CBFs are quite efficient from strength and stiffness considerations and are used widely in lower SDCs A and B.
However, they are of questionable value in seismic regions because of their poor inelastic behav-ior. Although moment-resistant frames exhibit considerable energy dissipation characteristics, they are relatively flexible when sized from strength considerations alone. Eccentric bracing is a unique structural system that attempts to combine the strength and stiffness of a braced frame with the inelastic energy dissipation characteristics of a moment frame. The system is called eccentric because deliberate eccentricities are designed with in the system, typically with in the beam segment.
The eccentric beam element designed as a fuse limits large forces from entering the braces. The eccentric segment of the beam, called the link, undergoes flexural or shear yielding prior to buck-ling of compression members. Thus, the system maintains stability even under large inelastic defor-mations. The required stiffness during wind storms or minor earthquakes is maintained because no plastic hinges are formed under these loads and all behavior is elastic. Although the deformation is larger than in a concentrically braced frame because of bending deformation of the “fuse,” its con-tribution to deflection is not significant because of the relatively small length of the fuse. Thus, the elastic stiffness of an eccentrically braced frame can be considered the same as the concentrically braced frame for all practical purposes.
Shown in Figure 1.19 are some common EBF configurations with links at one end of brace.
1.4.1 Behavior
Eccentrically braced frames can be configured in various forms as long as the brace is con-nected to at least one link. The underlying principle is to prevent buckling of the brace from large overloads that may occur during major earthquakes. This is achieved by designing the link to yield either in shear or in bending.
The shear yielding of beams is a relatively well-defined phenomenon; the corresponding shear yielding load of a beam of given dimensions can be calculated quite accurately. The resulting axial
22 Structural Analysis and Design of Tall Buildings: Steel and Composite Construction
Using certain overload factors, explained shortly, the braces and columns are designed conserva-tively to assure that in the event of a large earthquake, it is the link that behaves as a fuse without seriously overloading the columns or braces.
Whether the link develops plastic hinges or yields in shear is a function of its length. Links longer than twice the depth tend to develop plastic hinges while shorter links tend to yield in shear.
Accordingly, the links can be identified either as short or long. Short link experiences moderate rotation, while the longer, a relatively larger rotation.
The cyclic shear yielding is an excellent energy dissipation mechanism because large cyclic deflections can take place without failure or deterioration in the hysteretic behavior. This is because yielding occurs over a large segment of the beam web and is followed by a cyclic diagonal field.
The web buckles after yielding in shear, but the tension field action takes over the load-carrying mechanism to prevent failure, resulting in a robust hysteric loop representative of good energy dis-sipation characteristics.
1.4.2 deFleCtion CharaCteristiCs
The lateral deflection of an eccentrically braced frame can be estimated as the sun of three com-ponents: (1) deflection due to axial shortening or elongation of the brace; (2) deflection due to axial strain in the columns; and (3) the deflection due to bending deformation of the link. Because the braces and columns are designed to remain elastic in a design earthquake, their deflection contribu-tions are very nearly the same even after the shear yielding of the link. The beams in EBFs are much heavier than in a concentrically braced frame. Therefore, the bending deformation of the link is likely to contribute very little to the overall deflection of the frame. Hence, an eccentrically braced frame is not an unreasonably flexible system as compared to a concentric frame.
(f)
FIGURE 1.19 Eccentric bracing system: (a–f) Links at one end of brace.
Lateral Load Resisting Systems for Steel Buildings 23
1.4.3 seismiC design Considerations
It is now well-recognized that eccentrically braced frames can provide two distinct benefits: (1) an elastic stiffness that is comparable to that of special concentrically braced frames (OCBF), particu-larly when short link lengths are used and (2) excellent ductility and energy dissipation capacity in the inelastic range, comparable to that of SMFs, provided that the links are not too short.
The distinguishing characteristic of an EBF is that at least one end of every brace is connected so that the brace force is transmitted through shear and bending of a short beam segment called the link. Inelastic action in EBF under seismic loading is restricted primarily to the links. Cyclic yielding in the links can, therefore, occur in a stable manner while the diagonal braces, columns, and portions of the beam outside of the link remain essentially elastic under the forces that can be developed by fully yielded and strain-hardened links.
In some bracing arrangements, as shown in Figure 1.20, with links at each end of the brace, links may not be fully effective. If the upper link has a significantly lower design shear strength than that for the link in the story below, the upper link will deform inelastically and limit the force that can be developed in the brace and to the lower link. When this condition occurs, the upper link is termed an inactive link. The presence of potentially inactive links in an EBF increases the difficulty of analy-sis. Thus, an EBF configuration that ensures that all links will be active, such as those illustrated in Figure 1.19 is recommended.
