Abstract: The proper choice of raw materials and manufacturing parameters for Cross Laminated Timber is essential to promote the proper bonding of the lamellas, aiming at their application in construction. However, few Brazilian species are currently used in the production of Cross Laminated Timber. The aim of this work was to characterize the bonding quality of four Brazilian reforestation species (Pinus elliottii (pino ellioti), Eucalyptus grandis (eucalipto), Toona ciliata (toona) and Acrocarpus fraxinifolius (lazcar)) in the manufacture of Cross Laminated Timber with two-component polyurethane adhesive and five different pressure levels (from 0,1 MPa to 1,3 MPa). Bonding quality was evaluated through delamination and glue line shear tests based on the European standard. Delamination was affected by the wood species, and the best adhesion occurred for the Cross Laminated Timber manufactured with Pinus elliottii (pino ellioti) and Acrocarpus fraxinifolius (lazcar) at the bonding pressure of 0,7 MPa. Cross Laminated Timber bonding pressure did not affect the percentage of wood in the shear test fractured surface, whereas higher density Cross Laminated Timber showed higher percentages.

ABSTRACT To simplify the characterization of wood species, the Brazilian standard document ABNT NBR 7190-1 (2022) establishes the determination of mechanical properties employing the characteristic strength in the compression parallel to grain (fc0,k). This mechanical property is estimated using the linear relation given by the following expression fv0,k = 0.12·fc0,k Brazilian and European standard documents support the estimation of fv0,k using relations among properties. However, the European guidelines in the EN 384 (2019) have used the conventional characteristic strength in the static bending test (fM,k). Thus, this study aimed to investigate the efficiency of the ratio fv0,k = 0.12·fc0,k for adopting 30 hardwoods. The variance analysis results demonstrate the divergence among the experimental outcomes and those values estimated using the relation cited. Therefore, regression models at two parameters were considered to obtain more accurate estimates of fv0,k by adopting fc0,k, and fM,k as independent variables. Regarding the results, the geometric (R² = 80.80%) and linear (R² = 74.19%) models were the most accurate for the estimates of fv0,k in terms of fc0,k, and fM,k, respectively. This fact evinces the good accuracy of the models under consideration, which may provide a more rigorous structural design compared to the correlation currently prescribed by the ABNT NBR 7190-1 (2022).

RESUMO Para simplificar a caracterização de espécies de madeira, o documento normativo brasileiro ABNT NBR 7190-1 (2022) estabelece a determinação de propriedades mecânicas por meio da resistência característica na compressão paralela às fibras (fc0,k). Essa propriedade mecânica é estimada utilizando-se da relação linear dada pela expressão a seguir fv0,k = 0.12·fc0,k. Ambos os documentos normativos europeu e brasileiro prescrevem a estimativa da fv0,k empregando-se relações entre propriedades, embora as diretrizes da europeia contidas na EN 384 (2019) utilize a resistência característica convencional obtida no teste de flexão estática (fM,k). Assim, esse estudo teve o objetivo de investigar a eficiência da relação fv0,k = 0.12·fc0,k para 30 espécies folhosas. Os resultados da análise de variância demonstram a divergência entre os resultados experimentais e aqueles estimados utilizando-se da relação citada. Portanto, modelos de regressão em função de dois parâmetros foram considerados para se obter estimativas mais precisas da fv0,k através da adoção da fc0,k e fM,k como variáveis independentes. Com relação aos resultados, os modelos geométrico (R² = 80.80%) e linear (R² = 74.19%) foram os mais precisos para a estimativa da fv0,k em termos da fc0,k e fM,k, respectivamente. Este fato evidencia a boa precisão dos modelos em questão, o que pode proporcionar um dimensionamento estrutural mais rigoroso quando comparado à correlação atualmente prescrita pela ABNT NBR 7190-1 (2022).

