This paper introduces a novel model-based approach for virtual sensing of wind turbine support structures for full-field strain estimation using a single DC-capable accelerometer. It enables displacement and strain estimation in the quasi-static frequency band, which accounts for a large proportion of accumulated fatigue damage in offshore wind turbine support structures, while saving costs by relying solely on accelerations from a single accelerometer as input. The introduced method extends the modal decomposition and expansion by using displacement estimations based on tilt-error compensated acceleration time series, utilising the tower's static bending line. It is applied here in two validation case studies: a small-scale laboratory experiment and a full-scale offshore wind turbine. In both cases, the estimated strain is validated against strain measurements conducted at various locations along the structure. The results show excellent agreement between the estimated and measured strains for both case studies. In the laboratory experiment, both displacements and strains are estimated accurately with errors below 2.2 % and 1.2 %, respectively. For the offshore wind turbine, the damage equivalent loads at the tower can be estimated with a maximum error of 21 % in the worst case and 6 % in the best case. The presented approach offers an improvement over established methods for strain estimation, achieving similar accuracy with fewer sensors, resulting in a low-maintenance load monitoring.