LATERAL-FORCE DESIGN 9.21 FIGURE 9.11 Photograph of crack through the column flange and into the column web or panel zone of connection. of these buildings collapsed and there was no loss of life, but the economic loss was con- siderable. This unexpected damage has caused a new evaluation of the design of moment frame connections through the SAC Steel Project. SAC is a joint venture of SEAOC, ATC (Applied Technology Council), and CUREE (California Universities for Research in Earth- quake Engineering), and the joint venture is funded by FEMA. This work is still in progress, but it is clearly leading structural engineers in new directions in the design of special steel moment frame buildings. The work shows that great ductility is possible, but it also shows that the engineer must exercise great care in the selection and design of members and con- nections. The requirements that are evolving for special moment frames are briefly sum- marized in Art. 9.7.1. Concentric braced frames, defined in Art. 9.4, economically provide much larger strength and stiffness than moment-resisting frames with the same amount of steel. There are a wide range of bracing configurations, and considerable variations in structural perform- ance may result from these different configurations. Figure 9.12 shows some concentric bracing configurations. The braces, which provide the bulk of the stiffness in concentrically braced frames, attract very large compressive and tensile forces during an earthquake. As a result, compressive buckling of the braces often dominates the behavior of these frames. The pinched cyclic force-deflection behavior shown in Fig. 9.9b commonly results, and failure of braces may be quite dramatic. Therefore, concentrically braced frames are regarded as stiffer, stronger but less ductile than steel moment-resisting frames. In recent years, research has shown that concentrically braced frames can sustain relatively large inelastic deformation without failure if greater care is used in the design and selection of the braces and the brace connections. Concentrically braced frames, which are designed to these higher ductility stan- dards, can be designed for smaller seismic design forces and are called special concentrically braced frames. Different design provisions are required for ordinary concentrically braced frames and special concentrically braced frames. These are summarized in Art. 9.7.2. Eccentric braced frames, defined in Art. 9.4, can combine the strength and stiffness of concentrically braced frames with the good ductility of moment-resisting frames. Eccentric braced frames incorporate a deliberately controlled eccentricity in the brace connections (Fig. 9.13). The eccentricity and the link beams are carefully chosen to prevent buckling of the brace, and provide a ductile mechanism for energy dissipation. If they are properly designed, eccentric braced frames lead to good inelastic performance as depicted in Fig. 9.9c, but they require yet another set of design provisions, which are summarized in Art. 9.7.3. Dual systems, defined in Art 9.4, may combine the strength and stiffness of a braced frame and shear wall with the good inelastic performance of special steel moment-resisting frames. Dual systems are frequently assigned an R value and seismic design force that are 9.22 SECTION NINE FIGURE 9.12 Typical configurations of concentric braced frames. intermediate to those required for either system acting alone. Design provisions provide limits and recommendations regarding the relative stiffness and distribution of resistance of the two components. Dual systems have led to a wide range of structural combinations for seismic design. Many of these are composite or hybrid structural systems. However, steel frames with composite concrete floor slabs are not commonly used for developing seismic resistance, even though composite floors are commonly used for gravity-load design throughout the United States. 9.7 SEISMIC-DESIGN LIMITATIONS ON STEEL FRAMES 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 LATERAL-FORCE DESIGN 9.23 FIGURE 9.13 Typical configurations of eccentric braced frames. See also Fig. 9.16. included in the 1997 UBC, but the 1997 AISC seismic provisions are discussed in this article since they are more current. 