ABSTRACT The objective of this work was to determine the physical and mechanical properties of paricá (Schizolobium parahyba var. amazonicum (Huber x Ducke)) LVL panels bonded with urea-formaldehyde resin. Six LVL panels were produced with 17 sheets of 2.5 mm thick, 14 sheets of paricá and 3 sheets of marupá (Simarouba amara Aubl.). For the standard temperature condition of 12%, tests were carried out on moisture content, apparent and basic densities (physical characterization), resistance to resistance parallel and perpendicular to the fibers, traction parallel to the fibers, shearing in the glue line and flatwise static bending and edgewise (mechanical characterization). In addition, saturation tests parallel to the fibers and shear tests were carried out in the LVL glue line in the condition of total saturation of the wood. The results appreciated that the LVL panels fall within the D30 strength class and medium density. The brittle type failure mode was observed in all mechanical tests, except in the parallel and perpendicular compression tests to the fibers. The increase in moisture content, due to the total saturation of the wood, negatively influences the resistance to the slope parallel to the fibers and to the shear strength in the glue line. The LVL presented a mechanical performance compatible with the substitute.

RESUMO O trabalho teve como objetivo determinar as propriedades físicas e mecânicas de painéis LVL de paricá (Schizolobium parahyba var. amazonicum (Huber x Ducke)) colados com resina ureia-formaldeído. Foram produzidos 6 painéis LVL com 17 lâminas de 2,5 mm de espessura, sendo 14 lâminas de paricá e 3 lâminas de marupá (Simarouba amara Aubl.). Para a condição de umidade padrão de 12%, foram realizados ensaios de teor de umidade, densidades aparente e básica (caracterização física), resistências à compressão paralela e perpendicular às fibras, tração paralela às fibras, cisalhamento na linha de cola e flexão estática flatwise e edgewise (caracterização mecânica). Na condição de saturação total da madeira, foram realizados ensaios de compressão paralela às fibras e cisalhamento na linha de cola do LVL. Os resultados mostraram que os painéis LVL se enquadram na classe de resistência D30, caracterizado com média densidade. Foi observado o modo de ruptura do tipo frágil em todos os ensaios mecânicos, exceto nos ensaios de compressão paralela e perpendicular às fibras. O aumento do teor de umidade, decorrente da saturação total da madeira, influenciou de forma negativa nas resistências à compressão paralela às fibras e ao cisalhamento na linha de cola. O LVL apresentou desempenho mecânico compatível com as solicitações estruturais.

RESUMO Neste trabalho avaliou-se numericamente a influência do módulo de elasticidade paralelo às fibras da madeira na estabilidade de arcos treliçados, considerando uma análise não linear geométrica baseada no Método dos Elementos Finitos (MEF). Essa abordagem foi realizada conforme uma formulação posicional do MEF, atribuindo-se os nós da estrutura como variáveis principais do sistema de equações não lineares, cuja resolução foi alcançada pelo método de Newton-Raphson. Ao todo, sete modelos de arco foram avaliados adotando-se madeiras coníferas e folhosas, com propriedades definidas segundo as classes de resistência da norma brasileira ABNT NBR 7190. Subrotinas foram desenvolvidas em linguagem MATLAB para resolução do sistema de equações não lineares e processamento da análise, incluindo a representação gráfica dos resultados e configurações do arco treliçado. Valores de esforços internos e deslocamentos foram determinados, assim como as forças de instabilidade dos arcos treliçados. Verificou-se que a força de instabilidade do arco constituído pela madeira folhosa mais rígida (D60) foi aproximadamente igual a 700% da força de instabilidade referente à classe conífera C20, e equivalente a 257,8% da força associada à classe folhosa D20. Concluiu-se que o módulo de elasticidade apresentou influência significativa no comportamento não linear geométrico do arco treliçado de madeira. Além disso, a análise não linear geométrica possibilitou o cálculo de parâmetros mais precisos e a verificação da estabilidade do sistema estrutural.

ABSTRACT In this work, it was numerically evaluated the influence of the modulus of elasticity parallel to the wood grain on the stability of trussed arches considering a nonlinear geometric analysis based on the Finite Element Method (FEM). This approach was carried out according to a positional formulation of the FEM, considering the structural nodes as main variables of the nonlinear equations system, whose resolution was obtained using the Newton-Raphson method. Altogether, seven arch models were evaluated, consisting of coniferous and hardwoods, with properties defined according to the strength classes of the Brazilian standard ABNT NBR 7190. The subroutines were written in MATLAB to solve the system of nonlinear equations and perform the analysis, including the graphical representation of the results and configurations of the trussed arch. Internal loads and displacements were obtained, in addition to the instability loads of the trussed arches. It was found that the instability load of the arch made with the stiffest hardwood (D60) was approximately equal to 700% of the instability load of the C20 coniferous class and equivalent to 257.8% of the D20 hardwood class-related load. It was verified that the modulus of elasticity significantly influences the nonlinear geometric behavior of the timber trussed arch. Furthermore, the nonlinear geometric analysis allowed calculating more accurate parameters and the verification of the stability of the structural system.

