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Effect of Elliptic or Circular Holes on the Stress Distribution in Plates of Wood or Plywood Considered as Orthotropic materials.

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This is a mathematical analysis of the stress distribution existing near a hole in a wood or plywood plate subjected to tension, as, for example, near holes in the tension flanges of wood box beams. It is assumed that the strains are small and remain within the proportional limit. In this analysis a large, rectangular, orthotropic plate with a small elliptic hole at the center is subjected to a uniform tension along two opposite edges. By taking equal axes for the elliptic hole, the theoretical stress distribution in the neighborhood of a circular hole is obtained. The analysis shows that for a circular hole in a plain-sawn plate of Sitka spruce a maximum tensile stress of 5.84S is attained, S being the uniform tension applied in the direction of the grain. The maximum stress occurs on the edge of the circular hole at the ends of the diameter perpendicular to the direction of the uniform tension. Although this stress concentration may be greater than that found in isotropic materials, it is much more sharply localized and is relieved by plastic flow when the stress exceeds the proportional limit. For the reader who does not wish to follow the mathematical details of this report, the formula for computing this maximum stress for wood or plywood and an explanation of the constants involved is given in the appendix. The formula has not been confirmed by an extensive series of tests, but it was found to be in reasonably satisfactory agreement with the only test made. It is also demonstrated that for the Sitka spruce plate mentioned the maximum shear stress attained is 0.71S.

Subject Categories:

  • Ceramics, Refractories and Glass
  • Mechanics

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