Large-Scale Experimental Evaluation of Post-Tensioned

Large-Scale Experimental Evaluation of Post-Tensioned Coupled Shear Wall Systems

for Seismic Regions

Structural Engineering Research Report

Civil and Environmental Engineering and Earth SciencesUniversity of Notre Dame

Notre Dame, Indiana

January 2015

S.M. Barbachyn, Y.C. Kurama, and M.J. McGinnis Report #NDSE-2015-01

EAST

-4 40

0

2500(560)

tota

l bas

e sh

ear

forc

eV

tota

l [k

N (k

ips)

]

average 3rd floor drift, Δ3 (%)

-2500(-560)

loadingeast

loadingwest

measuredpredicted

approx. roof driftΔr = +4.35%

Specimen 2

approx. roof driftΔr = -3.22%

approx. roof driftΔr = +3.25%

approx. roof driftΔr = -4.10%

slab

minimalcracking

concentratedcrack at end

coverspalling

beam damage stateafter θb,max=10.5%

piercoupling

beam

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Large-Scale Experimental Evaluation of Post-Tensioned Coupled Shear Wall Systems

for Seismic Regions

Structural Engineering Research Report

Civil and Environmental Engineering and Earth SciencesUniversity of Notre Dame

Notre Dame, Indiana

January 2015

bySteven M. BarbachynUniversity of Notre Dame

Yahya C. Kurama

Report #NDSE-2015-01

University of Notre Dame

Michael J. McGinnisUniversity of Texas at Tyler


TABLE OF CONTENTS

ACKNOWLEDGMENTS .............................................................................................. iii ABSTRACT ..................................................................................................................... iv CHAPTER 1: INTRODUCTION .....................................................................................1 1.1 Overview ........................................................................................................................1 1.2 Research Objectives .......................................................................................................2 1.3 Project Scope .................................................................................................................2 1.4 Project Significance .......................................................................................................3 1.5 Organization of Report ..................................................................................................4 CHAPTER 2: BACKGROUND .......................................................................................5 2.1 Previous Research ..........................................................................................................5 2.2 ACI Validation Requirements........................................................................................6 CHAPTER 3: FULL-SCALE PROTOTYPE STRUCTURE ........................................9 3.1 Prototype 8-Story Structure ...........................................................................................9 3.2 Design Methodology ....................................................................................................10 CHAPTER 4: ANALYTICAL MODELING & EXPERIMENTAL PROGRAM ....13 4.1 Analytical Model .........................................................................................................13 4.2 Pre-Test Validation ......................................................................................................16 4.3 Experimental Program .................................................................................................17 4.3.1 Analytical Simulation ...............................................................................................17 4.3.2 Specimen Loading ....................................................................................................18 CHAPTER 5: TEST SPECIMEN 1 ...............................................................................20 5.1 Specimen Detailing ......................................................................................................20 5.2 Instrumentation ............................................................................................................23 5.3 Measured Behavior ......................................................................................................24 5.3.1 System Behavior .......................................................................................................25 5.3.2 Damage at Completion of Test .................................................................................27 5.3.3 Coupling Beam Behavior ..........................................................................................30 5.3.4 DIC Results ...............................................................................................................33 CHAPTER 6: TEST SPECIMEN 2 ...............................................................................36 6.1 Specimen Detailing ......................................................................................................36 6.2 Instrumentation ............................................................................................................40 6.3 Measured Behavior ......................................................................................................40 6.3.1 System Behavior .......................................................................................................40 6.3.2 Damage at Completion of Test .................................................................................43 6.3.3 Coupling Beam Behavior ..........................................................................................44 6.3.4 DIC Results ...............................................................................................................49

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CHAPTER 7: SUMMARY OF RESULTS AND REMAINING WORK...................54 7.1 Comparisons with ACI ITG-5.1 Validation Requirements .........................................54 7.2 Comparisons with Design Predictions .........................................................................55 7.3 Main Findings and Conclusions...................................................................................56 7.4 Remaining Work ..........................................................................................................59 REFERENCES .................................................................................................................61 LIST OF TECHNICAL REPORTS ...............................................................................63

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ACKNOWLEDGMENTS

Funding for this research was provided by the National Science Foundation (NSF) under Grant No. CMMI 1041598 as a part of the “George E. Brown, Jr. Network for Earthquake Engineering Simulation (NEES) Research (NEESR).” This award is a part of the National Earthquake Hazards Reduction Program (NEHRP). Support of the NSF Program Director Dr. J. Pauschke is gratefully acknowledged. This project was a collaborative effort that included the University of Notre Dame, the University of Texas at Tyler, and Lehigh University. At the University of Texas at Tyler, students M. Lisk and M. Holloman worked on the development of the multiple digital image correlation sensor protocol. At the Lehigh University NEES equipment site, laboratory staff (C. Bowman, P. Bryan, D. Fritchman, T. Marullo, G. Novak, and E. Tomlinson), faculty members (R. Sause, S. Pakzad, and J. Ricles), graduate students (K. Kazemibidokhti, K. Peterson, G. Shahidi, and M. Tillotson), REU students (A. Breden, M. Davis, E. Salazar, and F. Tao), and other undergraduate students (K. Brinkhoff and C. Fallon) worked on the construction, instrumentation, and testing of the coupled wall specimens. The design of the test specimens was conducted in collaboration with practicing engineers from Magnusson Klemencic Associates (D. Fields, A. Haaland, and J. Mouras). The contributions of K. Bondy, consulting structural engineer, to the project are also acknowledged. Construction of the specimens was made possible through material donations from the following companies: Essroc Italcementi Group, Hayes Industries, Ltd., Sumiden Wire Products Corporation, A.H. Harris & Sons, Inc., Suncoast Post-Tension, Dayton Superior, and Casilio Concrete. The opinions, findings, and conclusions expressed in this report are those of the authors and do not necessarily reflect the views of the NSF or the other organizations/individuals acknowledged above.


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ABSTRACT

The seismic design, analysis, and large-scale experimental evaluation of a novel multi-story coupled shear wall system with post-tensioned coupling beams are presented. In this new system, high-strength unbonded post-tensioning (PT) strands are used to couple (i.e., link) reinforced concrete (RC) shear wall piers for primary lateral load resistance in building structures. Reversed-cyclic quasi-static testing of two 40%-scale coupled wall specimens with the proposed details was conducted to evaluate the system according to the requirements of the American Concrete Institute (ACI). The laboratory specimens represented the most critical bottom three stories of an eight-story prototype structure, consisting of two C-shaped wall piers, six coupling beams (two beams at each floor level), tributary slabs at each floor, and the foundation. The other (less critical) regions of the eight-story structure were simulated analytically. Overall, both test specimens performed well and significantly better than conventional RC coupled shear wall structures. The specimens achieved ductile behavior through the completion of three full cycles exceeding the “validation-level” lateral roof drift prescribed by ACI, thus demonstrating the classification of these structures as “special” RC shear walls. In addition to a dense array of conventional sensors, the deformations of the specimens were monitored using up to 14 two- and three-dimensional digital image correlation (DIC) sensors, providing unprecedented near-full-field response data of the most critical regions of the structures. Ultimately, the high-fidelity data from these tests support the ACI validation of the design procedures and modeling/prediction tools for the use of post-tensioned coupled shear wall structures as primary lateral load resisting systems in moderate and high seismic regions of the U.S.


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CHAPTER 1: INTRODUCTION

1.1 Overview Reinforced concrete (RC) coupled shear wall structures are common primary lateral load resisting systems for medium and high-rise buildings in regions of moderate and high seismicity. The typical coupled wall system consists of two or more vertical wall piers connected by relatively short and deep beams (called coupling or link beams) at the floor and roof levels. Properly designed and detailed coupled walls can provide large strength, stiffness, and energy dissipation under lateral loads; however, the design and construction of the coupling beams are challenging due to the presence of large reversed-cyclic rotation demands under large shear forces. To meet these demands in a ductile manner, the primary reinforcement for typical RC coupling beams in seismic regions consists of two intersecting groups of large diagonal reinforcing bars [Fig. 1.1(a)] passing through the beam and anchored into the wall piers (Barney et al. 1978; Tassios et al. 1996; Bristowe 2000; Galano and Vignoli 2000; Adebar et al. 2001; Kwan and Zhao 2002; Canbolat et al. 2005; Wallace 2007; Fortney et al. 2008). This conventional system is difficult to construct and can experience considerable damage under seismic loading despite being detailed according to ACI 318 (2011) design requirements.

In comparison, the primary reinforcement in the coupling beams of the proposed system consists of unbonded post-tensioning (PT) strands placed in one or two tendons near the beam centroid, greatly simplifying construction [Fig. 1.1(b)]. The use of post-tensioning to couple RC shear walls represents a significant innovation and transformation, but one that can be realistically achieved by utilizing the widely-used post-tensioned floor slab construction technology. The lateral deformations in a post-tensioned coupling beam occur primarily in the form of concentrated cracks at the ends, rather than distributed cracks over the entire span, resulting in reduced damage as the structure displaces during a large earthquake. After the earthquake, the PT tendons provide a restoring force that closes the cracks and pulls the structure back toward its undeformed, plumb position.

(a) (b)

Figure 1.1 RC coupling beams: (a) diagonally reinforced beam (courtesy, Magnusson Klemencic Associates); (b) post-tensioned beam [with energy dissipating

(ED) mild steel bars]

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The single major barrier to the use of post-tensioned coupled shear wall structures in seismic regions is the lack of experimentally-validated design methods, construction procedures, and numerical simulation models for multi-story structures. Previous tests on the use of this technology are limited to isolated floor-level coupling beam subassemblies (Kurama et al. 2006; Weldon and Kurama 2007, 2010, 2012). To fill this knowledge gap, two large-scale physical laboratory experiments integrated with computer simulations of multi-story coupled wall structures were conducted as part of this NEESR project. The coupled wall specimens were built and tested at the NEES laboratory site operated by Lehigh University. In addition to a dense array of conventional sensors (load cells, strain gauges, displacement/rotation transducers), the deformations of the laboratory specimens were monitored using up to 14 two- and three-dimensional digital image correlation (DIC) sensors, providing unprecedented near-full-field response data of the most critical regions in the wall piers, floor slabs, and coupling beams. Ultimately, the results from this research project support the implementation of post-tensioned coupled wall structures as “special” RC shear walls in medium and high seismic regions of the U.S. in accordance with the evaluation and validation requirements set forth by the American Concrete Institute (ACI).

