Experimental evaluation of mode II fracture properties of Eucalyptus globulus L.

research projects BIA 2015-64491-P. UIDB/00667/2020 (UNIDEMI).Eucalyptus globulus Labill is a hardwood species of broad growth in temperate climates, which is receiving increasing interest for structural applications due to its high mechanical properties. Knowing the fracture behaviour is crucial to predict, through finite element models, the load carrying capacity of engineering designs with possibility of brittle failures such as elements with holes, notches, or certain types of joints. This behaviour can be adequately modelled on a macroscopic scale by the constitutive cohesive law. A direct identification of the cohesive law of Eucalyptus globulus L. in Mode II was performed by combining end-notched flexure (ENF) tests with digital image correlation (DIC) for radial-longitudinal crack propagation system. The critical strain energy release for this fracture mode, which represents the material toughness to crack-growth, was determined by applying the Compliance Based Beam Method (CBBM) as data reduction scheme and resulted in a mean value of 1.54 N/mm.publishersversionpublishe

Measuring the cohesive law in mode I loading of Eucalyptus globulus

This work was undertaken during a short-term scientific stay by the first and second authors at the University of Tras-os-Montes e Alto Douro, within the framework of the research project BIA 2015-64491-P Analysis of the stress relaxation in curved members and new joints solutions for timber Gridshells made out of Eucalyptus globulus, co-financed by the Ministry of Economy and Competitiveness of the Spanish Government and ERDF funds. The short-term stay was supported by a STSM Grant from COST Action FP1402 Basis of Structural Timber Design-from research to standards, ref. COST-STSM-ECOST-STSM-FP1402-091116-080058. This work is also supported by: European Investment Funds by FEDER/COMPETE/POCI-Operacional Competitiveness and Internacionalization Programme, under Project POCI-01-0145-FEDER-006958 and National Funds by FCT-Portuguese Foundation for Science and Technology, under the project UID/AGR/04033/2013.Assessing wood fracture behavior is essential in the design of structural timber elements and connections. This is particularly the case for connections with the possibility of brittle splitting failure. The numerical cohesive zone models that are used to simulate the fracture behavior of wood make it necessary to assume a cohesive law of the material that relates cohesive tractions and crack opening displacements ahead of the crack tip. This work addresses the determination of the fracture cohesive laws of Eucalyptus globulus, a hardwood species with great potential in timber engineering. This study centres on Mode I fracture loading for RL and TL crack propagation systems using Double Cantilever Beam tests. The Compliance-Based Beam Method is applied as the data reduction scheme in order to obtain the strain energy release rate from the load-displacement curves. The cohesive laws are determined by differentiating the relationship between strain energy release rate and crack tip opening displacement. The latter is measured by the digital image correlation technique. High strain energy release rates were obtained for this species, with no big differences between crack propagation systems. The difference between the crack systems is somewhat more pronounced in terms of maximum stress that determines the respective cohesive laws.publishersversionpublishe

Mechanical Properties of Small Clear Specimens of Eucalyptus globulus Labill

Eucalyptus globulus Labill stands out as one of the hardwood species produced in Europe with prominent mechanical properties, which is undergoing a growing interest in extending added value. The development of engineered wood products with this species and its application in timber structures involving numerical finite element simulations requires knowledge of the mechanical properties for the different orthotropic material directions. The aim of the present study is to determine the main mechanical properties of E. globulus from small clear specimens, necessary for the development of finite element models. The work provides experimental results on the ultimate capacity and modulus of elasticity considering different stresses: tension parallel and perpendicular to the grain, compression parallel and perpendicular to the grain (in radial and tangential directions), shear and longitudinal static bending. The work is complemented with experimental data on timber-to-timber friction coefficients for 0°, 45°, and 90° orientation angles, which are useful in the modeling of traditional joints. Very high values of ultimate stress and modulus of elasticity for the different mechanical properties were obtained, highlighting the great potential of this species for structural applicationsThe work has been developed within the framework of the research project BIA2015-64491-P Analysis of the stress relaxation in curved members and new joints solutions for timber Gridshells made out of Eucalyptus globulus, co-financed by the Ministry of Economy and Competitiveness of Spain Government and ERDF fundsS

Shear traction‐separation laws of European beech under mode II loading by 3D digital image correlation

