Transfer learning techniques for structural health monitoring in bridge-type structures are investigated, focusing on model generalizability and domain adaptation challenges. Finite element models of bridge-type structures with varying geometry were simulated using the OpenSeesPy platform. Different levels of damage states were introduced at the midspans of these models, and Gaussian-based load time histories were applied at mid-span for dynamic time-history analysis to calculate acceleration data. Then, this acceleration time-history series was transformed into grayscale images, serving as inputs for a Convolutional Neural Network developed to detect and classify structural damage states. Initially, it was trained and tested on datasets derived from a Single-Source Domain structure, achieving perfect accuracy (1.0) in a ten-label multi-class classification task. However, this accuracy significantly decreased when the model was sequentially tested on structures with different geometry without retraining. To address this challenge, it is proposed that transfer learning be employed via feature extraction and joint training. The model showed a reduction in accuracy percentage when adapting from a Single-Source Domain to Multiple-Target Domains, revealing potential issues with non-homogeneous data distribution and catastrophic forgetting. Conversely, joint training, which involves training on all datasets except the specific Target Domain, generated a generalized network that effectively mitigated these issues and maintained high accuracy in predicting unseen class labels. This study highlights the integration of simulation data into the Deep Learning-based SHM framework, demonstrating that a generalized model created via Joint Learning utilizing FEM can potentially reduce the consequences of modeling errors and operational uncertainties unavoidable in real-world applications.