PerfBasedSeismicDesign (Edge Buckling)

PERFORMANCE-BASED SEISMIC DESIGN OF BRACED-FRAME CONNECTIONS

Charles Roeder is Professor of Civil Engineering at the University of Washington (UW). He has served on the faculty for 26 years, and he has performed a range of research related to the seismic performance of steel and composite structures.

Dawn Lehman has been an Assistant Professor of Civil Engineering at the UW since 1998. She has completed research projects related to performance based seismic design (PBSD) of bridges and buildings.

Jung Han Yoo is currently a graduate student at the UW. The authors are conducting research to investigate and improve the seismic performance of braced frame gusset plate connections. The study is funded by the National Science Foundation (CMS-0301792).

ABSTRACT

Performance-based seismic design (PBSD) results in structures that meet multiple performance objectives. Special concentrically braced frames (SCBFs) and buckling restrained concentrically braced frames (BRCBFs) are stiff, strong structures which is desirable for serviceability limit states. These systems can be detailed to achieve stable cyclic inelastic response, however different response mechanisms must be considered. With SCBFs, stable cyclic inelastic behavior requires satisfactory post-buckling behavior of the brace. Braces in BRCBFs yield in both tension and compression without buckling and they are expected to readily satisfy inelastic deformation requirements. In both cases, achieving this ideal behavior requires compliant performance of the gusset plate connections used to connect the brace to the frame. A shortcoming of current seismic design provisions for braced frames is the design of the gusset plate connection. Current design provisions attempt to ensure good inelastic connection performance primarily by requiring a connection strength that exceeds the capacity of the brace. However, recent experimental studies suggest that considering only the strength of the connection does not provide stable, reliable performance. Improved connection design procedures are needed.

An analytical and experimental research

study is in underway to develop improved PBSD methods for SCBF and BRCBF connections. The proposed procedures balance desirable yield mechanisms in the brace and connection and restrict undesirable failure modes. To develop reliable design procedures, expressions are needed to accurately predict the yield and failure mechanisms. Initially, an extensive database of past experimental data from braced frame and connection tests is used to evaluate the accuracy of existing models for predicting the yield mechanisms and failure modes of the brace and its connection. These initial results are presented here. Potential design criteria are also discussed and the data from the database is used to demonstrate the variability in existing design methods. In future phases of the research, these proposed design criteria will be evaluated experimentally. The resulting data will be used to develop improved design criteria.

INTRODUCTION

Steel concentrically braced frames (CBFs) are stiff, strong structures which makes them an economical system for seismic design. The inelastic lateral response of the frame is dominated by the post buckling behavior of the braces. Therefore steel braces and braced frames have been studied for many years (e.g., Popov et al. 1976). More recently, research has shown that innovative bracing systems, such as unbonded or buckling restrained braces, hold promise for improved seismic performance. In both cases, the complete response of CBF systems depends on the brace, the connection, and the framing members. Current seismic design provisions are intended to result in a connection strength that exceeds the strength of the brace. These design provisions can result in large, cumbersome connections which limits the inelastic response of the connection and the brace. To achieve a superior level of seismic performance, the design of the connection must be balanced to meet strength and deformation demands while permitting the brace to develop the desired elastic and inelastic performance. An improved seismic framing system can result if the seismic response of the connection, including inelastic action, is considered.

BRACED FRAME BEHAVIOR Special concentrically braced frames (SCBFs) (AISC, 2002) are the most commonly used braced frames

for seismic design. and they develop the majority of their cyclic inelastic deformation capacity through post-buckling deformation of the brace. Brace post-buckling behavior is illustrated in Fig. 1. The brace provides significant lateral stiffness to the steel frame, and so the brace attracts large axial forces during earthquake loading. These axial demands typically cause the brace to buckle in compression and yield in tension, 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 length of the brace after buckling, as a result of second-order (P-δ) effects. These hinges can cause permanent plastic deformations and deterioration of resistance in the brace. After this occurs, significant axial deformation is required to achieve the full tensile stiffness and resistance of the brace (as shown in Zones B-C, C-D and D-E). This behavior leads to one-sided axial force-deflection behavior of the braced seen in Fig. 1a and, as a result of this response mechanism, SCBFs use braces in opposing pairs, which results in the inelastic hysteretic behavior illustrated in Fig. 1c.

