STEEL BRACINGS: Increasing the stiffness (e.g. addition of bracing or shear walls) or reducing the mass (e.g. lightweight floors, lightweight concrete) both reduce the structural period, and of course the reverse is also true. However, period depends on the square root of mass divided by stiffnesses, (T =2 π√M/k ) so large changes in mass and stiffness are needed for a significant change in period. By contrast mounting the building on flexible bearings can dramatically increase the period. Moment-resisting (i.e. unbraced) frames derive their lateral strength, not from diagonal bracing members, but from the rigidity of the beam–column connection. CONCENTRICALLY BRACED FRAMES (CBFs): CBFs are conventionally designed braced frames in which the centre lines of the bracing members cross at the main joints in the structure, thus minimising residual moments in the frame. The pros and cons of braced frames are essentially the opposite of moment frames; they provide strength and stiffness at low cost but ductility is likely to be limited and the bracing may restrict architectural planning.
(a)
(b)
(c)
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(d)
(e)
(f)
Fig-1-Examples of bracing schemes for concentrically braced frames: (a) Xbraced; (b) diagonally braced; (c) alternative diagonally braced; (d) Vbraced; (e) inverted V-braced; and (f ) K-braced Figure 5.2 distinguishes between various types of braced frame, the seismic resistance of which can be markedly different. X-BRACED FRAME: An X-braced frame (Fig. 1(a)) has bracing members in tension for both directions of loading, and if these are sized to yield before the columns or beams fail, ductility can be developed. DIAGONAL BRACES: Single bays of diagonal braces (Fig. 1(b) and (c)) respond differently according to the direction of loading. Configuration (b) may be much weaker and flexible in the direction causing compression in the braces, while configuration (c) will be weaker and more flexible in the storeys with compression braces, leading to the possibility of soft-storey formation. This is clearly not satisfactory. With more than one diagonally braced bay, the performance can revert to that of X-bracing if a suitable arrangement of bracing direction is chosen. Eurocode 8 requires a balance of compression and tension braces at each level. Single bays of diagonal braces (Fig. 1(b) and (c)) respond differently according to the direction of loading. Configuration (b) may be much weaker and flexible in the direction causing compression in the braces, while configuration (c) will be weaker and more flexible in the storeys with compression braces, leading to the possibility of soft-storey formation. This is clearly not satisfactory. With more than one diagonally braced bay, the performance can revert to that of X-bracingif a suitable arrangement of
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bracing direction is chosen. Eurocode 8 requires a balance of compression and tension braces at each level. V-BRACINGS: The V-braced arrangements of Fig. 1(d) and (e) suffer from the fact that the buckling capacity of the compression brace is likely to be significantly less than the tension yield capacity of the tension brace. Thus there is inevitably an out-of balance load on the horizontal beam when the braces reach their capacity, which must be resisted in bending of the horizontal member. This restricts the amount of yielding that the braces can develop, and hence the overall ductility. Where the horizontal brace has a large bending strength which can resist the out-of-balance load, the hysteretic performance of V-braced systems is improved. K-BRACES: The same out-of-balance force applies to K-braces (Fig. 1(f )) when the braces reach their capacity, but this time it is a much more dangerous horizontal force applied to a column – dangerous because column failure can trigger a general collapse. For this reason, K-braces are not permitted in seismic regions. ECCENTRICALLY FRAMES:
BRACED
FRAMES
(EBFS)
AND
KNEE-BRACED
In EBFs, some of the bracing members are arranged so that their ends do not meet concentrically on a main member, but are separated to meet eccentrically
FIG 3
The eccentric link element between the ends of the braces is designed as a weak but ductile link which yields before any of the other frame members. It therefore provides a dependable source of ductility and, by using capacity design principles, it can prevent the shear in the structure from reaching the level at which buckling occurs in any of the members. The link element is relatively short and so the elastic response of the frame is similar to that of the equivalent CBF. The arrangement thus combines the advantageous stiffness of CBFs in its elastic response, while providing much greater ductility and avoiding problems of buckling and irreversible yielding which affect CBFs in their post-yield phase. Arrangements such as (a) and (b) in Fig above also have architectural advantages in allowing more space for circulation between bracing members than their concentrically braced equivalent. An alternative arrangement with similar characteristics is the knee-braced frame.
Knee-braced frame The yielding element here is the ‘knee brace’, which remains elastic and stiff during moderate earthquakes, but yields to provide ductility and protection from buckling in extreme events. Unlike the link in the EBF, the
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knee brace does not form part of the main structural frame, and could be removed and replaced if it is damaged in an earthquake. ARRANGEMENT OF TENSION AND COMPRESSION BRACES Within any plane of bracing, the compression diagonal braces should balance the tension diagonal braces at each bracing level, in order to avoid tension braces contributing most to lateral resistance in one direction and compression braces in the other. This is to satisfy the general principle that the diagonal elements of bracings should be placed in such a way that the load–deflection characteristics of the structure are the same for both positive and negative phases of the loading cycle. DISTRIBUTION OF DUCTILITY DEMAND IN BRACES: It is important to ensure a reasonably uniform distribution of ductility demand in the braces over the height of the structure. If this is not achieved, and the braces at one level yield well before the others, a weak storey might form, concentrating most of the ductility demand at that level. To avoid this, Eurocode 8 places a restriction on the ratio of bracing member strength to strength required from the seismic design. The ratio between maximum and minimum values of this ratio must not exceed 125%. There is no similar requirement in AISC. DIFFERENT BRACING SYSTEMS: X-BRACED SYSTEMS: These are generally designed assuming that the compression braces do not contribute stiffness or strength. Eurocode 8 places upper and lower limits on the slenderness of diagonal braces in X-braced systems. The upper limit corresponds to a slenderness l=ry of around 180 (depending on yield strength), and is designed to prevent the strength and stiffness degradation shown for a slender strut in Fig. 1. The lower limit of around 110 is intended to prevent column overloading; columns to which the diagonal braces are connected will be sized to resist the full yield strength of the tension brace assuming no force in the compression brace, but higher axial forces might occur in the columns before very stocky braces have buckled. In AISC, there is a similar limit on upper bound slenderness, but no lower limit. DIAGONAL AND V-BRACED SYSTEMS: These systems rely on both compression and tension braces for stability, and so the stiffness and strength of the compression braces must be explicitly accounted for. The same upper bound limits on slenderness
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apply, but there is no lower bound limit in Eurocode 8, because the concern about neglecting the compression brace force does not apply. In V-braced systems, the horizontal brace is subjected to an out-of-balance force when the compression brace begins to buckle, and in Eurocode 8 this must be designed for. Also, the horizontal brace must be designed to carry any gravity loads without support from the diagonal braces, and the AISC rules are similar. K-BRACED SYSTEMS: These are not permitted, because buckling of the compression brace imposes an out-of-balance force not on the horizontal beam (as in the case of V-braced systems) but on the column, and this is clearly unacceptable. The design procedure for EBFs in both Eurocode 8 and AISC is similar. For an elastic analysis, the links are sized from the actions obtained from the seismic analysis, using the specified q or R factor. They can then be classified on the basis of their length e, shear strength Vp and flexural strength Mp as follows.
Typical details of a short link(from AISC)
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