Analysis of civil infrastructure using machine learning algorithms, such as Artificial Neural Networks and Deep Neural Networks, has gained popularity in recent years. The finite element method is robust and accurate; however, it requires greater computational time and effort for high-fidelity meshes when performing repeated simulations for design optimization, inverse problems, or structural health monitoring applications. A Graph Neural Network (GNN) is a type of deep learning method that operates over graph-based data. Several existing GNN-based methodologies for solving truss problems aim to learn physical laws, such as the equilibrium equation, constitutive laws, and compatibility conditions, within a single GNN model [1, 2]. Combining the above equations that connect distinct concepts in mechanics into a single GNN requires retraining the entire pipeline whenever the constitutive relation changes, making such a machine learning algorithm data-hungry. Instead, the current study proposes separating the equilibrium equation and the constitutive law into GNN and artificial neural network (ANN)-based models, respectively, and treating the compatibility condition as a separate GNN model. This novel methodology is used to solve planar trusses. The first GNN (G1) takes applied forces and nodal coordinates as node features, and the orientation and length of the truss members as edge features. The output of the first GNN is the member forces with the nodal equilibrium incorporated as a loss function. Further, an ANN (A1) is trained to simulate the constitutive law, with member forces, cross-sectional area, and truss member length as inputs and member elongation as the output. The obtained member elongation and member length serve as edge features for the second GNN (G2), while the nodal coordinates and boundary conditions serve as node features. The output of the GNN (G2) gives nodal displacements of the entire truss. Currently, three types of trusses, namely, Warren, Howe and Pratt trusses, are used to generate the training and test data set. The R^2 value in prediction on 500 samples of test data for G1 and G2 models is 0.998 and 0.999, respectively, for the linear elastic constitutive relation.