ABSTRACT The present research intended to propose and evaluate regression models which estimate toughness property as a function of physical, chemical properties of thermally modified hardwood and thermal treatment temperature, using linear, quadratic, cubic, exponential, logarithmic, geometric and multiple linear models. Commercial thermally modified woods were used on the study, being characterized for all referred properties, totalizing 450 experimental determinations. The analyzed models presented a low and moderate coefficient of determination, indicating the impossibility to use such models in the estimation of toughness as a function of physical and chemical factors

Abstract The Brazilian Code ABNT NBR 7190 (1997) is currently under review process and one of the proposals is the change and add of some test procedures. Several specimen geometric configurations and test conditions have been evaluated by the study committee CE-02:126.10. The aim of this paper was the analysis of the tensile strength perpendicular to the grain through the current Brazilian Code and from an adaptation of ISO 13910 (2005). Pine and Indian Cedar were used and simplified relationships were proposed. Numerical simulations were performed to identify the stress distributions in the specimens. The results obtained by ISO 13910 (2005) did not differ statistically for the two species. Brazilian standard method cedar had a higher strength value than pine. The simplified ratios obtained ranged between 0,017 and 0,123. The numerical simulations of ISO 13910 (2005) specimens showed predominant failure by tension in the lower fiber due to stress concentration.

Abstract: This research intends to evaluate the relation, aided by the Brazilian Standard and statistical analysis (Kruskal-Wallis ANOVA and bootstrap technique), between physical and mechanical properties of Cambará-Rosa wood harvested from three different regions: Vera, Mucajaí and South Rondonia. In addition, the possibility to estimate (regression models) physical and mechanical properties in function of apparent density was analyzed. Different climate and soil conditions which tree thrives may influence its growth and, consequently, its properties values. The results of ANOVA indicated an elevated equivalence index for all three regions. The bootstrap technique led to similar results for Vera and Mucajai regions, and for South Rondonia region, equivalence index equals to 89 %. The ANOVA results to estimate physical and mechanical properties in function of apparent density indicated that it is not possible to perform such estimates for Cambará-Rosa wood species.

RESUMO Este estudo teve como objetivo avaliar a influência do tratamento térmico comercial no Eucalyptus grandis considerando suas propriedades físicas, químicas e mecânicas. As amostras de madeira foram tratadas termicamente em autoclave com vapor saturado e aplicação de pressão em quatro diferentes temperaturas: 155, 165, 175 e 185 º C. As propriedades físicas, químicas e mecânicas foram alteradas devido ao tratamento térmico. O teor de extrativos variou entre 6,06% e 28,75%; lignina entre 28,93% e 37,96%; holocelulose entre 65,01% e 38,12%. As propriedades mecânicas reduziram significativamente com o aumento da temperatura do tratamento térmico. Com o conjunto de dados obtidos, foi possível gerar modelos de regressão significativos e de alta precisão capazes de estimar tais propriedades para temperaturas de tratamento térmico não estudadas experimentalmente, possibilitando a determinação da temperatura de tratamento térmico mais adequada para atingir determinado valor de propriedade do tratado madeira.

ABSTRACT This study aimed to evaluate the influence of commercial thermal treatment on Eucalyptus grandis considering its physical, chemical, and mechanical properties. The wood samples were heat-treated in an autoclave with saturated steam and pressure application at four different temperatures: 155, 165, 175, and 185 ºC. The physical, chemical, and mechanical properties were altered due to the heat treatment. The extractives content varied between 6.06% and 28.75%; lignin between 28.93% and 37.96%; holocellulose between 65.01% and 38.12%. The mechanical properties reduced significantly with the increase of the heat treatment temperature. Through the set of data obtained, it was possible to generate significant and high precision regression models capable of estimating such properties for heat treatment temperatures not studied experimentally, enabling the determination of the most suitable temperature of heat treatment to achieve a certain property value of the treated wood.

