Time-variant reliability of timber beams according to Eurocodes considering long-term deflections

ABSTRACT

In order to achieve a consistent level of failure probability, structural design codes are optimized using probabilistic methods. This optimization process traditionally focuses on the ultimate limit states (ULS). However, in the design of timber structures the performance of the structural members is often governed by the serviceability limit state (SLS) associated with different load levels than applied in the ULS. The probability of serviceability failure is strongly dependent on the loading sequence and the time-dependent response of timber; therefore, a time-variant probabilistic model is recommended to estimate them properly. This study aims to investigate the time-dependent reliability for long-term deflections of timber office and residential floor beams according to the specifications of the Eurocodes. A simple creep model is used to calculate the deflections and Monte Carlo simulation is carried out to determine the reliability index. It was found that the creep factor and the suggested deflection limits given in Eurocode 5 might not be appropriate to achieve the expected target reliabilities. To obtain a more consistent reliability, more suitable values for the mentioned parameters were suggested. However, the primary aim was to present a framework to determine appropriate deflection limits for structural codes.     

Mechano-sorptive effects on timber creep

Summary Fick's law of predicting the moisture content of beams, combined with a simple mechano-sorptive model is applied to the analysis of creep resulting from moisture variations due to changing environmental conditions. The natural climatic conditions are modelled with the daily and annual cyclic variations represented by sine waves. As the moisture change responding to varying climatic conditions is always greater near the boundaries of a timber section, the creep rate close to the surface layer is higher than that in the middle of the cross-section. Therefore with time, an increased portion of the load will be carried by the inner part of the material.     

Non-linear creep caused by slip plane formation

Summary The minute compression failures of the cell walls known as slip planes are quantified with respect to their occurrence in the compression side of beams subjected to mechano-sorptive creep. It is shown that slip planes occur at values of stress/strain lower than previously assumed. The slip plane intensity proves to be linearly related to creep and non-linearly related to stress. A permanent increase, S, of longitudinal shrinkage /swelling results from slip plane formation, and this parameter therefore serves as a substitute for slip plane intensity, which is not easily measured. Slip plane intensity is considered a measure of accumulated damage, and the substitute parameter S is used to quantify the accumulated damage of structural timber beams. The load level experienced by structural timber beams subjected to mechano-sorptive creep is shown to be reflected in the accumulated damage as assessed by S.The project is a part of a USDA funded project Initiation and Propagation of Failure in Wood. Support is also provided by the Danish Technical Research Council. The N.C. Brown Centre for Ultrastructure Studies, CESF, SUNY, Syracuse provided research facilities. The support is gratefully acknowledged     

Fibre morphological effects on mechano-sorptive creep

The increased creep rate of paper under load during moisture cycling conditions as compared to that at high constant humidity is a problem in the use of packaging materials. In order to investigate the influence of morphological factors of the fibres on the occurrence and magnitude of this phenomenon, i.e. the occurrence of mechano-sorptive creep, studies on wood fibres isolated from different parts of spruce wood were performed. Thus, creep properties were studied on earlywood and latewood fibres from both juvenile wood and mature wood. In general, latewood fibres showed a higher degree of mechano-sorptive creep than earlywood fibres, and mature wood showed a higher degree of mechano-sorptive creep than juvenile fibres. The difference in mechano-sorptive creep rate between different fibres was shown to be correlated to the differences in fibril angle. The smaller the fibril angle the higher was the mechano-sorptive creep ratio. It was suggested that at fibril angles approaching 45° wood fibres do not exhibit mechano-sorptive creep.     

Use of Leicester's “rheological model for mechano-sorptive deflections of beams”

Summary The model for mechano-sorptive deformation proposed by Leicester is used to predict stress relaxation of wood drying under constraint from apparent creep of drying wood under constant load. The predictions are compared with measurements on four pairs of beams, one beam in each pair being tested under constant load, the other at constant deflection. Agreement was sufficiently close to demonstrate the value of the model.     

Long term bending creep of wood in cyclic relative humidity

Summary Long term creep and recovery test results of wood under a bending load of 10 MPa stress and subjected to relative humidity cycling are presented. In spite of the vast number of humidity cycles during these tests, the results do not give evidence of an existence of a mechano-sorptive creep limit. The results also indicate that the recovery is not complete on unloading when the humidity is cycled. A mechano-sorptive model that fits the test results is proposed. According to the model, the elastic bending deflection in a cyclic load of 10—3 MPa and subjected to natural outdoor relative humidity can be about doubled to account for the creep under ten years loading.     