1.2 Research Objectives Addressing the research need on the seismic design, analysis, and behavior of multi-story RC coupled shear wall systems with post-tensioned coupling beams, the primary objectives of this project were to develop:

(1) a validated seismic design procedure for the new system; (2) validated analytical models and design tools that can accurately predict

performance; (3) sufficient experimental and analytical evidence demonstrating the

classification of these structures as “special” RC shear walls per ACI 318 (2011); and (4) practical seismic guidelines and recommendations summarized in a Design

Procedure Document that includes a full-scale numerical design example.

1.3 Project Scope To meet the research objectives above, experimental tests of two 40%-scale post-tensioned coupled shear wall structures were conducted. The required validation criteria used in the experiments were adapted from ACI ITG-5.1 (2007), which provides guidelines for the seismic testing and assessment of unbonded post-tensioned precast concrete shear walls, including coupled wall systems. The Equivalent Lateral Force (ELF) procedure from ASCE/SEI 7 (2010) was used to determine the design forces for an 8-story prototype structure that formed the basis of the 40%-scale test specimens. Existing seismic design methods and guidelines were utilized as much as possible to facilitate the adoption of the new system in practice. The structure was designed to be

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ductile up to a validation-level roof drift of 3.0% per ACI ITG-5.1 requirements, but with little over-capacity in force or displacement so as to critically assess the limits of the design procedure, tools, approximations, and assumptions. The design procedure included specific steps to determine the PT steel areas, confined concrete detailing in the coupling beams, and mild steel areas and locations in the wall piers to satisfy the performance requirements. Some of the reinforcement detailing guidelines were adapted from the design recommendations for post-tensioned precast concrete shear walls in ACI ITG-5.2 (2009). To validate the design methodology, selected design parameters were varied between the two test specimens. The two primary parameters were: (1) coupling beam depth; and (2) use of energy-dissipating (ED) mild steel reinforcement crossing the beam-to-wall joints (i.e., partially post-tensioned versus fully post-tensioned coupling beams). The test specimens included the first three floors, tributary post-tensioned floor slabs, and the foundations of the 8-story prototype building. This represented the most critical regions of the structure where the nonlinear behavior in the wall piers was expected to concentrate and the axial and shear forces in the coupling beams were expected to be the largest. The less critical upper 5 stories of the prototype structure were modeled analytically. The primary lateral load resisting system consisted of two C-shaped wall piers with two coupling beams at each floor level. The inclusion of the floor slabs and the foundation in the test specimens allowed for the designs of both the wall-to-foundation joints and wall-to-slab joints to also be assessed. Per ACI ITG-5.1, a pre-test analytical study was conducted to evaluate the design and expected performance of the proposed coupled shear wall system. The DRAIN-2DX (Prakash et al. 1993) structural analysis program was used to construct the numerical models, which formed the basis for the pre-test and post-test analyses of the two specimens. Comparisons between the predicted and measured behaviors of the specimens were used to validate and refine (as necessary) the analytical models after each test. Additionally, the validated models provided further insight into the behavior of these structures beyond what could be measured in the laboratory. 1.4 Project Significance This research project was a joint effort between the University of Notre Dame, University of Texas at Tyler, and Lehigh University. It also included an advisory group of practicing engineers to ensure the design and testing of realistic structures. The goal was to arrive at structures with significantly simpler detailing and improved seismic behavior as compared to conventional RC coupled shear wall systems, but otherwise consistent with current design and construction methods in order to facilitate the rapid adoption and implementation of the new system in practice. As previous experimental work related to this project is limited to isolated floor-level coupling beam subassemblies, the research presented herein on multi-story systems represents a significant and relevant contribution to the design of earthquake-resistant post-tensioned coupled shear wall structures. Ultimately, the experimental and analytical results from the research will be organized into a validated Design Procedure Document. This document will contain

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design and analysis guidelines to be used by practicing structural engineers for the implementation of the new system in moderate and high seismic regions of the U.S. The eventual adoption of this system in practice would lead to improved construction economy and better mitigation of losses from future earthquakes. 1.5 Organization of Report The remainder of this final project report is organized as follows: Chapter 2 – Background: An overview of previous research on RC coupled shear walls and post-tensioned coupling beams is provided, followed by a summary of the applicable ACI code validation requirements. Chapter 3 – Full-Scale Prototype Structure: The design and layout of the full-scale prototype structure that formed the basis for the laboratory experiments is described.

Chapter 4 – Analytical Modeling and Experimental Program: A nonlinear fiber-element analytical model for multi-story post-tensioned coupled shear wall structures is presented, including pre-test validation of the model using previous test results of a conventional RC coupled wall structure. The experimental program and laboratory setup used to evaluate the new system are also described.

Chapter 5 – Test Specimen 1: The first test specimen with partially post-tensioned

coupling beams is discussed. The results from this experiment led to revised design recommendations for the second test specimen.

Chapter 6 – Test Specimen 2: Details on the second specimen with fully post-

tensioned coupling beams are presented, including results from the experimental evaluation.

Chapter 7 – Summary of Results and Remaining Work: This chapter provides a

summary and conclusions from the research to date, including an overview of the remaining work.

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CHAPTER 2: BACKGROUND

This chapter presents background information relevant to the project. An

overview of previous research on RC coupled shear walls and post-tensioned coupling beams is provided, followed by a summary of current ACI code validation requirements. 2.1 Previous Research To date, no large-scale tests are available on RC coupled shear wall structures with post-tensioned beams beyond the experimental evaluations described herein. However, as part of this research project, a simplified, small-scale (15%-scale) specimen was built and tested at the University of Texas at Tyler to validate the multiple DIC monitoring approach (McGinnis et al. 2013). This is the first known test of a multi-story post-tensioned coupled shear wall system. All other previous tests have been limited to isolated floor-level subassemblies. Weldon and Kurama (2007, 2010, 2012) conducted a series of subassembly experiments in which each specimen included a post-tensioned precast concrete coupling beam and the adjacent RC wall pier regions at 50% scale. The results from these experiments demonstrated the advantages of post-tensioned coupling beams, showing that properly-designed beams outperformed monolithic cast-in-place RC beams with diagonal reinforcement found in the literature (Barney et al. 1978; Tassios et al. 1996; Bristowe 2000; Galano and Vignoli 2000; Canbolat et al. 2005). Additional tests of diagonally-reinforced concrete coupling beams, beyond those used for comparison in Weldon and Kurama (2010), can be found in Adebar et al. (2001), Kwan and Zhao (2002), Wallace (2007), and Fortney et al. (2008). Building on the results from the previous floor-level subassembly experiments of post-tensioned coupling beams, system-level multi-story experimental evaluations are needed to address some of the limitations inherent in the subassembly tests. The primary limitations are: 1) the underestimation of axial restraint on the coupling beams (i.e., wall piers in a multi-story system are stiffer and more restraining, especially near the foundation); and 2) the exclusion of floor slabs. The testing of the two large-scale multi-story structures described in this report directly addresses these limitations. The experimental evaluations also inform on the interaction between the wall pier bases and the foundation in a coupled shear wall system. Weldon and Kurama (2012) present a nonlinear analytical model that accurately predicted the behavior of isolated floor-level subassemblies of post-tensioned coupling beams. In this model, fiber beam-column elements are used to represent the wall pier regions as well as the coupling beams. Three truss elements with initial tensile forces to simulate the PT force are connected at the beam-to-wall interfaces to model each beam PT tendon. This analytical model is used as the basis for the development of a multi-story coupled wall analytical model for the proposed system in Chapter 4. Previous research on the testing of conventional multi-story RC coupled shear wall systems is limited to structures with planar or T-shaped wall piers, conventional

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reinforcement in the coupling beams, and no large, integrated floor slabs (Santhakumar 1974; Shiu et al. 1981; Ozselcuk 1989; Turgeon 2011; Lequesne et al. 2013; Lehman et al. 2013). As such, the experimental evaluations of the new system with post-tensioned beams, C-shaped wall piers, and tributary post-tensioned floor slabs in this report represent a number of firsts in structural engineering research. An experiment by Aktan and Bertero (1984) featured a similar loading setup to the one used in this project. In the previous experiment, a conventional 4-story planar RC coupled shear wall specimen was tested. The 1/3-scale specimen represented the most critical regions (bottom 4 stories) of a taller (15-story) building, with four vertical actuators to apply overturning moments and axial forces at the top of the wall piers. Due to the similarities in loading approach, the results from Aktan and Bertero (1984) provided a basis for validating the pre-test analytical models for the new coupled shear wall system with post-tensioned beams. Another important reason for selecting this previous experiment for the pre-test validation in the current study was the availability of measured results for the base shear forces in the individual wall piers, in addition to the total base shear force for the coupled structure. 2.2 ACI Validation Requirements According to Chapter 21 of ACI 318 (2011), the new shear wall system with post-tensioned coupling beams investigated in this research requires experimental validation and analysis prior to its use in practice. Specifically, the ACI 318 building code states that the evaluations must demonstrate that “the proposed system shall have strength and toughness equal to or exceeding those provided by a comparable monolithic reinforced concrete structure satisfying this chapter.” To satisfy this requirement, ACI ITG-5.1 prescribes a testing methodology and recommended structure performance limits for post-tensioned precast concrete shear walls, including coupled walls. This document was adopted to evaluate and validate the new system. ACI ITG-5.1 requires the development of a design procedure for the structure prior to experimental testing. The design procedure shall ensure that the structure can achieve the prescribed validation-level lateral drift in a ductile manner with sufficient energy dissipation. Requirements regarding the specimen testing procedure per ACI ITG-5.1 include the following: (1) each specimen shall be subjected to a sequence of lateral displacement cycles; (2) three fully-reversed cycles shall be applied at each lateral drift angle; (3) the initial drift angle shall be applied within the essentially linear-elastic response range for the specimen; and (4) testing shall continue with gradually increasing drift angles (between 1.25 and 1.5 times the preceding set of cycles) until the drift angle equals or exceeds the validation-level drift defined as:

(1)

where, hw is the height to the top of the wall piers and lw is the length of a pier. For coupled walls, hw/lw in Eq. (1) is taken as the smallest value of hw/lw for any of the individual wall piers being coupled. The wall drift, Δw is defined as the lateral displacement at the top of the wall piers divided by the pier height measured from the top

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of the foundation. Based on the definitions above and the dimensions of the prototype structure, the validation-level drift used in the design and experimental evaluations in this research report is Δwm=3.0%. According to ACI ITG-5.1, the test specimen has demonstrated satisfactory performance when the following criteria are met for both directions of loading (i.e., positive and negative drift directions):

(1) The overall peak lateral strength in each direction of loading is at least 90% and not greater than 120% of the probable peak lateral strength calculated using the pre-test design procedure.