Resumo As gridshells são estruturas leves, que permitem a obtenção de grandes vãos livres, além de uma ampla variedade de formas arquitetônicas. No entanto, no Brasil, não existem registros da construção desse tipo de estrutura (em caráter permanente) nem muitas informações bibliográficas sobre o seu comportamento estrutural. Neste manuscrito, são apresentados os principais aspectos teóricos, como também os detalhes de projeto e de construção de uma gridshell, construída em madeira, em escala real. Os custos de construção também foram relacionados neste caso. Na confecção da estrutura utilizou-se uma configuração de malha quadrangular plana, formada por ripas duplas de madeira de Lyptus (Classe D40), unidas ortogonalmente entre si por parafusos com diâmetro de 6,35 mm. A malha plana (com dimensões totais de 9 m x 9 m) foi deformada até a obtenção da forma curva desejada e, posteriormente, travada por contraventamentos diagonais. A bagagem de conhecimento adquirida como resultado dessa aplicação prática levou a um aperfeiçoamento significativo da ideia de projeto inicial, relacionada ao controle da forma da estrutura durante as fases de montagem e à otimização das estratégias executivas. As recomendações de construção aqui apresentadas enriquecerão a literatura nacional sobre o assunto tendo-se em vista a carência de textos dessa natureza.

Abstract Gridshells are light structures that allow the obtention of large spans, as well as the use of a wide variety of architectural shapes. However, in Brazil, there are no records of the construction of this type of structure, neither literature available on this type of structural composition. This paper presents the main theoretical aspects, as well as design and construction details of a gridshell built in wood in real scale. The construction costs are also reported. The structure was built by using a quadrangular flat mesh configuration, formed by double slatted Lyptus wood (Class D40), joined orthogonally, using 6.35 mm diameter screws. The plane mesh (with total dimensions of 9 m x 9 m) was bent until the desired curve was achieved. The system was subsequently locked by diagonal bracing elements. The knowledge obtained through this practical application led to a significant improvement in the original design idea related to controlling the shape of the structure during the building phase and the the optimisation of the executing strategies. The building recommendations presented in this paper will be a contribution to the scarce literature on the subject currently available in Brazil.

RESUMEN Este trabajo describe la aplicación de un modelo de calidad de agua para la simulación de metales pesados en sistemas fluviales. La estrategia propuesta incluye un enfoque de modelación 1D con la extensión del modelo QUASAR-ADZ para la representación del comportamiento de los metales pesados, buscando fortalecer su capacidad predictiva a partir de la integración de variables que juegan un papel importante en la adsorción y desorción de estos compuestos por las partículas en solución. La metodología se implementó en un tramo del río Negro (oriente de Antioquia, Colombia), utilizando cromo, cobre y níquel como metales pesados, debido a que son estos los metales pesados representativos de las corrientes en el área de estudio. En los resultados se muestra la capacidad de predicción de la metodología del comportamiento de sustancias de interés ambiental con cierto grado de incertidumbre, lo que la constituye en una herramienta de gestión importante.

ABSTRACT This work describes a water quality model for heavy metals simulation in river systems. The proposed strategy comprises an 1D modeling approach with an ADZ-QUASAR extension to represent the behavior of heavy metals. This methodology seeks to strengthen their predictive capability based on the integration of variables which play an important role in the adsorption and desorption of these particles. The methodology was implemented in a reach of the Negro river (eastern side of Antioquia, Colombia), using Chromium, Copper and Nickel as heavy metals, because these are the heavy metals representative of the currents in the study area. Results are showing, with some degree of uncertainty, the capacity of the methodology to predict the behavior of environmental interesting substances, which makes it an important management tool.

ABSTRACT This paper presents two numerical models for the evaluation of the distribution of stresses in corrugated sheets of fibre cement subjected to uplift load. The numerical simulations, in this case, were made from three-dimensional models using the software SAP2000Nonlinear, version 7:42, which has as base the finite elements method (MEF). Corrugated sheets with thickness of 5 mm considering two different spans, i.e., 1100 mm and 1530 mm were evaluated. The sheets had the 2nd and 5th high waves fixed. The load of suction applied on the sheets was 10 kN/m2, and it was verified that the stresses on the sheets are distributed heterogeneously in a more complex pattern than for the bending stresses for vertical loads. The sheets suffer bending in transverse and longitudinal directions for the suction load applied, and the attachment points of sheets present concentration of stresses. The numerical results of the stresses showed good agreement with the results obtained from other researchers and these results can be used to predict the behavior of corrugated sheets of fibre cement subjected to wind load suction.

