Stability of Structures under Emergency Loads

This article covers the issues of local and general stability of multi-storey buildings and high-rise constructions under emergency loads (explosions, tornadoes, tsunamis, earthquakes). It provides the differential equations that describe threedimensional translational and three-dimensional rotational oscillations. It defines the dependence of the assessment of the local and general stability. It gives a numerical example that takes into account the local stability of the highest forms of oscillations. Besides that it evaluates the behavior of the real 16-storey skeleton-type building in the Leninakan earthquake in Spitak December 7, 1988. It provides the main causes of loss of stability and destruction.

Multimass Dynamic Systems
The article provides the results of studying the stability of high-rise buildings that are modeled by a multi-mass dynamical system. The three-dimensional translational and rotational oscillations of the multi-mass system under emergency loads are described by differential equations. During the dynamic analysis the highest vibration modes of constructions with an allowance for attenuation were taken into consideration.

The analysis of the effects of severe earthquakes in Spitak (Armenia, 1988); Kobe (Japan, 1995); Concepcion (Chile, 2010); Port-au-Prince (Haiti, 2010); Christchurh (New Zealand, 2011); the state of California (USA, 1992) and many others shows that in many cases destruction is caused by the loss of the stability (local and general) of the building, framework or separate floors.

Figure 1 is a photo that illustrates buildings losing stability during earthquakes, which is caused by the tilt (slope) or dephased rotation of the building.In structural mechanics the scenarios of loss of stability are divided into 2 major types: local and general. Some authors characterize these types of loss of stability as “minor” and “major”; local and global, etc.

Structural mechanics and bifurcation theory assume that the “local” loss of stability can only occur under an aliquant critical load. Thus, in this case the loss of stability takes place under the slightest critical load Рmin. The system can come back to its below-critical state by means of the internal stored energy, possibly with the help of the energy of the neighboring elements or accumulated retroactive internal energy. Further on if the structure (element) does not come back to its critical state, with the increasing external load it experiences a supercritical state and in the system there occurs a second stage of the loss of stability under the load Рcr2. In this case, the general loss of stability takes place.

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Text: OLEG PONOMAREV, PhD in Technical Sciences, Advisor of RAASN, Principal Director of Scientific Research;
ARAMAIS MINASYAN engineer (TSNIISK named after V.A.Kucherenko Open Joint-Stock Company Scientific Research Centre “Stroitelstvo”)