A wide range of special seismic design requirements are specified for steel frames to ensure that they achieve the ductility and behavior required for the structural system and the design forces used for the system. Use of systems with poor or uncertain seismic performance is restricted or prohibited for some applications. Most of these requirements are specified in the ‘‘Seismic Provisions for Structural Steel Buildings’’ of the AISC. These provisions are either adopted by reference or they are directly incorporated into the UBC and NEHRP provisions. However, UBC also includes supplemental provisions and clarifications which supplement the AISC provisions. This article will provide a summary of the provisions for moment-resisting frames, concentrically braced frames and eccentrically braced frames for seismic applications. It should be noted that the 1992 AISC seismic provisions are directly included in the 1997 UBC, but the 1997 AISC seismic provisions are discussed in this article since they are more current.
Limitations on Moment-Resisting Frames
Structural tests have shown that steel moment-resisting frames may provide excellent ductility and inelastic behavior under severe seismic loading. Because these frames are frequently quite flexible, drift limits often control the design. The UBC recognizes this ductility and assigns R 8.5 to special moment-resisting frames (Art. 9.4).
Slenderness Requirements. Special steel moment-resisting frames must satisfy a range of slenderness requirements to control buckling during the plastic deformation in a severe earthquake.
The unsupported length, Lb , of bending members must satisfy
provides a lower limit beyond which Eq. (9.21b) need not be applied. For these equations, Pu and Py are the factored applied compressive load and the yield load of the member, is the resistance factor, and d and tw are the depth and web thickness of the member. These latter equations are required to control web buckling during the plastic deformation expected during a severe earthquake. These limits are somewhat more conservative than the normal compactness requirements for steel design, because of the greater ductility demand of seismic loading.
Seismic Loads for Columns. The columns and column splices must be designed for the possibility of uplift and extreme compressive load combinations. Two special factored load combinations are required for this purpose when the factored axial load on the column exceeds 40% of the nominal capacity. For axial compression, columns should have the strength to resist
and horizontal components of earthquake loading, respectively. The factor, , is an overstrength factor which is 3.0 for steel moment-resisting frames.
Beam-to-Column Connections. In special moment-resisting frames, beam-to-column connections have historically been designed as prequalified, welded flange, bolted web connections as depicted in Fig. 9.14a. The connections were used because experiments performed 20 to 30 years ago indicated that good ductility was achieved with such connections. However, as noted in Art. 9.6, cracking occurred in a number of these connections during the Northridge earthquake. The cracking was more frequently noted in new buildings and in buildings with relatively heavy members. There are a number of probable contributing factors to this observed damage, and the building codes have responded to these factors. First, the damage was more common in buildings where the lateral resistance was concentrated in limited portions of the structure, since this concentration produces larger member sizes. The redundancy factor described in Art. 9.4 was partly motivated by this observation. Second, the expected yield stress of modern structural steels often widely exceeds the nominal yield stress. This limits the ability to control the yield mechanism during severe seismic loading and thus, may increase the potential for cracking and brittle modes of failure. As a result, the AISC seismic design provisions now include an expected strength factor, Ry , defined as the ratio of the expected yield stress, Fye, to the specified yield stress, Fy:
This Ry value can be established through testing or, in the absence of test data, specification defined values of between 1.1 and 1.5 are provided. Ry is used to evaluate both the uncertainty in material properties and how this affects the seismic performance of the building.
Many other issues including the weld electrode, the basic connection geometry, and the construction practices used, are believe to have contributed to the observed damage. The SAC Steel Project was started to address these issues and its goals are to develop reliable methods of seismic design, repair, and retrofit for steel moment frames. This project is completing a wide range of experimental and analytical research regarding the seismic performance of steel frame buildings. The work is still in progress, but significant recommendations are forthcoming. However, ‘‘Interim Guidelines: Evaluation, Repair, Modification and Design of Welded Steel Structures’’ and ‘‘Interim Guidelines Advisory No. 1’’ by FEMA (FEMA 267 and 267A) include many recommendations arrived at to date regarding special steel moment-resisting frame connections. It is expected that a number of new and improved connection types will be prequalified by this research work. However, for the present, the structural engineer is left with a great deal of responsibility regarding the acceptability of connections for special steel moment-resisting frames. In general, the UBC and the AISC seismic provisions permit the use of a wide range of connections, but require that prototype connection tests be completed to verify seismic performance of the connection before it is used in construction. This testing requires time and the cost is not inconsequenttial. However, the testing may often produce significant savings in the final construction cost and it relieves the engineer of considerable uncertainty regarding the seismic performance of the building.
The testing may be avoided, if past test results of the selected connection with the same general member sizes as used in the subject building, can be provided.
