In structural optimizations through meta-heuristic algorithms, analyses of structures are performed formany times. For this reason, performing the analyses in a time saving way is precious. The importanceof the point is more accentuated in time-history analyses which take much time. To this aim, peakpicking methods also known as spectrum analyses are generally utilized. However, such methods donot have the required accuracy either done by square root of sum of squares (SRSS) or completequadratic combination (CQC) rules. The paper presents an efficient technique for evaluating thedynamic responses during the optimization process with high speed and accuracy. In the method, firstby using a static equivalent of the earthquake, an initial design is obtained. Then, the displacements inthe modal coordinates are achieved. The displacements are herein called basic modal displacements(MBD). For each new design of the structure, the responses can be derived by well scaling each of theMBD along the time and amplitude and superposing them together using the corresponding modalmatrices. To illustrate the efficiency of the method, an optimization problems is studied. The resultsshow that the proposed approach is a suitable replacement for the conventional time history andspectrum analyses in such problems.