ABSTRACT
Structures in practice are subjected to a variety of forces, both static and dynamic. Static forces, such as gravity forces, remain constant with time. Structures are also subjected to dynamic forces, which vary with respect to time. Some of these forces can act over a long period of time while others act over a relatively short period. Typical of forces which act over a long period of time are vehicular loading on a bridge and wind loads on buildings. On the other hand, forces due to an earthquake or an explosion act over a fairly short period of time. In the vast majority of design situations, the dynamic forces affect the serviceability limit state. For example, vibrations could cause discomfort to users of a structure such as a building or a bridge. In some cases vibrations could lead to the malfunctioning of delicate apparatus. In extreme cases, dynamic forces could affect the ultimate limit state by causing collapse due to violent shaking during an earthquake or cause fatigue failure of joints and components. As will be shown later, dynamic properties of a structure are governed mainly by the mass and stiffness of the structure. Many design advances of recent years, such as the use of higher strength materials, the use of welding or friction grip bolts in steel structures, the wide spread use of prestressed concrete, the emergence of flexible structures such as long span bridges and tall buildings, have all made structures more sensitive to dynamic forces. Many of the changes in construction practice have also reduced the inherent damping present in structures, making them more susceptible to vibration. It is for these reasons that the study of structural dynamics has assumed great importance. The nature of the dynamic forces that act on a structure vary widely. Some, such as the force due to a rotating machine, can be described almost completely as a function of time both in magnitude and direction. Such forces are deterministic forces. On the other hand, forces due to wind can only be described in terms of statistical properties, such as mean and standard deviation. Such forces are called stationary random forces. Forces due to an earthquake are even more complicated. Each earthquake is almost unique. Earthquake forces cannot be described even in statistical terms. Such forces are called non-stationary random forces. In this book, only analysis of structures subjected to deterministic force is considered.
