This paper proposes a vibration-based damage detection method designed for structural elements subjected to important vertical loads, as columns or pillars. The method is based on the relation existing between the energy stored in the pillar in several vibration modes and the corresponding natural frequencies. For a certain mode, this energy results as the sum of the energies stored in all pillar slices, being dependent on the rigidity and the squared of the corresponding mode shape curvature. This means that the energy distribution along the pillar is different for each mode. Thus, reducing the rigidity of one slice due to damage, the frequencies will decrease in different ways, depending on the slice location. This fact permits to contrive patterns able to characterize the effect of damage at any location along the pillar. Since the mode shapes (and the natural frequencies) are influenced by inertial forces, but in the meantime by the compression and shear forces induced by the top mass, the patterns have to be derived for each load case. The paper presents a simple mathematical expression able to predict frequency changes if damage occurs at any location along the pillar and for any top mass value. Patterns that characterize the damage location are consequently derived by using the squared mode shape curvatures of the healthy beam. The damage location becomes an inverse problem, it being found by interpreting the results of frequency measurements for the healthy and damaged state. The process of damage location is exemplified by numerical simulations.