performance-based seismic design of braced-frame...

PERFORMANCE-BASED SEISMIC DESIGN OF BRACED-FRAME GUSSET PLATE CONNECTIONS

C.W. Roeder, U. of Washington, Seattle, WA, USA D.E. Lehman, U. of Washington, Seattle, WA, USA

J. H. Yoo, U. of Washington, Seattle, WA, USA

ABSTRACT Performance-based seismic design (PBSD) produces structures that meet multiple performance objectives. Economical application of PBSD produces structures that:

• have adequate strength and stiffness to remain serviceable during small, frequent earthquakes, and

• develop cyclic nonlinear deformations while assuring life safety and collapse prevention during large infrequent earthquakes.

Special concentrically braced frames (SCBFs) and buckling restrained concentrically braced frames (BRCBFs) can meet these diverse objectives if the gusset plate connection provides adequate performance. Current connection design provisions attempt to ensure adequate connection resistance to avoid premature failure, but the resulting connections may be massive and uneconomical or provide unacceptable performance. An analytical and experimental research study to develop improved design methods for these gusset plate connections is described. A rational, PBSD procedure is proposed. Future directions of the research study are noted.

INTRODUCTION Large, infrequent earthquakes induce huge elastic forces in building structures. Therefore, seismic design of buildings employs relatively small earthquake design forces to assure that the structure remains serviceable during frequent seismic events, and cyclic, inelastic ductility is used to prevent loss of life and structural collapse during large seismic events. This concept is simple and results in economical design, but it is difficult to reliably and accurately apply in engineering practice. Performance based seismic design (PBSD) is a recently developed design concept that formalizes this procedure for meeting multiple design objectives. Concentrically braced frames (CBFs) are stiff, strong steel structures, which are economical systems for seismic design. The inelastic lateral response of CBFs is dominated by axial yielding and post buckling deformation of the braces, and special concentrically braced frames (SCBFs) are designed under guidelines which are intended to assure good inelastic performance from the brace. These SCBF requirements control the local and global slenderness of the brace to prevent concentration of local damage during post buckling deformations. They require that the strength of the connection be greater than the yield capacity of the brace, and they establish geometric clearances intended to develop the connection rotations needed to develop brace buckling. Innovative bracing systems, such as unbonded or buckling restrained braced frames (BRCBFs), have also been proposed, since they hold promise for improved seismic performance. The seismic performance of these CBF systems depends on the brace, the connection, and the framing members. To achieve a superior level of seismic performance, the design of the connection

Connections in Steel Structures V - Amsterdam - June 3-4, 2004 167

must be balanced to meet strength and deformation demands while permitting the brace to develop the desired elastic and inelastic performance. The connections are normally gusset plate connections, and the connection seismic performance of this connection is the focus of this paper. BRACED FRAME SEISMIC BEHAVIOR SCBFs (AISC, 2002) provide economical strength and stiffness and are commonly used for seismic design. The brace provides lateral stiffness to the frame, and so the brace attracts large axial forces during earthquake loading. As a result, the cyclic inelastic deformation of an SCBF is achieved through post buckling deformation and tensile yield of the brace as illustrated in Zones 0-A, A-B, B-C, C-D and D-E in Figs. 1a and 1b. Plastic hinges form within the brace after buckling, because of the P-δ moments. These hinges cause permanent plastic deformations and ultimately deterioration of brace resistance. When the brace is subjected to a tensile force during load reversals (Zones B-C, C-D and D-E) significant axial deformation is needed to recover the full tensile stiffness and resistance. This leads to the one-sided axial force-deflection behavior of the brace seen in Fig. 1a, and SCBFs use braces in opposing pairs to achieve the system inelastic hysteretic behavior illustrated in Fig. 1c.

Figure 1. Behavior of special concentrically braced frames (Popov et al. 1976).

Braces are normally joined to the beams and columns of the frame through gusset plate connections as illustrated in Fig. 2. SCBF brace post-buckling behavior places significant cyclic load and deformation demands on these connections as illustrated by the brace end rotation shown in Zone A-B of Fig. 1b. These connection rotation demands vary depending upon whether the brace has in-plane or out-of-plane buckling. Figure 3 is a photo of a buckled braced from a steel frame damaged during a past earthquake, and it shows the large end rotations that can occur during inelastic seismic deformations.

