A theoretical, or geometric, stress-concentration factor Kt or Kts is used to relate the actual maximum stress at the discontinuity to the nominal stress. The factors are defined by the equations:
(Eq1)
Kt =
σmax
σ0
and:
(Eq2)
Kts =
τmax
τ0
where Kt is used for normal stresses and Kts for shear stresses. The nominal stress σ0 or τ0 is more difficult to define. Generally, it is the stress calculated by using the elementary stress equations and the net area, or net cross section. But sometimes the gross cross section is used instead, and so it is always wise to double check your source of Kt or Kts before calculating the maximum stress.
The subscript t in Kt means that this stress-concentration factor depends for value only on the geometry of the part. That is, the particular material used has no effect on the value of Kt. This is why it is called a theoretical stress-concentration factor.
The analysis of geometric shapes to determine stress-concentration factors is a difficult problem, and not many solutions can be found. Most stress-concentration factors are found by using experimental techniques. Though the finite-element method has been used, the fact that the elements are indeed finite prevents finding the true maximum stress. Experimental approaches generally used include photoelasticity, grid methods, brittle-coating methods, and electrical strain-gauge methods. Of course, the grid and strain-gauge methods both suffer from the same drawback as the finite-element method.