Distributions of Moe and Mor in a Full Lumber Population

Owens, Frank C.; Verrill, Steve; Shmulsky, Rubin; Kretschmann, David E.

doi:10.22382/wfs-2018-027

Cited by 14 publications

(16 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Moreover, the GEV model has not been applied for MOE and MOR assessment so far, according to the available literature. The distributions often used for MOE and MOR in the literature (Gupta et al 1992;Owens et al 2018), W3 proved to be the best. Normal and W2 distributions were difficult to adapt to changes in the shape of empirical distribution.…”

Section: Distribution Fittingmentioning

confidence: 98%

“…The normal distribution is most often assumed for the MOE distribution, and a normal, log-normal, and Weibull distribution for the MOR distribution (Gupta et al 1992;Owens et al 2018). The application of the Weibull's model for strength properties is based on the theoretical "weakest link" concept.…”

Section: L-moment Ratio Diagramsmentioning

confidence: 99%

“…These relations are still used today in several American standards (Evans et al 2019). However, in a recent study, Owens et al (2018) presented the results of a research of MOE and MOR distribution testing for "a full lumber population of southern pine 2" × 4", produced in a single mill on a single day" subjected to the static bending test. These authors fit several distributions to the MOR and MOR data and found that neither MOE nor MOR was well-fit by a Weibull distribution.…”

Section: L-moment Ratio Diagramsmentioning

confidence: 99%

See 2 more Smart Citations

Loading rate effects on MOE and MOR distributions in testing of small clear beech wood specimens

Mihailović

Miric-Milosavljević

Djurković

et al. 2022

BioRes

View full text Add to dashboard Cite

Distributions of the modulus of elasticity (MOE) and modulus of rupture (MOR) were characterized at three loading rates for small clear beech specimens in static bending. The correlation between MOE and MOR for all three loading rates was significant, but it weakened with increasing load rates. The analysis of the characteristics of empirical distributions, as well as the preliminary selection of the theoretical distributions for MOE and MOR, were performed on the basis of L-moments and L-moment diagrams. According to the standard for testing small specimens, MOE and MOR are determined as the arithmetic mean of the sample. Usage of the arithmetic mean is justified when the analyzed quantity is symmetrically distributed. It was found that the distribution of MOE and MOR is not always symmetric. The loading rate influences the shapes of the MOE and MOR empirical distributions, and consequently the choice of theoretical distribution. The general extreme value distribution stood out as the best one for both MOE and MOR, regardless of the loading rate, and the second overall ranked distribution is the three-parameter Weibull distribution. The loading rate affected the value of the fifth percentile in MOR, when determined from both the empirical and theoretical distributions.

show abstract

Section: Distribution Fittingmentioning

confidence: 98%

Section: L-moment Ratio Diagramsmentioning

confidence: 99%

Section: L-moment Ratio Diagramsmentioning

confidence: 99%

See 1 more Smart Citation

Loading rate effects on MOE and MOR distributions in testing of small clear beech wood specimens

Mihailović

Miric-Milosavljević

Djurković

et al. 2022

BioRes

View full text Add to dashboard Cite

show abstract

“…Using these estimators, it is possible to determine the graphical slope of the representation, that is, the Weibull modulus, which represents the reliability of the material. Previous studies show the growing interest in using this tool to determine the reliability of different types of wood [43,44]. The origin and type of defects found can vary by specimen, thus, designing components for structural applications using wood is more complicated than for other materials, such as metals, whose Weibull modulus is high [45].…”

Section: Reliabilitymentioning

confidence: 99%

Analysis of Mechanical Behavior through Digital Image Correlation and Reliability of Pinus halepensis Mill.

Villarino

López-Rebollo

Antón

2020

Forests

View full text Add to dashboard Cite

The mechanical behavior of test pieces extracted from two specimens of Pinus halepensis Mill., from the same geographical area and close to each other, was examined in this study. Using a methodology based on Digital Image Correlation (DIC) and implemented during compression strength testing, the modulus of elasticity in compression parallel to the grain (MOEc) was obtained. In addition, the value of compressive strength (MORc) was obtained for this type of wood. The research was complemented with a reliability study, determined using the Weibull modulus, from the MORc values. A microstructural and behavioral study of the most representative pieces after failure was also conducted to correlate breakage with the behavior of the pieces during the tests monitored by DIC, to link both studies. DIC was shown to be an ideal and low-cost technique for the determination of the studied properties, and obtained average values of MOEc of 50.72 MPa and MORc of 9693 MPa. These values represent fundamental data for design and calculations of wooden structures. A reliability value of between 11 and 12 was obtained using the Weibull modulus for this type of wood.

show abstract

“…However, these assumptions are based on the work of researchers who were fitting distributions to grades of lumber (as in the In-Grade work) rather than to mill run populations. This fact, and the need for an accurate estimate of the MOR probability density function in reliability calculations, led us to perform the experiment described in Verrill et al (2017) and Owens et al (2018) -an experiment designed to yield estimates of mill run bivariate stiffness-strength distributions (which, in turn, yield estimates of pseudo-truncated MOR distributions).…”

Section: A Fit Of a Mixture Of Bivariate Normals To Lumber Stiffness-...mentioning

confidence: 99%

A fit of a mixture of bivariate normals to lumber stiffness–strength data

Verrill¹,

Owens²,

Kretschmann³

et al. 2018

Self Cite

View full text Add to dashboard Cite

It has been common practice to assume that a two-parameter Weibull probability distribution is suitable for modeling lumber strength properties. In a series of papers published from 2012 to 2018, Verrill et al. demonstrated theoretically and empirically that the modulus of rupture (MOR) distribution of a visual grade of lumber or of lumber that has been "binned" by modulus of elasticity (MOE) is not a twoparameter Weibull. Instead, the tails of the MOR distribution are thinned via "pseudo-truncation." The theoretical portion of Verrill et al.'s argument was based on the assumption of a bivariate normal-Weibull MOE-MOR distribution for the full ("mill run") population of lumber. Verrill et al. felt that it was important to investigate this assumption. In a recent pair of papers, they reported results obtained from a sample of size 200 drawn from a mill run population. They found that normal, lognormal, three-parameter beta, and Weibull distributions did not fit the sample MOR distribution of these data. Instead, it appeared that the MOR data might be fit by a skew normal distribution or a mixture of two univariate normals. In this paper, we investigate whether the joint MOE-MOR data from Verrill et al.'s recent mill run study can be well modeled as a mixture of two bivariate normals.

show abstract

Distributions of Moe and Mor in a Full Lumber Population

Cited by 14 publications

References 6 publications

Loading rate effects on MOE and MOR distributions in testing of small clear beech wood specimens

Loading rate effects on MOE and MOR distributions in testing of small clear beech wood specimens

Analysis of Mechanical Behavior through Digital Image Correlation and Reliability of Pinus halepensis Mill.

A fit of a mixture of bivariate normals to lumber stiffness–strength data

Contact Info

Product

Resources

About