In this environment, the coverplated connection depicted in Fig. 9.14b and the reduced beam section depicted in Fig. 9.14c are being used with some frequency since there is a reasonable experimental data base for both connection types. The coverplated connection significantly strengthens the connection with the goal of forcing yielding into the beam at the end of the coverplate. This modification has worked very well in a number of past tests, but it is an expensive connection and there also have been a few undesirable fractures with this connection. The reduced beam section cuts away a portion of the beam flange at a short distance from the welded flange connection so that yielding occurs within the reduced flange area, well before large stresses develop at the welded connection. This alternative has also performed well, but testing is in progress to evaluate the effects of composite slabs and the lateral-torsional stability of the reduced section. These and other alternatives are discussed in the FEMA 267 documents, and partial design procedures are provided there. At the end of the SAC Steel Project, a number of different steel frame connections will likely be prequalified for use in seismic design by structural engineers. These will clearly include a number of different bolted connections as well as welded connections. However a study of these connections is incomplete and the design procedures for the connections are not fully developed. As a result, the structural engineer must currently rely on the experimental evaluation requirements of the seismic design specification.
Other Connection and Frame Issues. While many issues of connection design are now loosely defined because of the Northridge damage, some important issues are still well defined in the seismic specifications. Seismic bending moments in the beam cause large shear stresses in the column web in the panel zone of the connection (Fig. 9.15). The panelzone shear strength, kips, may be computed from
where dz and wz are the depth between continuity plates and width between column flanges in the panel zone. Doubler plates must be stitched to the web of the column with plug welds to prevent local buckling of the plate, otherwise dz cannot be included in Eq. (9.27).
Panel-zone requirements often control the lateral resistance of steel moment-resisting frames. However, this may cause some difficulties for structural designers. The UBC requires computation of the story drift due to panel-zone deformation, and there is no clear, simple method for calculating story drift in frames dominated by panel-zone yielding.
Special moment-resisting frames provide superior performance when yielding due to severe seismic loading occurs in the beams rather than the columns. This strong-column, weakbeam behavior is required, except in special cases. To ensure this behavior, the following relationship must be satisfied, except as indicated below.
where Zb and Zc are the plastic section modulus, in3, of the beam and the column. This requirement need not be met when ƒa specified by Eqs. (9.22) and (9.23), and any of the following conditions hold:
1. The joint is at the top story of a multistory frame with fundamental period greater than 0.7 second.
2. The joint is in a single-story frame.
3. The sum of the resistances of the weak-column joints is less than 20% of the resistances for a specific story in the total frame and the sum of the resistances of the weak-column joints in a specific frame is less than 33% of the resistances for the frame.
Research suggests that yielding of the columns results in concentration of damage in the structural frames (Fig. 9.10) and reduces the available ductility in the structure while increasing the ductility demand. However, many structural configurations quite naturally lead to weak-column, strong-beam behavior. In addition, the issue is further complicated by concern that panel-zone yielding may lead to an equivalent of weak-column, strong-beam behavior even though Eq. (9.28) is satisfied.
Ordinary Moment Frames. Some steel moment-resisting frames, known as ordinary moment frames, are not designed to satisfy all of the preceding conditions. In many cases, these frames are used in less seismically active zones. Sometimes, however, they are used in seismically active zones with larger seismic design forces; that is, they are designed with R = 4.5. As a result, the design forces would be nearly twice as large as required for special moment frames, but the detailing requirements are reduced. Ordinary moment-resisting frames must satisfy some of the requirements noted above, depending upon the seismic zone and the design forces in the structure.
Limitations on Concentric Braced Frames
Concentric braced steel frames are much stiffer and stronger than moment-resisting frames, and they frequently lead to economical structures. However, their inelastic behavior is usually inferior to that of special moment-resisting steel frames (Art. 9.6). One reason is that the behavior of concentric braced frames under large seismic forces is dominated by buckling.
Furthermore, the columns must be designed for tensile loads and foundation uplift as well as for compression.
Figure 9.12 shows some of the common bracing configurations for concentric braced frames. Seismic design requirements vary with bracing configuration.
X bracing, for example, usually is very slender and has large tensile capacity and little compressive buckling capacity. It may be an economical design for lateral loads, but it permits concentration of inelastic deformations, and energy dissipation during major earthquakes is poor. As a result, X bracing is restricted to use in less seismically active zones or very short structures in more active zones.
K bracing causes yielding in the columns during severe seismic loading. One diagonal is in compression while the other is in tension, and the compression diagonal buckles well before the tensile brace yields. The buckling introduces large shears and bending moments in the columns. As a result, K bracing is prohibited in the more seismically active regions.
Because of these considerations, diagonal and chevron bracing are the primary systems for major structures in seismically active regions of the United States.
