Dapped end prefabricated concrete purlins (PCPs) suffer from shear damages due to coating, snow, wind load and also their dead loads. In this present study, a series of numerical modelling is performed with the aid of finite element program ABAQUS in order to investigate this behavior of PCPs through parametric study. In addition to the mechanical properties of the PCPs, the strengthening of the PCPs with the help of carbon fiber reinforced polymers (CFRP) is considered as a parameter in the models. Pursuant to this aim, longitudinal steel reinforcement ratio, shear friction reinforcement ratio, bending reinforcement ratio, suspension reinforcement ratio, concrete and steel mechanical properties, pre-stressing level, CFRP ply orientation, the number of CFRP plies and material properties of CFRP composite were selected as the parameters. First of all, numerical models were verified using experimental test data of three PCP test specimens and five CFRP coupon tests. Later, a total of 50 different numerical models was created to investigate the behavior of PCPs thoroughly. Vertical load- displacements curves are compared and explained in detail. The result of the parametric study revealed that the effects of the parameters related to reinforced concrete except longitudinal reinforcement and material properties of concrete are very limited when compared to the effects of the parameters related to CFRP. The effect of FRP ply orientation is the most effective parameter that increases significantly the shear capacity of PCPs. More importantly is the general FRP layout is proposed to delay or prevent shear cracks for the beams and the proposed layout is proved through numerical analyses. [±45°] fiber orientation is recommended to use to prevent shear damage.