Question

What is the meaning torsion of structure when it is at first mode ? please explain detailedly.

Answer 1

The deformed shape of the building associated with oscillation at fundamental natural period is termed its first mode shape. Similarly, the deformed shapes associated with oscillations at second, third, and other higher natural periods are called second mode shape, third mode shape, and so on, respectively.

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, non- uniform 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.

For the study of modes in structure, placement of structural walls in the building plays an important role.It is not sufficient to just provide structural walls in buildings; however their location in a building governs the overall response of the building. Consider three buildings with same number and size of structural walls but at different locations; structural walls at periphery, structural walls in inner bays, and structural walls forming a core at the center of the building. The buildings are subjected to gravity loads and lateral force equal to 10% of building weight in the two plan directions. While introduction of structural walls cause reduction in (a) lateral displacement, and (b) natural periods of oscillation, placing the same structural walls towards the center of the building allows flexibility for buildings to undergo torsion. In the extreme case, where the four structural walls are interconnected at the center to form a core, torsion becomes the first mode of oscillation and is not desirable. Clearly, structural walls are most effective when placed at the periphery of buildings.