed Matlab code based on the finite element toolbox CALFEM. The predicted results expressed in time-domain by the building model incorporating SSI effect are compared with the corresponding model results ignoring soil flexibility effect. The results show that the effect of surrounding soil medium leads to significant changes in the obtained dynamic response of the considered systems and hence cannot be simply ignored in damage assessment and response time-histories of structures where it increases response and amplifies damage of structures subjected to blast loads. Moreover, the numerical results provide an understanding of level of damage of structure through the computed damage indices.

• Steel and Composite Structures
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• v.2 no.1
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• pp.21-34
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• 2002

A model of the process of local buckling in tubular steel structural elements is presented. It is assumed that this degrading phenomenon can be lumped at plastic hinges. The model is therefore based on the concept of plastic hinge combined with the methods of continuum damage mechanics. The state of this new kind of inelastic hinge is characterized by two internal variables: the plastic rotation and the damage. The model is valid if only one local buckling appears in the plastic hinge region; for instance, in the case of framed structures subjected to monotonic loadings. Based on this damage model, a new finite element that can describe the development of local buckling is proposed. The element is the assemblage of an elastic beamcolumn and two inelastic hinges at its ends. The stiffness matrix, that depends on the level of damage, the yielding function and the damage evolution law of the two hinges define the new finite element. In order to verify model and finite element, several small-scale frames were tested in laboratory under monotonic loading. A lateral load at the top of the frame was applied in a stroke-controlled mode until local buckling appears and develops in several locations of the frame and its ultimate capacity was reached. These tests were simulated with the new finite element and comparison between model and test is presented and discussed.

• Journal of Korea Water Resources Association
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• v.45 no.2
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• pp.203-215
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• 2012

The objective of this study is to develop a catchment hydrologic cycle assessment model which can assess the impact of urban development and designing water cycle improvement facilities. Developed model might contribute to minimize the damage caused by urban development and to establish sustainableurban environments. The existing conceptual lumped models have a potential limitation in their capacity to simulate the hydrologic impacts of land use changes and assess diverse urban design. The distributed physics-based models under active study are data demanding; and much time is required to gather and check input data; and the cost of setting up a simulation and computational demand are required. The Catchment Hydrologic Cycle Assessment Tool (hereinafter the CAT) is a water cycle analysis model based on physical parameters and it has a link-node model structure. The CAT model can assess the characteristics of the short/long-term changes in water cycles before and after urbanization in the catchment. It supports the effective design of water cycle improvement facilities by supplementing the strengths and weaknesses of existing conceptual parameter-based lumped hydrologic models and physical parameter-based distributed hydrologic models. the model was applied to Seolma-cheon catchment, also calibrated and validated using 6 years (2002~2007) hourly streamflow data in Jeonjeokbigyo station, and the Nash-Sutcliffe model efficiencies were 0.75 (2002~2004) and 0.89 (2005~2007).

• Computers and Concrete
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• v.6 no.4
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• pp.319-341
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• 2009

A new formulation based on lumped plasticity and inelastic hinges is presented in this paper for nonlinear analysis of Reinforced Concrete (RC) frame structures. Inelastic hinge behaviour is described using the principles of Continuum Damage Mechanics (CDM). Member formulation contains provisions to model stiffness degradation due to cracking of concrete and yielding of reinforcing steel. Depending on its nature, cracking is classified as concentrated or distributed. Concentrated cracking is accounted through a damage variable and its growth is defined based on strain energy principles. Presence of distributed flexural cracks in a member is taken care of by modelling it as non-prismatic. Plasticity theory supported by effective stress concept of CDM is applied to describe the post-yield response. Nonlinear quasi-static analysis is carried out on a RC column and a wide two-storey RC frame to verify the formulation. The column is subjected to constant axial load and monotonic lateral load while the frame is subjected to only lateral load. Computed results are compared with those due to experiments or other numerical methods to validate the performance of the formulation and also to highlight the contribution of distributed cracking on global response.

• Nuclear Engineering and Technology
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• v.53 no.8
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• pp.2696-2707
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• 2021

The purpose of this study is to investigate the efficiency of various structural modeling schemes for evaluating seismic performances and fragility of the reactor containment building (RCB) structure in the advanced power reactor 1400 (APR1400) nuclear power plant (NPP). Four structural modeling schemes, i.e. lumped-mass stick model (LMSM), solid-based finite element model (Solid FEM), multi-layer shell model (MLSM), and beam-truss model (BTM), are developed to simulate the seismic behaviors of the containment structure. A full three-dimensional finite element model (full 3D FEM) is additionally constructed to verify the previous numerical models. A set of input ground motions with response spectra matching to the US NRC 1.60 design spectrum is generated to perform linear and nonlinear time-history analyses. Floor response spectra (FRS) and floor displacements are obtained at the different elevations of the structure since they are critical outputs for evaluating the seismic vulnerability of RCB and secondary components. The results show that the difference in seismic responses between linear and nonlinear analyses gets larger as an earthquake intensity increases. It is observed that the linear analysis underestimates floor displacements while it overestimates floor accelerations. Moreover, a systematic assessment of the capability and efficiency of each structural model is presented thoroughly. MLSM can be an alternative approach to a full 3D FEM, which is complicated in modeling and extremely time-consuming in dynamic analyses. Specifically, BTM is recommended as the optimal model for evaluating the nonlinear seismic performance of NPP structures. Thereafter, linear and nonlinear BTM are employed in a series of time-history analyses to develop fragility curves of RCB for different damage states. It is shown that the linear analysis underestimates the probability of damage of RCB at a given earthquake intensity when compared to the nonlinear analysis. The nonlinear analysis approach is highly suggested for assessing the vulnerability of NPP structures.

• Journal of the Korea institute for structural maintenance and inspection
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• v.23 no.7
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• pp.145-151
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• 2019

The fragility analyses for the partially filled horizontal cylindrical tank having a flexible wall were conducted to evaluate seismic performance. An equivalent simplified model with two lumped masses representing to impulsive and convective masses was used to represent the liquid storage system. This simplified model was validated by comparing its time history analysis results with the 3D FSI model results. The horizontal tank was analyzed under bi-directional excitations. Seismic fragility curves for the stability were developed in transverse and longitudinal directions. Fragility curves show that seismic damage for the horizontal storage system is more susceptible in the transverse direction.