Hankinson's equation

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Hankinson's equation (also called Hankinson's formula or Hankinson's criterion) [1] is a mathematical relationship for predicting the off-axis uniaxial compressive strength of wood. The formula can also be used to compute the fiber stress or the stress wave velocity at the elastic limit as a function of grain angle in wood. For a wood that has uniaxial compressive strengths of parallel to the grain and perpendicular to the grain, Hankinson's equation predicts that the uniaxial compressive strength of the wood in a direction at an angle to the grain is given by

Wood grain

Wood grain is the longitudinal arrangement of wood fibers or the pattern resulting from this.

Contents

Even though the original relation was based on studies of spruce, Hankinson's equation has been found to be remarkably accurate for many other types of wood. A generalized form of the Hankinson formula has also been used for predicting the uniaxial tensile strength of wood at an angle to the grain. This formula has the form [2]

Spruce genus of plants

A spruce is a tree of the genus Picea, a genus of about 35 species of coniferous evergreen trees in the family Pinaceae, found in the northern temperate and boreal (taiga) regions of the Earth. Spruces are large trees, from about 20–60 m tall when mature, and have whorled branches and conical form. They can be distinguished from other members of the pine family by their needles (leaves), which are four-sided and attached singly to small persistent peg-like structures on the branches, and by their cones, which hang downwards after they are pollinated. The needles are shed when 4–10 years old, leaving the branches rough with the retained pegs. In other similar genera, the branches are fairly smooth.

where the exponent can take values between 1.5 and 2.

The stress wave velocity at angle to the grain at the elastic limit can similarly be obtained from the Hankinson formula

where is the velocity parallel to the grain, is the velocity perpendicular to the grain and is the grain angle.

See also

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References

  1. ↑ Hankinson, R. L., 1921, Investigation of crushing strength of spruce at varying angles of grain, Air Force Information Circular No. 259, U. S. Air Service.
  2. ↑ Clouston, P., 1995, The Tsai-Wu strength theory for Douglas fir laminated veneer , M. S. Thesis, The University of British Columbia.
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