Braces are normally joined to the beams and columns of the braced frame through gusset plate connections. Brace post-buckling behavior places significant cyclic load and deformation demands on these connections. These demands depend on the mode of buckling, in-plane or out-of-plane. For example, the deformed shape shown in Zone A-B of Fig. 1b would result in significant end rotations which must be sustained by the connection. With out-of-plane buckling, these end rotations may result in significant deformation demands on the connection. The gusset plate connection behavior depends upon the strength and stiffness of the plate relative to the brace. Theoretically, the brace and the gusset plate will straighten on load reversal (Zone B-C and C-D of Fig. 1b), and this may further exacerbate the inelastic strain demands. Figure 2 shows an example of these end rotation demands. The photograph shows a buckled brace in a steel frame damaged during an earthquake, which demonstrates the large end rotations that can occur during inelastic seismic deformations

Past research shows that SCBFs can provide good seismic performance if the cross-sectional geometry, local slenderness, global slenderness, and connection design are properly controlled (e.g., Kahn and Hanson 1976, Foutch et al. 1987, Astaneh-Asl et al. 1982, Lee and Goel 1987, and Aslani and Goel 1989). As a result of this research, the AISC Seismic Design Requirements for the SCBF system (AISC 2002) define slenderness limits for the brace and different brace geometry and configuration requirements. The design specifications also require that the tensile capacity of the connection be designed to be stronger than the brace capacity, and geometric limits are established in cases of out-of-plane buckling to accommodate the expected end rotation. These design rules lead to the common conception that a stronger, stockier gusset plate connection is better, and some very uneconomical, poor performing connections have resulted. The frame performance suggests the improved connection design philosophies may lead to improved braced frame response.

Figure 1 Behavior of Special Concentrically Braced Frames (Popov et.al. 1976)

Figure 2. Connection Rotation Due to Brace Buckling

To minimize the pinched hysteretic behavior shown in Fig. 1a and 1c and the resulting strength deterioration, innovative unbonded or buckling restrained bracing systems (BRCBFs) have been developed. Unbonded braces are patented braces where the axial member yields in tension and compression without brace buckling. This is accomplished by encasing the slender brace bar with concrete or other fill within the tube to prevent lateral deformation and buckling without bonding the bar to the fill. This assures that the yield strength of the bars is similar in tension and compression which improves axial yield performance. The resulting brace can tolerate large inelastic axial deformations. As a result, unbonded braces are highly regarded by engineers and have been used with increasing frequency in recent design practice. A significant body of research (Clark et al. 2000, Ando et al. 1993, Connor et al. 1997, Inoue et al. 2001) has been completed on their performance, but this research

has primarily focused on axial load and deformation capacities of isolated braces. Figure 3 shows a typical axial force-deformation hysteretic curve for one buckling restrained brace element. The hysteresis curves are full with large energy dissipation and no visible deterioration in stiffness and resistance. As a result, many engineers believe that BRCBFs may provide seismic performance that is far superior to that of traditional bracing systems. However, achieving this idealized performance requires true truss behavior of the brace (i.e., the brace does not sustain an end moment). However, if bending moment demands do result, the brace demands may exceed the connection capacity and the resulting performance may not meet the original design objectives.

Figure 3. Axial Force-Deformation Hysteresis Curve for an Unbonded Brace (Clark et al. 2000)

As with SCBFs, the seismic performance of BRCBFs also depends on the connection design. Figure 4 shows a typical BRCBF connection, and this connection may have significant rotational restraint. BRCBF connections must support the full tensile and compressive force capacities of the brace during cyclic inelastic deformation demands. The connection must have adequate stability and lateral restraint to prevent out-of-plane deformation, and it clearly cannot buckle or fracture prior to the development of the full resistance and ductility of the brace if the idealized behavior shown in Fig. 3 is to be achieved. Rotation or out-of-plane deformation of the BRCBF connection cannot be tolerated, because these actions may restrict development of system resistance and ductility. However, limited yielding in the connection may be acceptable under extreme conditions.

Figure 4. Typical BRCBF Gusset Plate Connection

Design and analysis of BRCBF systems is complicated by the differences between the assumed and actual

frame behavior as depicted in Fig. 5. Buckling-restrained braces have large axial deformation capacity, which is advantageous in meeting to seismic design requirements if the beam-column joints respond as pinned joints as illustrated in Fig. 3b. However, for connections with rotational stiffness, the flexural stiffness of the buckling-restrained brace, including the moment of inertia of the surrounding tube, must be considered. As a result, the deformations of the frame may result in significant bending moments in the gusset plate and the buckling restrained brace due to flexural deformation of the frame as depicted in Fig. 5c. The inelastic deformation demands of the

BRCBF may place large stress and strain demands on the gusset plate connection. These demands are not considered in the connection design and the resulting deformation and strength capacities may be inadequate. Figure 6 is a photograph of a gusset plate in a BRCBF test frame. The gusset plates in this frame are sufficient in that they meet current seismic design provisions. However, the gusset plate buckled early at relatively modest inelastic frame deformations. The buckling restrained brace also buckled because of the resulting connection deformation.

Figure 5. Deformation Mechanisms of BRCBF systems

Figure 6. Photograph of Buckled BRCBF Brace and Gusset Plate

The previous discussion has demonstrated the need to understand and improve the seismic design methods for gusset plate connections in BRCBF and SCBF systems. To ensure proper implementation, reliable design and analysis models are needed which assure that the full performance of the brace can be achieved. However, strength and stiffness values that exceed the design needs or modeling assumptions are not only undesirable, they may lead to undesirable behavior of the brace. Therefore, upper bounds on these properties and properly balancing of the brace and connection yield modes must be specified as well.