RESUMEN Este artículo presenta dos modelos numéricos para evaluación de la distribución de tensión en planchas onduladas de fibrocemento sometido a una carga de succión. Las simulaciones numéricas en este trabajo, se hicieron a partir de modelos tridimensionales utilizando el software SAP2000Nonlinear, versión 7:42, que se basa en el método de elementos finitos (MEF). Se evaluó planchas onduladas con espesor de 5 mm, teniendo en cuenta dos tramos diferentes, 1100 mm y 1530 mm. Las planchas tuvieron las 2a y 5a olas altas fijas. La carga de succión aplicada en de las planchas fue de 10 kN/m2, fue encontrado que las tensiones de planchas en la succión se distribuyen heterogeneamente un estándar más complejo de lo que los esfuerzos de flexión obtenidos para cargas verticales. Las planchas sufren flexión en direcciones transversales y longitudinales en la carga de succión aplicada, y los puntos de fijación de las planchas tienen concentración de esfuerzos. Los resultados numéricos de las tensiones mostraron buena concordancia con los resultados de otros investigadores y estos resultados se pueden utilizar para predecir el comportamiento de planchas onduladas de fibrocemento sometidos a cargas de viento de aspiración.

RESUMO Este trabalho teve a finalidade de avaliar o perfil de temperatura em duas vigas mista de madeira e concreto com seção transversal T e sistema de conexão metálico submetida à altas temperaturas. O sistema de conexão, neste caso, foi efetuado por barras de aço comum, com 12,5 mm de diâmetro, igualmente espaçadas ao longo da interface madeira-concreto. A seção transversal T da viga foi composta por uma alma de madeira com dimensões 5 cm x 15 cm e mesa de concreto com 30 cm x 5 cm. Foi considerado para as vigas mistas um tempo de exposição ao fogo de 40 minutos. A simulação numérica foi realizada a partir da utilização do software ANSYS [1], versão 10.0. Os resultados das simulações numéricas foram comparados com os resultados experimentais de temperatura obtidos para as duas vigas mistas, as quais foram instrumentadas com termopares e submetidas à altas temperaturas em um forno horizontal de ensaios construído na EESC/USP para tal finalidade. Os resultados numéricos e experimentais apresentaram uma boa concordância neste caso. Como resultado, são apresentados os perfis de temperatura na seção transversal para vários tempos de aquecimento, assim como toda estratégia de modelagem numérica e os elementos finitos utilizados na determinação dos perfis de temperatura.

ABSTRACT The aim of this work was the evaluation of the temperature profile in two composite timber and concrete beam with cross-section T and metallic connection system subjected to high temperatures. The connection system, in this case, was performed by use of steel bars with 12.5 mm diameter, equally spaced, along the concrete-timber interface. The cross section T of the beam consisted of a timber piece with dimensions 5 cm x 15 cm connected of a concrete slab with 30 cm x 5 cm. To the composite beams, a total time of fire exposure equal to 40 minutes was considered. The numerical modeling of the system was carried out using the ANSYS software [1], version 10.0. The results of numerical simulations were compared with the experimental results of temperature obtained by the two composite beam, which were instrumented with thermocouples and subjected to high temperature in a horizontal furnace constructed on EESC/USP for this purpose. The numerical and experimental results showed good agreement in this case. As a result, the temperature profiles are shown in cross section for various heating times and all numerical modeling strategy and the finite element used to determine the temperature profiles.

ABSTRACT The aim of this work was the study of embedment strength of dowels in reforested wood pieces. Analytical and experimental approaches were considered. Specimens for testing were made of Pinus elliottii (C30) and Eucalyptus saligna (C50) wood with steel rods with diameter of 6.35 mm (1/4"). The tests were performed according to the recommendations of ABNT NBR 7190:1997 and ASTM D5764:2007 Standards with subsequent comparison between the analytical and experimental results for embedment strength in the parallel and perpendicular directions to the grain. The results showed that the analytical and experimental values for embedment strength according to American Standard presented closer to each other compared to the Brazilian Standard in this case. Moreover, the American Standard recommended test specimen dimensions, which facilitate the manufacture, especially in the direction perpendicular the to wood fibers.