Mechanical response of wood perpendicular to grain when subjected to changes of humidity

This paper describes the deformations caused by stress and humidity interaction, mechano-sorption, in the cross grain directions of wood and the relaxation or accumulation of internal stresses caused by these deformations. Long-term tests on small clear specimens in cyclic climates with both tensile and compressive loads were carried out. The development of internal stresses in timber was measured indirectly at different times during the adsorption and desorption processes. Released deformations were measured from cross-sections after cutting them to small slices. These deformations were used to estimate the internal stresses caused by the humidity variations. Tests with constant loads and multiple humidity cycles show a mechano-sorptive strain that is ten times higher than the elastic strain. It is shown that existing models for describing mechano-sorption perpendicular to grain are inaccurate when applied to multiple humidity cycles. The present results demonstrate that if the mechano-sorptive behaviour and the moisture gradients in wood can be accurately described, it is possible to predict the stress distribution in a timber cross-section by knowing the climate history.     

Mechano-sorptive creep in wood fibres

In order to investigate the way in which fibre properties affect the mechano-sorptive creep phenomenon in paper, single wood fibres were exposed to tensile stresses at a constant humidity of 80% relative humidity (RH) and in a cyclic humidity environment varying between 80 and 30% RH. Contrary to earlier claims, it was demonstrated that single wood fibres exposed to a cyclic RH show a considerably higher creep than that corresponding to the highest RH experienced in the cycle, i.e., a mechano-sorptive behaviour. The creep strain rate at cyclic humidity was shown to be a function of the creep rate at constant climate, and to be an apparent linear function of the applied stress.     

Shear behaviour of bond lines in glued laminated timber beams at high temperatures

A comprehensive research project has been carried out at the Swiss Federal Institute of Technology (ETH) on the fire behaviour of timber-concrete composite slabs (Frangi and Fontana 2000). The glued laminated timber beams used for the fire tests were bonded with a one-component polyurethane (1-K-PUR) adhesive. As one fire test on a slab showed an unexpected shear failure of a glued laminated timber beam, a series of tests was carried out to study the shear behaviour of different types of adhesives at high temperatures. The first part of the paper describes the results of the shear tests at elevated temperatures, in the second part the shear test results are compared to the fire test on a slab.     

Cantilever experimental setup for rheological parameter identification in relation to wood drying

Wood exhibits a pronounced time dependent deformation behavior which is usually split into ‘viscoelastic’ creep at constant moisture content (MC) and ‘mechano-sorptive’ creep in varying MC conditions. Experimental determination of model rheological parameters on a material level remains a serious challenge, and diversity of experimental methods makes published results difficult to compare. In this study, a cantilever experimental setup is proposed for creep tests because of its close analogy with the mechanical behavior of wood during drying. Creep measurements were conducted at different load levels (LL) under controlled temperature and humidity conditions. Radial specimens of white spruce wood [Picea glauca (Moench.) Voss.] with dimensions of 110 mm in length (R), 25 mm in width (T), and 7 mm in thickness (L) were used. The influence of LL and MC on creep behavior of wood was exhibited. In constant MC conditions, no significant difference was observed between creep of tensile and compressive faces of wood cantilever. For load not greater than 50% of the ultimate load, the material exhibited a linear viscoelastic creep behavior at the three equilibrium moisture contents considered in the study. The mechano-sorptive creep after the first sorption phase was several times greater than creep at constant moisture conditions. Experimental data were fitted with numerical simulation of the global rheological model developed by authors for rheological parameter identification.     

Experimental indication of interaction between viscoelastic and mechano-sorptive creep

Summary This paper describes the study of possible interactions between the viscoelastic and mechano-sorptive creep inPinus sylvestris. When two periods of constant-moisture creep were separated by a period of mechano-sorptive creep, the expected creep rate during the second viscoelastic period was decreased. A similar effect was observed during creep recovery. These results were taken to indicate an interaction between the two types of creep, although not necessarily a common mechanism. During recovery with uniform moisture cycling, the effects of one extra low and one extra high humidity were observed. The low humidity showed no significant effect, but the high humidity significantly increased the recovery. This was attributed to a parallel effect to that of creep: namely, the creep acceleration that occurs at a higher moisture level than has previously been reached during the test.     

