[Show abstract][Hide abstract] ABSTRACT: Due to the natural growing process of wood, the mechanical properties of wooden boards are subject to high variability, mainly introduced by knots and the resulting deviation of the wood fibre directions around them. This variability has a great impact on the serviceability limit state performance of wood-based products, such as glued-laminated timber, and thus should be considered within design concepts. Numerous applications of random process models for numerically representing the fluctuation of the mechanical properties along wooden boards can be found in the literature. But, the corresponding mechanical probabilistic investigation, however, is limited almost exclusively to Monte Carlo simulations so far. For this reason, the focus of this work is laid on alternative probabilistic approaches, in particular the perturbation and the spectral stochastic finite element method. Both methods are combined with several discretization methods for the random process, programmed in a consistent environment, and compared to the Monte Carlo simulation, regarding computational effort as well as quality of results. For this purpose, the second-order moments (mean and standard deviation) of the system response of a glued-laminated timber beam with random lamination stiffness are computed. The performance of the different approaches is compared and, in particular, the influence of the variability of the ‘raw’ material on the structural response is shown. Well-known effects, such as the decrease in the variability of effective properties of GLT with increasing number of lamellas, are numerically reproduced and quantified. Moreover, a significant influence of the correlation length, specifying the rate of material property fluctuation within each lamella, on the effective stiffness of the resulting glued-laminated timber beams is demonstrated.
Full-text · Article · Jan 2016 · Archive of Applied Mechanics
[Show abstract][Hide abstract] ABSTRACT: The mechanical properties of structural timber—particularly in terms of stiffness and strength—are subject to high variability, which also affects the properties of timber products made from structural timber, e.g., glued laminated timber (GLT). In this paper, the influence of the longitudinal stiffness variability of wooden lamellas on the effective stiffness of GLT is investigated. In a first step, the local fiber orientation on the surfaces of 350 lamellas of Norway spruce was determined by an optical scanning device. This fiber angle information in combination with a micromechanical model for wood was used for the generation of a longitudinal stiffness profile of each lamella. Recording the position and orientation of each lamella, a total number of 50 GLT beams were assembled (with 4, 7, and 10 laminations) and tested under four-point bending. Knowing the stiffness profile of each board and its location within the GLT beam allowed for an accurate numerical finite element model, which is able to predict the effective GLT stiffness with high accuracy. Interesting insights into the relation between the stiffness of lamellas and the resulting GLT beams could be gained, and finally, a numerical simulation tool which is able to reproduce the experimental results appropriately was obtained.
[Show abstract][Hide abstract] ABSTRACT: As a result of the natural growing process of wood, each timber lamella shows a high variability in its mechanical properties, particularly strength and stiffness. It is assumed that those properties are governed by a random process and, subsequently, that the effective stiffness of glued laminated timber also varies randomly. Therefore, a probabilistic approach is necessary. Hence, the latest achievements in probabilistic timber engineering are reviewed and compared. Numerous works rely on random process models for the representation of stiffness and/or strength distributions in single timber lamellas. The statistical evaluation of those random process models, however, is limited almost exclusively to Monte Carlo simulation (MCS) so far. Therefore, this work aims at giving an overview of alternative ways to compute the effective stiffness, by reviewing the framework of stochastic finite element methods. Random process models for the representation of the stiffness distribution in single lamellas are discussed, and the two most promising alternatives to the MCS for computation of effective stiffness parameters, the perturbation and the spectral stochastic finite element method, are evaluated in terms of accuracy and efficiency. Finally, this paper shows alternative and more efficient ways of exploring the stochastic nature of wood, delivering a new basis for more reliable design concepts for timber products.
Full-text · Article · Jun 2015 · Wood Science and Technology
[Show abstract][Hide abstract] ABSTRACT: The naturally grown material wood exhibits, in addition to its orthotropic material structure, several types of inhomogeneities, where most of them can be allocated to knots and the resulting local fiber deviations. Since they generally lead to a reduction in strength properties, wooden boards must be subjected to a grading process before they can be used as load-bearing elements. Within this process so-called indicating properties are recorded and used to assess the wooden board strength. Common indicating properties are almost exclusively based on surface information of wooden boards while the 3D position and orientation of knots within a board is hardly considered. Thus, algorithms for the 3D reconstruction of wooden boards based on already available surface scans, laser scanning, X-ray or computer tomography data are assessed first within this work. This new knot information allows then the development of novel indicating properties, which consider the knots, the resulting fiber deviation regions and, for bending conditions, the knot location information using height-dependent weighting functions. The statistical evaluation of combinations of the new indicating properties, separately for tensile and bending load conditions, shows that the correlations to experimentally obtained strength properties could be improved significantly with such an approach.
