• Structural Engineering and Mechanics
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• 제56권2호
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• pp.169-188
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• 2015

There are two types of nonlinear analysis methods for building frameworks depending on the method of modeling the plastification of members including lumped plasticity and distributed plasticity. The lumped plasticity method assumes that plasticity is concentrated at a zero-length plastic hinge section at the ends of the elements. The distributed plasticity method discretizes the structural members into many line segments, and further subdivides the cross-section of each segment into a number of finite elements. When a reinforced concrete member experiences inelastic deformations, cracks tend to spread form the joint interface resulting in a curvature distribution. The program IDARC includes a spread plasticity formulation to capture the variation of the section flexibility, and combine them to determine the element stiffness matrix. In this formulation, the flexibility distribution in the structural elements is assumed to be the linear. The main objective of this study is to evaluate the accuracy of linear flexibility distribution assumed in the spread inelasticity model. For this purpose, nonlinear analysis of two reinforced concrete frames is carried out and the linear flexibility models used in the elements are compared with the real ones. It is shown that the linear flexibility distribution is incorrect assumption in cases of significant gravity load effects and can be lead to incorrect nonlinear responses in some situations.

• Computers and Concrete
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• 제20권1호
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• pp.11-22
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• 2017

There are two methods to model the plastification of members comprising lumped and distributed plasticity. When a reinforced concrete member experiences inelastic deformations, cracks tend to spread from the joint interface resulting in a curvature distribution; therefore, the lumped plasticity methods assuming plasticity is concentrated at a zero-length plastic hinge section at the ends of the elements, cannot model the actual behavior of reinforced concrete members. Some spread plasticity models including uniform, linear and recently power have been developed to take extended inelastic zone into account. In the aforementioned models, the extended inelastic zones in proximity of critical sections assumed close to connections are considered. Although the mentioned assumption is proper for the buildings simply imposed lateral loads, it is not appropriate for the gravity load effects. The gravity load effects can influence the inelastic zones in structural elements; therefore, the plasticity models presenting the flexibility distribution along the member merely based on lateral loads apart from the gravity load effects can bring about incorrect stiffness matrix for structure. In this study, the linear flexibility distribution model is improved to account for the distributed plasticity of members subjected to both gravity and lateral load effects. To do so, a new model in which, each member is taken as one structural element into account is proposed. Some numerical examples from previous studies are assessed and outcomes confirm the accuracy of proposed model. Also comparing the results of the proposed model with other spread plasticity models illustrates glaring error produced due to neglecting the gravity load effects.

• 한국지진공학회논문집
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• 제26권6호
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• pp.227-235
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• 2022

For a member model in nonlinear structural analysis, a lumped plastic model that idealizes its flexural bending, shear, and axial behaviors by springs with the nonlinear hysteretic model is widely adopted because of its simplicity and transparency compared to the other rigorous finite element methods. On the other hand, a challenging task in its numerical solution is to satisfy the equilibrium condition between nonlinear flexural bending and shear springs connected in series. Since the local forces between flexural and shear springs are not balanced when one or both springs experience stiffness changes (e.g., cracking, yielding, and unloading), the additional unbalanced force due to overshooting or undershooting each spring force is also generated. This paper introduces an iterative scheme for numerical solutions satisfying the equilibrium conditions between flexural bending and shear springs. The effect of equilibrium iteration on analysis results is shown by comparing the results obtained from the proposed method to those from the conventional scheme, where the equilibrium condition is not perfectly satisfied.

• Structural Engineering and Mechanics
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• 제26권5호
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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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• 제6권4호
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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.

• Structural Engineering and Mechanics
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• 제28권6호
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• pp.727-747
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• 2008

In the framework of the SPEAR (Seismic PErformance Assessment and Rehabilitation) research Project, an under-designed three storey RC frame structure, designed to sustain only gravity loads, was subjected, in three different configurations 'as-built', Fiber Reinforced Polymer (FRP) retrofitted and rehabilitated by reinforced concrete (RC) jacketing, to a series of bi-directional pseudodynamic (PsD) tests under different values of peak ground acceleration (PGA) (from a minimum of 0.20g to a maximum of 0.30g). The seismic deficiencies exhibited by the 'as-built' structure after the test at PGA level of 0.20g were confirmed by a post - test assessment of the structural seismic capacity performed by a nonlinear static pushover analysis implemented on the structure lumped plasticity model. To improve the seismic performance of the 'as-built' structure', two rehabilitation interventions by using either FRP laminates or RC jacketing were designed. Assumptions for the analytical modeling, design criteria and calculation procedures along with local and global intervention measures and their installation details are herein presented and discussed. Nonlinear static pushover analyses for the assessment of the theoretical seismic capacity of the structure in each retrofitted configuration were performed and compared with the experimental outcomes.

• Earthquakes and Structures
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• 제13권3호
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• pp.267-277
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• 2017

Base-isolation is now being adopted as a retrofitting strategy to improve seismic behaviour of reinforced concrete (r.c.) framed structures subjected to far-fault earthquakes. However, the increase in deformability of a base-isolated framed building may lead to amplification in the structural response under the long-duration horizontal pulses of high-magnitude near-fault earthquakes, which can become critical once the strength level of a fire-weakened r.c. superstructure is reduced. The aim of the present work is to investigate the nonlinear seismic response of fire-damaged r.c. framed structures retrofitted by base-isolation. For this purpose, a five-storey r.c. framed building primarily designed (as fixed-base) in compliance with a former Italian seismic code for a medium-risk zone, is to be retrofitted by the insertion of elastomeric bearings to meet the requirements of the current Italian code in a high-risk seismic zone. The nonlinear seismic response of the original (fixed-base) and retrofitted (base-isolated) test structures in a no fire situation are compared with those in the event of fire in the superstructure, where parametric temperature-time curves are defined at the first level, the first two and the upper levels. A lumped plasticity model describes the inelastic behaviour of the fire-damaged r.c. frame members, while a nonlinear force-displacement law is adopted for the elastomeric bearings. The average root-mean-square deviation of the observed spectrum from the target design spectrum together with a suitable intensity measure are chosen to select and scale near- and far-fault earthquakes on the basis of the design hypotheses adopted.