The Transmissibility Function (TF) has gained considerable interest in structural damage detection because of its relatively high sensitivity to damage and robustness to excitation. This study proposed a distributed damage diagnosis method for beam-like structures based on a long-gauge static strain TF defined as the ratio of the Fourier transform of static strain response under moving loads from a target long-gauge sensor to that from the reference sensor. It has been discovered that each long-gauge static strain TF is independent of moving loads, making it an ideal damage indicator. It exhibits direct proportionality to the ratio of bending stiffness between the two measured zones covered by the target and reference long-gauge strain sensors while being unaffected by the stiffness of any other zones not covered by these two sensors. Moreover, the TF at zero frequency was proved to be equivalent to the ratio of static strain time history areas, relying solely on the stiffness of the covered zones. Leveraged by the physical properties of long-gauge static strain TF, an element-wise parallel deep neural network architecture was developed to decompose damage diagnosis into independent sub-tasks on the element level, utilizing a variational autoencoder (VAE) in the Bayesian inference framework for extracting features from the long-gauge strain TF and a regressor for mapping the features to elemental stiffness reduction. The divide-and-conquer strategy and element-wise parallel learning architecture allow for a significant reduction in the number of labeled training samples generated based on the updated numerical baseline model as it only requires simulated scenarios involving a single damage element. The efficiency and robustness of the proposed method were demonstrated through a numerical simply supported beam and a laboratory experiment on a two-span bridge.