The taller a building, the longer its natural period tends to be. But the height of a building is also related to another important structural characteristic: the building flexibility. Taller buildings tend to be more flexible than short buildings. (Only consider a thin metal rod. If it is very short, it is difficulty to bend it in your hand. If the rod is somewhat longer, and of the same diameter, it becomes much easier to bend. Buildings behave similarly) we say that a short building is stiff, while a taller building is flexible. (Obviously, flexibility and stiffness are really just the two sides of the same coin. If something is stiff, it isn’t flexible and vice-versa).
Ductility is the ability to undergo distortion or deformation without resulting in complete breakage or failure. To see how ductility can improve a building’s performance during an earthquake, see the above figure. In response to the ground motion, the rod bends but does not break. (of course, metals in general are more ductile than materials such as stone, brick and concrete) The ductility of a structure is in fact one of the most important factors affecting its earthquake performance. One of the primary tasks of an engineer designing a building to be earthquake resistant is to ensure that the building will possess enough ductility to withstand the size and types of earthquakes it is likely to experience during its lifetime.