PROPOSED IMPROVED SEISMIC DESIGN PROCEDURES FOR BRACED FRAMES

Comprehensive seismic design procedures for seismic design of SCBFs and BRCBFs are needed to provide efficient and economical means of achieving the strength and deformation capacities required in seismic design and rehabilitation. Current SCBF seismic design provisions do not consider the influence of the connection on the brace, and therefore frame, behavior. In addition, these provisions do not recognize the full range of the demands on the connection or the consequence of some connection failure modes, which may have a more adverse consequences than others. Instead, a simplified approach is taken in an attempt to achieve a yielding hierarchy in which tensile yielding of the brace precedes yielding of the connection by requiring that the strength of the connection is larger than the yield capacity of the brace. This simple connection resistance check leads to variable seismic performance which does not assure the most desirable connection behavior nor does it prevent less desirable response modes.

The objective of the proposed research program is to develop improved connection design procedures that ensure the desired performance of the brace and the connection are achieved. The design premise is the balancing of the yield mechanisms of the connection and the brace and the prevention of undesirable failure modes. Yield mechanisms produce significant changes in stiffness and inelastic deformation of the structure without significant loss in resistance while failure modes that result in structural fracture may cause significant loss in resistance and reduced inelastic deformation capacity. Although multiple failure modes may be required to produce complete failure of the connection, a single failure mode can produce a significant reduction in resistance and deformation capacity. Figure 7a summarizes the potential yield mechanisms for both the brace and connection; Figure 7b summarizes the potential failure modes. Proper balance of the yield mechanisms will lead to improved behavior and increased energy dissipation capacity. The desirable yield mechanism balance equation may be idealized as:

Brace Buckling (for SCBF) < Brace Yielding < Connection Yielding < Brace Tearing (Eq. 1)

This design philosophy has been adapted from design procedures that were developed to improve the performance of steel moment resisting frame connections as part of the SAC steel project (Roeder 2001 and 2002). In that project, design procedures were developed to balance desirable yield mechanisms, restrict undesirable failure modes, and achieve the desired seismic performance. During this research, similar types of design procedures are being developed to balance the brace and connection behavior, including explicit methods to restrict connection failure, to improve the performance of braced frame structures.

Figure 7 Yield Mechanisms and Failure Modes of CBF Components

It is possible that improvements could be made to existing SCBF and BRCBF requirements, but these issues have been researched extensively and are not the focus of this research. Instead, this research focuses on improving the connection design to insure good seismic performance of the system and the efficiency of the connection. For a SCBF, the controlling yield mechanisms are expected to be inelastic shortening due to post-

buckling deformation of the brace and tensile yielding of the brace. The axial load capacity of the BRCBF brace will be similar in tension and compression, and the brace should not buckle. In both framing systems, limited local yielding of the gusset plate may be tolerated in rare seismic events, since this behavior may improve the economy of the frame and increase the system inelastic deformation capacity. Possible failure modes for CBFs include tearing or fracture of the brace, net section fracture of the brace or gusset plate, weld fracture of the gusset plate welds, shear fracture of the bolts, block shear, excessive bolt bearing deformation, and buckling of the gusset plate.

The proposed design procedure must address these complex behavior mechanisms while retaining a simple design method. Results from the SAC steel project research (Roeder 2001) have shown that connection should be designed to balance the expected yield resistance of the controlling yield mechanism. This idea can be expressed as Eq. 2 where β is a balance factor.

Cy Fy Ag < β Rn (Eq. 2)

where Rn is the resistance for a single yield mechanism or failure mode, and Ag is the gross cross sectional area of the brace. Cy is a factor for adjusting the nominal yield stress, Fy, to the expected or average yield stress. (The critical buckling stress, Fcr, may be substituted for Fy when brace buckling is the controlling yield mechanisms in SCBFs.) Note that Cy appears as Ry in the AISC Seismic Design Specifications (AISC, 2002), but the notation is changed here to avoid confusion with resistance. The β factor 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 response mode and design equations. However, the factors are fundamentally different in that φ is based upon achieving a probability of failure for a given set of load factors, while β is based entirely upon balancing the expected inelastic seismic behavior mechanisms to achieve the desired seismic performance. A smaller value of β is required when a given failure mode is difficult to predict or has severe undesirable consequences. Larger β values are appropriate for failure modes which do not lead to sudden fracture or abrupt loss of resistance and have more reliable prediction methods. A series of such balance equations can be 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 to balance each yield mechanism and prevent each failure mode, which will provide the desired progression of yielding. The research will result in appropriate β values to balance the yield mechanisms and failure modes to achieve appropriate yielding hierarchies for both SCBF and BRCBF systems.

