Design of a Seismic-Resistant Self-Centering Concentrically-Braced Frame and Experimental Test Structure Ryan Ahn Pennsylvania State University at University Park REU Institution: Lehigh University REU Advisors: Dr. James Ricles and Dr. Richard Sause Graduate Student Mentors: Nathaniel Gonner and David Roke

Abstract The goals of the Self-Centering Concentrically-Braced Frame (SC-CBF) project are to achieve the performance based design criteria of creating a building frame that achieves Immediate Occupancy (IO) performance when subjected to a Design Basis Earthquake (DBE) seismic event, and achieves Life Safety (LS) performance when subjected to a Maximum Considered Earthquake (MCE) seismic event. These goals are accomplished by allowing gaps to open at the base of selected frame columns. These gaps are then closed using post tensioning bars that run the height of the structure. To date a test frame has been designed which calls for gusset plates to connect the braces to the columns and beams. The design of these gusset plates explored several different design criteria for positioning the brace on the gusset. These included a conventional 2tp linear clearance model as well as an 8tp elliptical model which had been proposed by researchers at the University of Washington. In the end the more conventional model was chosen due to its advantages of allowing for smaller gusset plates in almost every instance and the cases in which they did not there was not a significant size difference. The gussets were also checked for several different failure modes including: tension, compression, interaction, and block shear. Finally a completed test structure has been designed and will be constructed and tested within the next year.

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Table of Contents Abstract ......................................................................................................................................................... ii Table of Contents ......................................................................................................................................... iii Chapter 1 Introduction ................................................................................................................................. 1 1.1 General ................................................................................................................................................ 1 1.2 Motivation Behind the Project............................................................................................................ 1 1.3 Performance Based Design ................................................................................................................. 1 1.3.1 Seismic Performance Levels ......................................................................................................... 1 1.3.2 Seismic Hazard Levels .................................................................................................................. 3 1.3.3 SC-CBF Performance Based Design Criteria ................................................................................. 4 Chapter 2 Self-Centering Frames .................................................................................................................. 5 2.1 The Self-Centering Concept: ............................................................................................................... 5 2.2 Self-Centering Concentrically-Braced Frame (SC-CBF) ....................................................................... 5 Chapter 3 The Test Structure ........................................................................................................................ 7 3.1 Design of the Test Structure ............................................................................................................... 7 3.2 Scaling ................................................................................................................................................. 7 3.3 Final Component Dimensions ............................................................................................................. 7 Chapter 4 Gusset Plates ................................................................................................................................ 9 4.1 Design of Gusseted Connections ........................................................................................................ 9 4.2 Standard Clearance ............................................................................................................................. 9 4.3 Elliptical Clearance ............................................................................................................................ 10 4.4 Gusset Analysis ................................................................................................................................. 13 4.4.1 Compression Check .................................................................................................................... 14 4.4.2 Compression/Moment Interaction Check ................................................................................. 15 4.4.3 Tension Check ............................................................................................................................ 16 4.4.4 Tension/Moment Interaction Check .......................................................................................... 16 4.4.5 Block Shear Check ...................................................................................................................... 17 4.5 Final Gusset Plate Designs ................................................................................................................ 17 Chapter 5 Final Design and Further Work .................................................................................................. 19 5.1 Final Structure Design ....................................................................................................................... 19

5.2 Further Work..................................................................................................................................... 20 References .................................................................................................................................................. 21 Acknowledgements..................................................................................................................................... 22

