Equivalent single layer theories for layered beams effectively and accurately predict global displacements and internal force and moment resultants using a limited number of displacement variables. However, they cannot reproduce local effects due to material architecture or weak/imperfect bonding of the layers, such as zigzag displacement fields, displacement jumps at the layer interfaces and complex transverse stress fields, nor can they simulate delamination damage growth. In this work we will present some applications and discuss advantages and limitations of a recently formulated zigzag model. The model, through a modification of the equilibrium equations of an equivalent single layer theory, which maintains the same number of variables, reproduces local effects and delamination fracture under mode II dominant conditions. The approach is based on a local enrichment of the displacement field of first order shear deformation theory, the introduction of cohesive interfaces and homogenization.