(2) In cycling to the validation-level drift, significant strength degradation shall not occur. For any sequence of three cycles beyond the drift angle achieved at the measured overall peak lateral strength of the structure, the measured peak lateral strength during any of those subsequent three cycles shall not be less than 80% of the overall peak lateral strength in that loading direction.

(3) For cycling at a drift angle equal to or greater than the validation-level drift, the relative energy dissipation ratio, βh, for the 3rd drift cycle shall not be less than 0.125.

(4) For cycling at a drift angle equal to or greater than the validation-level drift, the secant stiffness between drift angles of -1/10 and +1/10 of the maximum applied drift angle shall be not less than 10% of the initial lateral stiffness (as defined by ACI ITG-5.1) in each direction of loading.

(5) The maximum relative horizontal displacement between the base of the wall piers and the foundation shall not exceed 1.5 mm (0.06 in.).

(6) At a displacement one half of the validation-level drift, the stress in any unbonded PT strand shall not exceed 90% of the measured stress of the PT steel at 1% elongation.

ACI ITG-5.1 defines the relative energy dissipation ratio, βh, as “the ratio of measured energy dissipated by the test module during reversing cyclic displacements between given measured drift angles to the maximum theoretical energy that can be dissipated for the same drift angles.” As shown in Fig. 2.1, βh is taken as the ratio of the hatched area within the measured hysteresis loop to the area within the dashed parallelograms. More information on the above acceptance criteria can be found in ACI ITG-5.1.

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Figure 2.1 Relative energy dissipation ratio, βh (adopted from ACI ITG-5.1)

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CHAPTER 3: FULL-SCALE PROTOTYPE STRUCTURE

A full-scale 8-story RC prototype building was designed to form the basis for the

40%-scale post-tensioned coupled shear wall test specimens. An overview on the design of this prototype structure is given in this chapter. 3.1 Prototype 8-Story Structure

The full-scale 8-story prototype structure was designed for an office building located in a site in Los Angeles, California with seismic response coefficients (ASCE/SEI 7-10) of Cs = 0.136g and Cs = 0.154g for Specimens 1 and 2, respectively. The plan and elevation views of the structure are shown in Figs. 3.1(a) and 3.1(b), respectively. The coupling beam depth was 610 mm (24 in.) for Specimen 1 [as shown in Fig. 3(b)] and 813 mm (32 in.) for Specimen 2, representing typical coupling beam geometries found in U.S. construction. The primary lateral load resistance was provided by a coupled core wall at the center of the building, consisting of two C-shaped RC shear walls connected by two post-tensioned coupling beams at each floor and roof level. The center core included two slab openings to simulate the elevator shafts and stairwells in the office building. These slab openings were centered inside the core to prevent any significant asymmetric behavior during testing. The widely-used unbonded post-tensioned RC slab technology was used for the floor slabs. The configuration, dimensions, and detailing of the prototype structure were chosen with the assistance of practicing engineers from Magnusson Klemencic Associates (MKA) in Seattle, Washington. The design strengths of concrete, mild steel, and PT steel were taken as f’c=41.4 MPa (6 ksi), fsy=469 MPa (68 ksi) [assuming typical material over-strength for Grade 420 (Grade 60) steel], and fpu=1862 MPa (270 ksi), respectively.

(a) (b) Figure 3.1 Prototype structure (full-scale): (a) building plan; (b) wall elevation

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3.2 Design Methodology To facilitate the adoption of the new system in practice, the detailing requirements in Chapter 21 of ACI 318 (2011) were used to design the reinforcement for the C-shaped wall piers. This included the confinement hoops at the toes of the piers, which also extended into the foundation. Similarly, ACI 318 specifications were used to design the post-tensioned floor slabs, but with some alterations to the mild steel reinforcement near the coupling beams. The beam shear reinforcement was designed and detailed according to the requirements in Sections 11.3 and 11.4 of ACI 318; however, new specifications were needed to design the beam axial-flexural reinforcement. These specifications included a procedure for selecting the steel areas across the beam-to-wall joints as well as providing adequate concrete confinement reinforcement at the beam ends. Some of the design guidelines presented in ACI ITG-5.2 (2009) for unbonded post-tensioned precast concrete shear walls were used in the design of the prototype structure. For example, confined concrete detailing guidelines for the toes of precast concrete shear walls were adapted for the confinement hoops at the ends of the post-tensioned coupling beams.

To facilitate direct comparisons, both test specimens were designed based on similar overall coupled wall design forces for the prototype structure. These seismic design forces were calculated using the Equivalent Lateral Force (ELF) procedure from ASCE 7-10 together with a response modification factor of R=6.0 for “special” RC shear walls within a building frame system (as defined by ASCE 7-10). A modal analysis of the prototype building was done using ETABS (CSI 2005) to determine the fundamental periods of the structure as T=0.74 s and T=0.65 s for Specimens 1 and 2, respectively. The ELF procedure resulted in a design total base moment, Mtotal, and total base shear force, Vtotal, which were distributed to the components of the coupled wall for both test specimens by making a number of design selections. First, a coupling degree of Rc=0.30 was chosen for both specimens, meaning that 30% of the design base moment was to be carried by the coupling action between the two wall piers. Second, the remaining total base moment was distributed evenly between the tension-side and compression-side piers resulting in the following moment relations:

(2)

(3)

where, Mc=base moment contribution from the coupling action, M1=tension-side wall pier base moment, and M2=compression-side wall pier base moment. Third, the coupling moment was then distributed to the post-tensioned coupling beams as a design shear force as follows:

(4)

where, Nc=axial force at the bases of the wall piers due to the coupling action, Lc=distance between the geometric centroids of the wall piers, and ΣVb=sum of the coupling beam design shear forces over the structure height.

Mtotal Mc M1 M2

M1 M2 (1 Rc )

2Mtotal

Mc Rc Mtotal NcLc Vb Lc

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Due to the uneven distribution of the coupling beam shear and moment demands over the height of the structure, a series of coupling beam design force adjustment factors, ri, were used to calculate the design forces for the different floor and roof levels. Preliminary coupled wall analytical models were used to determine these adjustment factors, resulting in different beam designs over the height. The adjustment factors for the coupling beams in Specimen 1 were found as: r1=1.14 for the 1st floor level and r2-8=0.98 for the 2nd-8th floor levels. Due to the increased coupling beam depth, different adjustment factors were determined for Specimen 2 as: r1=1.24 for the 1st floor level and r2-8=0.96 for the 2nd-8th floor levels. The adjusted design beam shear forces and end moments were then calculated using the following relationships:

(5)

(6)

where, Vb,i and Mb,i=adjusted coupling beam design shear forces and end moments, respectively, and =unadjusted (i.e., uniform) coupling beam design shear force and end moment, respectively, nb=number of coupling beams in the structure (nb=16 for the 8-story prototype structure with C-shaped wall piers); and lb=coupling beam length (clear span length).

The reinforcement details of the wall piers and coupling beams were selected to satisfy the calculated design forces at the design-level drift, Δwd, and achieve ductile behavior up to the validation-level roof drift of Δwm=3.0% for the 8-story structure. In the calculation of Δwd, a displacement amplification factor of Cd=5.0 for special reinforced concrete shear walls was applied to the linear-elastic drift, Δwe of the coupled wall structure. To estimate Δwe, the assumed effective (i.e., reduced) shear areas, Ave and moments of inertia, Ie in Table 3.1 for the wall piers and coupling beams were used in a linear-elastic representation of the structure. The effective shear areas for the wall piers and coupling beams in both structures were assumed to be 80% of the shear area, Av from the gross concrete sections. For the wall piers in both structures, an effective moment of inertia of Ie=0.35Ig was used based on the recommendations for cracked walls in Section 10.10.4.1 of ACI 318 (where Ig is the gross cross-section moment of inertia). In Specimen 1, an effective moment of inertia of Ie=0.50Ig was assumed for the coupling beams based on Section 8.8.2(b) of ACI 318 (where Ig was calculated based on assumed T-shaped beam cross-sections as discussed later). In Specimen 2, top and bottom energy-dissipating (ED) mild steel bars crossing the beam-to-wall joints were not used in the coupling beam design and, therefore, less of the gross beam cross section was assumed to be effective. As such, the effective moment of inertia factor was taken as half of that used for Specimen 1, resulting in Ie=0.25Ig for the beams in Specimen 2.

The C-shaped wall piers were designed according to the requirements in Section

21.9 of ACI 318 for special structural walls. The boundary element reinforcement layout

Vb,i riVb ri

Nc

nb

Mb,i ri Mb ri

Vb lb

2

ri

Nc lb

2nb

Vb Mb

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(i.e., toes of the wall piers) satisfied Section 21.9.6 and included the extension of the transverse reinforcement into the foundation. The post-tensioned floor slabs were designed by Magnusson Klemencic Associates (MKA) according to the requirements in Sections 18.12 and 21.11 of ACI 318 for prestressed concrete slab systems and structural diaphragms, respectively. As described in Chapter 5, modifications were made to minimize the restraining effect of the slab reinforcement to the opening of large, concentrated cracks at the beam ends under lateral loading.

Table 3.1 – Effective Linear-Elastic Shear Areas and Moments of Inertia Structure

Component Specimen 1 Specimen 2

Ie Ave Ie Ave

wall piers 0.35Ig 0.80Av 0.35Ig 0.80Av

coupling beams

0.50Ig 0.80Av 0.25Ig 0.80Av

The coupling beams were designed as T-beams with a total effective flange width

of 3.66 m (12 ft) consisting of the beam web, the lateral distance to the terminated slab edge outside of the core, and the portion of the recommended flange width (i.e., six times the floor slab thickness) from ASCE 7-10 inside the core. The effective flange width specified in Section 8.12.2 of ACI 318 was deemed too small relative to the beam web width (610 mm total ACI 318 effective flange width relative to the 457 mm wide beam web). The largest compression strains at the ends of the T-shaped beams were found to develop in the web under negative bending, requiring closely-spaced transverse hoops for concrete confinement. Due to the presence of the slab, a smaller amount of concrete confinement was required at the top of the beam cross-section. The confined concrete design method described in ACI ITG-5.2 (2009) for the toes of precast concrete shear walls was used to determine the size and spacing of the beam end hoops. In this method, the confinement reinforcement is designed for a specified beam end rotation. The post-tensioned coupling beams of the test specimens were designed for a maximum beam end rotation of θb=9.0%, which was determined from a preliminary analytical model of the 8-story structure displaced to the 3.0% validation-level roof drift.