Chevron bracing (V or inverted V, shown in Fig. 9.12) causes beam yielding during severe seismic excitation, whereas K bracing causes column yielding. Beam flexure with chevron bracing induces deformations of floors during a major earthquake but provides additional energy dissipation, which may improve the seismic response during major earthquakes.
but provides additional energy
Diagonal bracing acts in tension for lateral loads in one direction and in compression for lateral loads in the other direction. The ‘‘Uniform Building Code’’ requires that the direction of the inclination of bracing with the diagonal bracing system be balanced, since braces have much larger capacity in tension than in compression.
Buckling of Bracing. In general, the energy dissipation of concentric braced frames is strongly influenced by postbuckling brace behavior. This is quite different for slender braces than for stocky braces. For example, the compressive strength of a slender brace is much smaller in later cycles of loading than it is in the first cycle. In addition, very slender braces offer less energy dissipation but are able to sustain more loading cycles and larger inelastic deformation than stocky braces. In view of this, the slenderness ratio of bracing is limited, to
where L is the unsupported length, in; r is the least radius of gyration, in; and Fy is the yield stress, ksi.
The compressive strength of bracing members must also be limited to 80% of the factored nominal compressive capacity, @Pn, of the brace computed by the normal AISC LRFD design procedure. This reduction in compressive capacity is applied because of the loss of compressive resistance expected during cyclic loading after the initial buckling cycles. However, the reduction is not used in the evaluation of the maximum forces that can be transferred to adjacent members.
Bracing, contributing most of the lateral strength and stiffness to frames, resists most of the seismic load. It is tempting, for economy, to design bracing as tension members only, since steel is very efficient in tension. However, this results in poor inelastic behavior under severe earthquake loading, a major reason for excluding X bracing from seismically active regions. On the other hand, more energy is dissipated in a brace yielding in tension than in a brace buckling in compression. As a result, all bracing systems must be designed so that at least 30%, but no more than 70%, of the base shear [Eq. (9.5)] is carried by bracing acting in tension, while the balance is carried by bracing acting in compression.
The overall and local slenderness of bracing is important. The ratio b/t of width to thickness of single-angle struts or double-angle braces that are separated by stitching elements is limited to
where t is wall thickness of the tube, d is the diameter of circular tube, and b and hc are the width and depth in compression for a rectangular tube. Beyond the restrictions noted above, the bracing may be compact or non-compact, but they must not exceed the limit for slender members in the AISC LRFD provisions.
Strength of Connections. The strength of the connections should be stronger than the members themselves. This assures that the energy dissipation occurs in the members rather than the connections. For ordinary concentrically braced frames, this is achieved by first assuring that the connections are capable of developing the brace forces produced by the load combinations given in Eqs. (9.22) and 9.23) with the overstrength factor, , of 2.0. In addition, the connections must be designed to resist the maximum tensile strength of the brace considering the full uncertainty of the yield stress in the brace members. This is accomplished by assuring that the connection resistance also exceeds RyFyAg, where Ag is the gross area of the brace and Ry and Fy are as defined in the moment-resisting frame discussion (Eq. 9.24).
Selection of R. Once concentric bracing is selected for seismic design, the force reduction factor, R, must be chosen. The discussion to this point has focused on ordinary braced frames, which have R = 5.6, and also have the fewest restrictions on their application. This R value is somewhat smaller than that permitted for special steel moment-resisting frames, because concentrically braced frames are known to be dominated by brace buckling. As a result, their resistance may deteriorate and the brace may fracture under seismic loading. There are two major options for improving the behavior of concentrically braced frames. First, they may be used as a dual system with a special steel moment-resisting frame, and R = 6.5.
With this system, the moment frame must be able to resist the loads which are at least 25% of the total seismic design base shear. In addition, both the braced frame and the moment frame must be able to resist their appropriate portion of the loading in accordance with their relative stiffness. The braced frame is usually much stiffer than the moment frame, so that this requirement effectively means that the dual system has a greater total resistance than required by the basic design equations. A second alternative is the recently developed special concentrically braced frame. The seismic performance of concentrically braced frames can be improved if the brace can tolerate larger inelastic deformations without excessive deterioration and brace or connection fracture. However, additional special detailing requirements are needed to achieve this improvement. If these additional requirements are satisfied, R 6.4 for special concentrically braced frames, and R = 7.5 with dual systems of special concentrically braced frames and special steel moment frames.
Special Concentrically Braced Frames. Special concentrically braced frames require that the braced frame satisfy the requirements summarized above, but a few more restrictive requirements are added to ensure improved ductility of the system. The slenderness of bracing members must be limited to
where K, L and r are the effective length coefficient, the brace length, and the controlling radius gyration of the bracing. The bracing must be compact, and there is no reduction applied to the compressive load capacity as used for ordinary concentrically braced frames.
The requirements for the stitching of the members are somewhat more restrictive, and a strength analysis of the bracing member is required to ensure that the connections have adequate strength to fully develop the bracing members. It should be noted that the provisions for special concentrically braced frames were considerably more restrictive than the provisions for ordinary braced frames in previous versions of the seismic design specifications.