Full-text · Article · May 2015 · Wood Science and Technology
[Show abstract][Hide abstract] ABSTRACT: In this study, shear stiffness properties of 10 different hardwood species and their relation to the corresponding species-specific microstructure are investigated. For this purpose, shear stiffness of 10 different hardwood species is experimentally measured by means of ultrasonic testing. In addition, a micromechanical model for hardwood is applied in order to illustrate the influence of certain microstructural characteristics such as mass density and volume fractions of vessels and ray cells on the shear stiffness. Comprehensive microstructural and mechanical data from previous investigations of the same hardwood material support the interpretation of the microstructure-shear stiffness relationships. Mass density was confirmed to be the dominant microstructural characteristic for shear stiffness. Also, ultrasound shear wave propagation velocity increases with density, particularly in the radial-tangential (RT) plane. In addition to density, comparably higher shear stiffness GLR can be explained by comparably higher ray content and lower vessel content. As for GLT, a ring porous structure seems to lead to higher shear stiffness as compared to a diffuse porous structure. For this shear stiffness, vessel and ray content were found to have a less impact. Also, the rolling shear stiffness GRT was found to be higher for a diffuse porous structure than for a ring porous one. Moreover, the data supports that ray cells act as reinforcements in the RT plane and lead to higher GRT.
No preview · Article · Apr 2015 · Wood Material Science and Engineering
[Show abstract][Hide abstract] ABSTRACT: The stiffness evolution of binder ‘cement paste’ is triggering the stiffness of concrete. In the engineering practice, concrete formworks are typically removed 24 h after production. This underlines that knowledge on mechanical properties of cementitious materials during the second, third and fourth day after production is of high relevance for the ongoing construction process. This provides the motivation to perform early-age stiffness characterisation on hydrating cement pastes, by means of the following three test methods. Unloading modulus is determined using a novel setup for non-destructive uniaxial compression testing including overdetermined deformation measurements. Dynamic Young's moduli are obtained from ultrasonics experiments. Isothermal differential calorimetry allows for linking the observed temporal evolution of early-age stiffness to the hydration degree of cement. Pastes with three different compositions are investigated, defined in terms of the initial water-to-cement mass ratio w/c and the initial water-to-solid (binder) mass ratio w/s. Pure cement pastes exhibit w/c = w/s = 0.50 and w/c = w/s = 0.42, respectively. A fly ash-blended cement paste refers to a cement mass replacement level of 16%, and this is related to w/c = 0.50 and w/s = 0.42. Both unloading moduli and dynamic Young's moduli of all three materials increase practically linearly with increasing hydration degree, in the investigated regime of hydration degrees ranging from 40 to 60%. Fly ash does not contribute significantly to the early-age hydration of the material, i.e. it represents a quasi-inert part of the material's microstructure, exhibiting a significant stiffening effect.
[Show abstract][Hide abstract] ABSTRACT: A new type of semi-rigid timber beam-to-beam connection and its behavior under bending is presented. This connection consists of four identical steel parts, which are inserted into the timber beams in the tension and compression zone of the connection. These steel parts are easily connected by mounting bolts on the construction site. In order to avoid initial slip, gaps between the timber and the steel parts are filled using two different types of filler materials, namely cement based (CEM) or polyurethane based (PUR) filler. In this study, the connection is modeled by means of the Finite Element (FE) Method and the modeling results are compared to the results of an experimental assessment of the proposed connection under bending. The material model for timber encompasses a Hill criterion in combination with cohesive surface contact in order to depict both, yielding in compression and brittle failure in shear and tension perpendicular to the grain. The experimentally observed decisive failure mode, i.e. shear block failure, could be reproduced by the model. Subsequently, the FE model was used to investigate the effect of using different filler materials, or not considering the filler in the analysis at all. In addition, a particular influence of clamping bolts in the timber on the strength of the connection was revealed. The FE analysis excluding these bolts showed good agreement with the experiments in terms of the strength of the connection, while considering these bolts led to an overestimation of the strength. This is a consequence of the considerable influence of the clamping bolts on stresses perpendicular to the grain in the timber in the block-shear area, and therefore, on shear failure initiation. Using the CEM filler hardly changed the overall behavior of the connection as compared to the analyses without filler material, while the PUR filler leads to a less ductile overall behavior. This is well in line with experimental observations. The application of modeling approaches for timber has proven suitable for the analysis of such a type of timber beam-to-beam connection and, consequently, might be used for further optimization of this connection.