The full-scale prototype structure was intentionally designed not to have any

significant over-capacity in force or displacement (e.g., no capacity reduction factor was used for axial-flexural design) so as to critically assess the limits of the design procedure, tools, approximations, and assumptions (i.e., overly-conservative, not conservative, or reasonable design). The 40% scaling of the structure to determine the test specimen properties was also done to result in little or no over-capacity (e.g., actual provided steel areas close to the required scaled areas). The scaled specimen designs were then checked against the scaled design forces to ensure that all requirements were still met. Further information on the individual test specimen design and reinforcement details can be found in Chapters 5 and 6.

13

CHAPTER 4: ANALYTICAL MODELING AND EXPERIMENTAL PROGRAM

The development and preliminary validation of a nonlinear fiber-element analytical model for the multi-story coupled wall system is presented in this chapter. A description of the experimental program and laboratory test setup is also provided.

4.1 Analytical Model

The multi-story coupled wall analytical model was developed based on a previous model for unbonded post-tensioned precast concrete coupling beams (Weldon and Kurama 2012) using the DRAIN-2DX (Prakash et al. 1993) software. A typical floor-level coupled wall subassembly model is shown in Fig. 4.1 (○ markers depict nodal locations). Analytical models of the 8-story (full-height structure) and 3-story (laboratory specimen) coupled walls, both at full-scale and at 40%-scale, were constructed by combining the subassembly models for the different floor and roof levels. For example, Fig. 4.2 shows a typical 40%-scale 3-story test specimen model. Note that, for clarity, some of the model details illustrated in Fig. 4.1 have been omitted in Fig. 4.2.

To simplify the analysis, only one half of the coupled core wall structure was

modeled considering symmetry with respect to the E-W axis of the building [Fig. 3.1(a)]. Each wall pier was modeled using two sets of nonlinear fiber beam-column elements. The first set consisted of vertical elements, referred to as “wall-height elements,” at the centroid, c.g., of the pier cross-section (e.g., Nodes B and AD for the west and east piers, respectively, in Fig. 4.1) to model the behavior of the wall along its height. The second set of fiber elements, referred to as “wall-contact elements,” were placed in the horizontal direction to the left and right of each coupling beam to model the compression deformations of the pier concrete at these locations. The fiber cross-section properties of the wall-contact elements were determined from “effective” pier cross-sections in the vertical plane. The width and depth of the effective pier sections were taken as the beam web width, bw, and beam depth, hb, at each beam-to-wall interface, with the effective section size increasing away from the interface. The Y-translational degree-of-freedom (DOF) of each beam-to-wall interface node (e.g., Node G for west pier) was kinematically constrained to the corresponding wall pier centroid node (Node B). The rotational and X-translational DOFs of the interface nodes were not constrained.

The fiber cross-sections of the wall-height elements were modeled using

longitudinal (i.e., vertical) concrete and steel fibers with material properties that depicted the concrete and reinforcement present in the piers, including the effect of confinement. In an attempt to indirectly simulate the effect of the nonlinear shear deformations in the wall piers, the concrete fibers in the wall-height elements were assumed to have zero strength in tension.

14

Figure 4.1 Floor-level subassembly model for Specimen 1

Figure 4.2 Multi-story analytical model (40%-scale test specimen)

In comparison, the cross-sections for the wall-contact elements were modeled using concrete fibers only (i.e., with no steel fibers). The coupling beams were also modeled using nonlinear fiber beam-column elements with concrete fibers only. This approach was taken because the steel reinforcement crossing the beam-to-wall interfaces was not bonded to the concrete; and thus, this reinforcement was modeled separately using nonlinear truss elements. The coupling beams were modeled as T-sections considering the selected effective flange width from the beam design [i.e., 3.66 m (12 ft) and 1.46 m (4.8 ft) for the full-scale and 40%-scale structures, respectively]. To model

15

the large, concentrated cracks expected to develop at the beam-to-wall interfaces, zero tension strength was assumed for the concrete fibers at the beam ends. However, if numerical difficulties were encountered during the analysis, a very small amount of tension strength was added to these concrete fibers. Away from the beam ends, the concrete was assumed to be linear-elastic in tension because in a properly designed beam, the cracks within the beam span remain small and are not expected to significantly affect the behavior. This modeling approach is similar to the modeling of post-tensioned precast concrete coupling beams, which are governed by gap opening at the beam-to-wall interfaces, as described in Weldon and Kurama (2007). The result is a relatively simple analytical model when compared to the modeling of conventional RC coupling beams, which are often governed by distributed crack formation and its interactions with bonded steel reinforcement.

Three truss elements connected at the beam-to-wall interfaces were used to model

the beam PT steel. The two strands in each coupling beam of the test specimens were lumped into a single truss element (i.e., between Nodes A-H-Y-AE). The PT force was simulated by initial tensile stresses in the truss elements, which were equilibrated by compressive forces in the fiber elements modeling the coupling beams and the wall-contact regions. The PT element nodes at the beam-to-wall interfaces (Nodes H and Y) were free to move in the horizontal (i.e., X) direction since the PT strands were unbonded. However, these nodes were kinematically constrained in the vertical direction to the respective beam end nodes (i.e., Nodes G and X). These constraints modeled the angle change of the PT tendons at the beam-to-wall interfaces when the beam was rotated under lateral loading (to accurately capture second-order effects in the tendons). The end anchor nodes for the tendons were kinematically constrained to the corresponding wall pier nodes (e.g., Node A to Node B).

In addition to the PT steel, horizontal top and bottom mild steel reinforcement

crossing the beam-to-wall interfaces was used in the coupling beams of Specimen 1 (see Chapter 5). These energy-dissipating (ED) bars were deliberately unbonded from the concrete (by wrapping each bar inside a plastic sleeve) over a predetermined length at the beam ends to prevent the low-cycle fatigue fracture of the steel. In the analytical model, the unbonded length of each ED bar was represented using a nonlinear truss element. The total unbonded length included the wrapped length of the bar plus an additional length of “debonding” expected to develop during the reversed-cyclic lateral displacements of the structure. This additional debonded length, which was assumed to be equal to 2 times the nominal bar diameter (Smith et al. 2011), was modeled to remain constant from the beginning to the end of the analysis. The remaining bonded regions of the bars were represented by kinematically constraining the end nodes of the truss elements (e.g., Nodes F and K in Fig. 4.1) to the corresponding beam fiber-element nodes (Nodes G and L, respectively) at the same X coordinate.

In Specimen 2, ED bars were not used in the coupling beam design and therefore,

these elements were not included in the numerical model. However, as described in Chapter 6, the vertical mild steel bars in the wall pier toes were deliberately unbonded from the concrete at the top of the foundation (i.e., the unbonded lengths of the bars were

16

below the pier toes). To model these bars, nonlinear truss elements were added parallel to the wall-height elements with lengths equal to the unbonded bar length plus 2 times the nominal bar diameter (similar to the modeling of the beam ED bars for Specimen 1 in Fig. 4.1). As such, the vertical steel fibers representing these bars in the wall-height elements at the base of the structure were removed. 4.2 Pre-Test Validation

To validate the multi-story coupled wall analytical modeling approach prior to the testing of the 40%-scale post-tensioned coupled wall specimens, a similar model with fiber beam-column elements but no PT steel was used to analyze the conventional coupled wall specimen tested by Aktan and Bertero (1984). In this experiment, a 4-story planar RC coupled shear wall structure was tested under monotonic lateral loading. As illustrated in Fig. 4.3(a), two horizontal actuators were used to apply the lateral loads, and four vertical actuators (two on each pier) were used to apply overturning moments and axial forces at the top of the wall piers. The application of these pier overturning moments and axial forces was similar to the testing of the post-tensioned coupled wall specimens described in this report.

(a) (b) Figure 4.3 Preliminary model validation: (a) conventional coupled wall test setup

(Aktan and Bertero 1984); (b) analytical versus experimental results

The actual specimen dimensions, material properties, boundary conditions, and loading scheme described by Aktan and Bertero (1984) were used in the fiber-element modeling and analysis of the coupled structure. Fig. 4.3(b) shows the total and left wall pier base shear forces plotted against the displacement at the top of the specimen. The analytical model predictions were generally in reasonable agreement with the measured behavior, including the distribution of base shear forces between the two piers at large lateral displacements. The results from this preliminary validation allowed the use of the analytical model to determine the forces applied at the top of the 40%-scale post-tensioned coupled wall specimens as described below.

17

4.3 Experimental Program The construction and testing of the two 40%-scale post-tensioned coupled core wall specimens took place at the Lehigh University NEES equipment site. Figs. 4.4(a) and 4.4(b) show a 3D rendering and photograph, respectively, of the test setup, including the steel reaction frame surrounding the specimen. The setup shown in Fig. 4.4 is typical for both 40%-scale experiments. A description of the analytical simulation and specimen loading scheme that drove the experiments is provided below.

4.3.1 Analytical Simulation

To determine the applied loading on each 3-story test specimen, the corresponding 40%-scale 8-story structure was analytically subjected to a reversed-cyclic lateral displacement history. This lateral displacement history was based on the validation testing requirements prescribed in ACI ITG-5.1 (2007). The lateral load distribution over the height of the 8-story analytical model was based on the ASCE 7-10 Equivalent Lateral Force (ELF) profile used in design. This force distribution was also applied at the floor and roof level wall-height element nodes (e.g., Nodes B and AD in Fig. 4.1) except for the ELF forces at the 1st, 2nd, and 3rd floor levels. Because no lateral forces were applied at the 1st, 2nd, and 3rd floor levels of the test specimens as described in the next section, the ELF forces at these levels were lumped at nodes located at the same elevation as the horizontal actuators in the laboratory setup [i.e., Nodes 106 and 206 in Fig. 4.5(a)]

(a) (b)

Figure 4.4 Experimental setup (40%-scale): (a) 3D rendering; (b) photograph

18

in a manner to result in the same wall base moments (but slightly smaller base shear forces) as the full ELF profile (i.e., profile including the 1st, 2nd, and 3rd floor level forces).