Development of appropriate β factors to meet the performance requirements requires methods that reliably

predict the relevant yield mechanisms and failure modes of braced frame members and connections. To develop more reliable and improved connection design procedures, models that can predict the connection behavior must be developed and used to correlate the connection behavior to the required performance. The accuracy of various models for prediction connection yielding and failure resistances are unknown. Simple models are inherently limited when post buckling behavior is the expected yield mechanism or a controlling failure mode. For example, simplified buckling calculations assume that the brace and the gusset plates buckle independently using a model of full elastic end restraints. However, the brace and the gusset plate connection are in series, and the response of one may affect the buckling capacity of the other. These coupled buckling modes may result in significantly smaller buckling capacity than predicted by independent buckling calculations.

The objective the first phase of the research program, described herein, is to evaluate the accuracy of

existing connection design models. The following describes the initial research results which are based on existing experimental data. The results are used to evaluate existing design methods originally develop to calculate the capacities of gusset plate connections. Based on those results, the existing methods were modified to improve the predictions. These models will then be used to develop a first-generation expression that meets the balance conditions for braced frame systems.

PAST EXPERIMENTS ON GUSSET PLATE CONNECTIONS

With both the SCBF and BRCBF frames the controlling yield mechanism will be related to the tensile and

compressive yield (or buckling) capacity of the brace. Accurate models for predicting the failure mode resistance,

Rn, for each connection failure mode are required to achieve the balance requirement of Eq. 2. Experimental data can be used as a tool to verify the accuracy and reliability of these models. Experimental evidence as to the expected consequence of each failure mode on the gusset plate connection performance is also needed to establish the β values required for each failure mode. A number of past experiments on braced frame gusset plate connections have been performed, and this experimental data is a logical starting point for the detailed research study. Most past experimental studies considered monotonic loading, but nearly all possible failure modes have been observed in these past test programs.

Hu and Cheng (1987) examined the elastic buckling behavior of thin gusset plate connections. The effects of gusset plate thickness, geometry, boundary conditions, eccentricity and reinforcement were examined experimentally and analytically. Brown (1988) complete 24 gusset plate connection tests where the variation in failure mode was noted as a function plate slenderness, brace inclination angle, and bracing type. Yam (1994) and Yam and Cheng (2002) performed experiments where inelastic gusset plate buckling was noted. The above tests were all monotonically loaded, and they examined alternate design methods for evaluating connection performance.

Cyclic gusset plate connection tests also were performed (Bjorhovde and Chakrabarti, 1985, Rabinovitch and Cheng, 1993, and Grondin et al., 2000). Tests by Rabinovitch and Cheng and Grondin and others were inelastic cyclic load tests typical of seismic deformation. Bjorhovde and Chakrabarti (1985) examined the behavior of gusset plates when the brace was in both tension and compression, but the focus was stress and strain fields and monotonic connection behavior as opposed to ductility and failure modes. The cyclic tests commonly had gusset plate buckling, but tensile tearing or fracture after inelastic deformations also occurred. One study suggested that inelastic deformation provided by gusset plate buckling may be beneficial to in design, since significant energy was dissipated during the cyclic inelastic deformation. However, some specimens failed in tension at the net section of the gusset plate or in the plastically deformed area at relatively small axial deformations. Itani and Dietrich, 1999) tested double gusset plated connections, but these are not of primary interest to this work.

The above tests constitute a substantial body of experimental data on gusset plate connection performance. Further, a significant number of additional gusset plate test results are available from gusset plate failures noted in brace buckling experiments (Astaneh-Asl et al., 1982, El Tayeb, 1985). Most of these later tests experienced tensile tearing of the gusset plate or welds after inelastic bending of the gusset plate to permit brace end rotation during the brace buckling cycle. Table 1 summarizes this combined body of data. A wide range of failure modes and behaviors are noted. Many failure modes such as buckling of the gusset plate result in significant reduction in resistance after buckling occurred, but actual tearing or fracture of the gusset plate occurred in tensile load after significant inelastic strains had occurred.

Table 1. Summary of Gusset Plate Test Results Specimen

ID Brace

Section Length of Brace (in)

Gusset Plate Size

(inxin)

Thickness (in)

Whimore width (in)

Failure Mode Reference

1 2C8x11.5 20.5 15x15 0.251 9.196 Free edge buckling Brown (1988)



4 2C8x11.5 20.5 15x15 0.379 9.196 No failure Brown (1988)




8 2C4x7.25 17.5 15x15 0.188 8.66 Test stopped Brown (1988)




12 2C8x11.5 20.5 15x15 0.377 9.196 Buckling of brace Brown (1988)









21 2C8x11.5 20.5 15x15 0.378 9.196 Not failed Brown (1988)

22 2C4x7.25 17.5 15x15 0.379 8.66 Braces buckled Brown (1988)

23 2C4x7.25 17.5 15x15 0.378 8.66 Connection failed Brown (1988)