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Chapter 1 Introduction 1.1 General This paper presents research conducted on self-centering concentrically braced-frame (SC-CBF) systems. This research was conducted as part of a larger project investigating a variety of selfcentering damage-free seismic-resistant steel frame systems. The research so far has consisted of the design of a test structure which seeks to test and validate the SC-CBF concept. 1.2 Motivation Behind the Project One of the most important issues facing structural engineers in the US is the effect of seismic forces. There have been great leaps in our understanding of how seismic forces enter buildings and what happens to the buildings as they resist these forces. The Network for Earthquake Engineering Simulation research project investigating self-centering systems has the long term goal of designing and testing performance-based designs for building support structures that would allow a building to be immediately occupied after an earthquake. While previous systems were designed to keep a building standing after an earthquake in order to allow its occupants to survive, they were not specifically designed to allow the building to be occupied in the future, without extensive overhauls of the underlying support structure. This is extremely costly, due to the cost of repairs and the economic impact of not being able to use the structure. 1.3 Performance Based Design Performance based design (PBD) is an alternative to standard strength-based design in which performance objectives are specified according to structural limit states. For seismically active areas it is customary to use FEMA450 standards (BSSC 2003) to define performance objectives. FEMA450 identifies four seismic performance levels and several different earthquake hazards. 1.3.1 Seismic Performance Levels There are four different performance levels that can be used to characterize the level of protection for a building. They are: (1) operational (O), (2) immediate occupancy (IO), (3) life safety (LS), and (4) collapse prevention (CP). As defined by FEMA450 (BSSC 2003), O performance is as follows. “*T+he operational level represents the least level of damage to the structure. Structures meeting this level when responding to an earthquake are expected to experience only negligible damage to their structural systems and minor damage 1

to nonstructural systems. The structure will retain nearly all of its preearthquake strength and stiffness and all mechanical, electrical, plumbing, and other systems necessary for the normal operation of the structure are expected to be functional. “ FEMA 450 does not recommend designing for this standard as it is difficult to achieve while remaining economical. For this reason the SC-CBF will not try to achieve this standard. The next level of performance is the IO performance level, which is defined as follows. “The immediate occupancy level is similar to the operational level although somewhat more damage to nonstructural systems is anticipated. Damage to the structural systems is very slight and the structure retains all of its pre-earthquake strength and nearly all of its stiffness. Nonstructural elements, including ceilings, cladding, and mechanical and electrical components, remain secured and do not represent hazards. Exterior nonstructural wall elements and roof elements continue to provide a weather barrier, and to be otherwise serviceable. The structure remains safe to occupy; however, some repair and clean-up is probably required before the structure can be restored to normal service. In particular, it is expected that utilities necessary for normal function of all systems will not be available, although those necessary for life safety systems would be provided.” Since the building “retains all of its pre-earthquake strength and nearly all of its stiffness,” the SC-CBF project will use this level as a minimum design goal. LS is the next performance level and FEMA 450 (BSSC 2003) describes this as follows. “At the life safety level, significant structural and nonstructural damage has occurred. The structure may have lost a substantial amount of its original lateral stiffness and strength but still retains a significant margin against collapse. The structure may have permanent lateral offset and some elements of the seismicforce-resisting system may exhibit substantial cracking, spalling, yielding, and buckling. Nonstructural elements of the structure, while secured and not presenting falling hazards, are severely damaged and cannot function. The structure is not safe for continued occupancy until repairs are instituted as strong ground motion from aftershocks could result in life threatening damage. Repair of the structure is expected to be feasible, however, it may not be economically attractive to do so. The risk to life during an earthquake, in a structure meeting this performance level is very low.” This performance level will also be used in the project as a minimum design standard due to the fact that it is obtainable through current frame designs.

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The final performance level that has been defined is CP, which according to FEMA450 (BSSC 2003) is as follows. “At the collapse prevention level a structure has sustained nearly complete damage. The seismic-force-resisting system has lost most of its original stiffness and strength and little margin remains against collapse. Substantial degradation of the structural elements has occurred including extensive cracking and spalling of masonry and concrete elements and buckling and fracture of steel elements. The structure may have significant permanent lateral offset. Nonstructural elements of the structure have experienced substantial damage and may have become dislodged creating falling hazards. The structure is unsafe for occupancy as even relatively moderate ground motion from aftershocks could induce collapse. Repair of the structure and restoration to service is probably not practically achievable.” The goal of the SC-CBF is to avoid needing major structural repair and to allow the building to continue active use, so this level will not be used extensively for this project. Figure 1.1 graphically depicts the different performance levels and what a building might look like at each performance stage.

