CALCULATION OF STEPPED PORTICOES FREE OSCILLATIONS FREQUENCIES IN 2D BY STIFFNESS MATRIX METHOD

In the modern world, high-rise buildings are in vogue, each year more and more large buildings built. One of the most common schemes for high-rise buildings is portico system, formed by combination of vertical (columns) and horizontal (beams) supporting members. However, as building grows in height, it must have enough strength and stiffness to withstand lateral loads imposed by wind or moderate earthquakes. Over last ten decades, there was therefore significant renewed interest in structures stability problem subjected to time-dependent loads. Considering dynamic problems in civil engineering field is necessary to ensure structure reliability in many applications. But dynamics problems study is often complex for inertia forces come from structure displacements which in turn depend on structures free oscillations frequency. The coincidence of this frequency of free oscillation with that of the forced oscillations caused by the wind involves the phenomenon of resonance which is very dangerous for the structures. It is therefore necessary to know how to determine the frequency of the free oscillations of the systems which constitutes the starting point for a dynamic study. To do this, the stiffness matrix method was used to determine the free oscillation frequencies of the multi-storey portico structures. It has been observed, therefore, that the frequencies of free oscillations don?t depend on time, neither on the amplitude of the oscillations, nor on the phase angle, but rather on the rigidity and the mass of the structures.