Full-text · Article · Mar 2015 · Engineering Structures
[Show abstract][Hide abstract] ABSTRACT: Fungal degradation is among the greatest hazards for standing trees as well as timber constructions. Herein we aim at gaining more detailed insight into the degradation strategies of wood destroying fungi and the consequences on the mechanical performance of wood. At the macroscale, the occurring losses of mass and of mass density mask effects of altered chemical composition and microstructure. Thus, it is necessary to step down the hierarchical organization of wood to the cell wall scale in order to resolve these changes and their mechanical impact. We present a multiscale micromechanical model which is used to estimate the stiffnesses of the S2 cell wall layer and the compound middle lamella of fungal degraded wood. Data from a detailed chemical, microstructural and micromechanical characterization of white rot and brown rot degraded Scots pine sapwood is analyzed. Comparing predicted cell wall stiffnesses with measured ones confirms the suitability of the approach. The model enables to establish structure–stiffness relationships for fungal degraded wood cell walls and to test hypotheses on yet unknown effects of fungal decay. The latter include the evolution of porosity, modifications of the cell wall polymers resulting in changes of their stiffnesses, as well as increasing cell wall crystallinity. The model predictions in general showed good agreement with the predictions not considering pores in the cell wall. However, this finding does not rule out the formation of porosity. Other degradation related effects like modifications of the cell wall polymers as well as increased crystallinity have the potential to account for stiffness decreases upon the formation of pores.
[Show abstract][Hide abstract] ABSTRACT: In wooden boards, knots and the resulting fibre deviations in their vicinities are mainly responsible for qualitative downgrading of timber elements. Thus, the development of reliable numerical simulation tools for the determination of effective strength and stiffness properties of timber elements and, in a next step, for the development and evaluation of grading criteria is highly desirable. Due to the complexity of such tools, a comprehensive validation is required. Within this work, the suitability of full-field deformation measurements for four-point bending tests on wooden boards with knots is evaluated first. Next, the test series is used to validate a previously developed three-dimensional numerical simulation tool, which combines a geometrical model for the grain course and a micromechanical model for a density and moisture dependent characterisation of the clear-wood material. The digital image correlation technique proved to be capable to reproduce the strain fields in the vicinity of knots under bending load. Moreover, a very good correlation between numerical and experimental results was obtained.
[Show abstract][Hide abstract] ABSTRACT: Nachdem Holzwerkstoffe-insbesondere Brettsperrholz-zunehmend auch als Tragelemente im Bauwesen Eingang gefunden haben, hat sich der Bedarf nach geeigneten und zuverlässigen Bemessungsnormen für diese Produkte verstärkt. Für die Entwicklung bzw. Verbesserung von Bemessungskonzepten ist allerdings ein fundiertes Wissen uber das tatsächliche mechanische Verhalten derartiger Bauelemente unverzichtbar. Aus diesem Grund konzentriert sich die vor-liegende Arbeit auf die globalen Versagensmechanismen inklusive der zugehörigen Entwick-lung von Bruchformen in Brettsperrholzplatten in Abhängigkeit von geometrischen und mate-rialspezifischen Kenngrößen. Zu diesem Zweck wurden Versuche an 3-und 5-Schicht-Platten durchgeführt. In Ergänzung zu traditionellen Auswertemethoden wurden die Versuchskörper zusätzlich in kleine Würfel zerschnitten zwecks Identifikation der Bruchformen auch im Plat-teninneren. Dabei konnten Zonen mit ausgeprägtem Schub-, Zug-und Interface-Versagen sowie Mischformen lokalisiert und mit der Bauteilgeometrie bzw. Belastungskonfiguration in Verbindung gebracht werden. Auf diese Weise ist es gelungen, bisher zwar bekannte je-doch nicht näher erforschte Effekte wie z.B. duktiles Tragverhalten von Brettsperrholzplat-ten zu erklären. In diesem Zusammenhang wurden sowohl die Entwicklungsgeschichte des Publikation 2 94 Rollschubversagens als auch der Einfluss fortschreitender Rissbildung auf die Reduktion der Plattensteifigkeit untersucht und im Detail analysiert. Since wood products for structural elements, especially cross-laminated timber (CLT), have gained importance in the building sector, the need for appropriate and reliable design codes for such wood products has become essential. For the improvement and development of design concepts, a profound knowledge about the mechanical behaviour of these products is necessary. For this reason, this work focuses on global failure mechanisms and the corresponding evolution of different crack modes in CLT plates, depending on geometric and/or material related properties. Therefore, plate-bending experiments on 3-and 5-layered CLT plates were carried out. In addition to standard evaluation methods, each specimen was cut into small cubes to identify the failure modes inside the plates. Regions with dominant shear failure, tensile failure, delamination, and mixed failure modes could be captured and connected to geometry and loading situation. Based on this evaluation well known but not yet in detail described effects, such as the ductile structural behaviour of CLT plates, can be explained. Moreover, the evolution of rolling shear failure modes as well as from which point the progressive failure highly affects the plate stiffness is investigated and analysed in detail.
