where A is the area of the cross section of the tension diagonal and a is the slope of the diagonal to the horizontal.
In V-bracing, both tension and compression bracing members are needed to resist horizontal seismic forces effectively, hence both should be included in the elastic analysis of the frame. Also, the beams should be designed for gravity loading without considering the intermediate support of the diagonals, as ell as account for the possibility of an unbalanced vertical action after brace buckling. In other frames, only the tension diagonals are considered. However, accounting for both braces is allowed in E8 provided a non-linear static or tie-history analysis is used, both pre-buckling and post-buckling situations are considered and background
Figure 6.10 Symmetry of lateral resistance in concentrically braced frames studies justifying the models adopted are provided. It should be noted that ignoring the compression brace can have favourable or detrimental effects on the actual response, depending on the frame configuration and design situation (Elghazouli, 2003). On the other hand, K-bracing, such as that shown in Figure 6.7(d) where the diagonals meet at an intermediate point in the column, do not offer ductile behaviour due to the potential demand for a column yielding mechanism. Consequently, it is not appropriate for dissipative design and its use is not recommended in EC8.
In the design of the diagonal members, the non-dimensional slenderness X used in EC3 plays an important role in the behaviour. This is discussed in detail elsewhere (Elghazouli, 2003). In earlier versions of EC8, an upper limit of 1.5 was proposed to prevent elastic buckling. However, further modifications have been made in the current version of EC8 and the upper limit has been revised to a value of 2.0, which results in a more efficient design. Moreover, no upper limit is needed for structures up to two storeys high. On the other hand, in frames with X-diagonal braces X should be bettveen 1.3 and 2.0. The lower limit is specified to avoid overloading columns in the pre-buckling stage of diagonals. Satisfying this lower limit can, however, result in some difficulties in practical design. It should also be noted that in frames with non-intersecting diagonal bracings (e.g. Figure 6.7a), the code stipulates that the design should account for forces that may develop in the columns due to loads from both the tension diagonals and pre-buckling forces in the compression diagonals.
All columns and beams should be capacity designed for the seismic combination actions. In summary, the following relationship applies for the capacity design of non-diagonal members, where the design resistance of the beam or column under consideration, NEd (MEd), with due account of the interaction with the bending moment MEd_ is determined as:
where NEd G and NEd are the axial load due to gravity and lateral actions, respectively, in the seismic design situation, as illustrated in Figure 6.11; W is the minimum value of axial brace overstrength over all the diagonals of the frame and g is the material overstrength. However, W of each diagonal
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