Transient moisture effects on wood creep

To gain insight into the physical nature of the coupling between mechanical stress and humidity variations, the behaviour of thin wood strips was studied using specially developed apparatus for creep/recovery and relaxation/blotting-out tests in a controlled humidity environment. The load time and the rate of viscoelastic creep were found to have little influence on mechano-sorptive creep. Moreover, creep trajectory curves for specimens with continuous and interrupted humidity cycles indicated divergence from simple creep-limit behaviour. The effect of transient moisture was also modelled numerically at the molecular level using an idealized cellulose-based composite. Preliminary results suggest that: (i) during free shrinkage, the cellulose chains in elementary fibrils may bend perpendicular to the planes of the hydrogen bonded sheets which form the crystalline lattice; (ii) transient hydrogen bonding between the crystalline cellulose and amorphous polymer owing to the introduction or removal of water may accelerate shear slip between the two phases in the presence of an external load. Received 6 July 2000 The financial support of the Swiss Federal Office for Education and Science is gratefully acknowledged.     

Mechano-sorptive creep in pulp fibres and paper

The factors affecting mechano-sorptive creep of wood and paper have been investigated for a long time. It has also been argued that single wood fibres do not exhibit mechano-sorptive creep and that the reasons for the accelerated creep under moisture cycling conditions instead are related to the bonds between the fibres. In order to examine the relevance of this argument, measurements on single pulp fibres of different composition were performed in tension, and the mechano-sorptive creep was compared to that of papers made from the same source of pulp fibres. All fibres tested were found to exhibit an increased creep rate during moisture cycling as compared to constant humidity conditions. Thus, pulp fibres show mechano-sorptive creep and in this sense behave similar to solid wood or paper products made thereof. A linear relation between the creep strain rate during cyclic humidity and the creep strain rate at a constant humidity was also noted for both fibres and paper. This relation was not affected by changes in hemicelluloses content or composition, neither for fibres nor for papers made of these fibres. However, in all cases, papers showed a much higher mechano-sorptive creep than the corresponding fibres they were made of.     

Mechano-sorptive creep mechanism of wood in compression and bending

Summary A model is introduced which links the mechano-sorptive behaviour of wood subjected to moderate and high compression or bending stresses parallel to grain to the formation of slip planes in the cell wall. Slip plane formation is dependent on the breaking of hydrogen bonds, which process is directly related to the amount of moisture change. The dramatic change of microfibril orientation in slip plane zones cause an increase of the longitudinal shrinkage/swelling and a decrease of the modulus of elasticity. These features of slip plane formation account for both the magnitude and the oscillation of the excessive mechano-sorptive creep associated with compression and bending parallel to grain. A summary is given of the characteristics of the mechano-sorptive effects, and the model is discussed in the light of these effects.The paper is one of the results of a project on the influence of changing moisture content on the mechanical behavior of wood, currently underway in a co-operation between College of Environmental Science and Forestry, State University of New York, and the Technical University of Denmark. Support for this project is provided by the Danish Technical Research Council and by the USDA C--operative Research Program (proj. 85-FSTY-9-0112). The support is gratefully acknowledged     

Mechano-sorptive effects in wooden material

Summary The effects on wood of simultaneous mechanical and moisture loading are studied. In order to clarify the mechano-sorptive behaviour of wood, a review of different phenomena presented in the literature is included. Based on this review a constitutive model is proposed for the case of uniaxial stress in the longitudinal direction. The validity of the model is checked independently against test results. The calculations show that the model is capable of describing the response of wood with reasonable accuracy. Simulations indicate that the response of small test specimens is more difficult to describe than that of larger beams. Some differences in behaviour are found to depend on loading mode and nature of moisture cycling. Very large and fast moisture cycles seem to give larger mechano-sorption than smaller variations. The results of the simulations show that there is a significant influence of strain on the shrinkage and swelling response.     

Mechanical behaviour of finger joints at elevated temperatures

Finger joints are commonly used to produce engineered wood products like glued laminated timber beams. Although comprehensive research has been conducted on the structural behaviour of finger joints at ambient temperature, there is very little information about the structural behaviour at elevated temperature. A comprehensive research project on the fire resistance of bonded timber elements is currently ongoing at the ETH Zurich. The aim of the research project is the development of simplified design models for the fire resistance of bonded structural timber elements taking into account the behaviour of the adhesive used at elevated temperature. The paper presents the results of a first series of tensile and bending tests on specimens with finger joints pre-heated in an oven. The tests were carried out with different adhesives that fulfil current approval criteria for the use in load-bearing timber components. The results showed substantial differences in temperature dependant strength reduction and failure between the different adhesives tested. Thus, the structural behaviour of finger joints at elevated temperature is strongly influenced by the behaviour of the adhesive used for bonding and may govern the fire design of engineered wood products like glued laminated timber beams.     