Funding Information: Part of the work was undertaken during a short-term scientific stay by the first author at the Faculty of Engineering (University of Porto) in 2021, with the financial support provided by Programa Propio de I+D+i 2021 de la Universidad Politécnica de Madrid. The work is part of the R&D&I Project PID2020-112954RA-I00 funded by MCIN/AEI/10.13039/501100011033. The authors gratefully acknowledge also Fundação para a Ciência e a Tecnologia (FCT-MCTES) for the financial support of the Laboratório Associado de Energia, Transportes e Aeronáutica (LAETA) by the project MCIN/AEI/10.13039/501100011033 and the Research and Development Unit for Mechanical and Industrial Engineering (UNIDEMI) by the project UIDB/00667/2020. Publisher Copyright: © 2022, The Author(s).An experimental and numerical study on mode II fracture behaviour of European beech (Fagus sylvatica L.) in the RL and TL crack propagation systems is performed. It is a hardwood species that has attracted increasing interest for structural use in Europe in recent years. Three-point end notched flexure tests are performed. The R-curves of both crack propagation systems are obtained, from which the critical strain energy release rate (GIIc) is derived by applying the compliance-based beam method. This data reduction scheme avoids crack length monitoring during its propagation, which is an advantage in wood. Using a direct method, the shear traction‐separation laws in mode II loading are determined. Full field displacements around the crack tip are monitored by 3D digital image correlation technique, and the crack tip shear displacements are analysed. The proposed method is numerically validated by finite element analysis. Cohesive zone models are developed implementing a shear traction–separation law with exponential damage evolution zone and the average value of the experimental elastic and fracture properties. The numerical results for the different properties including upper and lower limits represent well the experimental data.publishersversionepub_ahead_of_prin

Evaluation of R-curves and cohesive law in mode I of European beech

This work addresses the determination of the cohesive laws in Mode I and tangential–longitudinal (TL) crack propagation system of Fagus Sylvatica L. This species is one of the ever-growing and most widely used hardwood species in Europe for engineered timber products. Double Cantilever Beam (DCB) tests are performed. The strain energy release rate ( G I) is derived from the R-curves by applying the Compliance-Based Beam Method (CBBM), which has the advantage of not requiring the measurement of the crack length during propagation, but only the global load–displacement curves. The cohesive law of the material is determined from the relationship between G I, and the crack tip opening displacement (CTOD) monitored for each specimen using Digital Image Correlation (DIC). Numerical finite element models are developed by implementing the average cohesive law through Cohesive Zone Models (CZM). An average G I value of 0.46 kJ / m 2 is obtained for this species. The numerical load–displacement curves are consistent with the experimental results, which demonstrates the suitability of the method for the identification of the cohesive laws in beech. The fracture properties obtained are essential in the development of advanced and reliable numerical models in timber engineering design using this species.publishersversionpublishe

Láminas reticulares de madera deformadas elásticamente : del material a la construcción = Elastic timber gridshells : from material to construction