[Show abstract][Hide abstract] ABSTRACT: Although cross-laminated timber (CLT) plates are increasingly used in high-performance building structures, a tailored composition of them or, at least, a performance-based classification scheme is not available. Especially, the influence of the quality of the ‘raw’ material (wooden boards) on the load carrying capacity of CLT elements is hardly investigated yet. For this reason, within this work, bending tests on 24 CLT plates consisting of wooden boards from three different strength classes have been carried out. The global mechanical response as well as the formation of failure mechanisms were investigated, including a full-field deformation measurement system, which allowed for a qualitatively as well as quantitatively identification of board failure modes. Interestingly, no influence of the board strength class on the elastic limit load of the CLT plates was observed, but the situation was different for the load displacement history beyond the elastic regime, where basically, two different global failure mechanisms could be distinguished. The obtained knowledge about the ‘post-elastic’ behaviour of CLT plates may serve as a basis for the optimisation of CLT products and the development or improvement of design concepts, respectively. Moreover, the obtained large ‘post-elastic’ capacity reserve of CLT consisting of high quality boards could lead to a better utilisation of the raw material.
[Show abstract][Hide abstract] ABSTRACT: The main failure mechanisms of flexible pavements, such as low-temperature cracking, fatigue failure, and rutting are strongly influenced by the viscoelastic properties of asphalt. These viscoelastic properties originate from the thermorheological behavior of bitumen, the binder material of asphalt. In this paper, the bitumen behavior is studied by means of a comprehensive experimental program, allowing the identification of viscoelastic parameters of a power-law type creep model, indicating two time scales (short-term and long-term) within the creep deformation history of bitumen. Moreover, these characteristics of the creep deformation transfer towards bitumen-inclusion mixtures, as illustrated for mastic, consisting of bitumen and filler. For this purpose, the aforementioned power-law creep model is implemented into a micromechanical framework. Finally, the activation of the different creep mechanisms as a function of the loading rate is discussed, using viscoelastic properties obtained from both static and cyclic creep tests.
[Show abstract][Hide abstract] ABSTRACT: Since wood products for structural elements, especially cross-laminated timber (CLT), have gained importance in the building sector, the need for appropriate and reliable design codes for such wood products has become essential. For the improvement and development of design concepts, a profound knowledge about the mechanical behaviour of these products is necessary. For this reason, this work focuses on global failure mechanisms and the corresponding evolution of different crack modes in CLT plates, depending on geometric and/or material related properties. Therefore, plate-bending experiments on three- and five-layered CLT plates were carried out. In addition to standard evaluation methods, each specimen was cut into small cubes to identify the failure modes inside the plates. Regions with dominant shear failure, tensile failure, delamination and mixed failure modes could be captured and connected to geometry and loading situation. Based on this evaluation, well-known but not yet in detail described effects, such as the ductile structural behaviour of CLT plates, can be explained. Moreover, the evolution of rolling shear failure modes as well as from which point the progressive failure highly affects the plate stiffness is investigated and analysed in detail.