24 2C4x7.25 17.5 15x15 0.376 8.66 Connection failed Brown (1988)

FR C1 W250x58 33.5x21.6 0.263 22.36 Buckling of gusset Cheng (1987,1994)




FX C1 W250x58 33.5x21.6 0.263 22.36 Free edge buckling Cheng (1987,1994)




FR E5 W250x58 33.5x21.6 0.263 22.36 Yielding of splice plate at the last row of bolts

Cheng (1987,1994)

FR E6 W250x58 33.5x27.6 0.263 22.36 Yielding of splice plate at the last row of bolts

Cheng (1987,1994)

FRS E5 W250x58 33.5x21.6 0.263 22.36 Yielding of splice plate at the last row of bolts

Cheng (1987,1994)

FRS E6 W250x58 33.5x27.6 0.263 22.36 Buckling of gusset Cheng (1987,1994)

FXS E5 W250x58 33.5x21.6 0.263 22.36 Yielding of splice plate at the last row of bolts

Cheng (1987,1994)

FXS E6 W250x58 33.5x27.6 0.263 22.36 Buckling of gusset Cheng (1987,1994)

GP1 19.7x15.8 0.524 12.22 Sway buckling of the gusset

Yam (1994)

GP2 19.7x15.8 0.386 12.22 Sway buckling of gusset Yam (1994)

GP3 19.7x15.8 0.256 12.22 Sway buckling of gusset Yam (1994)

GP1R 19.7x15.8 0.524 12.22 Free edge buckling Yam (1994)



SP1 33.5x27.6 0.524 18.59 Sway buckling of gusset Yam (1994)

SP2 33.5x27.6 0.386 18.59 Sway buckling of gusset Yam (1994)

AP1 19.7x15.8 0.524 12.22 Sway buckling of gusset Yam (1994)



MP1 19.7x15.8 0.524 12.22 Sway buckling of gusset Yam (1994)



MP3A 19.7x15.8 0.256 12.22 Sway buckling of gusset Yam (1994)

MP3B 19.7x15.8 0.256 12.22 Sway buckling of gusset Yam (1994)

EP1 19.7x15.8 0.524 12.22 Yielding of splice plate Yam (1994)



A-1 W250x67 21.6x17.7 0.367 15.40 Net section fracture of gusset

Rabinovitch (1993)


Rabinovitch (1993)


Rabinovitch (1993)

A-4 W250x67 21.6x17.7 0.243 15.40 Net section fracture of Rabinovitch (1993)

gusset A-5 W250x67 21.6x17.7 0.367 15.40 Net section fracture of

gusset Rabinovitch (1993)

T-1 W250x49 43.3 17.7x21.6 0.374 Buckling of gusset plate Grondin (2000)

T-2 W250x49 43.3 17.7x21.6 0.378 Buckling of gusset plate Grondin (2000)

T-3 W250x49 206.7 17.7x21.6 0.373 Buckling of brace Grondin (2000)

T-4 W250x49 206.7 17.7x21.6 0.375 Buckling of brace Grondin (2000)

Brace Tests with Gusset Plate Failure AW10 2L3x2x1/4 142 0.5 8.9 Fracture of Gusset Astaneh-Asl (1982)

AW14 2L31/2x21/2x1/2 142 0.75 8.2 Fracture of stitch & gusset Astaneh-Asl (1982)

AW16 2L31/2 x21/2x1/2 142 0.75 8 Fracture of gusset Astaneh-Asl (1982)

ABS8 2L31/2 x21/2x1/4 142 0.375 9.3 Fracture of gusset plate Aslani (1989)

AW0 L21/2x 21/2x1/4 71 0.4375 5.4 Fracture of gusset at base El-Tayem (1985)

AW3 L21/2x 21/2x5/16 71 0.4375 5.6 Fatigue fracture of gusset at the end of brace

El-Tayem (1985)

AW4 L21/2x 21/2x3/16 71 0.3125 5.3 Buckling of gusset plate Yamamoto (1988)

DESIGN MODELS FOR PREDICTING GUSSET PLATE PERFORMANCE Design models were developed from past research studies, and some studies compared computed

resistances to past experimental results. However, the relative accuracy of the various models has not been determined, and comparisons of individual models to experimental results have only been made for a limited family of test results. The first goal of this research program was to evaluate existing models, determine the most reliable models, and improve and simplify these models where possible. These existing models are briefly summarized here.