Figure 1.1 Depictions of Various FEMA450 Seismic Performance Levels (Taylor)

1.3.2 Seismic Hazard Levels

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In addition to protection levels, FEMA 450 (BSSC 2003) also defines three earthquake hazard levels, that are considered in this research: the design basis earthquake (DBE), the maximum considered earthquake (MCE), and the maximum probable event (MPE). A MCE is defined as a ground motion intensity that has a 2% probability of exceedence in 50 years, corresponding to a 2500-year return period. This would be a “reasonable representation of the most severe ground motion ever likely to affect a site.” A DBE is defined as a ground motion intensity that is two-thirds that of the maximum considered earthquake. The DBE has a return period of about 500 years. A MPE is defined as a ground motion intensity that has a 50% probability of exceedence in 50 years, corresponding to a 72-year return period. Often called a frequently occurring earthquake (FOE), this type of earthquake is often used to judge a structures ability to withstand frequent smaller events. This intensity is not used in the design criteria for the SC-CBF, because it is assumed that most current frame designs can withstand this level. 1.3.3 SC-CBF Performance Based Design Criteria The two major goals of the project are to achieve IO performance under a DBE load and to achieve LS performance under a MCE load. Table 1.1 (Roke 2008) further illustrates the specific objectives that have been established to determine if these levels have been exceeded.

Table 1.1 Summary of Performance Objectives (Roke 2008) Limit States Hazard Levels Performance Column PT Bar Member Member MPE DBE MCE Level Decompression Yielding Yielding Failure O x x IO x x x x LS x x x x x x

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Chapter 2 Self-Centering Frames 2.1 The Self-Centering Concept: The concept of self-centering frames is a relatively new idea that attempts to achieve performance based design by trying to soften lateral drift without inelastic deformation of structural members. This is achieved by allowing gaps to open at selected post-tensioned connections. These gaps then close, after the force is removed from the structure, due to the post tensioning re-centering the frame. Unlike in a traditional frame, energy dissipation is not due to damage of main structural members but from energy dissipating (ED) devices that dissipate energy due to friction or deformation of the devices.

2.2 Self-Centering Concentrically-Braced Frame (SC-CBF) The SC-CBF is similar to standard CBFs in that it consists of columns and beams that are braced together in a usual manner with the braces running from the lower column-beam interface to the midspan of the above beam (Figure 2.1a). However the SC-CBF also has post tensioning (PT) bars that allows the column to lift off its base under lateral loads. The frame configuration that will be used for this project includes two sets of columns: an outer set of gravity columns from the other bays of the building and an inner set of SC-CBF columns that experience the gap opening at the base. There is post-tensioning bars at midbay that permit self-centering after the lateral force is removed. This process can be seen in Figure 2.1

Figure 2.1 SC-CBF system: (a) schematic of members and loads; (b) elastic response prior to column decompression; (c) rigid-body rotation after column decompression. (Sause) 5

In addition to allowing the columns to uplift, there is also some ED device that allows energy to be dissipated due to friction or element deformation. An example of such a device is seen in Figure 2.2. This device is the actual friction device that will be used for this project. It is located between the SC-CBF columns and the gravity columns, and uses a series of friction bolts and plates to dissipate energy.

Figure 2.2 Energy dissipation device detail

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Chapter 3 The Test Structure 3.1 Design of the Test Structure Using the PBD objectives defined for the project, a prototype structure was designed using the International Building Code and ASCE7 by David Roke. It was then modeled in OpenSEES for nonlinear structural analysis. This information was then used to design an appropriate test structure which required scaling due to size limitations. 3.2 Scaling One of the most important considerations involved in the design of the test structure was the size of the test facility. This limitation dictated that a four story structure such as the one that was decided on needed to be constructed at three fifths scale. This meant that every member in the structure had to be scaled to three fifths its original size. This included not only length and width, but also area moment of inertia (I) and section modulus (S). Using the AISC Steel Construction Manual to find the original values each of these properties were scaled. After calculating the ideal characteristics for each member that had been called for in the initial design calculations, a member that was approximately the same size as the ideal characteristics was chosen. However, since steel is manufactured in standard shapes it was impossible to choose a member that exactly satisfied all the scaled properties. This led to some variation in the design of the scaled test specimen with respect to the full-scale prototype. However the scaled members provided a starting point for the test structure making the design process more efficient. An example of a scaled member is presented in Table 3.1. Table 3.1 Member Scaling

