A multiple-time-scale algorithm is developed to numerically simulate certain structural components in civil structures where local defects inevitably exist. Spatially, the size of local defects is relatively small compared to the structural scale. Different length scales should be adopted considering the efficiency and computational cost. In the principle of physics, different length scales are stipulated to correspond to different time scales. This concept lays the foundation of the framework for this multiple-time-scale algorithm. A multiple-time-scale algorithm, which involves different time steps for different regions, while enforcing the compatibility of displacement, force and stress fields across the interface, is proposed. Furthermore, a defected beam component is studied as a numerical sample. The structural component is divided into two regions: a coarse one and a fine one; a micro-defect exists in the fine region and the finite element sizes of the two regions are diametrically different. Correspondingly, two different time steps are adopted. With dynamic load applied to the beam, stress and displacement distribution of the defected beam is investigated from the global and local perspectives. The numerical sample reflects that the proposed algorithm is physically rational and computationally efficient in the potential damage simulation of civil structures. A multiple-time-scale algorithm is developed to numerically simulate certain structural components in civil structures where local defects inevitably exist. Spatially, the size of local defects is relatively small compared to the structural scale. Different length scales should be adopted considering the efficiency and computational cost. In the principle of physics, different length scales are stipulated to correspond to different time scales. A concept of the framework of this multiple-time-scale algorithm. A multiple-time-scale algorithm, which involves different time steps for different regions, while enforcing the compatibility of displacement, force and stress fields across the interface, is proposed. Also, a defected beam component is studied as a numerical sample. The structural component is divided into two regions: a coarse one and a fine one; a micro-defect exists in the fine region and the finite element sizes of the two regions are diametrica With dynamic load applied to the beam, stress and displacement distribution of the defected beam is investigated from the global and local perspectives. The numerical sample contrast that the proposed algorithm is physically and computationally efficient in the potential damage simulation of civil structures.