When a squared lumber such as a beam and/or a bearer is produced from a log, they often show warps. Warp of the sawn lumber is practically not serious when the pith is located at the center of the cross-section, as in the lumber-with-pith, but causes serious problems in the lumber-without-pith. In the present study, a mechanical model was introduced to explain lumber warping based on beam theory, and a numerical simulation using the introduced model examined how the magnitude and type of the residual stress distribution would affect the warps of the lumbers sawn from the four-sided cants with various sizes and shapes in their cross-sections, and how the different sawing patterns would affect the production efficiency of the straight lumber, which is manufactured from the four-sided cant by quartering and subsequent correction sawing. As a result, the following suggestions were obtained. The warp of the sawn lumber is affected by the type and the magnitude of the inherent strain distribution in the log and furthermore by the cross-sectional shape and/or size of the four-sided cant. Production efficiency of the straight lumbers differs depending on the sawing patterns. In the present study, two types of sawing patterns (a) and (b) were assumed. The sawing pattern (a) gave better production efficiency than the sawing pattern (b) in the sense that straight lumbers are produced with higher volumes as well as with less variation in dimension of the cross-section.

中文翻译：

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原木中残余应力分布对锯材翘曲的影响：基于梁理论的数值模拟

当用原木生产方形木材（例如横梁和/或承载木）时，它们通常会出现翘曲。当木髓位于横截面的中心时，锯材的翘曲实际上并不严重，如在有髓木材中，但在无髓木材中会导致严重问题。在本研究中，引入了一个力学模型来解释基于梁理论的木材翘曲，并使用引入的模型进行数值模拟检查残余应力分布的大小和类型如何影响从四个锯切下的木材的翘曲。由四边斜切和随后的校正锯切制成的直材，不同的锯切模式将如何影响直材的生产效率，以了解其横截面具有各种尺寸和形状的斜切面，以及不同的锯切模式如何影响直材的生产效率。因此，获得了以下建议。锯材的翘曲受原木中固有应变分布的类型和大小的影响，此外还受四边斜面的横截面形状和/或尺寸的影响。直材的生产效率因锯切模式而异。在本研究中，假设了两种类型的锯切模式 (a) 和 (b)。锯切模式 (a) 比锯切模式 (b) 提供更好的生产效率，因为直材的产量更高，横截面尺寸的变化更小。直材的生产效率因锯切模式而异。在本研究中，假设了两种类型的锯切模式 (a) 和 (b)。锯切模式 (a) 比锯切模式 (b) 提供更好的生产效率，因为直材的产量更高，横截面尺寸的变化更小。直材的生产效率因锯切模式而异。在本研究中，假设了两种类型的锯切模式 (a) 和 (b)。锯切模式 (a) 比锯切模式 (b) 提供更好的生产效率，因为直材的产量更高，横截面尺寸的变化更小。