Question

discuss the effect of modes to the overall behavior of the structure.

Answer 1

There are three basic modes of oscillation, namely, pure translational along X-direction, pure translational along Y-direction and pure rotation about Z-axis. Regular buildings have these pure mode shapes. Irregular buildings (i.e., buildings that have irregular geometry, nonuniform distribution of mass and stiffness in plan and along the height) have mode shapes that are a mixture of these pure mode shapes. Each of these mode shapes is independent, implying, it cannot be obtained by combining any or all of the other mode shapes. The overall response of a building is the sum of the responses of all of its modes. The contributions of different modes of oscillation vary; usually, contributions of some modes dominate. It is important to endeavor to make buildings regular to the extent possible. But, in regular buildings too, care should be taken to locate and size the structural elements such that torsional and mixed modes of oscillation do not participate much in the overall oscillatory motion of the building. One way of avoiding torsional modes to be the early modes of oscillation in buildings is increasing the torsional stiffness of building. This is achieved by adding in-plane stiffness in the vertical plane in select bays along the perimeter of the building; this addition of stiffness should be done along both plan directions of the building, such that the building has no stiffness eccentricity. Adding braces or introducing structural walls in select bays are some common ways in which this is done. Also, there are a number of possibilities in which buildings can oscillate along each direction of oscillation. Consider a building oscillating along the X-axis. It offers least resistance to motion while oscillating in its fundamental mode, and increased resistance to oscillation in the higher modes (second, third, and so on). A special situation arises in buildings that are perfectly symmetric in mass and stiffness distribution in both plan and elevation, say square in plan. Some fundamental or early modes of oscillation are along the diagonal direction and not along the sides of the building (i.e., along X- or Y-directions). Generally, in such cases, the torsional mode is also an early mode of oscillation. In such buildings, columns undergo bending about axes oriented along their diagonal. But rectangular columns have least resistance along their diagonal directions. Hence, their corners of the columns are severely damaged under this type of oscillation of buildings. This situation can be avoided by ensuring that the building (1) does not having the same structural configuration about BOTH plan axes (X and Y) passing through the center of mass, AND (2) is symmetric about EACH of the two plan axes (X and Y) individually passing through the center of mass.