168 Connections in Steel Structures V - Amsterdam - June 3-4, 2004

Figure 2. Typical gusset plate connections. Figure 3. Connection rotation due to brace buckling.

Brace buckling may result in deterioration of stiffness and resistance and pinched hysteretic behavior shown in Fig. 1a and 1c. BRCBFs have been developed to increase ductility and reduce deterioration in brace resistance. BRCBFs are patented systems where an axially loaded bar is encased into a stiff tube but is not bonded to the tube. As a result, the bar yields in tension and compression without brace buckling, and the resulting cyclic inelastic performance of the brace is symmetric without deterioration as illustrated in Fig. 4. Many engineers currently prefer BRCBFs for seismic design to SCBFs, because of this inelastic performance. A significant body of research (Clark et al. 2000, Ando et al 1993, Connor et al. 1997, and Inoue et al. 2001) has been completed on BRCBF performance. However, the past research and professional opinions on BRCBF braces are based on the assumption that braced frames behave as a truss, and the brace has pure axial deformation with no bending moment. This idealization is frequently not achieved in practice, because of the gusset plate performance.

Figure 4. Axial force-deformation hysteresis curve for an BRCBF (Clark et al. 2000).


BRACED FRAME GUSSET PLATE CONNECTION DESIGN REQUIREMENTS Past research (Kahn and Hanson 1976, Foutch et al. 1987, Astaneh-Asl et al. 1982, Lee and Goel 1987, and Aslani and Goel 1989) shows that SCBFs can provide good seismic performance if premature fracture or tearing of the brace and the connection is avoided. The AISC Seismic Design Requirements for the SCBF system (AISC 2002) provide guidelines toward meeting these goals. Slenderness limits for the brace and different brace geometry and configuration requirements are provided to avoid concentration of inelastic strain that leads to early tearing or fracture. The AISC seismic provisions also require that the connection be designed to be stronger than the brace, and with out-of-plane buckling, geometric limits are established to permit the expected end rotation on the connection. These design rules lead to the common conception that a stronger gusset plate connection is better, and some very uneconomical and impractical connections such as illustrated in Fig. 5 have been built. Further, it is difficult to satisfy the out-of-plane buckling geometry requirements for most practical gusset plate connections. The past performance of braced frames during earthquakes has been mixed. In some cases, economical and serviceable performance during earthquake loading has resulted, but in others, the apparent resistance and ductility were significantly smaller than expected when brace or connection failures such as illustrated in Fig. 6 occurred.

Figure 5. Photo of excessively large Figure 6. Photograph of brace fracture

gusset plate connection. noted from past earthquake damage.

Figure 7. Deformation mechanisms of BRCBF systems.


The seismic performance of BRCBFs also depends upon the gusset plate connection design. The BRCBF connection must support the full tensile and compressive force capacity of the brace during cyclic inelastic deformation demand, and it must have adequate stability and lateral restraint to prevent out-of-plane deformation. As a result, out-of-plane rotation or deformation, buckling, or fracture of the BRCBF connection cannot be tolerated, because the brace and gusset plate act in series and gusset plate deformation may negate BRCBF buckling restraint. BRCBF braces have large axial deformation capacity as long as the beam-column joints respond as pinned joints as illustrated in Fig. 7b. However, BRCBF braces have large flexural stiffness contributed by the moment of inertia of the surrounding tube. Further, the gusset plate connections have substantial flexural resistance and in-plane rotational restraint because of the size and geometry of the connection as illustrated in Fig. 2. As a result, BRCBF deformations may result in significant bending moment in the gusset plate and the BRCBF brace due to flexural deformation as depicted in Fig. 7c. These deformation demands may place large stress and strain demands on the gusset plate connection, and they may have negative impact on the seismic performance of the BRCBF system. Figure 8 is a photo of a BRCBF brace and gusset plate connection in a test frame. The gusset plate connection was clearly strong enough by the present seismic design reasoning. However, the gusset plate buckled at relatively modest inelastic frame deformations, and the BRCBF brace was damaged because of the resulting connection deformation.

