Calibrating wood products for load duration and rate: a statistical look at three damage models
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Calibrating wood products for load duration and rate: a statistical look at three damage models Samuel W. K. Wong1 Received: 11 February 2020 / Accepted: 17 September 2020 / Published online: 3 October 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Lumber and wood-based products are versatile construction materials that are susceptible to weakening as a result of applied stresses. To assess the effects of load duration and rate, experiments have been carried out by applying preset load profiles to sample specimens. This paper studies these effects via a damage modeling approach, by considering three models in the literature: the Gerhards and Foschi accumulated damage models, and a degradation model based on the gamma process. A statistical framework is presented for fitting these models to failure time data generated by a combination of ramp and constant load settings, and it is shown how estimation uncertainty can be quantified. The models and methods are illustrated and compared via a novel analysis of a Hemlock lumber dataset. Practical usage of the fitted damage models is demonstrated with an application to long-term reliability prediction under stochastic future loadings.
Introduction For nearly 70 years it has been recognized in the literature that the strength of wood changes over time due to applied stresses, as a function of both the duration of the load (Wood 1951) and the rate at which the load is applied (Liska 1950). These are known as the “duration-of-load” (DOL) and “rate-of-loading” (ROL) effects in lumber. In particular, the gradual weakening of lumber over time must be considered in the construction of wood-based structures, and this factor is governed by appropriate standards to ensure the long-term reliability of structures (American Wood Council 2018).
Electronic supplementary material The online version of this article (https://doi.org/10.1007/s0022 6-020-01227-9) contains supplementary material, which is available to authorized users. * Samuel W. K. Wong [email protected] 1
Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON, Canada
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Wood Science and Technology (2020) 54:1511–1528
Experiments have been carried out on lumber specimens to collect empirical data for assessing the extent of the DOL and ROL effects (e.g., Wood 1951; Madsen and Johns 1982; Foschi and Barrett 1982; Gerhards and Link 1987; Karacabeyli and Barrett 1993). Briefly, the common idea is to design a load profile 𝜏(t) under which a sample is to be stressed over time t ≥ 0 , and record the time to failure for each sample specimen. A ramp load test specifies 𝜏(t) = kt , that is, the load is increased linearly at rate k until the piece breaks. For a constant load test with level 𝜏c , the load is first increased linearly 𝜏(t) = kt for 0 ≤ t ≤ 𝜏c ∕k , after which the load is held at the constant level 𝜏c until either the specimen fails or a preset time T1 is reached, the latter usually being several months or years. The
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