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This paper proposes a specific parametric model order reduction (pMOR) scheme for the efficient evaluation of beam based structures. The model to be parameterized is a Finite Element (FE) model that represents a generic network of beams with a number of distinct cross-section types. The methodology considers geometrical parameters that describe the cross-section and the material properties of the beams as the design parameters of interest. An affine representation of the model is derived based on the description of the deformation of a uniform beam. This affine representation can be exploited for the hyper-reduction where the evaluation cost of the system matrices is reduced. The reduction of the system matrices is obtained through a projection based approach. For a given number of parameter combinations a modal basis is constructed. A global reduced order basis (ROB) is obtained through a principal component analysis of these local bases.