9.7.1 Limitations on Moment-Resisting Frames Structural tests have shown that steel moment-resisting frames may provide excellent duc- tility and inelastic behavior under severe seismic loading. Because these frames are fre- 9.24 SECTION NINE quently quite flexible, drift limits often control the design. The UBC recognizes this ductility and assigns R ϭ 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 earth- quake. The unsupported length, L b , of bending members must satisfy 2500 r y L Յ (9.19) b F y where r y is the radius of gyration about the weak axis of the member and is the specifiedF y minimum yield stress, ksi, of the steel. The objective of this limit is to control lateral torsional buckling during plastic deformation under cyclic loading. The flanges of beams and columns must have a slenderness less than b 52 ƒ Յ (9.20) 2 t ƒ ͙F y where b ƒ and t ƒ are the flange width and thickness, respectively. The purpose of this require- ment is to control flange buckling during the plastic deformation expected in a severe earth- quake. The webs of members must satisfy d 520 PP uu Ͻ 1 Ϫ 1.54 for Ͻ 0.125 (9.21a) ͫͬ t ␾ P ␾ P w ͙F yy y d 191 PP uu Ͻ 2.33 Ϫ for Ͼ 0.125 (9.21b) ͫͬ t ␾ P ␾ P w ͙F yy y except that d 253 Ͼ (9.21c) t w ͙F y provides a lower limit beyond which Eq. (9.21b) need not be applied. For these equations, P u and P y are the factored applied compressive load and the yield load of the member, ␾ is the resistance factor, and d and t w 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 1.0 P ϩ 0.5 P ϩ 0.2 P ϩ ⍀ P (9.22) DL LL S HE and for axial tension 0.9 P Ϫ ⍀ P (9.23) DL HE where P DL , P LL , P S and P HE are the column loads due to dead load, live load, snow load, LATERAL-FORCE DESIGN 9.25 and horizontal components of earthquake loading, respectively. The factor, ⍀, is an over- strength factor which is 3.0 for steel moment-resisting frames. Beam-to-Column Connections. In special moment-resisting frames, beam-to-column con- nections have historically been designed as prequalified, welded flange, bolted web connec- tions 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. How- ever, 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, R y , defined as the ratio of the expected yield stress, F ye , to the specified yield stress, F y : F ye R ϭ (9.24) y F y This value can be established through testing or, in the absence of test data, specificationR y defined values of between 1.1 and 1.5 are provided. R y 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 per- formance of steel frame buildings. The work is still in progress, but significant recommen- dations 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 9.26 SECTION NINE FIGURE 9.14 Typical beam-to-column connectoins for special moment-resisting frames. (a) Typical pre- Northridge connection. (b) Typical coverplated connection. (c) Typical reduced beam section connection. LATERAL-FORCE DESIGN 9.27 FIGURE 9.15 Forces acting on a column and beam in the panel zone in a typical moment-resisting connection during seismic loading. Forces in (a) are equivalent to those in (b). 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 pre- qualified 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 eval- uation 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 panel- zone shear strength, kips, may be computed from 2 3bt ccƒ V ϭ 0.6 Fdt 1 ϩ (9.25) ͫͬ yc c ddt bc F yc is the yield stress, ksi, of the panel-zone steel; d c is the overall column depth, in; t is the total thickness, in, of the panel-zone (including doubler plates); d b is the overall beam depth, in; b c is the width, in, of the column flange; and t cƒ the thickness, in, of the column flange. The panel-zone shear strength need not exceed 80% of the plastic bending capacity of the beams intersecting the column panel zone. Equation (9.25) takes into account the fact that the strength of the panel zone is enhanced by the strength and stiffness of the column flanges, and that panel- zone yielding provides good, stable energy dissipation and inelastic performance. Also, this equation encourages panel-zone yielding over many other types of plastic deformation. Equation (9.25), however, permits some plastic deformation of the panel zone at loads well below the design load, since V is sometimes considerably larger than the panel-zone yield capacity, 9.28 SECTION NINE V ϭ 0.55Fdt (9.26) syccw If the panel zone does not have the capacity required by Eq. (9.25), a doubler plate (Fig. 9.14a) or thicker column web is required. A minimum thickness t z for the combined doubler plate and column web is prescribed: d ϩ w zz t Ն (9.27) z 90 where d z and w z 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 d z 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 se- vere seismic loading occurs in the beams rather than the columns. This strong-column, weak- beam behavior is required, except in special cases. To ensure this behavior, the following relationship must be satisfied, except as indicated below. ͚Z (F Ϫ ƒ) cyc a Ͼ 1.0 ƒ Ն 0 (9.28) a ͚ZF byb where Z b and Z c are the plastic section modulus, in 3 , of the beam and the column. This requirement need not be met when ƒ a Ͻ 0.3F v c for all load combinations, except for those 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 in- creasing the ductility demand. However, many structural configurations quite naturally lead to weak-column, strong-beam behavior. In addition, the issue is further complicated by con- cern that panel-zone yielding may lead to an equivalent of weak-column, strong-beam be- havior even though Eq. (9.28) is satisfied. Ordinary Moment Frames. Some steel moment-resisting frames, known as ordinary mo- ment 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 ϭ 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. 