Figure 8. Photograph of buckled BRCBF brace and gusset plate.

PROPOSED PBSD DESIGN METHOD Prior discussion demonstrates the need to understand and improve the BRCBF and SCBF gusset plate connection design to efficiently and economically achieve multiple performance objectives for seismic design. The stiffness and strength of CBF systems clearly aid in satisfying the Operational and Immediate Occupancy performance levels, and they provide economical building design. However, the SCBF and BRCBF connections must accommodate significant inelastic deformation and strength demands for the Life Safety and Collapse Prevention performance levels. These later design limit states are less easily satisfied, because they place both force and deformation demands on the gusset plate


connection. A design strategy, which considers both connection strength and inelastic deformation capacity, is needed to meet these later design goals. A rational hierarchy of yield mechanisms within the frame and the connection are required to meet these diverse force and deformation demands, because a simple connection resistance check as presently used in SCBF seismic design leads to variable seismic performance. The simple resistance checks in the AISC requirements do not assure the most desirable connection behavior nor do they prevent the least desirable performance. The proposed design procedure must address this complex braced frame behavior while retaining a simple design method.

Figure 9. Yield mechanisms and failure modes of CBF components.

The proposed procedure employs concepts developed for PBSD of steel moment-resisting frames (Roeder 2001 and 2002) during the SAC Steel Project. This design procedure developed balance conditions to assure desirable yield mechanisms, restrict undesirable failure modes, and achieve the desired seismic performance. Occurrence of a yield mechanism changes the stiffness and provides inelastic deformation of the structure without significant loss in resistance. The occurrence of a failure mode can lead to fracture, loss in resistance, and reduced inelastic deformation capacity. A single failure mode will produce a significant reduction in resistance or deformation capacity, but multiple failure modes are usually required to produce complete connection failure. Similar design procedures are being developed to achieve the performance objectives of SCBF and BRCBF structures. The yield mechanisms and failure modes for the CBF systems as illustrated in Fig 9 are considered in this evaluation. The controlling yield mechanisms for SCBFs are expected to be inelastic shortening due to post-buckling deformation and tensile yielding of the brace. The axial load capacity of the BRCBF brace is similar in tension and compression, and the brace should not buckle. As a result, the controlling yield mechanism for BRCBF systems will be this axial yield deformation. Secondary yield mechanisms are also possible with braced frame gusset plate connections. These include local yielding of the gusset plate, local yielding of the beam and column adjacent to the gusset plate and elongation of boltholes in brace and gusset plate. These secondary yield mechanisms can contribute some plastic deformation during large earthquakes, but their deformation capacity is limited so that they are not capability of providing primary sources of inelastic deformation. CBFs have many different possible failure modes including tearing or fracture of the brace, net section fracture of the brace or gusset plate, weld fracture, shear fracture of the bolts, block shear, excessive bolt bearing deformation, and buckling of the gusset plate. A rational connection design procedure for seismic design can be based upon the expected or mean yield resistance of the controlling yield mechanism, and its comparison to the


expected resistance of the critical failure mode. As noted in prior discussion, favorable yield mechanisms should have a smaller resistance than less favorable or secondary yield mechanisms and all failure modes. Greater separation is warranted between the controlling yield mechanism resistance and failure mode resistance, when the failure mode results in poor seismic performance than that used for failure modes with better seismic performance and deformation capacity. As a result, good inelastic performance can be achieved for CFT gusset plate connections by balancing the controlling yield mechanism resistance with the resistances associated with all failure modes. This idea can be expressed as Eqs. 1a and 1b where β is a balance factor.

Ry Fy Ag < β Rfailure (Eq. 1a)

Ry Fcr Ag < β Rfailure (Eq. 1b)

Where Rfailure is the failure mode resistance for an individual failure mode, and Ag is the gross cross sectional area of the brace. Ry is a factor for adjusting the nominal yield stress, Fy and Fcr, to the expected or average yield and critical buckling stress, respectively. Two balance equations may be required for SCBFs because both brace buckling and tensile yield serve as controlling yield mechanisms for some failure modes. BRCBFs have identical yield resistance in both tension and compression, and so only Eq. 1a is required. The β factor used in these balance equations is similar to the φ factor in LRFD design (AISC 2001) in that both are less than 1.0 and both are based upon the performance and variability of the structural elements. However, φ is based solely upon strength, safety, and statistically extreme considerations, while β depends upon balancing the expected inelastic seismic behavior to meet the performance requirements and inelastic deformation capacity.