Las láminas reticulares de madera deformadas elásticamente son una solución estructural de gran eficiencia y expresividad arquitectónica, de interés para su aplicación en cubiertas ligeras de medias y grandes luces. Se construyen a partir de piezas de madera inicialmente rectas, de pequeña sección y gran longitud, las cuales se deforman en régimen elástico hasta alcanzar la forma objetivo generando una retícula estructural de elementos continuos. El empleo de piezas de madera idénticas y el uso de soluciones de unión sencillas confieren al sistema una alta capacidad de prefabricación y estandarización. Sin embargo, a pesar del enorme potencial de este tipo de estructuras, solo algunas obras singulares se han construido hasta la fecha. Esto es debido a que existen importantes dificultades durante el proceso de diseño y ejecución que impiden su popularización, como son la escasez de productos comerciales de madera adecuados, la insuficiencia de estudios sobre relajación de tensiones en láminas de madera curvadas, así como la falta de trabajos sobre modelos numéricos contrastados experimentalmente. El objetivo general de la presente tesis es generar conocimiento útil para conseguir salvar dichas dificultades y lograr la puesta en práctica de este tipo de estructuras con madera de Eucalyptus globulus Labill. Con este fin se establecen las principales directrices para producir madera maciza empalmada y madera laminada encolada de E. globulus de muy altas prestaciones para su aplicación en estructuras laminares reticulares deformadas elásticamente. Para ello se propone un sistema de clasificación de la madera maciza de eucalipto en diferentes perfiles resistentes, combinando criterios visuales y mecánicos. Así mismo, se establecen los parámetros de fabricación necesarios para obtener empalmes por unión dentada encolada de muy alta capacidad. Los resultados muestran que con E. globulus pueden fabricarse dos de los productos estructurales en base madera maciza de mayores prestaciones mecánicas del mercado europeo, suponiendo una alternativa de aplicación de gran valor añadido para esta especie cuyo destino habitual es la producción de pasta de papel. Un análisis comparativo con otros productos y especies de madera, en términos de radio de curvatura, rigidez del sistema de conexión y reserva estructural, pone de manifiesto la superioridad mecánica de los productos desarrollados y demuestra que con ellos pueden diseñarse estructuras laminares que no serían posibles con otras especies. De igual modo se realiza una revisión bibliográfica crítica relativa al fenómeno de la relajación de tensiones en láminas de madera curvadas en régimen elástico, en relación a los enfoques de análisis estructural empleados, los equipos y métodos de ensayos utilizados para su medición y los datos experimentales disponibles. Estos trabajos han derivado en la patente con examen de un novedoso equipo de ensayos, el cual elimina los inconvenientes de otros equipos empleados para el mismo fin. El nuevo equipo ha sido utilizado para medir la relajación de tensiones producida durante varios años en láminas de eucalipto curvadas con diferentes radios. Los resultados proporcionan datos de gran interés para el análisis estructural y sugieren la posibilidad de utilizar los valores normativos de fluencia en madera para estimar la relajación de tensiones en otras especies. Así mismo se propone un concepto innovador de lámina reticular de madera deformada elásticamente, el cual supone una importante contribución al diseño de este tipo de estructuras y abre nuevas e interesantes posibilidades de aplicación. Se basa en un esquema estructural de lámina alargada apoyada exclusivamente sobre sus lados cortos, el cual logra la rigidez a flexión fuera del plano mediante tres direcciones de láminas flectadas. Para analizar el comportamiento estructural del concepto propuesto, se desarrollan dos novedosos modelos numéricos de elementos finitos que incorporan los aspectos más importantes de este tipo de estructuras (excentricidad y deslizamiento en las uniones, y tensiones de curvado y su relajación). Ambos se basan en la modelización de las uniones de la estructura como una secuencia de acoplamientos rígidos con muelles en todos los planos de corte. El primero simula la geometría final a construir, pudiendo incorporar las tensiones iniciales debidas al proceso de construcción a través de momentos de curvatura deducidos de análisis geométricos. El segundo reproduce el proceso de construcción obteniendo las tensiones iniciales directamente de la simulación. A partir de los resultados numéricos obtenidos, se señalan los principales aspectos a considerar en el diseño y análisis estructural del concepto desarrollado. Por último, se construyen dos láminas reticulares de gran tamaño con el nuevo esquema estructural propuesto. La primera, un prototipo de laboratorio de 7.5 m de longitud, permite calibrar los modelos numéricos a partir de una prueba de carga. La segunda, una estructura de 24 m de longitud diseñada para cubrir el nuevo almacén de madera de PEMADE en el Campus de Lugo, es la primera lámina reticular de madera deformada elásticamente de carácter permanente construida en España y la primera del mundo realizada con E. globulus. Con esta actuación se llevan a cabo trabajos adicionales para conseguir láminas continuas de gran longitud sin uniones mecánicas, se desarrollan detalles estructurales novedosos y se propone un proceso de puesta en obra lámina a lámina, el cual permite disponer de tres direcciones de láminas continuas flectadas y evitar el uso de piezas de bloqueo de rasante. El diseño y construcción de esta cubierta demuestra definitivamente el potencial arquitectónico y estructural del Eucalyptus globulus Labill para su aplicación en láminas reticulares deformadas elásticamente y abre la puerta a nuevos caminos apasionantes aún por explorar. Los trabajos desarrollados en esta tesis se han llevado a cabo en el marco de tres proyectos de investigación: «Tecnificación de la cadena de valor para el desarrollo de productos de altas solicitaciones técnicas con madera de eucalipto» (Xilográcile), del Programa FEDER Innterconecta del Ministerio de Ciencia e Innovación del Gobierno de España; «Análisis de la relajación de tensiones en láminas curvadas y de nuevas soluciones de unión para estructuras tipo Gridshell realizadas con Eucalyptus globulus» (Eucagrid), del Programa Estatal de fomento de la investigación científica y técnica de excelencia, del Ministerio de Economía y Competitividad del Gobierno de España; y «Lugo+Biodinámico, Planificación de un barrio multiecológico