Several design models for braced frame gusset plate connections have been proposed. These models build

upon the basic concept of the Whitmore section (Whitmore, 1950). The Whitmore section postulates that the axial force of the brace can be distributed as a uniform stress over a defined width of the gusset plate as illustrated in Fig. 8a. The Whitmore method limited this uniform stress to the yield stress and distribution of the stress to the plate was permitted over the length of the bolt group at a 30o distribution angle as shown in the figure. This method is clearly deficient in predicting the compressive buckling failure mode of the gusset plate, since it does not consider the reduced buckling stress that occurs with slender elements. Further, steel design normally relates tensile failure to the ultimate tensile stress, Fu, of steel over a net section rather than the yield stress, Fy. Thornton (1991) adapted the Whitmore model so that it could address gusset plate buckling as well as tensile failure. The Thornton model used the Whitmore width and an average effective buckling length of the plate over this width to estimate compressive load capacity as illustrated in Fig. 8b. For this buckling calculation, the gusset plate was treated as an imaginary strip column with the rectangular cross section defined by the Whitmore width and the average length based on three measured length locations as shown in the figure. This effective length was measured from the centerline of the last row of bolts in the gusset plate connection, and an effective length coefficient of 0.65 was employed. This effective length coefficient essentially assumes that the effective length of the gusset plate is nearly fully restrained against rotation at each end, and sidesway buckling is prevented.

The Modified Thornton method as illustrated in Fig. 8c was proposed as an improvement to the Thornton

method. This method uses a modified Whitmore width, which is defined by a 45o projection angle as illustrated in Fig. 8c. This angle results in a larger width and a greater gusset plate capacity. However, the effective length for buckling of the gusset plate is taken as a single length of the plate along the centroidal axis of the brace from the end of the brace overlapping the gusset plate as shown in Fig. 8c. Other design models have been proposed for design of the gusset plate in tension and compression. Brown (Brown 1988) proposed a gusset plate model based upon the unsupported edge length as illustrated in Fig. 9. Astaneh-Asl (Astaneh-Asl, 1989) proposed another design model which uses another variation of this unsupported edge concept. All of these methods employ an effective width, and variations of the Thornton method are the most commonly used in engineering practice.

Figure 8. Typical Design Models for Gusset Plate Design

Figure 9. Unsupported Edge Length Concept of the Brown and Astaneh-Asl Models

Figure 7 shows that other gusset plate connection failure modes may occur. Bolt shear, bolt bearing, and

block shear failures are possible. Analytical methods for these failure modes are reasonably well understood. Generally the brace force is assumed to be uniformly distributed to all bolts, except for the special case of individual bolts with very close edge distance. Past gusset plate connection test results have not demonstrated a large number of these failure modes, but these failure modes (and the corresponding design assumptions) have been observed and evaluated in many other types of bolted connections. For example, bolted flange plate and bolted T-stub moment resisting beam-column connections have demonstrated these failure modes (Roeder, 2001, Swanson et al., 2000). In general, bolt shear can be relatively sudden and abrupt failure, but it is also predictable with reasonable accuracy and reliability except for very large bolt groups. Block shear and bearing failures are accompanied by significant local inelastic deformation, and the measured capacity typically exceeds the computed resistance. Only limited discussion of these failure modes is provided here for these reasons.

Tensile net section fractures of the brace at the last row of bolts away from the beam-column junction has

been noted in a number of braced frame connections. Net section failure of the gusset plate may also occur at the first row of bolts away from the beam-column junction. Failure at these location may be more likely to occur with the SCBF gusset plates, because brace buckling may induce large local inelastic strains in the region of this net section, because of out-of-plane brace buckling deformation. This failure has been observed in brace buckling tests with cyclic axial loading as noted in Table 1. In general, it is expected that the nominal resistance due to this failure is of the form

Rn = C Fu An (Eq. 3)

where Fu is the ultimate tensile strength of the steel, An is the area of the net section, and the constant C represents the variability of the tensile stress over the cross section of the brace and possible deterioration of the net section resistance caused by prior local inelastic deformation at the net section location.

Weld fractures of the gusset plate have been noted in some tests as shown in Table 1, but it is clearly not commonly noted in past test studies. The stress in the weld is relatively difficult to predict. The AISC LRFD Specification proposes several methods for estimating this weld force distribution, but they can produce significantly different results. This weld stress issue will be a focus of this research study, but little consideration has been given to this failure mode in this paper.

ANALYSIS OF PREVIOUS EXPERIMENTAL RESEARCH RESULTS Table 1 shows that there are significant test data for braced frame gusset plate connections, and a number of

failure modes are documented in these tests. The first part of this table shows results from tests that examined gusset plate failure modes. The later part of the table shows tests that had significant gusset plate failures, but the objectives of these tests were primarily to address brace post buckling and other behaviors. Prior discussion has noted that there is considerable variability in the models used to predict gusset plate connection behavior. Analysis of this past test data was completed, and the results were compared the alternate design models to evaluate the accuracy and reliability of simple models that may be used to predict brace frame and gusset plate connection performance.

