Structures show inelastic non-linear behaviour under cyclic loads associated with natural activities like earthquakes and wind, which impart the external kinetic energy to them, consuming in the lateral movement of structures, such movement may be responsible for the failure or collapse of these structures. To prevent such a collapse, it is necessary to recognize the non-linear behaviour of the structure and adopt a suitable mechanism to control the response of them and this may be possible by dissipating the seismic energy which imparts on them. The study is devoted to the development of an efficient, feasible and economical tuned mass damper for moderately high buildings. This tuned mass damper (TMD) is in form of a weak storey at the top of the buildings for square and rectangle in the plan. Incremental Dynamic Analysis (IDA) was implemented to investigate the benefits of the TMD on structural behaviour. Using ten earthquakes scaled up to a maximum target multiplier two, with ten increments, damage measures such as storey drift. The fragility curves in this study are represented by lognormal distribution functions with two parameters (i.e., the mean spectral displacement and the standard deviation) and developed as a function of spectral acceleration (Sa). Comparison of the fragility curves indicated that the TMD is marginally effective in attenuating seismic structural response under various earthquake ground motions.