Stochastic model for predicting the bending strength of glued-laminated timber based on the knot area ratio and localized MOE in lamina

The aim of this study was to develop a stochastic model for predicting the bending strength distribution of glued-laminated timber (GLT). The developed model required the localized modulus of elasticity (MOE) and tensile strengths of laminae as input properties. The tensile strength was estimated using a regression model based on the localized MOEs and knot area ratios (KAR) which were experimentally measured for lamina grades samples. The localized MOE was obtained using a machine stress-rated grader, and the localized KAR was determined using an image-processing system. The bending strength distributions in four types of GLTs were simulated using the developed GLT beam model; these four types included: (1) GLT beams without finger joints; (2) GLT beams with finger joints; (3) GLT beams with different lamina sizes; and (4) GLT beams with different combinations of lamina grades. The simulated bending strength distributions were compared with actual test data of 2.4 and 4.8 m-long GLTs. The Kolmogorov–Smirnov goodness-of-fit tests showed that all of the simulated bending strength distributions agreed well with the test data. Especially, good agreement was shown in the fifth percentile point estimate of bending strength with the difference of approximately 1%.     

A global rheological model of wood cantilever as applied to wood drying

In the process of wood drying inevitable stresses are induced. This often leads to checking and undesired deformations that may greatly affect the quality of the dried product. The purpose of this study was to propose a new rheological model representation capable to predict the evolution of stresses and deformations in wood cantilever as applied to wood drying. The rheological model considers wood shrinkage, instantaneous stress–strain relationships, time induced creep, and mechano-sorptive creep. The constitutive law is based on an elasto–viscoplastic model that takes into account the moisture content gradient in wood, the effect of external load, and a threshold viscoplastic (permanent) strain which is dependent on stress level and time. The model was implemented into a numerical program that computes stresses and strains of wood cantilever under constant load for various moisture content conditions. The results indicate that linear and nonlinear creep behavior of wood cantilever under various load levels can be simulated using only one Kelvin element model in combination with a threshold-type viscoplastic element. The proposed rheological model was first developed for the identification of model parameters from cantilever creep tests, but it can be easily used to simulate drying stresses of a piece of wood subjected to no external load. It can therefore predict the stress reversal phenomenon, residual stresses and maximum stress through thickness during a typical drying process.     

Creep in chipboard

Summary Previous linear and curvilinear regression models for predicting the creep deflection of timber and timber products have failed to provide an adequately good fit. However, this paper shows that the 4-element (and to a lesser degree the 3-element) rheological model provides an extremely good fit to chipboard creep data.A set of experiments has been carried out on the creep behaviour of five commercially-available types of chipboard under 3-point sustained loading at constant temperature and humidity. This range of board types encompassed three types of glue — UF, MF/UF and Pf- and was loaded at two stress levels-30% and 60% of the short term ultimate stress. The lifetime of these specimens ranged from 25 days to over 31/2 years until either failure occurred or the load was removed.Creep curves based on 3- and 4-element rheological models have been fitted to the data from each specimen using an iterative least squares computer program which we developed. The validity of the two models is discussed, together with studies on the comparative behaviour of different board types and the use of the models as predictive tools.     

Effects of temperature on mechano-sorptive creep of delignified wood

The effects of temperature on mechano-sorptive (MS) creep of delignified hinoki wood (Chamaecyparis obtusa Endl.) were investigated using longitudinal (L) and radial (R) specimens during adsorption and desorption over the temperature range of 20°–80°C. The results were compared with those of stepwise delignified specimens tested at a constant temperature of 20°C. It was found that the effects of temperature on the MS creep of delignified specimens are more remarkable than for untreated specimens. The tendencies of increasing MS creep with temperature, delignification, and their combination were observed. The increase in MS creep for L specimens was relatively small and almost equal in both adsorption and desorption processes, while for R specimens the MS creep was small in desorption, but significantly different in adsorption. In addition, good correlation was observed between the MS coefficient (K) and instantaneous compliance (J ₀). The increase in MS creep occurs as a result of temperature increase or decrease in lignin content, or their interacting effects. However, in the case of desorption for R specimens, the increase of MS creep was unexpectedly small due to a remarkably increased J ₀. Part of this report was presented at the 15th Annual Meeting of the Chubu Branch of the Japan Wood Research Society in Fukui, October 2005