modelo de resiliencia urbana», del Programa LIFE de la Unión Europea. La presente tesis doctoral se presenta por compendio de publicaciones. Su contenido se articula a través de seis de las contribuciones más relevantes realizadas por el autor en la temática: cinco artículos en revistas científicas Q1 o Q2 (uno de ellos en proceso de revisión) y una patente de invención con examen previo. ----------ABSTRACT---------- Elastic timber gridshells are a highly efficient and architecturally expressive structural solution of great interest for application in lightweight roofs of medium and large spans. They are built from initially straight pieces of wood, of small cross-section and great length, which are elastically deformed until they reach the target shape, resulting in a structural grid of continuous elements. The use of identical timber laths and simple connection solutions gives the system a high capacity for prefabrication and standardisation. However, despite the great potential of this type of structures, only a few singular realisations have been built to date. This is due to important difficulties during the design and construction process that prevent their popularisation, such as the scarcity of suitable commercial timber products, the insufficiency of studies on stress relaxation in bent timber laths, and the lack of work on experimentally verified numerical models. The general objective of the present PhD thesis is to provide useful knowledge to overcome these difficulties and to achieve the implementation of this type of structures using Eucalyptus globulus Labill wood. To this end, the main guidelines for producing high performance finger jointed solid timber and glued laminated timber of E. globulus for application in elastic gridshells are established. A grading system of eucalyptus solid wood into different strength profiles is proposed, combining visual and mechanical criteria. Manufacturing parameters necessary to get very high capacity finger-joints are also set up. The results show that E. globulus can be used to produce two of the highest mechanical performance solid wood-based products on the European market, representing a high added-value alternative application for this species, which is normally used for pulp production. A comparative analysis with other products and wood species, in terms of radius of curvature, stiffness of the connection system, and structural reserve, shows the mechanical superiority of the developed products and demonstrates that they can be used to design gridshell structures that would not be possible with other species. A critical literature review is also carried out on the phenomenon of stress relaxation in elastically bent timber laths, in relation to the structural analysis approaches, the equipment and test methods applied, and the available experimental data. This research has derived in a patent with examination of a novel test equipment, which eliminates the drawbacks of other devices used for the same purpose. The new equipment has been applied to measure the stress relaxation produced over several years in curved eucalyptus laths with different radii. The results provide data of great interest for structural analysis and suggest the possibility of using normative creep values to estimate stress relaxation in other species. An innovative concept of an elastic timber gridshell is also proposed, which makes an important contribution to the design of this type of structure and opens up new and interesting application possibilities. It is based on a structural scheme of a long gridshell supported exclusively on its short sides, which achieves out-of-plane bending stiffness by means of three directions of bent laths. To analyse the structural behaviour of the proposed concept, two novel numerical finite element models are developed which incorporate the most important aspects of this type of structure (eccentricity and slip at the joints, and bending stresses and their relaxation). Both are based on modelling the joints of the structure as a sequence of rigid couplings with springs in all shear planes. The first simulates the final geometry to be built, being able to incorporate the initial stresses due to the construction process by means of bending moments deduced from the geometrical analysis. The second reproduces the construction process by obtaining the initial stresses directly from the simulation. From the numerical results obtained, the main aspects to be considered in the design and structural analysis of the developed concept are pointed out. Finally, two large gridshells are built with the proposed new structural scheme. The first, a 7.5 m long laboratory prototype, allows the numerical models to be calibrated on the basis of a load test. The second, a 24 m long structure designed to cover the new wood warehouse of PEMADE on the Lugo Campus, is the first permanent elastic timber gridshell built in Spain and the first in the world to be made with E. globulus. Within this project, additional work was caried out to achieve continuous long laths without mechanical joints. Innovative structural details were also developed, and a lath-by-lath construction process was proposed, which allows three directions of continuous bent laths and avoids the use of shear blocks. The design and construction of this structure definitively demonstrate the architectural and structural potential of Eucalyptus globulus Labill for application in elastic gridshells and opens up new exciting avenues yet to be explored. The work developed in this thesis has been carried out in the framework of three research projects: "Technification of the value chain for the development of products with high technical solicitations with eucalyptus wood" (Xilográcile), from the FEDER Innterconecta Programme of the Ministry of Science and Innovation of the Spanish Government; "Analysis of the stress relaxation in curved members and new joints solutions for timber gridshells made out of Eucalyptus globulus" (Eucagrid), from the State Programme for the promotion of scientific and technical research of excellence, of the Ministry of Economy and Competitiveness of the Spanish Government; and "Lugo+Biodinamic, Planning of a multi-ecological neighbourhood model of urban resilience", from the LIFE Programme of the European Union. This doctoral thesis is presented as a compendium of publications. Its content is articulated through six of the most relevant contributions made by the author in the field: five articles in Q1 or Q2 scientific journals (one of them under review) and one patent with prior examination