To represent the gravity loads acting on the structure during a potential

earthquake, one half (since only one half of the structure was analyzed due to symmetry about the E-W axis) of the full 100% unfactored design dead loads plus 25% of the unfactored unreduced design live loads within the assumed tributary area of the core were scaled down (to achieve 40%-scale similitude) and applied at the floor and roof level wall-height element nodes (e.g., Nodes B and AD). Note that similar to the ELF forces, no superimposed gravity forces were applied at the 1st, 2nd, and 3rd floor levels of the test specimens. Thus, the tributary gravity loads from the 1st, 2nd, and 3rd floors, with the exception of the specimen self-weight, were also lumped at Nodes 106 and 206 of the analytical model.

4.3.2 Specimen Loading

During the testing of Specimen 1, the analytically-determined wall-height element forces and moments (i.e., Vlb, Nlb, Mlb) at Nodes 106 and 206 were applied to a near-rigid load block connected to the top of each pier using a set of hydraulic actuators. The directions shown in Fig. 4.5(a) for Vlb, Nlb, Mlb represent the positive directions assumed for the applied forces and moments. As shown in Fig. 4.5(b), in the horizontal direction, one 2670 kN (600 kip) servo-controlled hydraulic actuator was used to apply all of the lateral forces from the upper 5 floor/roof levels of the 8-story analytical model (i.e., 4th through 8th floors) as well as the lumped forces from the lower three floor levels. Two additional servo-controlled horizontal actuators were placed between the east and west loading blocks (one on each of the north and south sides of the loading blocks) to appropriately distribute the total applied lateral force between the west and east wall piers (i.e., Vlb,w and Vlb,e, respectively).

In the vertical direction, two servo-controlled hydraulic actuators were connected

to each loading block to simulate the axial force (Nlb,w, Nlb,e) and bending moment (Mlb,w, Mlb,e) from the upper 4th through 8th stories of the analytical model. The net axial force from these actuator pairs was equal to the sum of the coupling beam shear forces in the upper 5 floor/roof levels of the 8-story analytical structure (resulting in Nlb,e=-Nlb,w from the coupling effect). The remaining wall pier axial forces (i.e., gravity loads from the upper 5 stories as well as the lumped gravity loads from the lower 3 stories, with the exception of the specimen self-weight) were applied as constant loads (Glb,e=Glb,w) via two center-hole hydraulic jacks at the top of each load block. This resulted in the same axial forces at the bases of the laboratory wall piers as the bases of the analytical piers.

A simple control algorithm, combined with the load feedback from the center-

hole hydraulic jacks, was used to actively maintain the applied gravity loads as each specimen was displaced laterally (such that the applied loads remained within a pre-determined range of the target load, Glb,e=Glb,w). During the testing of Specimen 1, all seven of the servo-controlled actuators were individually operated in load-control to apply the analytically-determined forces throughout the experiment. Note, however, that

19

the forces applied by the horizontal 2670 kN (600 kips) actuator in Fig. 4.5(b) was limited by the actual lateral strength of the test specimen. As a result, there were deviations in the forces applied by this actuator towards the end of the test, while the other six hydraulic actuators still followed the analytically-determined forces. To eliminate this discrepancy, a different loading protocol was used during the testing of Specimen 2. In this protocol, the displacement and force histories from the analytical simulation were imposed to the specimen in a mixed-mode control scheme. In this scheme, the horizontal 2670 kN hydraulic actuator was used in displacement-control to apply the lateral displacement history from Node 106 of the 8-story analytical model. The remaining six hydraulic actuators were operated in load-control using force ratio histories from the analytical model together with the measured load feedback from the horizontal 2670 kN actuator to determine the forces to be applied during each step of the experiment. The force ratio histories from the analytical model were calculated as the ratios of the predicted loads in the load-controlled actuators to the predicted loads in the displacement-controlled actuator. The resulting mixed-mode control scheme was able to maintain the desired relative force distribution between all seven actuators while still accurately imposing lateral displacements that satisfied the ACI ITG-5.1 (2007) testing requirements. This makes the mixed-mode actuator control used in Specimen 2 a more accurate method for applying the effect of the upper 5 stories on the 3-story laboratory structure.

Figure 4.5 Load application: (a) analytical model; (b) test setup


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CHAPTER 5: TEST SPECIMEN 1

This chapter provides more detailed information on the first 40%-scale test specimen, including the selected reinforcement for the wall piers and coupling beams as well as the specimen instrumentation. An overview of the measured behavior from the experiment and the corresponding analytical predictions is also provided. 5.1 Specimen Detailing

Fig. 5.1(a) shows the wall pier reinforcement details at the base of the 40%-scale structure, which were symmetric in the N-S direction for each pier as well as in the E-W direction between the two piers. The pier reinforcement plan was selected to be similar to typical reinforcement details in RC shear walls according to ACI 318 (2011). An elevation view of the coupling beams is shown in Fig. 5.1(b), with detailed cross-section views at the ends of the 1st floor and 2nd/3rd floor beams provided in Figs. 5.1(c) and 5.1(d), respectively. Due to the smaller design shear and moment demands in the upper floors (as quantified using the coupling beam design force adjustment factors, ri discussed in Chapter 2), the PT steel was reduced from two 15.2 mm (0.6 in.) diameter strands [ASTM A416 (2013)] in the 1st floor coupling beams to two 12.7 mm (0.5 in.) diameter strands in the 2nd and 3rd floor beams. Each PT strand was anchored at the far ends of the wall piers and was placed inside an ungrouted duct to prevent bonding to the concrete, resulting in uniformly distributed strand strains over the entire length of the coupled core. Energy dissipation in each of the six coupling beams was provided by two No. M10 (U.S. #3) ED bars [ASTM A615 (2013), Grade 420 (Grade 60)] at the top and bottom of the beam, crossing the beam-to-wall interface at each end. Additionally, No. M10 (U.S. #3) mild steel “skin” reinforcement was placed along the side faces of each beam to control cracking within the span and support the transverse hoops. The skin reinforcement was not continuous across the beam-to-wall interfaces and satisfied the minimum longitudinal steel area required in Section 21.9.7.4(c) of ACI 318 (2011) for diagonally-reinforced beams.

A predetermined length of the ED reinforcement was unbonded from the concrete

by wrapping each bar in a plastic sleeve to limit the maximum tensile strains and prevent low-cycle fatigue fracture of the steel. Because the beams were designed as T-beams considering an effective flange width from the slab, greater ED steel tension strain demands and greater concrete compression strain demands were expected in the web. To meet these increased strain demands, a longer wrapped (unbonded) length for the bottom ED bars as compared to the top bars, as well as a larger amount of confinement reinforcement (by placing additional, smaller hoops) at the bottom as compared to the top of the cross-section were required [see Figs. 5.1(c) and 5.1(d)].

The deliberate lack of bond between the steel crossing the beam-to-wall interfaces

(i.e., PT and ED steel) and the surrounding concrete was intended to result in concentrated cracks at the beam ends rather than distributed cracks within the span. The PT steel was designed to create a large diagonal compression strut over the beam length,

21

essentially eliminating cracking in the mid-span regions. This compression strut also resulted in large compression stresses at the beam ends; and thus, closely spaced hoops [51 mm (2 in.) on centers] were placed for concrete confinement in these regions [Figs. 5.1(c) and 5.1(d)]. The transverse hoop spacing away from the beam ends was significantly increased [178 mm (7 in.) on centers]. The rectilinear orientation of the beam reinforcement and localization of damage under lateral loading represent significant improvements over diagonally-reinforced coupling beams.

(a) (b)

(c) (d) Figure 5.1 Specimen 1 (40%-scale): (a) wall pier bases; (b) typical coupling

beam elevation; (c) 1st floor beam ends; (d) 2nd and 3rd floor beam ends

The widely-used unbonded post-tensioned RC slab technology was used for the floor slabs. These slabs were designed following typical methods for coupled core wall structures, but with some adjustments to account for the new post-tensioned coupling beams. The reinforcement layout consisted of a top and bottom mat of mild steel bars (continuous into and through the wall piers) and unbonded PT steel in both the N-S and E-W directions of the slab (see Fig. 5.2). The slab PT tendons were banded in the N-S direction and distributed evenly along the slab length in the E-W direction. The main deviation of the test specimen from a typical post-tensioned slab design was in the termination of the No. M16 (U.S. #5) E-W mild steel bars running parallel to the coupling beams outside of the core. To prevent these slab bars from providing over-strength and interfering with the intended concentrated crack behavior at the beam ends,

22

the bars placed within the assumed slab effective width were terminated at the beam-to-wall interfaces (i.e., these slab bars were not continuous across the beam-to-wall interfaces). Similarly, the No. M10 (U.S. #3) mild steel bars running parallel to the coupling beams inside the core were moved away from the beams to the edges of the slab openings.

(a) (b)

(c)

Figure 5.2 Slab details (Specimen 1): (a) post-tensioning; (b) top reinforcement; (c) bottom reinforcement

The measured PT steel, mild steel, and concrete properties for the test specimen

are given in Tables 5.1, 5.2, and 5.3, respectively. The concrete strength, f’c and Young’s modulus, Ec were measured from ASTM C39M 100x200 mm (4x8 in.) cylinder tests in

23

compression. The concrete strengths, f’c, were mostly consistent between the various pours since the same concrete mix design was used throughout the construction of the specimen. The PT strands were tested in monotonic axial tension using sand-grip anchors to achieve free-length failure as described in Walsh and Kurama (2010). The mild steel strains were measured using two displacement transducers (to obtain an average elongation) and the concrete cylinder strains were measured using digital image correlation (Peterson et al. 2014). The stress-strain behaviors for the PT steel and ED steel reinforcement are shown in Fig. 5.3.

Table 5.1 – PT Steel Material Properties

Notes: n/a=not available. 1 MPa=0.145 ksi. 1fpl=limit of proportionality; 2εpl=strain at fpl [o markers in Fig. 5.3(a)]; 3Ep=modulus of elasticity; 4fpu=maximum (peak) strength at wire fracture; 5εpu=ultimate strain at fpu [ markers in Fig. 5.3(a)].

Table 5.2 – Specimen 1 Mild Steel Material Properties Material

Spec. No.