Table 1 shows that gusset plate buckling is a primary modes of failure, and so detailed comparisons of the

various models to these experimental results are provided. The basic Thornton, Brown and Astaneh-Asl design models were initially compared to the measured experimental results. Figure 10 shows the measured connection resistance divided by the predicted resistance of the Astaneh-Asl and Brown models for past experimental results. The ratio is plotted for all gusset plate connections with gusset buckling failure modes of the first part of Table 1 as a function of the kl/r ratio for the gusset plate. The ratio is greater than 1.0 when a conservative prediction is provided, and it is less than 1.0 when the model predicts a resistance that is smaller than that observed in the tests. The Brown and Astaneh-Asl models provide good comparisons for some test series, but they show significantly more variability than the Thornton models. In addition, the Thornton models is more commonly used in engineering practice. As a result, the reliability and accuracy of the Thornton models are the focus of this paper. The Thornton model also has scatter in the measured performance, but it is small compared to other two models. Figure 11 shows the measured connection resistance divided by the predicted resistance by the Thornton method. This figure shows that the Thornton model is quite conservative in estimating the gusset plate buckling capacity. On average, the experimental gusset plate resistance is 1.542 times the predicted Thornton buckling resistance, and the standard deviation the ratio, σ, is 0.195. Several factors may affect this conservatism. An increase in the 30o projection angle used to develop the effective Whitmore width would significantly increase the effective area of the gusset plate, and this would reduce the conservatism of the buckling capacity estimate. Reductions to the effective length of the gusset plate would also reduce the conservatism of the estimate, but it is difficult to rationally do this, because the Thornton model assumes nearly rigid end conditions.

The Modified Thornton method uses a larger projection angle and a slightly modified effective length, and

so this model was examined as a possible improvement to the performance estimates. Figure 12 shows the failure ratio for this Modified Thornton method with these same bucking gusset plate test results. The Modified Thornton method is still on average conservative, since the average ratio is 1.113 and σ is 0.149, but the conservatism is less extreme. The prediction is unconservative in a few cases, but the unconservative predictions primarily occur with very slender gusset plates, which are less common in seismic design. The mean and standard deviation values suggest that 89% of the gusset plates designed by the Modified Thornton method will have larger resistance than the computed capacity. From an LRFD strength design perspective the Modified Thornton method is quite attractive. However, PBSD is based upon the concept that we predict the behavior accurately. Conservatism is not desirable, because it leads to erroneous estimates of the failure mode for the structural system and erroneous predictions of the structural performance. Ideally, PBSD would be based upon an average ratio of measured to predicted resistance of 1.0 and a σ approaching zero. As a result, further adaptations of the Modified Thornton method were examined.

Figure 10. Comparison of the Astaneh-Asl and Brown Models to Past Experimental Results

Figure 11. Accuracy of the Thornton Model as a Function of Slenderness Ratio

A Modified Modified Thornton method was proposed. This method retains the 45o

projection angle for the modified Whitmore section as used in the Modified Thornton method, but it uses an average buckling length as employed with the basic Thornton method. The reasoning for this is that the average length may be significantly shorter than the centroidal length with some gusset plate geometries, and this shorter length will increase the buckling capacity of those gusset plate connections. Figure 13 shows an evaluation of this Modified Modified Thornton model. This model is a more accurate and reliable model for predicting gusset plate buckling behavior. The mean ratio for the buckled gusset plates described in the first part of Table 1 and Figs. 11 and 12 is 1.067 and the standard deviation is 0.142. This Modified Modified Thornton method provides a computed buckling resistance that is closer to the experimental value and it provides a smaller standard deviation of the observed performance. Further revisions to this model are under consideration. The model appears to overestimate the connection resistance primarily for larger slenderness ratios, and underestimate the resistance for slender plates. A slender gusset plate implies a thin gusset plate. A thin gusset plate is less able to distribute the stress uniformly over a wide width because of shear lag. As a result, it would be rational to expect that very thin gusset plates employ a

smaller modified Whitmore width (or distribution angle), because of this shear lag effect. This and other comparisons are presently under consideration in the research study.

Figure 12. Accuracy of the Modified Thornton Model as a Function of Slenderness Ratio

Figure 13. Accuracy of the Modified Modified Thornton Model as a Function of Slenderness Ratio

While the Modified Modified Thornton method compares well with past gusset plate connection test results, Fig. 13 also shows cause for concern when designing gusset plates for seismic design of braced frames. The gusset plate connections provided in the first part of Table 1 are all connections where the brace does not buckle or sustain significant inelastic deformation. In these tests, the brace sustained axial loading only, and the brace, beam, and out-of-plane movements are severely limited or restricted by the test setup. Earlier discussion describes seismic force and deformation demands in actual BRCBF and SCBF structural systems. Within these real systems, the brace experiences significant tensile and compressive yielding and may experience post buckling compressive deformation. Actual gusset plate connections may have significant rotational restraint, and this rotational restraint may induce significant bending moments into the gusset plate when frame deformations and eccentricities are considered. These factors may have a significant impact upon the buckling capacity of actual gusset plate connections. The 3 circled data points in Fig. 13 illustrate this. These three data points are preliminary data points (Tsai, 2003) from a recent full scale 3 story braced frame test completed at the National Center for Research in Earthquake Engineering in Taipei, Taiwan. A full scale 3-bay, 3-story, braced frame with buckling restrained braces was subjected to inelastic, seismic deformations. Gusset plates buckled (see Fig. 6) at each of the three

stories at relatively small inelastic deformations, and the gusset plate buckling led to buckling of the BRCBF braces. This resulted in dramatic reductions in the anticipated BRCBF performance. Only limited data is now available from this test program, but an initial analysis of these gusset plates indicate that they buckled at a compressive load that was between 40% and 60% of the predicted capacity by the Modified Modified Thornton method. The cause of this buckling requires further investigation, but this behavior strongly indicates the importance of considering the full seismic demands during the gusset plate connection design.

