Search results
Results from the WOW.Com Content Network
In two dimensions, the stress tensor at a given material point with respect to any two perpendicular directions is completely defined by only three stress components. For the particular coordinate system ( x , y ) {\displaystyle (x,y)} these stress components are: the normal stresses σ x {\displaystyle \sigma _{x}} and σ y {\displaystyle ...
The three stresses normal to these principal planes are called principal stresses. The components of the stress tensor depend on the orientation of the coordinate system at the point under consideration. However, the stress tensor itself is a physical quantity and as such, it is independent of the coordinate system chosen to represent it.
Components of stress in three dimensions Illustration of typical stresses (arrows) across various surface elements on the boundary of a particle (sphere), in a homogeneous material under uniform (but not isotropic) triaxial stress. The normal stresses on the principal axes are +5, +2, and −3 units. Combined stresses cannot be described by a ...
Visualisation of a Cauchy stress tensor σ in the Haight-Westergaard stress space. In continuum mechanics, Haigh–Westergaard stress space, or simply stress space is a 3-dimensional space in which the three spatial axes represent the three principal stresses of a body subject to stress.
Mohr's circle is used to determine which principal stresses will produce this combination of shear and normal stress, and the angle of the plane in which this will occur. According to the principle of normality the stress introduced at failure will be perpendicular to the line describing the fracture condition.
The theory models faulting in terms of these three principal stresses denoted as σ₁, σ₂, and σ₃. Two of these stresses are horizontal, on the plane, and one is vertical, normal to the plane, also known as S hmax, S hmin and S v, respectively. [2] All principal stresses are perpendicular to one another.
In this case, though all principal stresses are non-zero, the principal stress in the direction of the longest dimension can be disregarded for calculations. Thus, allowing a two dimensional analysis of stresses, e.g. a dam analyzed at a cross section loaded by the reservoir.
[1] are a set of tensor invariants that span the space of real, symmetric, second-order, 3-dimensional tensors and are isomorphic with respect to principal stress space. This right-handed orthogonal coordinate system is named in honor of the German scientist Dr. Walter Lode because of his seminal paper written in 1926 describing the effect of ...