No. M19 Reinforcing Bar No. M13 Reinforcing Bar No. M10 Reinforcing Bar 1fsy

(MPa)

2εsy (%)

3Es

(MPa)

4fsm

(MPa)

5εsm

(%)

6εsu

(%)

1fsy

(MPa)

2εsy

(%)

3Es

(MPa)

4fsm

(MPa)

5εsm

(%)

6εsu

(%)

1fsy

(MPa)

2εsy (%)

3Es

(MPa)

4fsm

(MPa)

5εsm

(%)

6εsu

(%)1 470 0.27 201386 711 10.9 15.7 476 0.24 197062 672 8.2 10.9 463 0.24 219586 747 10.8 12.12 472 0.21 227586 709 10.9 12.8 414 0.20 218541 671 11.8 15.0 457 0.31 206868 740 10.6 14.63 474 0.26 194800 710 11.4 11.7 418 0.22 203138 673 11.0 13.0 474 0.27 186207 752 9.4 14.14 471 0.28 215722 709 11.7 15.3 432 0.24 198363 687 11.1 13.4 472 0.27 196364 749 10.9 11.4

Notes: 1 MPa=0.145 ksi. 1fsy=yield strength; 2εsy=yield strain [o markers in Figs. 5.3(b-d)]; 3Es=modulus of elasticity; 4fsm=maximum (peak) strength; 5εsm=strain at fsm [ markers in Figs. 5.3(b-d)]; 6εsu=ultimate strain at bar fracture [ markers in Figs. 5.3(b-d)].

Table 5.3 – Specimen 1 Concrete Material Properties

Material Specimen

No.

Foundation 1st Story Walls and 1st Floor Beams 1st Floor Slab 28 day test day 28 day test day 28 day test day

1f’c

(MPa)

1f’c

(MPa)

2Ec

(MPa)

1f’c

(MPa)

2Ec

(MPa)

1f’c

(MPa)

2Ec

(MPa)

1f’c

(MPa)

2Ec

(MPa)

1f’c

(MPa)

2Ec

(MPa) 1 37.1 45.0 30165 45.1 28069 53.8 36542 45.1 33196 52.7 35866 2 36.6 48.0 36770 42.2 30617 49.4 33836 39.1 35939 51.9 33595 3 37.8 n/a n/a 44.3 n/a 53.1 33095 46.1 33490 n/a n/a

Notes: n/a=not available. 1 MPa=0.145 ksi. 1f’c=maximum (peak) strength of unconfined concrete; 2Ec= modulus of elasticity of unconfined concrete.

5.2 Instrumentation

A total of 29 load cells, 163 displacement/rotation transducers, and 214 strain gauges were used to monitor the behavior of the specimen. In addition, as shown in Fig. 5.4(a), 14 DIC sensors were used to provide near-full-field monitoring of critical regions in the wall pier bases, coupling beams, and floor slabs (McGinnis et al. 2014). The information that could be gathered from the available DIC cameras was maximized by operating some of the sensors in 2D, where out-of-plane displacements were expected to be small (e.g., north and south faces of the wall piers). Fig. 5.4(b) shows an example of a 3D sensor setup, and the patterns used in its field-of-view (FOV).

Material Specimen

No.

12.7 mm PT Strand 15.2 mm PT Strand 1fpl

(MPa)

2εpl (%)

3Ep (MPa)

4fpu (MPa)

5εpu (%)

1fpl (MPa)

2εpl (%)

3Ep (MPa)

4fpu (MPa)

5εpu (%)

1 1586 0.85 193160 1963 4.81 1586 0.83 197514 1979 6.86 2 1586 0.84 199148 1987 6.48 1586 0.84 195376 1974 6.42 3 n/a n/a n/a n/a n/a 1586 0.86 196387 1973 6.78

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Figure 5.3 Specimen 1 material behavior: (a) PT strand; (b) No. M19 bar; (c) No. M13 bar; (d) No. M10 bar (1 MPa=0.145 ksi; 1 mm=0.0394 in.)

(a) (b) Figure 5.4 DIC monitoring (Specimen 1): (a) locations; (b) example setup

5.3 Measured Behavior

This section discusses the measured results from the testing of Specimen 1 as follows: (1) system behavior; (2) damage at completion of test; (3) coupling beam behavior; and (4) DIC results.

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5.3.1 System Behavior

Figs. 5.5(a) and 5.5(b) show the measured average (from the east and west piers) 3rd floor drift, Δ3, history and the total base shear force, Vtotal, versus Δ3 behavior of the test specimen, respectively. Although minimal, the effects of foundation slip and rotation have been removed from the 3rd floor drift measurement. The testing started in the negative drift direction with the specimen displaced towards the east. The structure achieved maximum drift angles of Δ3=-2.70% (when displaced eastward) and +2.53% (when displaced westward) at the 3rd floor level during the validation-level drift series, reaching an overall peak base shear strength of -1922 kN (-432 kips) and +1850 kN (+416 kips) in the negative and positive directions of loading, respectively. The strength loss of the structure from the overall peak strength to the peak load during the last cycle of the test was 22.2% and 20.7% in the negative and positive directions, respectively. For comparison, a conventional coupled wall with diagonally-reinforced coupling beams tested by Lehman et al. (2013) failed due to core concrete crushing and buckling of vertical bars in the boundary (toe) region of the compression-side pier upon reaching a third floor drift of Δ3=2.27% for the first time. The lateral loading prior to failure in this recent study consisted of two cycles at each drift increment. Despite the application of a significantly greater number of load reversals (three cycles at each drift increment), the maximum 3rd floor drift achieved by Specimen 1 was nearly 20% greater than the maximum drift reached (but not repeated due to failure) by the conventional specimen tested by Lehman et al. (2013), demonstrating the higher performance of the new system.

(a) (b) Figure 5.5 Overall behavior of Specimen 1: (a) average 3rd floor drift; (b) total base

shear force versus 3rd floor drift

Note that the corresponding drifts at the roof of the full 8-story structure would be greater than the measured maximum 3rd floor drifts of -2.70% and +2.53% due to the nonlinear displaced shape of the building under lateral loads. Using the analytical model, these 8-story roof drift capacities were determined as Δr=-3.18% and +3.10% in the negative and positive directions, respectively, implying that the maximum roof drift of 3.0% used in the design of the structure was achieved. The reasonable comparison between the DRAIN-2DX model prediction (dashed line) and the measured behavior

26

(solid line) in Fig. 5.5(b) justifies the analytical extension of the 3rd floor measured drifts to the roof drifts for the full 8-story structure.

Fig. 5.6(a) shows the lateral shear force, Vlb (see Fig. 4.5), applied on the load

block at the top of each wall pier versus Δ3. As expected, there was a difference in the distribution of shear forces between the compression-side and tension-side piers. By the end of the test, the applied force at the top of the tension-side pier (e.g., west pier when the specimen was displaced towards the east) was approximately 30% greater than the force applied at the top of the compression-side pier. The greater forces in the tension-side pier likely occurred because of the unsymmetrical C-shaped cross-section of each pier [i.e., the piers were stronger with the flange (see Fig. 3.1) in tension than the toes in tension]. Note that the differences between the compression-side and tension-side wall pier shear forces were likely greater at the base of the structure; however, this was not measured during the test.

(a) (b)

(c) Figure 5.6 Specimen 1 applied load block forces: (a) shear forces; (b) axial forces;

(c) overturning moments

Fig. 5.6(b) shows the axial force, Nlb, imposed through the vertical actuator pair at the top of each load block (i.e., sum of the coupling beam shear forces from the upper 5

27

floor/roof levels of the 8-story structure). Likewise, the imposed overturning moment history, Mlb, at the top of each load block is shown in Fig. 5.6(c). Similar to the applied lateral shear forces, there was an uneven distribution of the overturning moments between the compression-side and tension-side wall piers. The overturning moment on the tension-side pier was approximately twice the moment on the compression-side pier during the final drift cycles of the test.

The primary sources of energy dissipation in the test specimen were the yielding

of the vertical mild steel bars at the wall pier bases and the yielding of the ED bars at the beam ends. To quantify the amount of energy dissipation, ACI ITG-5.1 defines the relative energy dissipation ratio, βh, as illustrated in Fig. 2.1. For validation purposes, ACI ITG-5.1 requires that βh be greater than βh,min=0.125 during the 3rd drift cycle at or greater than the validation-level drift. Fig. 5.7(a) shows the 3rd cycle from the final drift series during the test (which exceeded the validation-level 8-story roof drift of 3.0%), with the area, Ad, inside the hysteresis loop hatched. The βh ratio was calculated as the ratio of Ad to the area within the dashed parallelograms. The resulting βh ratios from the 3rd cycle in each drift increment are plotted against the average third floor drift, Δ3, in Fig. 5.7(b). It can be seen that the energy dissipation of the system was well above the minimum limit, βh,min, required by ACI ITG-5.1. The results also show that βh increased significantly as the reinforcement yielded more during the increasing drift cycles.

(a) (b) Figure 5.7 Specimen 1 energy dissipation: (a) third hysteresis loop from final drift

series; (b) relative energy dissipation ratio, βh

5.3.2 Damage at Completion of Test

Fig. 5.8 depicts the damage state of various components of the structure at the end of the test. The lateral strength loss (about 20% drop from the overall peak strength) during the 2nd and 3rd cycles of the final drift increment was largely caused by the low-cycle fatigue fracture (preceded by out-of-plane buckling) of the vertical No. M19 (U.S. #6) mild steel bars in all four wall pier toes at the base. Audio evidence of these bar fractures throughout the last two cycles of the final drift increment and post-test clean-up of the wall pier toe regions led to this conclusion. For example, Fig. 5.8(a) shows the

28

north toe region of the west wall pier base (after removal of the spalled concrete debris), depicting two fractured vertical bars above the foundation. These regions were designed according to current ACI 318 (2011) detailing specifications for special RC shear walls, implying that improved code requirements are needed to prevent the bar fractures. It should be noted that the buckling and fracture of the bars occurred in between the lowest hoop in the pier toes and the highest hoop in the foundation. In particular, the gradual degradation of the concrete at the top of the foundation contributed significantly to the buckling and subsequent fracture of the vertical mild steel bars (by extending the unsupported length of the bars into the foundation). This behavior can be prevented or delayed with revised reinforcement detailing to reduce both the steel and concrete strains within the top of the foundation as implemented in Specimen 2 (Chapter 6).

