Modelling of bending creep of low- and high-temperature-dried spruce timber

In the current project, a finite element model is developed to analyse the long-term behaviour of timber beams. The time-dependent response of wood subjected to bending and moisture changes is investigated in terms of strains and stresses. A rheological model is implemented to capture the effects of creep, mechano-sorption and hygroexpansion. The model is validated against test results from Bengtsson and Kliger (Holzforschung 57:95–100, 2003). The results of the analysis showed that the mechano-sorptive creep of low- (LT) and high-temperature-dried (HT) timber beams can be sufficiently modelled with a spring and a single Kelvin body. The different mechano-sorptive behaviour of LT- and HT-dried specimens is considered with different mechano-sorptive and shrinkage–swelling parameters. The presented model could be used to derive general mechano-sorptive parameters: (1) for better prediction of creep over the service life and (2) to provide a basis of time-dependent probabilistic calculations for structural-sized timber in serviceability limit state.     

Duration-of-load and creep effects in strand-based wood composite: a creep-rupture model

In order to investigate the creep and duration-of-load (DOL) effects in thick strand-based wood composite products, a creep-rupture model is proposed linking the accumulated damage to creep deformation. Results from long-term constant load tests have been interpreted by means of this creep-rupture model, which is capable of representing the time-dependent deflection and time-to-failure data at different stress levels. The predictions of the model have been verified using results from ramp load test at different rates of loading. The creep-rupture model incorporates the short-term strength of the material, the load history and predicts the deflection history as well as the time-to-failure. As it is a probabilistic model, it allows its incorporation into a time-reliability study of wood composites’ applications.     

Capacity prediction of welded timber joints

Linear vibration welding of timber structural elements provides new opportunities to potentially achieve structural joints. This paper investigates to which extent welded joints can be considered for load-bearing structural joints. On the basis of a series of experimental and numerical investigations on a series of welded single-lap joints, failure modes were identified, and the associated failure criterion was quantified. A probabilistic method subsequently allowed accurately predicting the capacity of the tested wood welded joints exclusively based on objective input data, including an estimate of the scattering due to the material’s inherent variability.     

Duration of load revisited

A duration of load study representing 13 years of testing was recently terminated. Preliminary results have been published over the years. This paper represents the final account of the study, which was focused on the influence of moisture content on time to failure for structural timber subjected to bending under constant load conditions. Two constant moisture conditions (MC = 11 and 20%) and one condition of varying moisture (MC between 11 and 20%) were applied. A total of 816 Norway spruce boards of dimensions 44 × 95 × 1,800 mm³ were included. Eight groups of non-destructively matched samples were formed. Four groups were subjected to short-term strength tests, and four groups were subjected to long-term tests. Creep and time to failure were monitored. Time to failure as a function of stress level was established and the reliability of stress level assessment was discussed. A significant mechanosorptive effect was demonstrated both in terms of increased creep and shortening of time to failure. The test results were employed for the calibration of four existing duration of load models. The effect of long-term loading was expressed as the stress level SL₅₀ to cause failure after 50 years of loading. SL₅₀ was found to be of the order 0.60 for MC = 11%, 0.50 for MC = 20% and 0.44 for MC varying between 11 and 20%. The test results revealed no evidence of a threshold stress level. A reliability based calibration of load-duration factors was performed using probabilistic models of loads and of the short-term and long-term strengths. For permanent and imposed library loads, reliability-based estimation of the load duration factor gave almost the same results as direct, deterministic calibration.     

Creep in chipboard

Summary Samples of five chipboards, one waferboard, one plywood, one fibre building board and Scots pine timber were loaded in four point bending at a stress equivalent to 60 per cent of the short term failing stress under five combinations of temperature and relative humidity for a period of six months, or until prior failure.Irrespective of whether creep behaviour was assessed in terms of total deflection, viscous component of deflection, relative creep, creep modulus, or deflection at, or time to failure, significant differences were obtained with variations both in temperature and relative humidity. The effect of temperature, at fixed humidity, was slightly greater between 20°C and 30°C than between 10°C and 20°C, while the effect of humidity was appreciably greater between 65% and 90% rh than between 30% and 65% rh. Fitting of hyperbolic curves to the data permitted the prediction of creep behaviour with a good degree of fit at any combination of temperature and humidity within the experimental range.Differences in response to environmental conditions existed among some of the boards. Thus the ranking order of the materials was slightly different under variable humidity than it was under variable temperature. It was possible to describe these differences in terms of the variation that occurred among the materials in the relative proportion of the elastic, viscoelastic and viscous components of deflection.     

