This paper deals with the estimation of fragility functions for acceleration-sensitive components of buildings subjected to earthquake action. It considers ideally coherent pulses as well as real non-pulselike ground-motion records applied to continuous building models formed by a flexural beam and a shear beam in tandem. The study advances the idea of acceleration-based dimensionless fragility functions and describes the process of their formulation. It demonstrates that the mean period of the Fourier Spectrum, Tm, is associated with the least dispersion in the predicted dimensionless mean demand. Likewise, peak ground acceleration, PGA-, and peak ground velocity, PGV-based length scales are found to be almost equally appropriate for obtaining efficient ‘universal’ descriptions of maximum floor accelerations. Finally, this work also shows that fragility functions formulated in terms of dimensionless Π-terms have a superior performance in comparison with those based on conventional non-dimensionless terms (like peak or spectral acceleration values). This improved efficiency is more evident for buildings dominated by global flexural type lateral deformation over the whole intensity range and for large peak floor acceleration levels in structures with shear-governed behaviour. The suggested dimensionless fragility functions can offer a ‘universal’ description of the fragility of acceleration-sensitive components and constitute an efficient tool for a rapid seismic assessment of building contents in structures behaving at, or close to, yielding which form the biggest share in large (regional) building stock evaluations.