STRESSES AND STRAINS
Normal Stresses and Strains:
Consider a cube of dimensions x 5 y 5 z that is subjected to forces Px, Py, Pz, normal to three adjacent sides, as shown in Figure The normal stresses are
Stresses and displacements due to applied loads
Let us assume that under these forces the cube compressed by Dx, Dy, and Dz in the X, Y, and Z directions. The strains in these directions, assuming they are small (infi nitesimal), are
The volumetric strain is
Shear Stresses and Shear Strains:
Let us consider, for simplicity, the XZ plane and apply a force F that causes the square to distort into a parallelogram, as shown in Figure 7.3. The force F is a shearing force, and the shear stress is
Simple shear strain is a measure of the angular distortion of a body by shearing forces. If the horizontal displacement is Dx, the shear strain or simple shear strain, gzx, is
Shear stresses and shear strains.
For small strains, tan gzx 5 gzx, and therefore
If the shear stress on a plane is zero, the normal stress on that plane is called a principal stress. We will discuss principal stresses later. In geotechnical engineering, compressive stresses in soils are assumed to be positive. Soils cannot sustain any appreciable tensile stresses, and we normally assume that the tensile strength of soils is negligible. Strains can be compressive or tensile.