Spalling of the cover concrete and subsequent buckling of the vertical mild steel

bars at the outer wall pier corners [i.e., intersection of flange and web of pier; see Fig. 2.1(a)] were also noted [Fig. 5.8(b)]. The buckling of these bars occurred in between the U-shaped bars placed at the outside corners of the wall piers, indicating that additional U-shaped bars may be needed in these regions as investigated in Specimen 2. The wall damage was significantly reduced away from the outer corners and toes of the C-shaped piers [Fig. 5.8(c)]. There was a well-distributed pattern of diagonal (shear) cracking observed over the first story height in the wall pier webs. These diagonal cracks extended downward into the web (at approximately 45° angles) from the outside east and west edges (i.e., flanges) of each pier. At the outside corners, the diagonal shear cracks intersected with horizontal flexural cracks that extended across the full length of each wall pier flange.

As shown for the bottom of the 1st floor slab in Fig. 5.8(d), significant cracking

and concrete spalling was observed in the post-tensioned slabs outside of the core wall. These cracks (and the corresponding spalling regions) propagated outward from the coupling beam ends, where the mild steel slab reinforcement was terminated to allow for the intended behavior with concentrated cracks at the beam ends, and extended to the terminated edges of the slab outside the core wall. Cracking in the slab was much smaller and better distributed with minimal concrete spalling inside the core where the slab was continuous between the wall pier webs and flanges. This may indicate that the greater slab damage that occurred outside of the core wall could be a result of the slab discontinuity along the outer edges of the test specimen. In an actual building, the continuation of the floor slabs further out from the core wall would eliminate this discontinuity and likely improve the performance of the slabs. The presence of cold construction joints in the slabs (perpendicular to the beam length and near each beam end) also contributed to the concrete damage in these regions outside the core. The cold joints should not be placed near the beam ends and a small amount of mild steel reinforcement can be added within the effective flange width to help reduce the slab damage. These potential improvements were investigated in Specimen 2.

29

(a) (b)

(c) (d)

(e) (f) Figure 5.8 Damage at completion of test (Specimen 1): (a) north toe of west wall pierbase; (b) south corner of west wall pier base; (c) south face of east wall pier base; (d) bottom of 1st floor slab outside of core; (e) 1st floor south coupling beam; (f) ED bar

buckling in 3rd floor north coupling beam

Overall, the post-tensioned coupling beams performed well during the test. The observed damage included localized crushing of the concrete at the beam ends [Fig. 5.8(e)], which was mostly limited to cover spalling, confirming the design of the confinement hoops. The large compression stresses at the beam ends resulted in concrete spalling in the adjacent wall pier regions. In the 3rd floor north coupling beam, buckling within the unbonded length of one of the bottom ED bars was also observed, which caused additional concrete spalling and splitting in this region [Fig. 5.8(f)]. This was the only ED bar in the structure that exhibited buckling. The ED bar buckling occurred

30

within the unbonded length and immediately outside of the closely-spaced hoop region, which may indicate the need for extending the closely-spaced hoops along the entire unbonded length of the ED bars. The damage shown in Fig. 5.8(e) is generally representative of all of the six coupling beams in the specimen. The beams underwent significant rotations (see next section) at the ends where large concentrated cracks formed. Minimal cracking was found in the rest of the span, validating the overall design philosophy for the post-tensioned system.

5.3.3 Coupling Beam Behavior

Fig 5.9 presents the measured absolute end rotation, |θb|, of each coupling beam versus the average 3rd floor drift, Δ3 of the test structure. The beam end rotation is defined as the relative rotation between the coupling beam and the adjacent wall pier at the beam-to-wall interface. This relative rotation was determined from two rotation transducers, one attached to the beam end and the other to the wall pier, located at the same structural elevation. The results show that the beams underwent large end rotations, increasing almost linearly with Δ3 and reaching a maximum of θb=8.5% in the 3rd floor south coupling beam [Fig. 5.9(c)]. This was consistent with the analytical model that showed a maximum beam end rotation of 9.1% at the same floor level of the structure. Despite these large rotations, which were nearly double the maximum measured rotations (θb =4.7% in the 3rd floor) in the conventionally-reinforced specimen tested by Lehman et al. (2013), the post-tensioned coupling beams performed well and demonstrated the advantages of the new system. The results showed that the beam end rotations increased from the 1st to the 3rd floor of the specimen. This behavior, which was also evident in the analytical results, occurred due to the larger restraining effect of the wall piers at the base and the nonlinear deflected shape of the structure over the height.

Fig. 5.10 shows the average PT strand stress in each coupling beam, calculated as

the total measured beam PT force, Fp (sum of the strand forces) divided by the total design ultimate strength of the strands, Fpu=ΣApfpu. Nonlinear behavior of the PT steel was negligible as all of the strand stresses were at or less than the limit of proportionality, fpl=0.85fpu. The largest average strand stress during the test was 0.86fpu, which occurred in the 3rd floor north coupling beam because of the larger beam rotations at the 3rd floor level and a slightly greater initial strand stress in this beam at the beginning of the test. Stresses in the other beam PT strands remained less than 0.80fpu.

The increases in the beam PT strand forces, Fp, from the initial forces occurred as

the horizontal distance between the wall piers increased (i.e., the wall piers separated outward) during the lateral displacements of the structure. Fig. 5.11(a) shows the maximum wall pier separation at the 1st peak of the 1st cycle in each drift series by plotting the increase in the horizontal distance between the pier flanges in line with the north and south coupling beams at each floor level. The maximum wall pier separation reflects the deformed shape of the coupling beams under lateral loading (i.e., beam rotation and the development of large concentrated cracks at the beam ends), which results in an increase in the distance between the PT strand anchorages. As such, the results in Fig. 5.11(a) are generally in agreement with those in Fig. 5.10. For example, the

31

largest pier separations were measured in the 2nd and 3rd floor levels of the structure, where the largest increases in Fp also occurred. Note that Fig. 5.10(b), in particular, shows an eventual reduction in the rate of increase in Fp at larger lateral displacements of the structure. Since the nonlinear behavior of the PT strands was minimal, this reduction was likely due to the crushing of the concrete at the beam ends and the adjacent wall pier regions under the large rotation demands.

Figure 5.9 Absolute beam end rotation versus 3rd floor drift (Specimen 1): (a) 3rd floor south; (b) 3rd floor north; (c) 2nd floor south; (d) 2rd floor north; (e) 1st floor

south; (f) 1st floor north

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Figure 5.10 Total beam PT force versus 3rd floor drift (Specimen 1): (a) 3rd floor

south; (b) 3rd floor north; (c) 2nd floor south; (d) 2rd floor north; (e) 1st floor south; (f) 1st floor north

Fig. 5.10 also shows that in all six coupling beams, a permanent increase in Fp

from the initial PT force occurred as the structure was returned to Δ3=0% from increasing nonlinear lateral displacements. This was primarily an outcome from the development of permanent (i.e., residual) plastic strains in the wall pier vertical mild steel bars during the reversed-cyclic lateral displacements of the structure. As the plastic strains accumulated in these mild steel bars, there was a permanent (residual) horizontal separation between the wall piers. Fig. 5.11(b) shows this permanent wall pier separation (measured between

33

the flanges along the same line as the coupling beams) upon returning to Δ3=0% after the completion of the 1st half cycle in each drift series. The permanent wall pier separation increased throughout the test, resulting in a gradual, permanent “elongation” of the coupling beams and corresponding elongation of the PT strands (and therefore, permanent increase in Fp) at Δ3=0%. Note that, based on strain gauge data, there was little accumulation of plastic strains in the coupling beam ED mild steel bars; and thus, the yielding of these bars did not contribute significantly to the permanent pier separation. This is discussed further in Section 6.3.3.

Figure 5.11 Measured separation between east and west wall piers (Specimen 1): (a) maximum; (b) residual

5.3.4 DIC Results

Fig. 5.12(a) shows the concentrated crack widths measured approximately 25 mm (1 in.) above the bottom corners of the coupling beams using DIC sensors 3D1, 3D2, and 3D3. These crack widths were determined as the horizontal displacement over the cracked zone between the end of each beam and the adjacent wall pier. The crack widths in each direction of loading are shown as the average values when the peak drift was reached during the 3 cycles for each wall drift increment, except for the last increment where the crack width from the peak of only the 1st cycle is shown. It can be seen that the concentrated crack widths increased almost linearly with increasing drift, similar to the beam end rotations in Fig. 5.9 and the maximum wall pier separations in Fig. 5.11(a). The 3rd floor beams had larger crack widths than the 1st floor beams, which also follows the trend for the beam rotations over the height of the specimen.

Fig. 5.12(b) shows the contributions from four deformation mechanisms to the 1st floor drift, Δ1 of the structure, as measured using DIC sensors 2D1 and 2D2, plotted against the corresponding 3rd floor drift, Δ3. These deformation mechanisms are: (1) rotation at the base of the wall piers with respect to the foundation; (2) shear slip at the base of the wall piers with respect to the foundation; (3) shear deformations over the 1st story height of the wall piers; and (4) axial-flexural deformations over the 1st story height of the wall piers. The foundation remained essentially rigid during the entire test. Thus, the rotation and slip at the base of each pier were computed using the DIC measurements

34

along a horizontal line directly above the foundation. Shear deformations of each pier within the 1st story height were computed through a comparison of DIC measurements along two diagonals, using the equations in Oesterle et al. (1976). The drift contributions were calculated for the east and west wall piers at the positive and negative peaks during the 3 cycles for each drift increment with available DIC data. The contributors to drift were consistent between the repeated cycles and the two directions of loading; and thus, they were averaged to generate the results in Fig. 5.12(b) (i.e., average of the east and west piers at the positive and negative drift peaks during the 3 cycles). The remaining 1st floor drift was attributed to the axial-flexural deformations over the 1st story height of the piers.

(a) (b)

(c) Figure 5.12 Specimen 1 DIC results: (a) beam end concentrated crack widths;

(b) contributions to 1st floor drift; (c) relative contributions to 1st floor drift

Fig. 5.12(c) shows the drift from each deformation mechanism normalized with respect to the total 1st floor drift, Δ1 (such that the sum of the four relative contributions is equal to 100%). It can be seen that the axial-flexural deformations of the wall piers provided the largest contribution (about 40%) to the 1st floor drift during the small 3rd

35

floor drift levels, but quickly diminished under increased Δ3. Pier base rotation dominated the response of the structure (about 50-60% contribution to the 1st floor drift) at the higher Δ3 levels. This means that the axial-flexural deformations localized at the pier-to-foundation joints as the 3rd floor drift was increased. The shear deformations of the wall piers and slip at the base joint provided consistent but smaller contributions to the 1st floor drift (around 25% and 10% for shear deformations and base slip, respectively).