Column 1st Story 1st Story Scaled 1st Story New Difference

Section W14X370 W10x112

Area (in2) Depth(in) 109 39.24 32.9 -19.27%

17.9 10.74 11.4 5.79%

Ixx (in4)

Sxx (in3)

Iyy (in4)

Syy(in3)

5440 705.024 716 1.53%

607 131.112 126 -4.06%

1990 257.904 236 -9.28%

241 52.056 45.3 -14.91%

3.3 Final Component Dimensions After scaling was completed and the structure underwent some further structural analysis, final member dimensions were decided upon. These can be seen in Table 3.2. Note that one column size and one beam size were picked for the entire height of the structure. This was done strictly to simplify the design and is not necessarily the best choice for all structures. 7

SC-CBF Components Component Story W-Section Length (ft) 1 W8X48 11.7 2 W8X35 10.6 Brace 3 W8X48 10.6 10.6 4 W8X58 1 W10X112 9 2 W10X112 7.5 Column 3 W10X112 7.5 7.5 4 W10X112 7.5 1 W12X50 7.5 2 W12X50 Beam 7.5 3 W12X50 7.5 4 W12X50 7.5 Strut 4 W8X48 Table 3.2 SC-CBF Components

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Chapter 4 Gusset Plates 4.1 Design of Gusseted Connections Gusset plates will be used to connect the braces to the columns and beams. There were several considerations when designing the plates. In general we wanted to limit the size of the plates to make the most economical design possible. One consideration was the minimum amount of material would be kept between the plate edge and the brace. This distance is shown as d1 in Figure 4.1.

Figure 4.1 Brace Location

The bare minimum for d1 was the size of the weld. However to ensure that there would not be an issue when welding in the event that the brace was not aligned precisely, and to simplify the process a gap of 1.5 inches was used on all plates. The next consideration was the length of the weld connecting the plate to the brace. This was dictated by the design criteria of the structure and was provided by Nate Gonner and David Roke. Finally it was decided that the gussets would not be tapered to further simplify the process. The process of defining the size and thickness of gusset plates follows.

4.2 Standard Clearance Standard gusset plate connection design is dictated by the design criteria of the AISC Uniform Force Method (UFM) (AISC, 2005a) and the AISC Seismic Design Provision (AISC, 2005b). There are several different methods of determining brace positioning for gusset plates that will resist seismic loading. The generally accepted method, as dictated the AISC Seismic Design Provision (AISC, 2005b), is to allow a separation greater than two times the plate thickness (tp) between 9

the end of the brace and an imaginary line parallel to the end of the brace that includes the nearest corner of the gusset plate. This is illustrated in Figure 4.2. The purpose of the gap is to allow for the end of the brace to rotate. If there was no gap the rotation at the end of the brace may be impeded by the column or beam. Based on this geometry the length of the beam and column connections were determined.

2tp Clearance

Figure 4.2 Standard 2tp Linear Clearance (Roeder and Lehman, 2006)

4.3 Elliptical Clearance The current provisions which call for a 2tp linear clearance can result in rather large, stiff gusset plates according a University of Washington paper (Roeder 2008). An alternative to this for seismic loads has been proposed by Professors Roeder and Lehman of the University of Washington. The alternative that they proposed is to use an 8tp elliptical clearance model which uses an ellipse that is 8tp from the end of the brace, curving into the corners of the plate, as seen in Figure 4.3. According to their research this results in smaller plates.

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8tp Clearance

Figure 4.3 Alternative 8tp Elliptical Clearance (Roeder and Lehman, 2006)

Using the formulas that were developed by Roeder and Lehman it is possible to calculate the size of the gusset plate. From their research the calculations should proceed as follows. All of the calculations refer to Figure 4.4.

Figure 4.4 8tp Elliptical Clearance (Roeder and Lehman, 2008)

After establishing an initial guess for a gusset plate size, the radii of the ellipse can be established as:

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;

(4-1)

then (4-2)

Finding ρ allows y` and x` to be found using the Equations (4-3) and (4-4):

(4-3) and (4-4)

This gives the exact clearance dimensions for the brace if the brace were to have no depth, but since the brace has a depth it is necessary to then approximate the needed dimensions using the following formulas.

