## Simplified estimation of the effects of accidental eccentricity

Clause The approach outlined in the previous section can also be applied when the lateral force

4.3.3.2.4(1) method is used for the analysis of the response to the two horizontal components of the seismic action. As already pointed out, in the context of the lateral force method this approach is indeed fully consistent with the concept of displacing the masses by the accidental eccentricity with respect to their nominal position. Within the spirit of simplicity normally associated with the lateral force method of analysis, Eurocode 8 allows in that case the effects of accidental eccentricities to be accounted for in a much simpler way: by multiplying by 1 + 0.6x/L the results of the lateral force analysis for each horizontal component of the seismic action, where x denotes the distance of the element of interest from the centre in plan and L the plan dimension, both normal to the horizontal component of the seismic action. This factor is derived assuming that:

• the torsional effects are fully taken up by the stiffness and resistance of the structural elements in the direction of the horizontal component considered, without assistance from the stiffness and resistance of these and other structural elements in the orthogonal horizontal direction

• the stiffness and resistance of the structural elements taking up the torsional effects are uniformly distributed in plan.

In fact, the term 0.6/L is (1) the total storey torsional moment due to the accidental eccentricity of 0.05L, namely 0.05L times the storey seismic shear, V, (2) divided by kBBL3/12, which is the moment of inertia of a uniform lateral stiffness, kB, per unit floor area parallel to side B in plan, and (3) further divided by the normalized storey shear, V/kBBL. Normally there is also lateral stiffness, kL ~ kB, per unit floor area parallel to side L in plan, which contributes with kLLB3/12 to the polar moment of inertia to be used in point 2. As the contribution of kh is neglected, the term 0,6x/L is conservative by a factor of 2, on average. If the designer considers this additional conservatism is too high a price to pay for the simplicity, then he or she may choose to use with the lateral force method of analysis the general approach outlined in the previous section.

The general approach of Section 4.8.2 can only be applied to a full 3D structural model. For buildings that meet the conditions of Section 4.3.2.1 or 4.3.2.2, the designer may opt for analysis - of the lateral force or the modal response spectrum type - with a separate 2D model for each horizontal component of the seismic action. As the general approach of Section 4.8.2 cannot be applied in that case, the effects of the accidental eccentricity can only be estimated through the simplified approach of the present section. In that case the second term in the amplification factor becomes 1.2x/L, to account also for the otherwise unaccounted for effects of any static eccentricity between the storey centres of mass and stiffness.

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