CHAPTER IL - Homogemous Stresses and Homogeneous Strains.
Def. A stress is said to be homogeneous throughout a body when equal and similar portions of the body, with corresporeding lines parallel, experience equal and parallel pressures or tensions an correspowlin, elements of their surfaces.
Cor. When a body is subjected to any homogeneous stress, the mutual tension or pressure between the parts of it on two sides of any plane amounts to the same per unit of surface as that between the parts on the two sides of any parallel plane; and the former tension or pressure is parallel to the latter.
A strain is said to lie homogeneous throughout a body, or the body is said to be homogeneously strained, when equal and similar portions, with corresponding lines parallel, experience equal and similar alterations of dimensions COP. All the particles of the body it, parallel planes remain in parallel planes, when the body is homogeneously strained in any way.
Examples. - A long uniform rod, if pulled out, or a pillar loaded with a weight, will experience a uniform strain, except near its ends. There will be a sensible heterogeneousness of the strain, because of the cud attachments, or other circumstances preventing the ends from expanding laterally to the some extent as the middle does.
A piece of cloth held in a plane, and distorted so that et warp and woof, instead of being perpendicular to one another, become two sets of parallels cutting eine another obliquely, experiences a homogeneous strain. The strain is heterogeneous as to intensity, Irom the axis to the surface of a cylindrical Is ire under torsion, and heterogeneous as to direction in different positions in a circle round the axis.