Abstract
In discussing forces in Chapters 2 and 5, we have already found it convenient to describe the intensity of forces acting across planes as the ratio of total force to the area of the plane. This ratio of force to area is the magnitude of the quantity called the stress on a plane. In Figure 5.1 the stress across the bottom surface of the quartzite cube is 12,600 kg/m2. We would get this same ratio of force to area if we consider only an nth part of the base of the cube. In this case the force acting is 12,600 kg/n and the area is 1 m2/n, so the ratio of force to area is still 12,600 kg/m2 no matter how small a segment of the base of the cube we consider. The assumption made here is that the surface forces are distributed uniformly along the plane in question.
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Notes and References
The rule for multiplication of a vector quantity by a scalar quantity is explained by Spiegel (1959, p. 2).
In emphasizing that the complete state of stress at a point is not a vector quantity, geological writers sometimes fail to make it explicitly clear that the traction or stress on any individual plane at a point is a vector quantity. This important idea is stated more clearly in books in the engineering literature (e.g., Jaeger and Cook, 1969, p. 10; Malvern, 1969, p. 69).
The complex inhomogeneous state of stress in granular materials is dramatically illustrated by Plate 1 (p. 52) in Price (1966). If the material were in a homogeneous state of stress, no photoelastic fringes would be visible. (The photoelastic fringes are the black zones within the grains). Photoelasticity is discussed by Jaeger and Cook (1969, pp. 286–289).
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© 1976 Springer-Verlag New York Inc.
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Means, W.D. (1976). Stress on a Plane. In: Stress and Strain. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9371-9_6
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DOI: https://doi.org/10.1007/978-1-4613-9371-9_6
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