9.7.2 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 LATERAL-FORCE DESIGN 9.29 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 earth- quakes 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 ad- ditional energy dissipation, which may improve the seismic response during major earth- quakes. 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 L 720 Յ (9.29) r ͙f y where L is the unsupported length, in; r is the least radius of gyration, in; and F y is the yield stress, ksi. The compressive strength of bracing members must also be limited to 80% of the factored nominal compressive capacity, ␾ c P n , 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. How- ever, 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. [...]... factor, ␾ 1.67 0.95 1.67 1.67 1.67 1.67 1.67 0.95 0.90 0.90 0.90 0.90 1.50 1.67 1 .85 2.00 1 .80 1.00 0.90 0.75 0 .80 0 .85 2.00 1.50 / 1.67 1 .80 0 .85 1.00 / 0.90 0 .85 1.67 1 .80 1.67 0.95 0 .85 0.90 / 0.95 1.67 1 .80 0.95 0 .85 1 .80 1.67 2.00 / 3.00 0 .85 0.90 / 0.95 0.50 / 0.65 250 2.50 2.50 0.90 0 .80 0.90 2.50 2.50 2.50 2.50 0.60 0.50 / 0.60 0.60 / 0.70 0.60 2.50 2.50 0.60 0.60 2.50 0.60 2.50 2.50 2.50 0.60... (Art 1.4) as applicable steels, as well several of the plate steels included in Table 1 (A36, A242, A 588 , and A572) A 283 and A529 plate steels are also included, as well as A500 structural tubing (Table 1.7) Other steels can be used for structural members if they meet the ductility requirements The basic requirement is a ratio of tensile strength to yield stress not less than 1. 08 and a total elongation... 10 .8 SECTION TEN TABLE 10.2 Moment of Inertia for Line Elements Source: Adapted from Cold-Formed Steel Design Manual, American Iron and Steel Institute, 1996, Washington, DC COLD-FORMED STEEL DESIGN 10.9 FIGURE 10.2 Local buckling of compression elements (a) In beams; (b) in columns (Source: Commentary on the Specification for the Design of ColdFormed Steel Structural Members, American Iron and Steel. .. connected part Shear, minimum edge distance Tension (c) Arc seam welds Shear, welds Shear, connected part (d) Fillet welds Welds Connected part, longitudinal loading Weld length / sheet thickness Ͻ25 Weld length / sheet thickness Ն25 Connected part, transverse loading ASD safety factor, ⍀ LRFD resistance factor, ␾ 1.67 0.95 1.67 1.67 1.67 1.67 1.67 0.95 0.90 0.90 0.90 0.90 1.50 1.67 1 .85 2.00 1 .80 1.00... 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... behavior be considered, and it is particularly important that the connection between the diaphragms and the structural elements be carefully designed These connections often involve a composite connection between a steel structural member and a concrete slab, wall, or other component The design rules for these composite connections are not as welldefined as those for most steel connections However, there... members for most application are designed in accordance with the Specification for the Design of Cold-Formed Steel Structural Members, American Iron and Steel Institute, Washington, DC Generally referred to as the AISI Specification, it applies to members coldformed to shape from carbon or low-alloy steel sheet, strip, plate, or bar, not more than 1in thick, used for load carrying purposes in buildings... always behave as the sum of the individual connectors SECTION 10 COLD-FORMED STEEL DESIGN R L Brockenbrough, P.E President, R L Brockenbrough & Associates, Inc., Pittsburgh, Pennsylvania This section presents information on the design of structural members that are cold-formed to cross section shape from sheet steels Cold-formed steel members include such products as purlins and girts for the construction... Resistance Factors Adopted by the AISI Specification (Continued ) Category (e) Flare groove welds Welds Connected part, longitudinal loading Connected part, transverse loading (f ) Resistance welds Bolted connections (a) Minimum spacing and edge distance* When Fu / Fsy Ն 1. 08 When Fu / Fsy Ͻ 1. 08 (b) Tension strength on net section With washers, double shear connection With washers, single shear connection... listed in the Cold-Formed Steel Design Manual, American Iron and Steel Institute, 1996, Washington, DC (AISI Manual ) Because the cross section of a cold-formed section is generally of a single thickness of steel, computation of section properties may be simplified by using the linear method With this method, the material is considered concentrated along the centerline of the steel sheet and area elements . 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 pre- qualified for use in seismic design by structural. LIMITATIONS ON STEEL FRAMES 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. 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.