Patrick J. Pellicane

Quality of timber products from Norway spruce

SummaryThe overall aim of this study and series of papers is to address the key variables for timber quality and to optimize the utilization of Norway spruce timber with respect to construction purposes. It is the end-users degree of overall satisfaction that determines the quality of a product. Therefore, the performance of structural timber cannot solely be defined by mechanical properties. Geometric performance (warp) must be improved if timber is to continue as an important building material.An experimental study of the spatial variation in warp and bending properties of fast-grown Norway spruce is introduced. In this paper, the growth characteristics are presented as a function of stand and location in the tree. The knot area ratio (KAR) was considerably higher in the core (0.31) compared with timber closer to bark (0.21). The top log studs had higher KAR (0.38) than the corresponding butt log studs (0.31). The average grain angle was 3.5% (≈ 2°) and appeared not to vary radially. The presence of compression wood was much more common in the top log timber (75%) than in the butt log (44%). However, no consistent radial variation in compression wood was found.

Goodness-of-fit analysis for lumber data

SummaryFour different probability distributions were studied to evaluate their relative goodness-of-fit in describing the modulus of rupture (MOR) and modulus of elasticity (MOE) of populations of dimension lumber. The distributions under consideration were the normal, lognormal, Weibull and Johnsons SB. The populations of lumber consisted of 96 data sets of various species groups, mechanical properties, sizes, structural grades and growth regions. The goodness-of-fit criteria selected in this study were the log likelihood, Kimball and Kolmogorov-Smirnov (K-S) tests. The K-S statistic was also calculated at the value of the random variable associated with the lower five percent exclusion limit of the empirical cumulative distribution. This value indicated the degree of goodness-of-fit at the lower tail of the distribution. The results indicated that the SB distribution generally provided the best fit to the data. The maximum likelihood test overwhelmingly recommended the SB distribution. The Kimball and Kolmogorov-Smirnov tests gave milder endorsements of the SB distribution. No distribution proved to be superior to the others in modeling the lower five percent exclusion limit of the populations.

Modeling wood pole failure

SummaryIn part 1 of this series, a three-dimensional, structural analysis, finite element program has been developed to predict the stress distribution in wood poles with and without spiral grain and variable material properties. This program serves as a basis for a model to predict the strength and failure location in full-size wood poles. Fundamental to this model is the ability to quantify the effects of key material and geometric properties of the pole. This paper deals with the enhancement of the program to quantify the effect of knots and their associated cross grain on the stress distribution of wood poles. The technique is based on the theoretical behavior of laminar fluid flow around an elliptical obstruction. The flow-grain analogy was employed to develop empirical relationships between knot diameter and pertinent variables (grain deviation angle near the knot and area of influence of the knot). Prior to the development of the empirical relationships, a study was conducted to determine the size and distribution of knots in Douglas-fir and western redcedar poles.The validity of the technique to describe knot behavior is reflected in the ability of the finite element model to predict the strength and failure location of wood poles. The results suggested that the flow-grain analogy is a rational mechanism to quantify the fiber orientation near a knot. Furthermore, this technique could have meaningful implication in improving visual grading methods for wood poles.

Application of the SB distribution to the simulation of correlated lumber properties data

SummaryWith the emergence of probabilistic design procedures, the need for precise knowledge of the entire probability distributions of load effects and material resistance has never been greater. In order to evaluate these distributions, simulation techniques have provided a reliable and cost and time effective alternative to large scale destructive testing. With the use of the Johnsons SB probability distribution, a closed-form, analytic procedure has been developed to model the inherent variability in strength, given some nondestructively evaluated parameter. This modeling procedure serves as the basis of a verified simulation process to predict a strength distribution, given a probability distribution of the NDE parameter. The approach presented here, represents a closed-form, analytic solution to a problem which has heretofore been treated in a more subjective fashion. This simulation procedure is complemented by a stratified sampling scheme.

A sampling strategy useful in full-distribution simulation

SummaryInherent in most simulation processes is a mechanism to sample from known probability distributions. This is most often accomplished with the aid of pseudo-random generation systems. Though, these generators produce sets of numbers which are usually statistically indistinguishable from a uniform distribution, the actual distribution of any individual one of these data sets exhibit peaks and valleys which, when used in simulations, somewhat misrepresent the desired probability distribution. A stratified approach to fulldistribution sampling is presented which represents a marked improvement over random number generated sampling in certain types of simulation procedures.

Sampling error in the bending strength distribution of dimension lumber

SummaryInformation is presented on the magnitude of errors associated with various sampling simulation schemes of the distribution of three different populations, representing actual bending strength of dimension lumber. Errors were determined between the simulated and actual distributions. Graphical evaluations indicated good fits with the three-parameter form of the weibull distribution for both original and simulated bending strength data, as well as with the resulting error terms. Error terms, based on the simulated versus actual distributions, were generated for the lower 5% exclusion limit, for the 50% exclusion limit and for the entire distribution curve. Simulations were carried out with the aid of Monte Carlo techniques using distribution functions fitted to actual test data for dimension lumber. The errors are expressed as functions of confidence levels. The comparison of the erro obtained through the various sampling schemes could provide some initial directions to choose an economical sampling plan for the presently ongoing in-grade lumber testing program.

