A simple expression using a critical fillet hoop stress (CFHS) model was derived to predict the capacity of a simply supported wood beam with a notch on the tension face between the supports. The derivation used the hypothesis that cracking initiates when the hoop stress tangent to the free surface of a round-cornered notch exceeds a critical value. This critical value is characteristic to the material. Finite element modeling was used to explore the effects of a broad range of notch geometries, notch locations, beam sizes, loading configurations, and material elastic properties on fillet hoop stress. The analyses assumed homogeneous, orthotropic, linear elastic behavior, and used a hybrid element to provide accurate results in the region of high stress gradients. Simplified, closed form expressions to predict maximum hoop stress were developed from the numerical results.
Notched beam tests included nine wood materials, encompassing hardwoods and softwoods in both green and kiln-dried conditions. A broad array of notch geometries was tested. A theoretical framework related the experimental failure loads with the calculated maximum fillet hoop stress values. The dependence of failure loads on notch geometry, location, and loading condition was described well by the predictive expression derived from the finite element modeling. The CFHS model can be applied to sharp-cornered notches when an appropriate effective fillet radius is substituted into the strength equation. Preliminary test results showed the effective fillet radius to be material dependent; theoretical analysis suggested a beam depth dependence as well.
The notched beam strength equation utilizes a single material constant which can be experimentally determined from tests of beams with a single notch geometry. The notched beam strength parameter, κ, was found to be strongly related to specific gravity and cross-grain tensile strength. The regression equation from this work can be used to estimate κ for solid wood materials outside of this study.
CFHS results compared favorably with those of earlier models shown to be accurate over a more limited set of cases. In addition to its broad applicability, the CFHS method benefits from its reliance on only one, easily determined, material parameter and avoids the need for directional fracture toughness and elastic parameter data which are very difficult to obtain. / Ph. D.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/54822 |
| Date | January 1989 |
| Creators | Zalph, Barry Louis |
| Contributors | Wood Science and Forest Products, McLain, Thomas E., Gerhardt, T.D., Holzer, Siegfried M., Ifju, Geza, Kline, D. Earl, Loferski, Joseph R. |
| Publisher | Virginia Polytechnic Institute and State University |
| Source Sets | Virginia Tech Theses and Dissertation |
| Language | en_US |
| Detected Language | English |
| Type | Dissertation, Text |
| Format | xii, 323 leaves, application/pdf, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
| Relation | OCLC# 20783273 |
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