Engineering method of calculating suspended buildings for seismic load

Abstract

Most often, dynamic vibration dampers are used to dampen vibrations under seismic loads. In this case, the vibration damper is a pendulum suspended within the building. In previous works by the authors of this article, it was proposed to suspend the entire building on a supporting frame. A dynamic scheme for calculating such a structure is proposed. However, the entire mass of the supporting frame is concentrated at its top.

To construct the equations of motion for such a system, the Lagrange equation of the second kind was used. In the dynamic scheme, it is assumed that the base oscillates according to the sine law. This scheme was compared with the traditional cantilever scheme, when the building is considered as a cantilever, at the end of which the entire mass of the building is concentrated. At the same time, the dynamic forces in the suspended and cantilever designs are significantly different.

The supporting frame is considered as one mass. However, when using suspended structures of two, thre,e or more floors, the supporting frame cannot be considered as a system with one mass. Such a simplification can lead to errors in determining dynamic forces. In this article, its equivalent mass is taken as the mass of the supporting frame. The equivalent mass is determined from the equality of kinetic energy for systems with one mass and many masses.

The article shows that the value of the equivalent mass has a significant impact on dynamic forces. Tables are provided to compare the maximum dynamic forces from base vibration depending on various factors. These reasons ae: the mass of the building, the mass of the supporting frame, and the rigidity of the frame. A graph of maximum dynamic force versus equivalent mass is presented. The construction of such graphs makes it possible to determine the structural design of the supporting frame to reduce dynamic forces.

The advantage of the engineering calculation method is that it is very simple and does not require the use of software packages. This method should be used for preliminary calculations. In preliminary variant calculations, the rigidity and mass of the supporting frame are determined from the point of view of the minimum dynamic force. After adopting a certain structural design of the load-bearing frame, its final calculation is performed using well-known programs for calculating seismic impacts.