### Calculation of normal and shear stress on a plane

Frequently it is necessary to calculate the normal and the shear stress on an arbitrary plane (with unit normal vector $$n$$) that crosses a rigid body in equilibrium. Faults or cracks that cross the rock mass and may lead to rock failure are cases that require the estimation of the stress components on a plane. Another example may be the calculation of the normal and shear stress on the failure surface of a specimen during a typical rock mechanics experiment.

The components of the stress vector $$T$$ acting on any plane crossing an arbitrary point inside …

### Transformation of a tensor to a new coordinate system

The transformation (rotation) of a tensor into a new coordinate system is a common problem in rock mechanics and in continuum mechanics in general. In this article we will present the necessary equations and an example case. We will use the stress tensor as example.

Consider a rigid body in equilibrium and a coordinate system. The stress state of any internal point of this body is given by the stress tensor (cf. Fig. 1):

$\sigma_{ij}=\left[\begin{array}{ccc}\sigma_{11} & \sigma_{12} & \sigma_{13}\\ \sigma_{21} & \sigma_{22} & \sigma_{23}\\ \sigma_{31} & \sigma_{32} & \sigma_{33}\end{array}\right]$
(1)