Origami robots self-reconfigure from a quasi two-dimensional manufactured state to three-dimensional mobile robots. By folding, they excel in transforming their initial spatial configuration to expand their functionalities. However, unlike paper-based origamis, where the materials can remain homogeneous, origami robots require varying payloads and controllability of their reconfigurations. Therefore, the mechanisms to achieve automated folding adapt flat thin panels and folding hinges that are often of different materials to achieve the folding. While the fundamental working principle of an origami hinge remains simple, these multi-component, multi-material origami joints can no longer be modeled by beam theory without considering the semi-rigid connections at the material interfaces. Currently, there is no comprehensive model to analyze physical behavior of an actuated folding hinge accurately. In this work, we propose a model based on the plate theory to predict the origami folding joint: we adapt a torsional spring to capture this semi-rigid connection, predict the folding stiffness and bending of origami joints. Herein, the semi-rigid connection is calibrated by quasi-static folding tests on a series of physical origami folding joints, and the accuracy of our model is compared to finite element simulations. With this analytical model, we can accurately simulate the mechanics of physical origami folding joints.