Questions 3.1 -3.1 0:
stress
- I Show how the stress state in a solid can be described via the stress
components (normal and shear) on an elemental cube of rock. Also,
show how these components are listed in the stress matrix. What do the
components in a row of the stress matrix have in common? What do the
components in a column of the stress matrix have in common?
43.2 When is a matrix symmetrical? Why is the stress matrix symmet-
rical?43.3 Explain the differences between scalar, vector and tensor quantit-
ies. Why is stress a tensor quantity?43.4 How are normal and shear stress components plotted on Mohr’s
circle?
43.5 What is a principal stress plane? What is a principal stress?43.6 What are the following stress states: uniaxial stress, biaxial stress,
triaxial stress, polyaxial stress, pure shear stress, hydrostatic stress?
43.7 Show how to add two tensors and hence how to calculate the
mean of n stress states. How would you calculate the mean of n different
stress states which were specified by their principal stresses and the
associated principal stress directions?
43.8 What are the first, second and third stress invariants?
43.9 By considering the rates of change of the stress components in
the answer to Q3.1, establish force equilibrium in the x, y and z direc-
tions and hence write down in differential form the three equilibrium
equations for an elemental cube.
Q3.70 Given an elemental cube with a normal stress component and
two shear stress components acting on all its faces, it is always possible