Application of the beam theory of cracks

For antiplane deformation of a thin rectangle with a crack (where the rectangle height is the small parameter) the necessary and sufficient conditions are stated under which the basic assumption of the crack theory in ″beam approximation″ is satisfied, i.e., the constraint requiring that the crack tips be immobile. An example where this condition is not satisfied is given. In that case, the difference between stress intensity factors calculated in terms of the beam theory and the asymptotic theory is as much as 32%.