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Annals of Warsaw University of Life Sciences - SGGW

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Calculated stress concentration factors for all observed elliptical hole halfaxises ratios<br />

and fiber orientations are given in Table 2.<br />

Table 2. Stress concentration factors<br />

Picea<br />

Stress concentration factor<br />

Excelsa a/b=5 a/b=2 a/b=1 a/b=1/2 a/b=1/5<br />

� � 0�<br />

1.85 3.13 5.26 9.53 20.61<br />

� � 90�<br />

1.13 1.33 3.13 4.37 6.26<br />

- 3.79 - 3.79 -3.79 -3.79 -3.79<br />

CONCLUSION<br />

When fibers orientation is along the x� – axis, (i.e.: �= 0°), compression stress ��<br />

around the elliptical hole is negligible. Locations with maximum values always occurs at<br />

� � 90�<br />

and 270°. Moreover, the maximum value <strong>of</strong> the stress concentration factor increases<br />

when the hole axes ratio a b decreases.<br />

In the case that wood fibers are perpendicular on loading stress direction, great<br />

concentration <strong>of</strong> stresses is caused by compression stress � � in locations about � � 0�<br />

and<br />

180°. These SCF are negative numbers, and moreover for all halfaxises ratios these ones are<br />

equal. Positive SCF increases when the hole axes ratio a b decreases but corresponding stress<br />

concentration factors are smaller as in the cases when �= 0°. Locations <strong>of</strong> the positive stress<br />

concentration factors change from angle � � 22�<br />

up to 158° and from 202° up to 338°.<br />

REFERENCES<br />

1. BARNETT D.M., LOTHE J. 1973. Synthesis <strong>of</strong> the sextic and the integral formalism<br />

for dislocations, Green’s function and surface waves in anisotropic elastic solids.<br />

Physica Norvegica, 7, 1973: 13-17.<br />

2. LECHNICKIJ S. G. 1957: Anizotropnyje plastinki. Moskva: Gostechizdat, Moskva-<br />

Leningrad: 1957, 463 pp.<br />

3. SAVIN G. N. 1951: Koncentacija naprjaženij okolo otverstij. Gostechizdat, Moskva-<br />

Leningrad: 1951, 496 pp.<br />

4. SOKOLNIKOFF I. S. 1956: Mathematical Theory <strong>of</strong> Elasticity. McGraw-Hill, New<br />

York: 1956.<br />

5. STROH A. N. 1958: Dislocations and cracks in anisotropic elasticity. Philosophical<br />

Magazine 7, 1958: 625- 646.<br />

6. TING T.C.T. 1996: Anisotropic Elasticity – Theory and Applications. Oxford Science<br />

Publications, New York: 1996.<br />

7. UKADGAONKER V. G., RAO D. K. N. 2000: A general solution for moments<br />

around holes in symmetric laminates. Composite Structures, 49, 2000: 41 –54.<br />

40

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