This paper presents an investigation of the effectiveness of the Simple Adaptive Control Method (SACM) in mitigating the dynamic response of steel moment-resisting frame buildings. The study aims to evaluate the performance of SACM in reducing the complexity of structural responses, which is measured by the Shannon entropy. Two building types, a 3-story and a 20-story, equipped with MR dampers installed at each story, are considered in this study and subjected to different earthquake loads. The Shannon entropy of acceleration, velocity, and displacement of each story is calculated for both controlled and uncontrolled responses. Results show that SACM is an effective control method in reducing the complexity of structural responses, which suggests its potential for practical applications in Structural Control and Health Monitoring.