In EBF systems, lateral forces are resisted by a combination of the flexure, shear, and axial forces in the framing members. Eccentrically braced frames are essentially a hybrid system, offering lat-eral stiffness approaching that of a concentrically braced frame and ductility approaching that of a moment frame system. The general concept is to have the centerline of a brace member coincide with the intersection of a beam-to-column joint at one end, while at the other end, it intersects the beam away from a column. The section of the beam transferring the vertical shear component of the eccentrically connected brace to the adjacent column or brace is called the “link.” The link becomes the focal point in the design and detailing of an EBF system, as it is intended to be the primary location for the inelastic behavior in the frame. The remainder of the members and connections in the EBF are intended to remain essentially elastic and are required to have sufficient strength to withstand forces corresponding to the link yield forces.
While EBF systems combine many concepts of both concentrically braced frames and moment frames, the technology of eccentrically braced frames is relatively new. The system was first devel-oped in Japan in the early 1970s. Research and development in the United States followed later that decade, continuing through the 1980s, with the first codified design procedure in the 1988 Uniform Building Code (UBC).
Column
Floor beam
Brace Link
(a) (b)
e e
e e
e e
e e
e e
24 Structural Analysis and Design of Tall Buildings: Steel and Composite Construction
1.4.3.1 Link Beam Design
The focal points in the design of an EBF link are as follows:
1. Limit the web width-to-thickness ration h/tw based on the ratio Pu/φbFy. See AISC Seismic, Section 15 for details.
2. Limit specified yield stress of link web to 50 ksi.
3. No double plates or penetrations permitted in the link zone.
4. The design shear strength, φVn is equal to lesser of ϕVn=0 90 0 6. × . F Ay w
ϕVn=0 90 2. × Mp/L
5. If Pu, the axial strength in the link exceeds 0.15Py, additional requirements apply. See AISC, seismic, Section 15.2b for details.
6. Limit the length, e of the link to a target value of 1.6Mp/Vp. This will keep the link length short enough to be controlled by shear. Observe shear yielding is much more reliable than flexural yielding.
7. When the link is directly adjacent to a column:
a. The connection is required to meet the provisions for SMRF, unless the connection is reinforced to force beam yielding to a location away from the column.
b. Laterally brace both top and bottom flanges of the link beams at the ends of link.
A composite floor system may be assumed to provide lateral bracing for the top flange but not for the bottom flange of the link. Provide independent bracing for the bot-tom flange. In all cases, lateral restraint against out-of-plane displacement and twist is required at the ends of link to ensure stable inelastic behavior of the link.
c. For EBF configuration shown in Figure 1.19f, provide lateral bracing at the intersection of the diagonal braces and the vertical link.
8. Limit the link rotation angle Vp to 0.08 rad for shear yielding links (e ≤ 1.6Mp/Vp) and 0.02 rad for flexural yielding links (e ≤ 2.6Mp/Vp). Use linear interpolation for links in the combined shear and flexural yielding range. See Figure 1.21 for the definition of link rota-tion angle for a link located at the center of a bay. Refer to AISC Seismic Commentary for other conditions.
Vp = Le θp θp
Δp
L
H
e
Vp
FIGURE 1.21 Link rotation angle λp: This is related to the plastic story drift Δp, and is strongly influenced by the link length. The limits of Vp are 0.08 and 0.02 radians for shear yielding and flexural yielding links.
L = Bay width, H = Story height, Δp = Plastic story drift (conservatively, may be taken equal to the design story drift), θp = Plastic story drift angle = Δp /H, Vp = Link rotation angle.
Lateral Load Resisting Systems for Steel Buildings 25
1.4.3.2 Link-to-Column Connections
Schematics of a link-to-column connection are shown in Figure 1.22. It should be understood, how-ever, that because of the problems observed in moment frame connections after the 1994 Northridge earthquake, the AISC Seismic Provisions require that the performance of link-to-column connec-tions be verified by testing, or by the use of prequalified link-to-column connecconnec-tions. The load and deformation demands at a link-to-column connection in an EBF are substantially different from those at a beam-to-column connection in an SMF. Link-to-column connections must therefore be tested in a manner that properly simulates the forces and inelastic deformations expected in an EBF.
