On the lumped damage modelling of reinforced concrete beams and arches

The analysis of reinforced concrete structures can be performed by means of experiments or numerical studies. The first way is usually quite expensive, so the second one sometimes is a good option to understand the physical behaviour of actual structures. Lumped damage mechanics appears as one of the latest nonlinear theories and presents itself as an interesting alternative to analyse the mechanical behaviour of reinforced concrete structures. The lumped damage mechanic applies concepts of the classic fracture and damage mechanics in plastic hinges for nonlinear analysis of reinforced concrete structures. Therefore, this paper deals with a novel physical definition of the correction factor γ for cracking evolution that ensures the presented lumped damage model depicts accuracy when it is compared to experimental observations of reinforced concrete beams and arches. Based on such experiments, the numerical analysis showed that γ value has upper and lower thresholds, depending on the physical and geometric properties of the reinforced concrete element. Notwithstanding, for γ values inside of the proposed interval, there is a best value of γ

Evaluation of the behaviour of reinforced concrete beams repaired with glass fibre reinforced polymer (GFRP) using a damage variable

The use of fibre reinforced polymers (FRP) for increasing the strength of RC structures became a usual method. FRP presents easy application and demands low space and provide significant strength increase. Usually, the decision for FRP use is made in terms of applied loads and deflections. However, such quantities can vary significantly depending on the characteristics of the structural element e.g. span, effective depth and concrete resistance. Therefore, this paper aims to present an alternative control variable to analyse the behaviour of RC beams repaired with glass fibre reinforced polymer (GFRP), called damage. Such damage variable accounts for concrete cracking and it was experimentally measured before and after the application of GFRP. Note that the application of GFRP increased the ultimate load for all repaired beams. The damage values of such beams also increased when collapse was reached. Furthermore, it was observed that the collapse mechanism shifted to shear and did not occurred the failure of the GFRP

Lumped damage mechanics as a diagnosis tool of reinforced concrete structures in service: case studies of a former bridge arch and a balcony slab

Reinforced concrete structures may need repair in order to ensure the designed durability. Such necessity vary in cause and effect, but the structural diagnosis serves as the basis for adopting intervention measures. The assessment of the structural condition usually is made in loco, but sometimes numerical analyses are required as a low cost and effective preliminary diagnosis. In general, numerical analyses use hundreds or thousands of finite elements and nonlinear theories that are not often used in engineering practice. As an alternative, lumped damage mechanics (LDM) uses key concepts of classic fracture and damage mechanics in plastic hinges throughout well-known quantities such as ultimate moment and cracking moment. Such theory describes the concrete cracking by a damage variable, which can be used as a diagnosis criterion. Therefore, this paper presents LDM as a diagnosis tool to analyse actual structures. The case studies presented in this paper are a former bridge arch tested in China and a balcony that collapsed in Brazil. The results show that LDM numerical response of those structures are quite close to laboratory observations (former bridge arch) and in loco measurements (balcony)

A nonlinear procedure for the analysis of RC beams

Abstract This work deals with the development of a computational method for the nonlinear analysis of reinforced concrete beams subjected to general loading and constraint conditions, able to catch crack formation and propagation. To this aim, a layered beam finite element is developed. The displacement field along beam axis and height is modelled through polynomial functions, whose number of terms is varied based on the complexity of the considered problem. The mechanical nonlinearity of the material is taken into account by implementing a smeared constitutive model for cracked reinforced concrete elements. The effectiveness of the proposed procedure, which can be applied to the analysis of both new and existing buildings, is proved through comparison with significant experimental data from technical literature, relative to both statically determinate and indeterminate beams

bending stiffness of truss reinforced steel concrete composite beams

This paper is concerned with a special steel-concrete composite beam in which the resisting system is a truss structure whose bottom chord is made of a steel plate supporting the precast floor system. This system works in two distinct phases with two different resisting mechanisms: during the construction phase, the truss structure bears the precast floor system and the resisting system is that of a simply supported steel truss; once the concrete has hardened, the truss structure becomes the reinforcing element of a steel-concrete composite beam, where it is also in a pre-stressed condition due to the loads carried before the hardening of concrete. Within this framework, the effects of the diagonal bars on the bending stiffness of this composite beam are investigated. First, a closed-form solution for the evaluation of the equivalent bending stiffness is derived. Subsequently, the influence of geometrical and mechanical characteristics of shear reinforcement is studied. Finally, results obtained from parametric and numerical analyses are discussed

