App4SHM is a mobile system for structural health monitoring (SHM) of bridges that aims to support routine inspections. It consists of a front-end smartphone application that is used to measure natural frequencies of vibration and to detect damage supported by a backstage server software, accessible through any internet browser. This paper focuses on the new module for stay cables, which directly converts natural frequencies into cable tension forces based on the cable's material and geometrical characteristics. The conversion uses an estimate of the forces from the taut string theory. Regardless of the module, App4SHM works in two modes. The training mode is used to collect observations composed of natural frequencies under normal operational and environmental conditions. The observations are used to train an unsupervised machine learning algorithm to learn the structure's normal behavior. The damage detection mode collects unlabeled observations, which are tested against normal behavior to detect abnormal performance that may be indicative of damage or excessive tension. The Edgar Cardoso Bridge — a large cable-stayed bridge in Portugal, undergoing rehabilitation and stay cables replacement — is used as a case study for the measurement of cable tension forces.