. A commentary on the scientific writings of J. Willard Gibbs. Gibbs, Joniah Willard, 1839-1908; Science; Thermodynamics. 400 RICE ART. K {du/dy')r}' and the angle QPM has for its trigonometrical tangent the value du/dy'. The figure shows that this strain is what is called a "; A bar shaped element of volume which is extended parallel to the axis OZ' (perpendicular to the plane of the paper) and whose section by the plane OX'Y' is P'Q'R'S' (Fig. 2), is displaced to a position whose section is PQRS. This is equivalent to a simple displacement of the bar as a whole from P'Q'R'S'
. A commentary on the scientific writings of J. Willard Gibbs. Gibbs, Joniah Willard, 1839-1908; Science; Thermodynamics. 400 RICE ART. K {du/dy')r}' and the angle QPM has for its trigonometrical tangent the value du/dy'. The figure shows that this strain is what is called a "; A bar shaped element of volume which is extended parallel to the axis OZ' (perpendicular to the plane of the paper) and whose section by the plane OX'Y' is P'Q'R'S' (Fig. 2), is displaced to a position whose section is PQRS. This is equivalent to a simple displacement of the bar as a whole from P'Q'R'S' to PMNS and a real strain or change of shape from PMNS to PQRS. This latter is the "shear" and its magnitude is measured by the tangent of the angle QPM (or simply by the angle itself when the strain is so small that the tangent of the angle and its radian measure are practically identical), , by du/dy'. If w is a linear function of y', the O'MO R'NR. Fig. 2 shear is homogeneous throughout the body; otherwise it is heterogeneous and the amount of shearing varies from point to point of the body. When we undertake a general analysis of strain these special cases give us a hint how to proceed. The point P' whose co- ordinates are x', y', z' experiences a displacement whose com- ponents we represent by u{x'^ y', z'), v{x', y', z'), w{x', y', z'), for the displacement must have some functional relationship with the position of P' if analysis is to be possible at all.* * Will the reader please note that we are, for the time being, referring the body before and after the strain to the same axes OX', OY', OZ'. Formally Gibbs' procedure is a little wider since he refers the body after. Please note that these images are extracted from scanned page images that may have been digitally enhanced for readability - coloration and appearance of these illustrations may not perfectly resemble the original Donnan, F. G. (Frederick George), 1870-1956; Haas, Arthur Erich, 1884-1
Size: 1823px × 1370px
Photo credit: © The Book Worm / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1900, booksubjectscience, booksubjectthermodynamics