Table 1. Overview of proposed performance based design strategy.

Different β values will be required for different design limit states and for different failure mode-yield mechanism combinations, because brace connection design must consider the full range of seismic behavior at all performance levels. Connection strength and stiffness must be adequate to insure serviceable seismic performance, but once this adequate


strength and stiffness is provided, system ductility and deformation capacity become the dominant concerns. As a result, smaller value of β is required when a given failure mode is difficult to predict or has undesirable consequences, and larger β values are appropriate for failure modes that provide larger inelastic deformation capacity or better and more predictable performance. Further, different seismic excitation demands may be warranted for different performance based design goals as illustrated in Table 1. The balance equations are used to ensure the desired progression of yielding, prevent premature failure, and ensure that undesirable failure modes are prevented. Appropriate β factors must be established for each failure mode to provide the desired progression of yielding and seismic inelastic performance. BRCBFs require that the connection satisfy these goals without local buckling or out-of-plane deformation, while the SCBF connections must tolerate large out-of-plane rotation while achieving the above resistance goals. Different β factors are likely needed for these two alternatives. Some failure modes may be controlled by prescriptive design measures. For example, fracture or tearing of the SCBF brace is theoretically controlled by global and local slenderness limits. In addition, geometric constraints are employed with SCBF gusset plate connections to assure that connection can tolerate brace end rotations due to post-buckling brace deformation. BRCBFs require great control over the connection deformation to avoid premature brace damage, and so additional constraints may be needed for out-of-plane stiffness of these BRCBF connections. This research work focuses on improving the seismic design of these gusset plate connections through:

• better understanding of these yield mechanisms and failure mode behaviors,

• development of simple but accurate models for prediction of the resistance associated with all of these yield mechanisms and failure modes,

• developing appropriate β factors for assuring adequate seismic performance of braced frame gusset plate connections with each of these yield mechanism and failure mode combinations, and

• application of these combined developments through balance conditions such as provided in Eqs. 1a and 1b.

These efforts are the continuing focus of the ongoing work. CONTINUING WORK This research work is in progress and will continue for the next two years. At present, past research is being compared and evaluated and this database will be used to develop and verify accurate but simple models for predicting connection behaviors. The inelastic performance achieved with different yield mechanism and failure mode conditions for SCBF and BRCBF systems in these past research studies will be assessed. Balance conditions (β values) necessary to assure the proper combination of behaviors are achieved in practice will then be developed to establish a proposed gusset plate connection design procedure. The proposed connection design procedure will then be evaluated experimentally. The experimental results will be used to modify the design procedure to assure that it provides the greatest design economy combined with good seismic performance at all performance levels. Follow-up experiments will be conducted to evaluate the design modifications.

The experiments will be designed to evaluate bolted and welded gusset plate connections. The test matrix will be developed to consider variation in the type of brace, type of


connection, and balance conditions. A schematic of the test configuration is depicted in Figure 10. The goal is to test approximately 25 specimens. Each specimen will consist of a large-scale braced bay typical of that expected in the bottom story of a 3 to 4 story building. One or more specimens will evaluate the expected performance with the existing SCBF design requirements [AISC (2002)] and will serve a reference specimen for that framing system. Another reference specimen will model a braced frame connection in a BRCBF. The remaining specimens will evaluate the proposed braced frame connection design criteria for SCBF and BRCBF systems. In these later tests different failure modes and yield mechanisms will be evaluated, and improved models for predicting their behavior will be examined and developed.