[Show abstract][Hide abstract] ABSTRACT: Wood is enjoying increasing popularity in the building sector. In order to fully exploit the potential of this material, particularly in two and three-dimensional structures, improved knowledge of the mechanical behavior of the material and more complex constitutive models are required. We herein present a holistic approach to mechanical material modeling of wood, including a multitude of length scales as well as computational and experimental efforts. This allows to resolve the microstructural origin of the macroscopic material behavior and to finally apply the gained knowledge to structural applications in a timber engineering framework. Focusing on elastoplasticity and viscoelasticity, exemplary results of the performed investigations are presented and their interrelations discussed. Regarding computational approaches, presented developments include multiscale models for prediction of elastic limit states and creep compliances of wood, macroscopic phenomenological models for wood plasticity and the time and moisture-dependent behavior, and their applications to investigations of dowel-joints and glued-laminated timber beams. Accompanying experiments provided additional input data for the computational analyses, therewith completing the set of material properties predicted by the multiscale models. Moreover, they served as the reference basis for model validation at both the material and the structural scale.
Full-text · Article · Oct 2013 · Computers & Structures
[Show abstract][Hide abstract] ABSTRACT: In the 1930s, Freyssinet presented a model describing that the strength of cement paste decreases with increasing capillary porosity. He proposed that uniaxial compressive strength of cement pastes is proportional to a volume quotient which is nowadays referred to as «gel-space ratio». In the 1970s, Fagerlund found out that capillary porosity is not the only governing factor because he observed that the final strength of substoichiometric cement pastes increases with decreasing initial water-to-cement mass ratio. However, due to limited microstructural insight, he could only propose an empirical description of the observed effect. We here provide more insight into how microstructural properties of cement paste influence its macroscopic compressive strength, based on the experimentally confirmed elasto-brittle micromechanics model of Pichler and Hellmich [CemConRes, 41(5) 467-476, 2011]. Gel-space ratio is shown to be equal to the solid volume fraction of a «hydrate foam» which is defined at the scale of a few microns and which exhibits a (quasi-)polycrystalline morphology of needle-shaped and isotropically oriented hydration products with capillary porosity filling the space in between. The model confirms that the material strength of cement pastes is not only determined by the capillary porosity, but unhydrated clinker grains (which are embedded, as inclusions, in the hydrate foam) act as reinforcements which increase the macroscopic strength; and that this is practically significant for substoichiometric mixes at large maturities, see Pichler et al. [CemConRes, 45(1), 55-68, 2013].
[Show abstract][Hide abstract] ABSTRACT: The material degradation of concrete subjected to fire events has a severe influence on the load-carrying capacity of support structures. Spalling of concrete layers, exposing the reinforcement bars and degradation of the material properties (Young's modulus, compressive strength) may lead to significant damage of the reduced cross-section and, therefore, cause failure of the structure. In order to understand the stress build-up at the heated surface caused by thermal expansion due to fire loading, finally leading to damage and spalling of concrete, the strain behaviour of cement paste and concrete exposed to combined thermo-mechanical loading is the focus of this work. Hereby, the evolution of thermal strains, Young's modulus and Poisson's ratio with increasing temperature are investigated experimentally. For this purpose, the specimens are loaded uniaxially while the temperature is increased up to 800 °C. The obtained results provide the proper basis for the development of realistic material models, allowing more sophisticated simulations of structures exposed to fire.
[Show abstract][Hide abstract] ABSTRACT: Many problems in engineering sciences can be described by linear, inhomogeneous, m-th order ordinary differential equations (ODEs) with variable coefficients. For this wide class of problems, we here present a new, simple, flexible, and robust solution method, based on piecewise exact integration of local approximation polynomials as well as on averaging local integrals. The method is designed for modern mathematical software providing efficient environments for numerical matrix-vector operation-based calculus. Based on cubic approximation polynomials, the presented method can be expected to perform (i) similar to the Runge-Kutta method, when applied to stiff initial value problems, and (ii) significantly better than the finite difference
method, when applied to boundary value problems. Therefore, we use the presented method for the analysis of engineering problems including the oscillation of a modulated torsional spring pendulum, steady-state heat transfer through a cooling web, and the structural analysis of a slender tower based on second-order beam theory. Related convergence studies provide insight into the satisfying characteristics of the proposed
No preview · Article · Jun 2013 · Advances in Applied Mathematics and Mechanics