The AISC Seismic Provisions permit the use of link-to-column connections without the need for qualification testing for shear yielding links when the connection is reinforced with haunches or other suitable reinforcement designed to preclude inelastic action in the reinforced zone adjacent to the column. An example of such a connection is shown in Figure 1.23.
1.4.3.3 Diagonal Brace and Beam outside of Links
The intent in seismic design is to ensure that yielding and energy dissipation in an EBF occur pri-marily in the links. Consequently, the diagonal brace and beam segment outside of the link must be designed to resist the loads developed by the fully yielded and strain-hardened link.
In most EBF configurations, the diagonal brace and the beam are subject to large axial loads combined with significant bending moments. Consequently, both the diagonal brace and the beam should be designed as beam–columns.
e Beam
Column
Eccentricity
Floor beam
Column M
Beam Gusset plate Spacer Doubler
plate Fuse
Brace Column
Top and bottom flange
FIGURE 1.22 Schematics of link-to-column connection: note that beam-to-column connections which qualify for use in an SMF may not necessarily perform adequately when used as a link-to-column connection in an EBF. Link-to-column connections must therefore be tested in a manner that properly simulates the forces and inelastic deformations expected in an EBF.
26 Structural Analysis and Design of Tall Buildings: Steel and Composite Construction A diagonal brace in a concentrically braced frame is subject to cyclic buckling and is the primary source of energy dissipation in such a frame. A properly designed diagonal brace in an EBF, on the other hand, should not buckle, regardless of the intensity of the earthquake ground motion. As long as the brace is designed to be stronger than the link, then the link will serve as a fuse to limit the maximum load transferred to the brace, thereby precluding the possibility of brace buckling. Consequently, many of the design provisions for braces in OCBF and SCBF systems intended to permit stable cyclic buck-ling of braces are not needed in EBF. Similarly, the link also limits the loads transferred to the beam beyond the link, thereby precluding failure of this portion of the beam if it is stronger than the link.
1.4.3.4 Link Stiffness
A properly detailed and restrained link web can provide stable, ductile, and predictable behavior under severe cyclic loading. Full-depth stiffeners are required at the ends of all links and to restrain the link web against buckling.
The maximum spacing of link intermediate web stiffeners in shear yielding links is dependent upon the size of the link rotation angle with a closer spacing required as the rotation angle increases.
Intermediate web stiffeners in shear yielding links are provided to delay the onset of inelastic shear buckling of the web. Flexural yielding links are required to have an intermediate stiffener at a dis-tance from the link end equal to 1.5 times the beam flange width. This is to limit strength degrada-tion due to flange local buckling and lateral–torsional buckling. Links of a length that are between the shear and flexural limits are required to meet the stiffener requirements for both shear and flexural yielding links. When the link length exceeds 5Mp/Vp, link intermediate web stiffeners are not required. Link intermediate web stiffeners are required to extend full depth to effectively resist shear buckling of the web and to effectively limit strength degradation due to flange local buckling and lateral–torsional buckling. Link intermediate web stiffeners are required on both sides of the web for links 25 in. in depth or greater. For links that are less than 25 in. deep, the stiffener need be on one side only. All link stiffeners are required to be fillet welded to the link web and flanges and should be detailed to avoid welding in the k-area of the link.
Shown in Figures 1.24 and 1.25 are schematics of EBFs with W-shape and HSS bracing.
1.4.3.5 Columns
Similar to the diagonal brace and beam segment outside of the link, the columns of an EBF should be designed to resist the maximum forces developed by the fully yielded and strain-hardened links.
The maximum shear force developed by a fully yielded and strain-hardened link can be estimated as 1.25Ry times the link nominal shear strength Vn, where the 1.25 factor accounts for strain harden-ing. It is permitted however to reduce the strain hardening factor to 1.1. This relaxation reflects the view that all links above the level of the column under consideration particularly in tall buildings, will not likely reach their maximum shear strength simultaneously. Consequently, applying 1.25
Link length = e
Steel beam
W-shape brace Intermediate stiffeners, full
depth, both sides of link for link depth ≥25 in.
W-shape brace
End stiffeners
FIGURE 1.24 EBF with W-shape bracing.
Lateral Load Resisting Systems for Steel Buildings 27
strain hardening factor to all links above the level of the column under consideration is likely too conservative for a multistory EBF. However, for a low-rise EBF with only a few stories, designers should consider using strain hardening factor of 1.25 for capacity design of the columns, since there is greater likelihood that all links may simultaneously reach their maximum shear strength.
1.4.3.6 Schematic Details
Shown in Figures 1.26 through 1.28 are key connection details for a typical EBF.