## S Simplified design of frames with X bracings

In a standard design, the following simplified approach may be used:

• The analysis of the structure is realized considering that only one diagonal in each X bracing is present, the other diagonal being considered as already buckled and unable to provide strength. This corresponds to an underestimation of both the stiffness and the strength of the structural system at the initial (pre-buckling) stage, but to a safe-side estimate at the post-buckling stage. e The beams and columns are capacity designed according to the real yield strength of the diagonals, for bending with axial force given by equation (D6.1) and bending moment from the analysis for the combination of the design seismic action with gravity loads according to Section 4.4.1.

However, this simplified approach could be dangerous for the stability of the structure, if it does not take into account that action effects of compression in columns and beams at the pre-buckling stage are higher than in the post-buckling stage envisaged in the analysis. Indeed, if the buckling loads of the diagonals are close to their yield load in tension, the initial shear resistance Vinit of the X bracing is underestimated by a model where only one diagonal is considered present. If low-slenderness diagonals are used, Fimt can be close to double the value of Vpi Rd computed with the hypothesis of one active (yielded) diagonal. The only way to prevent this unsafe situation is to design slender diagonals having their buckling load at most around 0.5A^p, Rd. This condition is behind the prescribed lower bound limit value of 1.3 for the slenderness A. The prescribed upper bound limit max(A) = 2 in clauses 6.7.3(1) to 6.7.3(3) is justified by the aim to avoid shock effects during the load reversal in diagonals. This limitation is removed for low-rise structures (up to two storeys); this means that rods or cables can be used as diagonals in such buildings.

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