Keywords: torsion effects, staircases, stair slabs, modal-spectral analysis, reinforced concrete frames, reinforced concrete buildings.

Under seismic loading, the stairs of the building are not usually included in the model of the structure for the analysis. The effect of the stairs can be very important in buildings which structures are constituted by frames. The study has been carried out in buildings constituted by reinforced-concrete frames, with one-way slabs. The main frames of the buildings support the gravity loads, and also the seismic loads acting in this direction. When acting in the direction of the ribs, frames, constituted by beams joining the columns, support the seismic loads in that direction. This disposition of the structure is very typical in Spain and in many countries from the South of Europe. The stairs are usually supported with a 15-20 cm thickness reinforced-concrete slab, connecting each floor level. In this paper the location of the stairs inside the buildings for the analysis is centred in one main facade of the building. The study has been carried out on a three-storey building and on a six- storey building. First, the buildings have been dimensioned (the sections of their columns and beams) considering the non-existence of the stair slabs (as usually done in projects), under gravity and seismic loads, according to Spanish Codes [4]. After, three-dimensional elastic modal-spectral analyses have been performed in the buildings, considering the location of the stair slabs, obtaining and comparing forces and displacements, for both lateral directions ( and ) of the seismic action [1,2,3].

The main conclusions of this study are:

1. Analyzing the global results of the buildings, torsion effects and local rigidity effects take place when considering the stair slabs, with an important change in the distribution of shears and flexural moments. In -direction seismic attack (with regard to which the stairwell is centred) the stair slabs cause a decrease in the sum of shears and moments of the column reactions. Local rigidity effects take place around the stairwell, generating a "shear-wall effect" in the columns surrounding the stairwell. In -direction seismic attack (whit regard to which the stairwell is eccentric) the stair slabs cause a decrease in the sum of shears and moments of the columns reactions in -direction, but torsion effects take place in the structure, resulting in new shears and moments in -direction. All these effects are of less importance in the six-storey building, because of the greater stiffness of columns and beams (the stiffness introduced by the stair slabs is a constant (same thickness) in both buildings).
2. Analyzing the individual results, it is observed how the stairwell and the columns to which the stair slabs are joined create a rigid substructure inside the building. The axial forces are increased in the columns surrounding the stairwell, reaching very high values in these columns. This behaviour is showed in both directions of the seismic attack. Depending on the configuration of the structure (number of columns, length of bays) this effect will be more or less strong. For the configuration of the buildings studied in this paper, the columns surrounding the stairwell are alternatively subjected to high compression forces and tensile forces (gravity loads already included), with strength and ductility demands not considered in an analysis without the stairwell. On the other hand the magnitude of the shears and axial values are of great importance in the beams connected with the stair slabs, with high strength and ductility demands, not taking into account if the stair slabs are not introduced in the structure.
3. All these effects are of great importance about all in the frames just surrounding the stairwell, where the stair slabs are joined. In the rest of the frames of the building the effects are not so important. Nevertheless, the disposition of the stairwell is adopted in this study centred in one main facade of the building. With other locations (in one corner of the building for example) the torsion effects may be of much more importance in frames located far from the centre of torsion.
4. Presumably, the local rigidity effects and torsion effects caused by the stair slabs should be of less importance in dual systems (where shear-walls collaborate with frames), because normally the stiffness introduced by the shear-walls are very great. Nevertheless in frame buildings the stair slabs can not be ignored, so they must be introduced in the analysis of the structure.

1

Ansys, Revision 5.7. Universitary Version, Swanson Analysis Systems, Inc., 1998.

2

Chopra, A.K., "Dynamics of Structures", Prentice Hall, 2001.

3

Der Kiureghian, A., "A Response Spectrum Method for Random Vibration Analysis of MDF Systems", Earthquake Engineering and Structural Dynamics, 9, 419-435, 1981. doi:10.1002/eqe.4290090503

4

NCSE-02 (Norma de Construcción Sismorresistente de Estructuras), Ministerio de Fomento, 2002.

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