Repair and strengthening of timber cantilever beams

This research aims to study the feasibility of repair and strengthening of timber cantilever beams used in historic buildings. It is conducted to investigate the feasibility of using different valid materials and techniques to repair and strengthen timber cantilever beams in new and historic timber buildings. The study is performed in terms of structural performance as well as historic and architectural values. An experimental program of several different materials and techniques is executed. The results are driven in terms of initial cracking load, crack propagation for the tested samples at different loading stages, deflection values, and failure load for each repaired or strengthened material and technique. The main variables are timber types (new and historic), repair and strengthening materials (steel plates, Glass Fiber Reinforced Polymer wrap, and Carbon Fiber Reinforced Polymer laminates), repair or strengthening techniques (near surface mounted and externally bonded system), and cantilever length (1000 and 1250?mm). Test results indicated that using steel plates, glass fiber wrap, and carbon fiber laminates increases the value of failure loads and decreases the deflection at both; repaired and strengthened timber cantilever beams compared to control beams.     

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.     

Creep in chipboard

Summary Although previous papers in this series have shown that a 4-element rheological model can provide a very good representation of the creep deflection of chipboard in bending, a new set of long-term data shows that it has certain limitations as a model for predicting deflection up to 3^1/2 years. It was deduced in a earlier paper (Pierce et al. 1979) that the linear viscous flow component was likely to predict higher than actual deflections over a long period. This paper shows that view to be correct, and puts forward a modified 4-element model in which the viscous component is non-linear with respect to time. The resulting 5-parameter model is shown to be superior to the 4-parameter model for long-term predictions of creep deflection particularly at the lower stress levels, although it appears that the viscoelastic and viscous components of deflection are not as realistic as in the 4-parameter representation.     

Withdrawal capacity of washers in bolted timber connections

Abstract

The European yield model (EYM) has been accepted to determine the load-carrying capacity of structural timber connections. However, experiments of bolted connections are still not in agreement with the EYM unless the additional bearing capacity offered by the washers is taken into account. This bearing capacity is depending on the compressive strength perpendicular to grain of the structural timber. Tests results carried out with M16 and M24 washers on solid and glued laminated timber are used to verify the reliability of three strength capacity predicting models, one of which is an analytical model while the other two are empirical. It was concluded that the analytical model is the superior one. This model should be incorporated in all new structural timber design code revisions.     

Creep of the beam in Japanese conventional structures composed of green and kiln-dried timber II: predictive model for relative deflections

We conducted creep tests to evaluate creep behaviors of conventional Japanese framing (jikugumi) structures as reported in a previous article. We measured beam deflections of two structures: one of them was composed of only green timbers (G) and the other with only kiln-dried timbers (D). Besides the two structures, we prepared green and kiln-dried beams to measure moisture content (MC), weight, and dynamic Young’s modulus (E _f) by the longitudinal vibration method. We attempted to predict deflections of beams in the structures by using experimental data for single beam specimens. The proposed simple predictive model was derived from two equations: a relation between MC and equilibrium moisture content calculated with temperature and relative humidity, and a relation between MC change and relative deflection change. Beam deflections were traced for 2.5 years, while the predictions were based on experimental data from loading to the 11th day of the test. It was assumed that sensitivity of deflection change to MC should differ during desorption or adsorption. Although annual cyclic changes were observed in E _f, there was no obvious relationship between E _f and beam deflection. Part of this article was presented at the Annual Meeting of the Architectural Institute of Japan, Kyushu, September 1998     

Creep in chipboard

Summary Samples of five chipboards, one waferboard, one plywood, one fibre building board and redwood timber (Pinus sylvestris) were loaded in 4-point bending under four stress levels: 30, 45, 67.5 and 75% of the short term ultimate, thereby extending earlier work at 60% stress level. Five environmental conditions were used at each stress level: 10°C 62% relative humidity (rh); 20°C 30% rh; 20 °C 65% rh; 20°C 90% rh and 30°C 68% rh. Deflections were recorded at least on a daily basis for a period of 6 months, unless failure of the sample occurred earlier. Values for the elastic, viscoelastic and viscous components of creep deflection were calculated for two time periods using the 4-element rheological model developed in an earlier paper: comparisons were made on the basis of the percentage contribution of each component. The relative proportions of the elastic, viscoelastic and viscous components making up total deflection were found to vary considerably with time, temperature, relative humidity, stress level and material. The relationships were complex with strong interactions occurring among environmental condition, stress level and material. Thus, for example, the effect of high temperature, or high relative humidity, in determining the magnitude of the viscous component was much greater at higher levels of stressing: waferboard appeared to be less sensitive to high humidity and solid timber more sensitive to high temperature than the other materials. T-tests further confirmed the complexity of the relationships. It is concluded that much of the variability in creep deflection recorded in Part 8 of this series is primarily due to changes in the percentage contribution of the viscous component.     