RESUMEN El objetivo de este trabajo fue estudiar la resistencia al aplastamiento de pernos de acero en cuerpos de pruebas de madera de reforestación. Dos enfoques principales han sido considerados: analítico y experimental. Las muestras para los ensayos estaban hechas de madera de Pinus elliottii (C30) y Eucalyptus saligna (C50) y los pernos de acero común con 6,35 mm (1/4") de diámetro. Los ensayos se realizaron de acuerdo con las recomendaciones de las normas ABNTNBR 7190:1997y ASTM D5764:2007 con posterior comparación entre los resultados analíticos y experimentales, que se obtuvieron para las resistencias al aplastamiento en las direcciones paralela y perpendicular a las fibras de la madera. Los resultados mostraron que los valores analíticos y experimentales obtenidos para la resistencia al aplastamiento de acuerdo con la norma técnica americana, se mostraron menos dispersos entre sí en comparación con los de la norma brasileña. Además, la norma técnica americana recomienda dimensiones para los cuerpos de prueba que hace que sean más fáciles de ser fabricados, principalmente en los cuerpos de dirección normal a las fibras de la madera.

Abstract The study of connections for timber structures has been the subject of intense research in Brazil. This work aimed to study the embedment strength of connections made by steel pins (dowels) in specimens of reforested woods. Analytical and experimental evaluations were considered in this study. Initially, tests on specimens made from Pinus elliottii (Class C30) and Eucalyptus salligna (Class C50) woods with dowels, type 1020, with diameter of 6.35 mm (1/4") were performed. The tests were performed according to the ANBT NBR 7190 (1997) and Eurocode 5 (2004) Standards with subsequent comparison between the analytical and experimental results for embedment strengths. The values of the embedment strength showed that the Eurocode 5 (2004) Standard had greater agreement between experimental and analytical results when compared to the results of the ABNT NBR 7190 (1997) Standard.

RESUMO Neste trabalho avaliou-se numericamente, a partir da utilização do software ANSYS, versão 10.0, o comportamento de ligações metálicas efetuadas por parafusos auto-atarraxantes com diâmetro igual a 11 mm, dispostos em X, em corpos de prova confeccionados com madeira de reflorestamento do tipo Eucalipto urograndis. A rigidez k (força versus deslizamento) do sistema de ligação foi avaliada, neste caso, por meio da simulação de ensaios de cisalhamento direto (direct shear), considerando-se 1/2 estrutura com carregamento aplicado até a ruptura do corpo de prova. A estratégia de se utilizar 1/2 estrutura simétrica teve o objetivo de reduzir o tempo de processamento numérico do modelo de corpo de prova. Na modelagem da madeira e dos conectores de aço foi utilizado o elemento finito solid45. Os resultados da análise numérica foram comparados com resultados obtidos a partir de ensaios experimentais realizados em corpos de prova de madeira com a mesma configuração e carregamentos utilizados na análise experimental. A calibração do modelo numérico foi realizada a partir da comparação da curva numérico-experimental "força aplicada" versus "deslizamento obtido". Os resultados numéricos obtidos para a resistência e rigidez k do sistema de ligação X mostraram uma boa concordância com os resultados experimentais, sendo que os resultados experimentais foram relativamente mais conservadores que os resultados numéricos. Como resultado apresenta-se, principalmente, a estratégia de modelagem numérica utilizada, neste caso.

ABSTRACT In this work was evaluated by numerical simulation, from the use of ANSYS software, version 10.0, the behavior of steel connections made by self-tapping screws with diameter of and 11 mm, in X position, in specimens made with reforested wood of the type Eucalyptus urograndis. The stiffness k (force versus displacement) of the connection system was evaluated, in this case, by direct shear testing simulation (direct shear), considering 1/2 structure with applied load until the rupture of the specimen. The strategy of using 1/2 symmetrical structure of specimen aimed to reduce the time of numeric processing of the specimen. In the modeling of wood and steel connectors was used the finite element solid45. The numerical analysis results were compared with results obtained from experimental tests on wood specimens with same configuration and loadings used in experimental analysis. The calibration of the numerical model was made from the comparison of numerical and experimental curves "applied force" versus "obtained displacement". The numerical results for the strength and stiffness k of the connection system analyzed X showed a good agreement with the experimental results and the values of experimental results were fairly smaller than the numerical values. As a result presents mainly the entire numerical modeling strategy used in this case.