Evaluating the severity of structural damage is a critical component of Structural Health Monitoring (SHM). Convolutional Neural Networks (CNNs) have been used before to detect structural damage and evaluate its severity by utilising only raw vibration data. However, these vibration-based CNN applications were limited to discrete user-defined levels of damage. To provide a more accurate representation of structural damage, this paper aims to design and validate a framework for evaluating structural damage severity within a continuous range of damage levels, using 1D CNNs and distributed raw acceleration data. To this purpose, a simple Finite Element (FE) cantilever model with non-rigid rotational spring support was adopted. Damage was simulated at the support as reduction of the rotational spring stiffness. The performance of the proposed framework was assessed under different excitation scenarios and data pre-processing techniques. The results demonstrate the ability of 1D CNNs to evaluate damage severity with high accuracy. By estimating the reduced value of the rotational spring stiffness, the proposed framework can also be used towards FE model updating in parallel with damage severity evaluation.