However, recent changes to the seismic design specifications such as the expected yield strength factor, Ry , and the overstrength factor, , have narrowed the differences between special and ordinary braced frames. As a result, the special concentrically braced frame is an incresingly attractive option.
Eccentric Braced Frames
These combine the strength and stiffness of a concentric braced frame with the inelastic performance of a special moment-resisting frame (Fig. 9.9c). The UBC permits use of an R of 7 or 8.5 for an eccentric braced frame. This results in seismic design forces comparable to those required for special moment-resisting frames if the fundamental period of vibration is the same. However, braced frames are invariably stiffer than moment-resisting frames of similar geometry and have a shorter period. This results in a somewhat larger design load than for special moment-resisting frames under comparable conditions. (C. W. Roeder, and E. P. Popov, ‘‘Eccentrically Braced Steel Frames for Earthquakes,’’ Journal of Structural Division, March 1978, American Society of Civil Engineers.)
General Requirements for Ductility. There are a number of special design provisions that must be satisfied by eccentric braced frames. As defined in Art 9.4, a link must be provided at least at one end of each brace. The link beam should be designed so that it is the weak link of the structure under severe seismic loading. This is done by selecting the size of the steel section and the length of the link beam to match seismic-load design requirements. The weak link is assured by the requirement that the brace be designed for a force at least 1.25 times the brace force necessary to yield the link beam considering the expected yield strength (Ry Fy ). Yielding or buckling of the columns must also be avoided. Therefore, the column must be designed for the combined axial force of 1.1 times the sum of the yield forces for all link beams considering the expected yield strength. In addition, the columns must be designed for the normal factored load combinations from the AISC LRFD Specification.
These brace and column design forces are needed to ensure that the brace and column do not buckle as the link beam strain hardens during inelastic deformation.
Link Beam. Eccentrically braced frames develop good inelastic behavior because yielding in the link beam occurs well before brace buckling or inelastic deformation of the columns, and this yielding permits large inelastic deformations and great energy dissipation during severe earthquakes. The link beam may yield in shear, flexure or a combination of the two depending upon the size of the beam and the length of the link. The normal yield shear of
are controlled by flexural yield behavior, and they have a maximum plastic link rotational angle of 0.02 radians. Link beams with lengths between these two limits are intermediate links and their rotational limit is determined by interpolation. The rotational limit must be compared to the maximum rotation predicted for the link in the analysis of the system under seismic loading.
Stiffeners and Lateral Support of the Link Beam. The link beam is subject to both high bending stress, high shear stress and significant inelastic deformation. As a result, it must have lateral support to both the top and bottom flanges at both ends of the link beam. The lateral supports must have adequate resistance to develop 6% of the expected flange force (Ry Fy bƒ tƒ ). The beam must also satisfy all of the web and flange slenderness requirements previously noted for special moment resisting frames. Full depth web stiffeners are also required at each end of the link beam as illustrated in Fig. 9.16. The high shear stress in the web of the link beam results in the potential for web buckling during large inelastic cycles, and intermediate web stiffeners are also likely to be required as shown in Fig. 9.16. Spacing s for intermediate stiffeners for link beams with link rotation angle of 0.08 radians is
For link beams with link rotation angle between 0.02 and 0.08 radians, the spacing must be determined by interpolation. The web stiffeners must all be full depth stiffeners, however, the intermediate stiffeners may sometimes be lighter than the end stiffeners.
Beam Outside the Link. Special considerations are also required for the beam outside the link. The beam outside the link must be designed for forces which are 1.1 times those caused by the brace force necessary to yield the link beam considering the expected yield stress (Ry Fy ) of the link beam. Lateral support and slenderness requirements are required for the beam outside the link.
Eccentrically Braced Frames in Dual Systems. The preceding discussion has covered eccentrically braced frames with R = 7.0. Eccentrically braced frames may also be designed as part of dual systems with special moment-resisting frames and R = 8.5. With dual systems, the special moment-resisting frame must be able to resist loads which are at least 25% of the total seismic design base shear. In addition, both the eccentrically braced frame and the moment frame must be able to resist their appropriate portion of the loading in accordance with their relative stiffness.
General Comments. Doubler plates and holes or penetrations are not permitted in the link beams. The connections must be strong enough to develop fully the plastic capacity of the link beams. Link beams that are directly connected to columns require the same experimental verification as is presently required for special steel moment-resisting frames.
Eccentrically braced frames are a rational attempt to design steel structures that fully develop the ductility of the steel without loss of strength and stiffness due to buckling. The design of these frames is somewhat more complicated than that of some other steel frames, but eccentric braced frames offer advantages in economical use of steel and seismic performance that cannot be duplicated by other systems.