Design Framework for Selection of Grid Topology and Rectangular Cross-Section Size of Elastic Timber Gridshells Using Genetic Optimisation

This work presents a design framework for the selection of the topology and cross-section size of elastic timber gridshells, taking as constraints the shape of the structure and the maximum value of bending stress that can be reached in a given area of the gridshell. For this purpose, a parametric design environment and a genetic optimisation algorithm are used, which provides a set of solutions (optimal and near-optimal) that can be examined by the designer before adopting the final solution. The construction of the parametric mesh model is based on a geometric approach using an original adaptation of the Compass Method by developing two algorithms. The first one plots geodesic curves on a surface given a starting point and a direction. The second algorithm adapts the accuracy of the Compass Method to the local curvature of the surface, substantially minimising the computation time. The results show that the optimisation process succeeds in significantly reducing the initial bending stresses and offers an interesting solution space, consisting of a set of solutions with sufficiently diverse topologies and cross-section sizes, from which the final solution can be chosen by the Decision Maker, even according to additional non-programmed structural or aesthetic requirements. The design framework has been successfully applied and verified in the design of the PEMADE gridshell, an innovative elastic timber gridshell recently realised by the authors. Finally, the most relevant details of its construction process carried out to ensure the exact position of the timber laths are presented

Fotogrametría SfM de bajo costo para monitorización de ensayos sobre estructuras laminares reticulares de madera deformadas elásticamente a escala real

Para validar modelos numéricos de resistencia de estructuras, es necesario medir su deformación bajo carga. La dificultad de dicha medición aumenta con su tamaño y su complejidad. En el presente estudio se determina la geometría de una estructura laminar reticular de gran tamaño tras una prueba de carga. La estructura fue cargada en sus cinco nodos centrales con un peso suspendido de 105 kg por nodo. Se generó el modelo 3D de la estructura sin carga y bajo carga, empleando fotogrametría usando software PhotoModeler Scanner y Metashape. El error máximo en la medida de las distancias sobre la escena fue 1,31 mm, que corresponde al 0,17 % respecto a la diagonal de la base de la estructura. El mayor error medio se dio bajo carga máxima, 0,70 mm de acuerdo a Metashapee y 0,44 mm en PhotoModeler Scanner. El perfil de la estructura bajo carga es coherente con la deformación prevista. La calidad de medida del modelo 3D resultó ser altamente uniforme. Este estudio releva el uso de fotos que han sido tomadas varios años después, a través de la fotogrametría utilizando softwares avanzados

Splitting capacity of Eucalyptus globulus beams loaded perpendicular to the grain by connections

R&D&I Project BIA2015-64491-P funded by MCIN/AEI/"http://sci-hub.tw/10.13039/501100011033In timber structures, knowledge of the splitting capacity of beams loaded perpendicular to the grain by dowel-type connections is of primordial importance since brittle failure can occur. In the present work, single- and double-dowel-type connections following different loaded edged distance arrangements are experimentally investigated to derive the splitting behaviour of Eucalyptus globulus L., which is a hardwood species of increasing interest for structural use due to its high mechanical performance, fast growth, and good natural durability. The correlation of experimental failure loads with those theoretically predicted by the expression included in Eurocode 5 and by eight analytical models based on an energetic approach is discussed. Most of the analytical models studied overpredict the splitting capacity. However, the code splitting expression, derived from softwoods, proves to be very conservative in predicting the eucalyptus splitting failure load.publishersversionpublishe