(4-5)

and (4-6)

which finally yields

(4-7)

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Due to the nature of the equations, it was necessary to iterate to determine the final dimensions. That is, first a starting gusset plate size was chosen and the size was adjusted to figure out the smallest possible gusset plate.

After calculating the size of each gusset using both the standard 2tp linear model and the alternate 8tp elliptical model and comparing the two sets of gussets it was determined that the standard 2tp linear gussets were better for our force and magnitude configuration, due to the fact that they were either smaller than or roughly the same size as the 8tp elliptical gussets in every case. The thickness of the gussets was the same for both standards, but the height and width of the plates designed using the 2tp criterion were significantly smaller. This can be seen in the Figure 4.5 below which shows the third story gusset plates. The plates on the left were created using the 8tp elliptical standard and the ones on the right were created using the more conventional 2tp standard. When viewed this way it is obvious that the 2t p standard is a better choice for this project. In addition to providing little size reduction the elliptical clearance model required far more calculations and thus was impractical and time consuming. Elliptical

Standard

Figure 4.5 Third Floor Gusset Comparison

4.4 Gusset Analysis Each gusset was subjected to a variety of checks using AISC standards and equations to verify its strength and to determine the required gusset plate thickness (AISC 2005a). Each check was done starting with a thickness that was an eighth of an inch larger than the weld size to account for the amount of material needed to allow for a sound weld. If the strength checks failed, the plate thickness was increased and the checks were repeated. These checks included a compression check, a compression / moment interaction check, a tension check, a tension / 13

moment interaction check and a block shear check. Throughout the calculations a Whitmore section was used to determine to effective section of the plate. The Whitmore section was calculated by taking a thirty degree angle from the start of the weld to the end of the weld. This was done on each side of the connection. The enclosed area by these two points is the Whitmore section. This can be seen in Figure 4.6.

Figure 4.6 Whitmore Section 4.4.1 Compression Check The first check that was conducted was a check to see if the gusset plate would fail in compression. First the Euler buckling stress was calculated using the following equation:

(4-8)

Next it was determined if the gusset underwent elastic or inelastic buckling using the following inequality. If it is true it will be subject to inelastic buckling. In all cases the gusset would experience inelastic buckling:

(4-9) 14

Given that this is true the critical buckling stress is calculated by the following eqation. If Equation 4-9 had been false an alternate equation would have been used.

(4-10)

As per AISC provision E1 criterion the design compressive strength for Load Resistance Factor Design (LRFD) is nine tenths the nominal compressive strength, so if: (4-11) the plate will not fail in compression. 4.4.2 Compression/Moment Interaction Check To understand the interaction between the compressive force and the moment exerted on the gusset plate, the plate was modeled as a rectangular bar. Thus the interaction present is that for a doubly-symetric, single axis flexural member. Therefore, the yield moment was calculated a follows: (4-12)

If

the plastic moment is calculated by: (4-13)

If not then it is calculated by: (4-14) The momement capacity is determined using the following equation:

(4-15)

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Where

. If it is greater than Mp:

(4-16)

Finally the interaction is checked using the following equation, which if true means the gusset will not experience an issue with the interaction of compression and momement:

(4-17)

4.4.3 Tension Check The next check that was performed was a tension check to make sure the plate did not fail in tension. The first thing cheked was to make sure the plate did not experience gross section yeild (GSY). To check this the GSY capacity was checked using the AISC provison D2-1 (AISC 2005a): (4-18)

If the GSY capacity is greater than the tension demand then the section will not yield. After it was determined that GSY was not an issue for a given thickness of plate the next check that was perfomed was whether or not it would experience net section fracture (NSF). This was done by using the AISC table D3.1 to calculate effective area, then using the following equation to calculate the NSF capacity:

(4-19)

If this is greater then the tension demand than the gusset will not fail under tension.

4.4.4 Tension/Moment Interaction Check

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The intereraction between the tensile force and the moment was checked to make sure that these two did not intereract in a way that would cause the system to fail. This was done by calculating the nominal moment capacity (Mn), then using inequality (4-20), which if true meant the plate was sufficently thick to not cause issues between the tension and moment.

