The structural complexity of design components (e.g. Classes) is proportional to design quality at the system level and is quantified via the object-oriented metrics. The frequent use of design patterns causes of too much abstraction and can increase the structural complexity of design components. Though, in our previous work, we have empirically investigated the impact of use intensity of design pattern on the system level quality attributes. However, the empirical investigation of the effect of usage of design patterns on the design properties is still required. In this regard, we conduct an empirical study and perform a case study which includes the analysis 1) the existence of a correlation between design pattern usage and design metrics, 2) the confounding effect of system size (number of classes) on the correlation, and 3) how the change in number of employed design pattern instances affects the structural complexity in the subsequent releases of a system. The result of this study suggests that structural complexity associated with aggregation, coupling, functional abstraction design properties has a significant relationship with the employed instances of Template, Adapter- Command, Singleton, and Factory Method design patterns.