Abstract
The application of the rigorous methods of analysis embodied in the theory of elasticity is naturally of interest to engineers. Within this largely theoretical subject, it is of interest to introduce the fundamental basis of such applications, namely, the comparison of the analytical results obtained from an elasticity solution to the expected capacity of the resisting material.
Traditionally, the capacity of a specific material has been stated in terms of a failure criterion or strength, whereby exceeding a critical value of a controlling parameter marks the limit of the functional range. It is recognized that other failure mechanisms, such as serviceability exceedence or fatigue, may govern. Here, only pointwise criteria in consort with elasticity theory are presented and discussed.
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Notes
- 1.
To plot a point within the grid defined in (12.23) on Fig. 12.2b, we find σ(1) on the +σ(1)-axis and move down the grid parallel to the −σ(3)-axis. Then we find σ(3) on the −σ(3)-axis and move along the grid parallel to the +σ(1)-axis to locate the intersection. Note that the arbitrary σ(1) and σ(3) points represented by the large dots fall within the yield surface, so do not indicate failure. Values of σ(1) and −σ(3) corresponding to the heavier lines on the grid would place the point on the yield surface indicating failure.
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Gould, P.L., Feng, Y. (2018). Strength and Failure Criteria. In: Introduction to Linear Elasticity. Springer, Cham. https://doi.org/10.1007/978-3-319-73885-7_12
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DOI: https://doi.org/10.1007/978-3-319-73885-7_12
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