Infrastructural aging is a significant challenge in managing civil infrastructures throughout their service life. As outlined in the 2023 statistics report issued by the Ministry of Land, Infrastructure, Transport and Tourism (MLIT) of Japan, the percentage of 50-year-old bridges is expected to surge to about 61% in the coming decade. There have been many hurdles in applying structural health monitoring technologies to bridges such as ease of sensor installation, test vehicles for excitation, and data reliability. Over the past few years, static-response-based techniques have been gaining considerable interest due to their simplicity. In this paper, a novel bridge damage detection methodology for simply supported girder bridges using displacement responses of girder ends, is proposed by constructing a two-dimensional (2D) Euler-Bernoulli beam model subjected to quasi-static vehicle load. On-site measurement is implemented at a steel box girder bridge in Japan under changing operational and environmental conditions. The bridge monitoring system is designed with the installation of displacement transducers and accelerometers. Displacements and acceleration are measured at the ends of the box girder, and the feasibility of the proposed methodology for the evaluation of structural soundness is examined by investigating the position of the existing neutral axis.