A wide range of other failure modes are possible with braced frame gusset plate connections. Simplified design models for these alternate connections are also being investigated to determine the accuracy and reliability of the model for PBSD. Tensile failure modes such as:

• net section fracture of the brace net section, • fracture of the gusset plate net section, • tearing of the gusset plate in the region where large inelastic rotations in the gusset plate occur due to

brace buckling, and • weld fracture of the gusset plate

are of particular interest, because these failure modes may result in dramatic loss of resistance and brittle performance. Many such failures were noted in braced frame connection tests, and gusset plate connection failures noted in the bottom portion of Table 1 are of interest in the evaluation of these later failure modes. These failure modes are based upon tensile yield stress and ultimate tensile stress, and the design models consider net section where required. Figure 14 shows an initial comparison of the ratio of the measured connection resistance to the resistance predicted by simplified design calculations. This figure shows that there is again scatter in the test results, and the scatter is particularly large with slender brace elements. the comparison shows that the basic models for predicting tensile failure appear to be reasonably conservative for stocky brace elements. The estimated resistance may be quite unconservative for very slender braces. Fracture of the net section of the gusset plate and the gusset plate are particularly susceptible to reduced strength with slender braces. This may occur because slender braces place large deformation demands on the gusset plate when brace buckling occurs. These gusset plate deformation demands are concentrated into a small locations, and large cyclic inelastic strains may occur.

Figure 14. Model Comparison for Other Failure Modes

Brace buckling is an essential element of PBSD for the SCBF system. The ability to predict the brace

buckling load and to estimate the maximum tensile capacity in the brace after brace buckling has occurred are also important to PBSD for this system. Hundreds of brace buckling experiments have been performed, and the buckling loads obtained in these experiments have been compared to the measured buckling load in Fig. 15. This figure includes all brace buckling tests with adequate data to describe the buckling load, test specimen geometry, materials, and boundary conditions. The ultimate measured compressive load of the brace divided by the AISC predicted

buckling load of the specimen are shown in the figure, and the final failure mode of the brace or connection are identified in the graph. There is considerable variation in the ability of the models to predict the maximum buckling resistance achieved in these past experiments. In all cases, buckling occurred, and it is logical to expect that the AISC design equations with resistance factors removed would provide a realistic estimate (a ratio of approximately 1.0) of the maximum compressive load. This scatter is important in the design of SCBF frames because it shows that there is considerable uncertainty in the prediction of the brace buckling load, and this buckling load is a critical element in the prediction of the yield mechanisms for the frame. This inaccuracy is largely caused by uncertainty in the effective length coefficient, K, of the brace rather than uncertainty in the AISC design equations. The K-factor depends on an accurate assessment of the end restraint which depends on the gusset plate connection stiffness and restraint.

Figure 15. Comparison of Measured Brace Buckling Loads to Predicted Brace Buckling Loads

These comparisons demonstrates the importance of evaluating the seismic deformation demands of SCBF

systems as well as BRCBfs. The combined discussion of the Taiwan tests and these other failure modes illustrate the importance of recognizing the full seismic demands in gusset plate connection design.

FUTURE DIRECTIONS This research work is in progress and will continue for the next two years. The ultimate goal of the

research is development of consistent and reliable PBSD procedures for braced frame gusset plate connections. This will be done by developing and verifying 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 will be assessed. Balance conditions necessary to assure that the proper combination of behaviors are achieved in practice will then be developed. The proposed connection design procedure will be evaluated experimentally. The 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 16. The goal to test approximately 25 specimens. One will evaluate the expected performance with the existing SCBF design requirements [AISC (2002)] and will serve a reference specimen for that framing system. A second reference specimen will model a braced frame connection in a BRCBF. The remaining specimens will evaluated the proposed braced frame connection design criteria for SCBF and BRCBF systems.

Figure 16 Schematic of Proposed Test Assembly

A load frame will be constructed and attached to the laboratory strong floor as depicted in Figure 16. The specimen will consist of end gusset plates attached to a brace. The frame will be constructed to permit multiple tests from a single frame. This configuration should result in reasonable economy in fabrication and installation of specimens, while insuring 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.

ACKNOWLEDGEMENTS

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 Manager for this research. This financial support is gratefully acknowledged.

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