Monitoring critical defects of creep rupture in oriented strandboard using acoustic emission: incorporation of EN300 standard

This creep rupture study in commercial oriented strandboard (OSB) used a 4-point flexural test to evaluate the dynamic property changes of a 300×1,000-mm specimen using an acoustic emission (AE) system. Compared to deflection, AE events were more sensitive to damage accumulation than deflection to final failure. Specimens were artificially notched on either the tension- or compression-side and were subjected to 80% stress level at ambient conditions. Defects on the compression side of the bending specimen were found to be more critical than on the tension side in creep-rupture. The in-plane fractures followed patterns of the valleys of low-density spots as defect trenches, demonstrating adverse effects of high variation in horizontal density. An impetus and rationale to incorporate regulatory quality inspection standards and product certification of structural OSB based on the control limits of ±10% panel density as stipulated in EN300 standard is discussed.Experiment conducted at the former University of California Forest Products Laboratory (Nondestructive Evaluation Center), Richmond, CA 94804, USA.     

Creep of four tropical hardwoods from Cameroon

Summary The knowledge of the behaviour of wood over time is important in the design of timber structures. This study, which is part of a program to better understand the behaviour of tropical woods, aims at showing the effect of creep in wood. Observations were made on the development of the deflection in a uniformly stressed beam under controlled temperature and humidity conditions. The results obtained show that for stresses not greater than 35% of the stress at failure, the behaviour of the species tested is linear. In these cases, the total relative creep is not more than 35%. Similar results have been obtained for four cameroonian species: Azobe, Tali, Sapelli and Movingui.This research was carried out in the Structural Analysis Laboratory of the Department of Civil and Urban Engineering, National Advanced Polytechnic School of Engineering. Yaounde. Director: Dr. A. Foudjet     

Creep in chipboard

Summary The effect of moisture and level of stressing on the rate of creep and time to failure is studied for UF and MUF bonded particleboard. Response curves were fitted to a 4-element rheological model with a high degree of accuracy for four levels of stressing and for three levels of relative humidity at 20°C. Values of relative creep increased with time and also with increased levels of stress and r.h. The ratio of stress to deflection — presented either as the creep modulus or as isochronous curves — decreased rapidly with time. Particleboard is demonstrated to exhibit non-linear viscoelastic properties, particularly at the higher levels of stress. Deflection was increased and time to failure decreased when r.h. was raised from 65 to 90 per cent, but no significant statistical change was noted between 30 and 65 per cent r.h. Increased levels of stress caused a decrease in both deflection and time to failure. Greater deflection at failure and longer time to failure were recorded for MUF board, but for the UF board the 90 per cent r.h. had a more pronounced effect in increasing deflection and decreasing the time to failure. Predictions are made on the long-term stress loadings for different humidity conditions.     

Statistical and reliability analysis for mixed-mode fracture tests applied to wood material

The integrity of timber structures is mainly related to its capacity to resist crack propagation under various load conditions. However, this phenomenon is random by nature, and the need to incorporate statistical information is mandatory for practical use in structures. This paper aims at defining a probabilistic model in order to characterize the scatter of the toughness test results of timber. The instantaneous failure tests are performed using the mixed-mode crack growth specimen. The crack tip growth is recorded by a video camera for mixed-mode ratios of 15°, 30° and 60°, where the relative displacement of loading points is recorded by LVDT sensor. The experimental energy release rate is evaluated by the compliance method. As large scatter of the energy release rate is observed, the statistical analysis is performed by using the bootstrap simulation, in order to characterize the probabilistic models in the opening and shear crack modes. The reliability analysis is then performed in order to underline the impact of the statistical uncertainties on the rupture of wood material.     

Reliability analysis and duration-of-load strength adjustment factor of the rolling shear strength of cross laminated timber

In this study, the duration-of-load effect on the rolling shear strength of cross laminated timber (CLT), with different cross-sectional layups (five-layer and three-layer), was evaluated. A stress-based damage accumulation model is chosen to evaluate the duration-of-load strength adjustment factor of the rolling shear strength of CLT. This model incorporates the established short-term rolling shear strength of material and predicts the time to failure under arbitrary loading history. The model has been calibrated and verified based on the test data from low cycle trapezoidal fatigue tests (damage accumulation tests) in the previous study. The long-term rolling shear behaviour of CLT can then be evaluated from this verified model. As the developed damage accumulation model is a probabilistic model, it can be incorporated into a time based reliability assessment of the CLT products, considering short-term, snow, and dead load only loading cases. The reliability analysis results and factors reflecting the duration-of-load effect on the rolling shear strength of CLT are compared and discussed. The characteristic of this modeling theory lies in that the verified model is also able to predict the duration-of-load behaviour of CLT products under arbitrary loading history, such as long-term dead load case; then, these predictions of time to failure from the damage accumulation model can elucidate duration of load by the stress ratio evaluation approach. The results suggest that the duration-of-load rolling shear strength adjustment factor for CLT is more severe than the general duration-of-load adjustment factor for lumber; this difference should be considered in the introduction of CLT into the building codes for engineered wood design.     