(4-20)

4.4.5 Block Shear Check The next check that was performed was to check for failure because of block shear. Block shear is the failure due to the tearing of a block of material. It involves either a combination of tension rupture and shear yield or a combination of shear rupture and tension yield. This check was done by first caculating the shear area using the following equation: (4-21)

This was used to calulate the nominal shear strength (Rn) using the following equation:

(4-22)

This is then multipiled by φ (0.75 for LRFD) and if the shear demand is less than this value the gusset will not suffer failure from block shear.

4.5 Final Gusset Plate Designs After completing the above mentioned design procedure the eight gusset plate designs necessary for the construction of test structure, the gusset plates are shown below in Figure 4.7 (note that dimensions of individual gussets are listed in Table 4.1):

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Figure 4.7 Gusset Plates Table 4.1 Final Gusset Plate Dimensions Story

Location

Beam

Brace

"tp"(in)

Fourth Fourth Third Third Second Second First First

Center End Center End Center End Center End

W12X50 W12X50 W12X50 W12X50 W12X50 W12X50 W12X50 W18X55

W8X58 W8X58 W8X48 W8X48 W8X35 W8X35 W8X48 W8X48

1.25 1.25 1 1 0.75 0.75 1 1

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Welds and Lengths (in) W1 0.6875 0.6875 0.625 0.625 0.4375 0.4375 0.625

0.625

L1 6 6 5 5 6 6 5 5

L2 21.25 21.625 18.0625 18.5 19.125

L3 23 21 24.125 19.0625 25.25

19.1875

19.75

16.25 19.625

19.875 19.6875

Chapter 5 Final Design and Further Work 5.1 Final Structure Design The final test structure with gusset plates and critical dimensions is pictured in Figure 5.1.

Figure 5.1 The SC-CBF Test Structure

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5.2 Further Work There is still a great deal of work to be done on the SC-CBF. First of all the design of the test structure must be finalized. While a great deal has already been done, the incomplete tasks include: Determining the positioning of ED elements Determining the positioning and detailing of hydraulic actuators to push the structure Designing a base structure to support the test structure After the design is completed a testing plan will be developed and the results of the tests analyzed to determine how well the structure performed. Finally a plan to distribute the results of this research to the structural engineering community at large will be developed. This research could then be incorporated into the existing codes and could potentially provide substantial economic impact if it could to be used on the building that was subject to seismic loading.

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References AISC (2005a). Steel Construction Manual, 3rd Edition. American Institute of Steel Construction, Chicago, IL. AISC (2005b). Seismic Provisions for Structural Steel Buildings, American Institute of Steel Construction, Chicago, IL. BSSC. (2003). “The 2003 NEHRP Recommended Provisions For New Buildings And Other Structures Part 1: Provisions (FEMA 450)”, Washington, D.C. Hamburger, R. (2007). "Codes and Standards for Performance-Based Design," Proc. of Sessions of the 2007 Structures Congress”, Long Beach, California, USA. ICC (2000). International Building Code, International Code Council, Washington, DC. Roeder, C., Lehman D., Johnson D., Herman D., and Yoo J. (2006). “Seismic Performance of SCBF Braced Frame Gusset Plate Connections,” Proc. Of Sessions of the 4th International Conference on Earthquake Engineering”, Taipei Taiwan. Roeder, C and Lehman D. (2008). “Seismic Design and Behavior of Concentrically Braced Steel Frames,” Structure Magazine February 2008, 37-9. Roke, D. (2008 in preparation). “Un-Titled” Ph.D. thesis, Civil Engineering Dept., Lehigh University, Bethlehem, Pennsylvania. Sause, R., Ricles, J., Roke, D., Seo, C-Y., and Kyung-Sik Lee, K-S. (2006). “Design of Self-Centering Steel Concentrically-Braced Frames,” Proc. Of Sessions of the 4th International Conference on Earthquake Engineering”, Taipei Taiwan. Taylor Devices Inc. (2008). http://www.taylordevices.com

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Acknowledgements I would like to thank the people that made this project possible. I would like to thank the National Sience Foundation and the Network for Earthquake Engineering Simulation for the funding the provided for the project. Also I would like to thank the project PIs, Professors Ricles and Sause and the REU coordinator Gary Novak, as well my co-workers and the graduate students. I would like to especially thank my mentors Nate Gonner and Dave Roke for all the guidance and help.

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