Questions and answers: stress 33LIniuxiu2 stress. One principal stress is applied, i.e. one principal stress
has a non-zero value, a1 # 0, a2 = a3 = 0.
Biaxial stress. Two principal stresses are applied, i.e. two principal
stresses have non-zero values, (TI # 0,02 # 0,q = 0.
TriuxiaE stress. Three principal stresses are applied but two have the surne
value. This term came into use during the development of laboratory
testing: a cylinder of rock is compressed by one principal stress along
its axis and a fluid pressure is applied to the sides, equivalent to a
stress state g1 # 0, a2 = a3 # 0. The term is correct in that three stress
components are applied along three axes, but somewhat misleading
because two of the components have the same value.
Polyuxid stress. Three principal stresses are applied, i.e. the three
principal stresses have non-zero values, 01 # 0, a2 # 0, a3 # 0. These
three stresses are usually unequal.
Pure shear stress. This term is used to denote a stress state where
there is only shear stress on a plane (i.e. there is no normal stress on
the plane). This occurs within a specimen when equal compressive and
tensile stresses are externally applied, a1 = some value, say k, 02 = -k,
a3 = 0. The plane with a state of pure shear is then at 45" to the applied
stresses, as shown below.
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?
A3.7 Two tensors, representing stress states A and B, are averaged (as-
suming the average is the mean value) by adding their corresponding
components and dividing by two.