Effect of Moisture Content and Temperature on the Mechanical Properties of Wood: An Analysis of Immediate Effects

Mechanical properties of wood increase as moisture content decreases below fiber saturation point, at least down to about 5% MC, and as temperature decreases. This report summarizes the relevant studies reported in the literature on the immediate effects of moisture content and temperature on several mechanical properties of clear wood. Recommendations are made for future research

A Note on Load Duration of Douglas-Fir 2 by 4s Under Repeated Loads

Douglas-fir specimens matched to specimens previously tested under sustained constant bending loads were subjected to two different repeated load cycle tests to evaluate the effect of repeated bending loads on load duration of lumber. There was no clear evidence that repeated loading gave different results than sustained constant loading

Bending Creep and Load Duration of Douglas-Fir 2 By 4S Under Constant Load

Douglas-fir 2 by 4 beams of different grades were tested under various constant-load levels in a controlled environment to evaluate load duration and creep behavior. A two-parameter equation was used to model relative creep of wood beams free of partial fracture. Both parameters M and N of this equation vary considerably between specimens but can be highly correlated with each other, depending on the time base used to determine N. Stress level was partially correlated with M and N together, but with neither parameter alone.Additional matched beams were tested at near design loads in an unheated building to determine the effect of an uncontrolled environment on load duration and creep. Based on load duration results for the controlled environment already reported, load durations do not appear to have been shortened by the uncontrolled environment, although relative creep was considerably increased.The most important result of this study, which has implications for the safety of wood structures, is that more beams failed when loaded at near design stress than are commonly assumed would fail. This result, coupled with results from a previous study, suggests that Douglas-fir bending allowable properties should reflect greater load duration reduction factors or shorter load durations. This research is important to structural engineers and to code groups responsible for the safe design of wood structures when establishing new design criteria for load duration and deflection limits

A Cumulative Damage Model to Predict Load Duration Characteristics of Lumber

The exponential damage model dα/dt = exp[-a + bσs(t)/σs] is used in this paper to describe duration-of-load data on lumber tested in bending where dα/dt is rate of damage, σs is static strength, σ(t) represents applied load history, and a and b are parameters. A specially selected set of Douglas-fir 2 by 4s was divided into six 49-specimen groups having similar distributions of edge knot size and modulus of elasticity. Each group was randomly assigned to one of three rates of ramp loading or one of three levels of constant loading.The lognormal distribution σs = σoexp(wR) provided a reasonable description of static strength of the 2 by 4s where σo is the median static strength, w is a measure of variability, and R is a normal random variable. With b' = b/σo, the model used to fit the ramp and constant load experimental data by nonlinear least squares was dα/dt = exp[-a + b'σo(t)/exp(wR)]; thus a, b', and w were parameters that were estimated. The model fit some but not all of the ramp and constant load data reasonably well. The estimates of variability (w) were slightly greater under ramp loading than under constant loading. Residual strength of specimens surviving constant load was less than expected. A greater duration-of-load effect was observed for the edge knot 2 by 4 lumber than that previously indicated for small clear-wood specimens; however, the difference does not appear to be statistically significant

Decomposition of L2L^{2}-vector fields on Lipschitz surfaces: characterization via null-spaces of the scalar potential

For $\partial \Omega$ the boundary of a bounded and connected strongly Lipschitz domain in $\mathbb{R}^{d}$ with $d\geq3$, we prove that any field $f\in L^{2} (\partial \Omega ; \mathbb{R}^{d})$ decomposes, in an unique way, as the sum of three silent vector fields---fields whose magnetic potential vanishes in one or both components of $\mathbb{R}^d\setminus\partial \Omega$. Moreover, this decomposition is orthogonal if and only if $\partial \Omega$ is a sphere. We also show that any $f$ in $L^{2} (\partial \Omega ; \mathbb{R}^{d})$ is uniquely the sum of two silent fields and a Hardy function, in which case the sum is orthogonal regardless of $\partial \Omega$; we express the corresponding orthogonal projections in terms of layer potentials. When $\partial \Omega$ is a sphere, both decompositions coincide and match what has been called the Hardy-Hodge decomposition in the literature

Unique reconstruction of simple magnetizations from their magnetic potential

Inverse problems arising in (geo)magnetism are typically ill-posed, in particular {they exhibit non-uniqueness}. Nevertheless, there exist nontrivial model spaces on which the problem is uniquely solvable. Our goal is here to describe such spaces that accommodate constraints suited for applications. In this paper we treat the inverse magnetization problem on a Lipschitz domain with fairly general topology. We characterize the subspace of $L^{2}$-vector fields that causes non-uniqueness, and identify a subspace of harmonic gradients on which the inversion becomes unique. This classification has consequences for applications and we present some of them in the context of geo-sciences. In the second part of the paper, we discuss the space of piecewise constant vector fields. This vector space is too large to make the inversion unique. But as we show, it contains a dense subspace in $L^2$ on which the problem becomes uniquely solvable, i.e., magnetizations from this subspace are uniquely determined by their magnetic potential

On the approximation of spatial structures of global tidal magnetic field models

The extraction of the magnetic signal induced by the oceanic M2 tide is typically based solely on the temporal periodicity of the signal. Here, we propose a system of tailored trial functions that additionally takes the spatial constraint into account that the sources of the signal are localized within the oceans. This construction requires knowledge of the underlying conductivity model but not of the inducing tidal current velocity. Approximations of existing tidal magnetic field models with these trial functions and comparisons with approximations based on other localized and nonlocalized trial functions are illustrated.</p