The modelling of time-dependant deformation in wood using chemical kinetics

Summary The development of rheological models to predict creep has led to the derivation of quite complex equations that can predict creep reasonably accurately. However, these models are conceptual and are not based on a fundamental understanding of the actual deformation processes occurring within the material. The concept of modelling creep using a chemical kinetic approach is one that attempts to understand creep in wood at a molecular level and, from this, to develop models that more accurately predict creep deflections.This paper presents two models developed from chemical kinetic theory, that describe the time-dependant deformation of wood. The validity of applying these models to experimental data has been assessed by stress relaxation tests on thin samples of Sequoia sempervirens. Two stages of experimentation were carried out. In stage 1, both models were applied to the results of stress relaxation tests on 6 samples. Similar values of activation energy and activation volume were calculated by both models and a single energy barrier was found to dominate the deformation process.In stage 2, the effect of varying the initial applied stress on activation energy and activation volume was assessed by carrying out stress relaxation tests at stress levels of 25%, 30% and 35% of the short-term strength. Values of activation energy and activation were found to increase as the applied stress level decreased.Both models describe the time-dependent behaviour of wood well, however their ability to predict long-term creep deflections may be limited. Future work will develop these models further in order to improve long-term creep prediction and then apply them to the results of both creep and stress relaxation tests at a variety of stress levels and moisture contents in order to test their validity.     

Structural analysis of tree trunks and branches: tapered cantilever beams subject to large deflections under complex loading

The dimensions, deflections and support costs of tree trunks and branches can be deduced using the structural theory for cantilever beams. However, elementary theory applies only as long as deflections are small, and complex analytical solutions are required to account for complex taper and patterns of loading. This paper describes a method that copes with large deflections, any patterns of taper, and any patterns of distributed loading, point loading or externally applied bending moments. A beam is considered to be composed of a series of short segments, such that each has only a small deflection, and each can have specified dimensions, Young's modulus and loading. The transport matrix method of structural analysis is used to determine the end conditions of each segment and of the whole beam. The method is verified by comparing predicted deflections with deflections (a) calculated using an analytical solution by Bisshopp and Drucker (1945), (b) calculated and measured for sapling tree trunks by Leiser and Kemper (1968), and (c) measured on tapered and untapered plastic rods.     

Modelling the long-term strength of timber columns

Summary This paper studies the influence of the used creep function, and the duration of the experimental sustained loading from which the creep function was derived, in modelling the long-term buckling strength of timber columns. The sensitivity of this buckling strength to creep and initial deflection is numerically studied using an energy approach that takes into account the initial deflection. Various creep functions — power laws as well as exponential laws — derived from bending experiments of different durations are used for the numerical simulation. The crucial need for experimental results issued from very long load period experiments is identified. Such experiments may lead to a more credible creep analysis of timber structures.Symbols i radius of giration - s stress level - E_L effective MOE - E₀ instantaneous MOE - I inertia moment - K,K geometrical matrices - L length of beam or column - L_f effective length - N_cr axial force, buckling load - U elastic strain energy - W external forces work - t time variable - u moisture content (m.c.) - v total deflection - v_c, v_e, v₀ creep, instantaneous elastic and initial deflections respectively Greek Letters (t) time function - , _e, ₀ total, instantaneous and initial strains respectively - twist rotation - (t) creep coefficient or fractional creep or relative creep - (x) shape function - load factor - longitudinal shortening - total potential energy - creep factor - relaxation time     

Seismic performance of post-and-beam timber buildings II: reliability evaluations

This paper presents an approach to evaluate the performance reliability of post-and-beam timber buildings under seismic excitation. The uncertainties considered include those associated with the earthquake ground motions, the structural mass and shear wall characteristics. The approach uses a verified structural model called “PB3D” for the creation of a database of seismic responses, which are then represented by appropriate response surfaces. These, in turn, are used to formulate explicit performance functions for the reliability analysis. Performance is studied in terms of peak inter-story drift, and polynomial functions are used to represent the seismic response surfaces. Non-performance probabilities are evaluated with respect to different performance expectations, using FORM and importance sampling methods. Case studies for two multi-story post-and-beam buildings are also presented.