MODELO DE DANO CONCENTRADO APLICADO À MODELAGEM MECÂNICA DE ESTRUTURAS EM CONCRETO ARMADO

O comportamento fisicamente não linear de estruturas em concreto armado pode ser representado por meio dos modelos da teoria do dano contínuo. Tal abordagem visa a descrição dos processos de degradação mecânico-material, os quais são correntemente acoplados à métodos numéricos. Nos modelos de dano contínuo, a avaliação do dano material é efetuada ao longo de todo o domínio estrutural, o que eleva consideravelmente seu custo computacional. Alternativamente, a teoria do dano concentrado permite a modelagem precisa do comportamento mecânico fisicamente não linear do concreto armado sem a necessidade da representação do dano ao longo de todo o domínio estrutural. Esta teoria alia conceitos da mecânica da fratura ao fenômeno de formação de rótulas plásticas, sendo aplicada com precisão em elementos estruturais unidimensionais. Neste trabalho, esta teoria é aplicada na análise mecânica de uma viga e de um pórtico plano em concreto armado. Os resultados obtidos com o modelo de dano concentrado são comparados com respostas numéricas e experimentais disponíveis na literatura. Boa concordância é observada entre os resultados apresentados pelas referências e pelo modelo de dano concentrado

Elasto-plastic and damage modeling of reinforced concrete

Modeling the mechanical behavior of Reinforced Concrete (RC) is still one of the most difficult challenges in the field of structural engineering. The Nonlinear Finite Element Analysis (NFEA) and modeling of the behavior of RC members are the primary goals of this study. The macroscopic components of RC, Concrete material and reinforcing steel, are represented herein by separate material models. These material models are combined together using a model that describes the global effect of interaction between reinforcing steel and concrete in order to simulate the behavior of the composite RC material. A thermodynamically consistent constitutive model for concrete that incorporates concrete-plasticity and fracture-energy-based continuum damage mechanics is presented. An effective stress space plasticity yield criterion, with multiple hardening functions and a non-associative plasticity flow rule, is used simultaneously with two (tensile and compressive) isotropic damage criteria. The spectral decomposition of the stress tensor into tensile and compressive components is utilized in all criteria in order to simulate different responses of the material under various loading patterns. The damage criteria are based on the hydrostatic-deviatoric sensitive damage energy release rates in tension and compression derived from the Helmholtz free energy function. Three dissipation mechanisms are defined, one for plasticity and two for damage, to control the dissipation process of the material model. Elastic-plastic models that account for isotropic perfectly-plastic and plastic-strain-hardening (linear, bilinear and nonlinear) of the steel reinforcement are provided as well. The global effect of bond-slip is incorporated into the stress-strain diagram of the reinforcing bars in an attempt to describe this interaction phenomenon in a stress-strain driven environment. The Numerical implementation and application are important parts of this study. A suitable elastoplasticity-implicit/damage-explicit scheme is adapted here for the integration of the incremental constitutive equations. The elastic-predictor, plastic-corrector and damage-corrector steps are used to facilitate the integration procedure. The constitutive approach is implemented, through numerical algorithms; in the advanced FE software ABAQUS via user defined material subroutine UMAT to analyze and better describe the overall behavior of such a composite material. Concrete and RC beams subjected to static-short-term-monotonic loading are analyzed in an assumed isothermal environment. The simulated results are compared to experimental studies conducted by other researchers