Application of the SB distribution to the prediction of concomitant wood properties

SummaryIt is frequently the case that multiple strength properties of structural wood members are simultaneously needed in design or research. A method has been developed to predict the probability distribution of concomitant material properties of wood from a knowledge of some correlated, nondestructive material property. The method developed in this study is based on properties of the univariate SB distribution and the bivariate SBB distribution. The technique involves a priori knowledge of the correlation relationship between a nondestructive parameter and the strength parameter for the two concomitant properties in question. A relationship is developed between the two nondestructive parameters and a simulation procedure is presented to predict either concomitant property from a single nondestructive measurement. The results showed that when a single parameter was predicted directly from a correlated variable, the simulated and experimental distributions were very similar (average error ≤3–4%). This result confirms previous findings. For the prediction of the concomitant property from an indirect relationship with another parameter, the absolute value of the average error was about 13%.It is frequently the case that multiple strength properties of structural wood members are simultaneously needed in design or research. A method has been developed to predict the probability distribution of concomitant material properties of wood from a knowledge of some correlated, nondestructive material property. The method developed in this study is based on properties of the univariate SB distribution and the bivariate SBB distribution. The technique involves a priori knowledge of the correlation relationship between a nondestructive parameter and the strength parameter for the two concomitant properties in question. A relationship is developed between the two nondestructive parameters and a simulation procedure is presented to predict either concomitant property from a single nondestructive measurement. The results showed that when a single parameter was predicted directly from a correlated variable, the simulated and experimental distributions were very similar (average error ≤3–4%). This result confirms previous findings. For the prediction of the concomitant property from an indirect relationship with another parameter, the absolute value of the average error was about 13%.

Load-slip behavior of nailed joints in seven Amazonian hardwoods

Two hundred ninety-two nailed joints in seven species of Amazonian hardwoods were tested to evaluate their load-slip (P-Δ) behavior when subjected to lateral loading. The seven species commonly used in Brazilian light-frame construction had a range of specific gravities from 0.36 to 0.85 (based on an oven-dry volume) Four sizes of common wire nails were used to construct joints with main and side members of the same species. From these tests, embedding strength values associated with a 5% offset load were obtained from the experimental (P-Δ) curves and equations derived from the European Yield Theory. The results suggest that the behavior of nailed joints made with tropical hardwoods is similar to that found in temperate zone species. Wood moisture content, in the range studied, did not meaningfully affect joint P-Δ behavior. In addition, embedding strength was influenced by the specific gravity of the connected material. However, no species effect was observable between species of similar specific gravity. Finally, an effect of nail diameter on embedding strength was seen; however, the lack of homogeneity of test materials precluded the accurate prediction of this effect. Since the embedding strength data demonstrated some degree of positive skewness, three commonly used statistical distributions (log-normal, three-parameter Weibull, and Johnsons SB) were evaluated to quantify the variability of this parameter. All three distributions were excellent descriptors of behavior. Therefore any of these mathematical models would be a rational choice for representing embedding strength.

A stress transformation approach to predicting the failure mode of wood

SummaryA simple model, based on the use of transformations of second-order tensors, is presented in this paper to predict the failure mode of wood members stressed in various degrees of parallel-and perpendicular-to-grain tension and parallel-to-grain shear. This type of loading is indicative of structural wood members with cross grain or grain deviations in the vicinity of knots subjected to bending or tension. The model is based on the assumptions that failure is dictated by the presence of any of the aforementioned stresses that exceed the clear wood strength in that mode and that failure does not result from stress interactions. The magnitudes of the applied stresses are normalized relative to the wood strength in that mode. The ratio of applied stress to material strength that is greatest at any particular angle of load to grain is presumed to be the failure mode at that angle. To verify model predictions, optical and microscopic analyses of surfaces of failed specimens loaded in uniaxial tension at angles between 0° and 90° to grain were compared to previously obtained, or otherwise known, surfaces of specimens tested in tension and shear. Specimens tested at various angles to grain demonstrated failed surfaces very much like those associated with specimens loaded in the modes predicted by the model.

Comparison of Optically and Mechanically Measured Deformations in a Finger-Jointed Wood Tension Specimen

An advanced finite element program was developed to predict the elastic stresses and strains in a specimen of finger-jointed lumber subjected to uniaxial tension. In this study, two techniques were examined to experimentally determine the deformations in the finger joint. The first method involved photographing at incrementally increasing load levels, predefined targets mounted on the finger joint and measuring the changing distances between targets using stereoscopic instruments. The second method consisted of placing microstrain gages at key locations in the finger-jointed region of the lumber. The results showed that even when the most sensitive film was used with a camera and planar lens, the photographic technique lacked the sensitivity to accurately measure the small deformations in the finger joint. The actual errors in deformation measurement were approximately twice the magnitude expected from an analysis of the properties of the film being used. Much of the error was due to the thermal expansion of the film in the stereoscopic instrument used to measure deformation. The microstrain gage technique was shown to be sufficiently sensitive to measure the deformations in the finger joint. However, the time, effort, and cost required to mount the tiny sensors with appropriate attention to their alignment made this technique impractical for any experiment other than those that involved placing only a modest number of sensors on a small number of specimens.