The test specimens will be constructed and attached to the laboratory strong floor as depicted in Figure 10. Each specimen will consist of end gusset plates attached to a brace and the surrounding beam and column framing. This configuration should insure realistic boundaries for the test specimens. The imposed displacement history will include cyclic deformation with multiple cycles of increasing story drift such as employed with the ATC-24 testing protocol. Initial cycles will be at deformations below the initial yield and buckling loads of the brace to examine Operational and Immediate Occupancy performance limit states. Subsequently, multiple cycles will be completed at and slightly above the buckling load and tensile yield load of the brace. Finally multiple cycles will then be completed with increasing inelastic story drift until ultimate failure of the brace or the connection occurs. These later cycles will be documented with emphasis upon the Life Safety and Structural Collapse Prevention performance limit states. Work on these tests will begin in Spring 2004.

Figure 10. Schematic of proposed test assembly.

ACKNOWLEDGEMENT This research work is funded by the National Science Foundation through Grant CMS-0301792, Performance-Based Seismic Design of Concentrically Braced Frames. Dr. Steven L. McCabe is the Program Manage for this research. This financial support is gratefully acknowledged.


NOTATION Ag gross cross sectional area of the brace Rn failure mode resistance for an individual failure mode Ry factor for adjusting the nominal yield stress Fcr critical buckling stress Fy expected or average yield stress β balance factor φ resistance REFERENCES (1) Ando, N. Takahasi, S. and Yoshida, K., (1993) "Behavior of Unbonded Braces

Restrained by Reinforced Concrete and FRP," ASCE, Composite Construction II, New York, pgs 869-882.

(2) AISC (2001) "Manual of Steel Construction, Load and Resistance Factor Design," 3rd Edition, American Institute of Steel Construction, Chicago, IL.

(3) AISC (2002). "Seismic Provisions for Structural Steel Buildings," American Institute of Steel Construction, Chicago, IL.

(4) Astaneh-Asl, A., Goel, S.C., and Hanson, R.D., (1982) "Cyclic Behavior of Double Angle Bracing Members with End Gusset Plates," Research Report UMEE 82R7, Department of Civil Engineering, University of Michigan, Ann Arbor, MI.

(5) Clark, P.W., Kasai, K., Aiken, I.D., and Kimura, I., (2000) "Evaluation of Design Methodologies for Structures Incorporating Steel Unbonded Braces for Energy Dissipation," Proceedings 12th WCEE, Auckland, New Zealand.

(6) Connor, J.J., Wada, A., Iwata, M., and Huang, Y.H., (1997) " Damage-Controlled Structuresl I: Preliminary Design Methodology for Seismically Active Regions," ASCE, Journal of Structural Engineering, Vol. 123, No. 4, pgs 423-31.

(7) Foutch, D.A., Goel, S.C. and Roeder, C.W., (1987) Seismic testing of a full scale steel building - Part I, Journal of Structural Division, ASCE, No. ST11, Vol. 113, New York, pgs 2111-29.

(8) Goel, S.C. (1992). "Earthquake Resistant Design of Ductile Braced Steel Structures," Stability and Ductility of Steel Structures Under Cyclic Loading, edited by Y. Fukumoto and G.C. Lee, CRC Press, Boca Raton, Florida.

(9) Inoue, K., Sawaizumi, S., and Higashibata, Y., "Stiffening Requirements for Unbonded Braces Encased in Concrete Panels, ASCE, Journal of Structural Engineering, Vol 127, No.6, pgs 712-19.

(10) Kahn, L.F., and Hanson, R.D., (1976). "Inelastic Cycles of Axially Loaded Steel Members," Journal of Structural Division, ASCE, No. ST5, Vol. 102, pgs 947-59.

(11) Lee, S., and Goel, S.C., (1987). "Seismic Behavior of Hollow and Concrete Filled Square Tubular Bracing Members," Research Report UMCE 87-11, Department of Civil Engineering, University of Michigan, Ann Arbor, MI.

(12) Popov, E.P. Takanashi, K., and Roeder, C.W. (1976) Structural Steel Bracing Systems, EERC Reprot 76-17, University of California, Berkeley, 1976

(13) Roeder, C.W., (2001) “State of Art Report – Connection Performance”, FEMA 355D, Federal Emergency Management Agency, Washington, D.C.

(14) Roeder, C.W., (2002) "Connection Performance for Seismic Design of Steel Moment Frames," approved for publication, ASCE, Journal of Structural Engineering.


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