Bidirectional resistance and stiffness

Seismic motion is a multi-directional phenomenon. In particular, its bi-directionality in the horizontal plan has to be considered in the conceptual design of the structure of a building. Accordingly, it is not surprising that Eurocode 8 requires that a building must be able to resist horizontal actions in any direction.

A very straightforward - and indeed the most common - way to achieve this is to arrange the structural elements in an orthogonal in-plan structural pattern. It is furthermore very desirable that such a pattern of structural elements ensures similar resistance and stiffness characteristics of the building as a whole in these two main orthogonal directions.

Provided that the building has resistance and stiffness in all horizontal directions, other structural arrangements in plan but not following an orthogonal pattern are naturally also acceptable, but normally they correspond to more complex seismic behaviours and require more sophisticated methods of analysis and dimensioning.

The choice of the stiffness characteristics of the structure is also an important step in the conceptual design phase. In fact, the stiffness characteristics control the dynamic response of the building to future seismic events, and while it may be attempted to decrease the seismic forces by reducing the stiffness (i.e. by 'moving' the structure into the longer-period range where the spectral accelerations are smaller), their choice should also limit the development of excessive displacements that might lead to either instabilities due to second-order effects or excessive damage.

In this respect, it should be pointed out that in the conversion of Eurocode 8 from its previous pre-standard version (ENV 1998) into the full European standard (EN 1998-1) the influence of the lateral displacements of a building on its overall seismic response has been recognized. Thus, the emphasis that is given to an accurate evaluation of the displacements at the design level is reflected for instance in the deformation checks required for the verification of the damage limitation state and in the prescription that in reinforced concrete structures the structural analysis model should use the cracked stiffness of elements.

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