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CHAPTER 6: TEST SPECIMEN 2

Information regarding the detailing and measured behavior of the second 40%-scale test specimen is provided in this chapter. 6.1 Specimen Detailing

As described in Chapter 5, the primary reinforcement in the coupling beams of Specimen 1 [see Fig. 6.1(a)] included unbonded PT strands near the centroid as well as horizontal energy-dissipating (ED) mild steel bars crossing the beam-to-wall joints near the top and bottom of the cross-section, resulting in a partially post-tensioned design. Specimen 2 differed from Specimen 1 in six main ways: (1) the coupling beams [see Fig. 6.1(b)] were deeper with a reduced length-to-depth aspect ratio of 3.0 (the previous aspect ratio was 4.0); (2) the coupling beams were fully post-tensioned (i.e., with no mild steel ED bars crossing the beam-to-wall joints), resulting in most of the energy dissipation of the specimen to be provided by the yielding of the vertical (flexural) mild steel bars at the wall pier bases; (3) the vertical mild steel bars at the toes of the wall pier bases were deliberately unbonded from the concrete within the top of the foundation (by wrapping the bars inside plastic sleeves); (4) additional closely-spaced U-bars were placed at the outside corners of the C-shaped wall pier bases; (5) changes were made to the slab reinforcement details and slab construction near the coupling beams; and (6) additional horizontal reinforcement was placed in the wall pier regions across from the beam ends. More information on the details of Specimen 2 is given below.

The significant energy dissipation observed in Specimen 1 [see Fig. 5.7(b)] led to

the elimination of the ED bars in the coupling beams for Specimen 2. The goal in eliminating these bars was to further simplify the coupling beam design and construction as well as reduce the damage in the beam-to-wall joint regions, while still providing adequate energy dissipation to the structure through the yielding of the vertical mild steel bars at the wall pier bases. Another change to the beam-to-wall joint regions was the addition of two horizontal No. M13 (#4) bars inside the wall piers across from the bottom of the beam confined concrete [see Fig. 6.1(b)] to improve the performance of the wall pier concrete adjacent to the beam ends. This additional horizontal pier reinforcement was not continuous into the coupling beams.

Detailed cross-section views of the ends of the 40%-scale 1st floor and 2nd/3rd

floor coupling beams are shown in Figs. 6.2(a) and 6.2(b), respectively. Because the coupling beams in Specimen 2 were deeper, the design force adjustment factors were different than those used in Specimen 1, requiring larger shear and moment strengths in the 1st floor beams (r1=1.24 versus r1=1.14 in Specimen 1). Due to the lower demands in the upper floors of the structure, the PT steel [ASTM A416 (2013)] was reduced from two 15.2 mm (0.6 in.) diameter strands in the 1st floor coupling beams to two 12.7 mm (0.5 in.) diameter strands in the 2nd and 3rd floor beams. Each PT strand was anchored at the far ends of the wall piers and was placed inside an ungrouted duct to prevent bonding to the concrete. As with Specimen 1, No. M10 (U.S. #3) mild steel “skin” reinforcement

37

terminated at the beam-to-wall interfaces was placed along the side faces of each beam to control cracking and support the transverse hoops along the beam span. Similarly, closely-spaced confinement hoops [51 mm (2 in.) on centers] were required at the beam ends due to the concentration of large compression stresses and strains when the structure was displaced laterally.

(a)

(b)

Figure 6.1 Coupling beam comparison: (a) partially post-tensioned (Specimen 1); (b) fully post-tensioned (Specimen 2)

Figure 6.2 Specimen 2 coupling beam details: (a) 1st floor beam ends; (b) 2nd and 3rd floor beam ends

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The wall pier reinforcement details in Specimen 2 were identical to those shown in Fig. 5.1(a) for Specimen 1 with two main changes. First, a 254 mm (10 in.) length of the 6 No. 19 (U.S. #6) bars within the confined regions at the wall pier toes was unbonded from the concrete within the top of the foundation to improve the performance of the concrete in these regions and delay the low-cycle fatigue fracture of the bars. Second, additional closely-spaced U-bars were placed at the outside corners of the C-shaped wall piers within the first 305 mm (12 in.) above the foundation to prevent the buckling of the vertical mild steel bars that was observed in Specimen 1 [see Fig. 5.8(b)].

The detailing of the post-tensioned floor slabs in Specimen 2 was similar to the reinforcement layout shown in Fig. 5.2 for Specimen 1 with two main changes in an attempt to reduce the damage to the slab concrete in these regions. First, the cold construction joints in the slabs were moved further away from the beam ends. Second, as shown in Fig. 6.3, a single No. M10 (U.S. #3) mild steel bar crossing the beam-to-wall interfaces was placed near the bottom of the slab on each side of the web in the T-shaped beam. A predetermined length of these bars [taken as the beam length plus 2 times the wall thickness (1.35 m)] centered at the beam mid-length was unbonded from the concrete to minimize the steel strains, thereby allowing the large concentrated cracks to open at the beam ends and limiting the contribution of the slab bars to the beam strength.

Figure 6.3 Slab mild steel bars crossing the beam-to-wall interfaces (Specimen 2)

The measured steel and concrete properties for Specimen 2 are provided in Tables 6.1 and 6.2, respectively. These material properties were determined using the same testing methods described for Specimen 1 in Section 5.1. The stress-strain behaviors for the three mild steel bar sizes used in the structure are shown in Fig. 6.4. Overall, the properties of the mild steel bars used in Specimen 2 were similar to the properties of the bars used in Specimen 1 [see Figs. 5.3(b-d)]. Similarly, the concrete strengths, f’c, were

39

mostly consistent between the two structures and between the various pours since the same concrete mix design was used throughout the project. The PT steel properties for Specimen 2 were the same as those for Specimen 1 since the material was taken from the same strand spools [see Table 5.1 and Fig. 5.3(a)].

Table 6.1 – Specimen 2 Mild Steel Material Properties

Material Spec. No.

No. M19 Reinforcing Bar No. M13 Reinforcing Bar No. M10 Reinforcing Bar 1fsy

(MPa)

2εsy (%)

3Es

(MPa)

4fsm

(MPa)

5εsm

(%)

6εsu

(%)

1fsy

(MPa)

2εsy

(%)

3Es

(MPa)

4fsm

(MPa)

5εsm

(%)

6εsu

(%)

1fsy

(MPa)

2εsy (%)

3Es

(MPa)

4fsm

(MPa)

5εsm

(%)

6εsu

(%)1 454 0.22 217476 676 9.9 10.5 437 0.22 224138 705 9.9 10.2 493 0.26 224234 774 8.4 10.12 453 0.24 193855 676 11.812.3 429 0.23 215310 698 9.8 10.6 504 0.24 213793 780 9.5 10.03 457 0.25 189455 681 10.413.6 433 0.25 210335 699 8.6 10.8 475 0.22 220690 755 10.7 10.94 459 0.25 184483 681 10.210.5 n/a n/a n/a n/a n/a n/a 483 0.26 187586 768 9.5 10.3

Notes: n/a=not available. 1 MPa=0.145 ksi. 1fsy=yield strength; 2εsy=yield strain [o markers in Figs. 6.4(a-c)]; 3Es=modulus of elasticity; 4fsm=maximum (peak) strength; 5εsm=strain at fsm [ markers in Figs. 6.4(a-c)]; 6εsu=ultimate strain at bar fracture [ markers in Figs. 6.4(a-c)].

Table 6.2 – Specimen 2 Concrete Material Properties

Material Specimen

No.

Foundation 1st Story Walls and 1st Floor Beams 1st Floor Slab 28 day test day 28 day test day 28 day test day

1f’c

(MPa)

1f’c

(MPa)

2Ec

(MPa)

1f’c

(MPa)

1f’c

(MPa)

2Ec

(MPa)

1f’c

(MPa)

1f’c

(MPa) 1 47.1 49.2 42359 40.1 44.7 31876 37.9 43.1 2 45.0 49.9 34945 44.9 47.6 31241 42.0 43.1 3 47.9 49.4 n/a 44.8 47.3 37738 n/a n/a

Notes: n/a=not available. 1 MPa=0.145 ksi. 1f’c=maximum (peak) strength of unconfined concrete; 2Ec=modulus of elasticity of unconfined concrete.

Figure 6.4 Specimen 2 mild steel behavior: (a) No. M19 bar; (b) No.

M13 bar; (c) No. M10 bar (1 MPa=0.145 ksi; 1 mm=0.0394 in.)

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6.2 Instrumentation

A total of 29 load cells, 156 displacement transducers, 46 rotation transducers, and 252 strain gauges were used to monitor the behavior of Specimen 2. In addition, 9 three-dimensional digital image correlation (DIC) sensors were used to provide near-full-field monitoring of critical regions in the wall pier bases and coupling beams. Experience gained from the DIC monitoring of Specimen 1 led to the revised layout illustrated in Fig. 6.4(a). The DIC sensor layout for Specimen 2 differed from that for Specimen 1 in three main ways: (1) only 3D-DIC sensors were used due to uncertainty with some of the 2D data collected during the testing of Specimen 1; (2) the sizes of the DIC sensor field-of-views (FOV) around the coupling beams were reduced and smaller DIC pattern mesh sizes were used in these regions to obtain more detailed (refined) measurements (e.g., to capture the neutral axial depth and initiation of cracking at the beam ends); and (3) DIC monitoring (using sensors 3D1 and 3D4) was conducted on the outside east/west faces of the wall piers near the base to determine the effectiveness of the wall pier flanges in contributing to the lateral strength and behavior of the coupled wall structure. Fig. 6.4(b) shows an example of a 3D sensor setup and the patterns used in its FOV.

Figure 6.4 DIC monitoring (Specimen 2): (a) locations; (b) example setup 6.3 Measured Behavior

This section discusses the measured behavior of Specimen 2 with an emphasis on the overall system behavior, observed damage at the completion of the test, coupling beam behavior, and results from DIC monitoring.

6.3.1 System Behavior

Figs. 6.5(a) and 6.5(b) show the measured average (from the east and west piers) 3rd floor drift, Δ3, history and the total base shear force, Vtotal, versus Δ3 behavior of Specimen 2, respectively. Different from Specimen 1, the testing of Specimen 2 started in the positive drift direction with the wall displaced towards the west. The structure demonstrated ductile behavior through maximum drift angles of Δ3=+2.68% (when

41

displaced westward) and -2.53% (when displaced eastward) at the 3rd floor level during the validation-level drift series. The strength loss of the structure from the overall peak strength to the peak load during the 3rd cycle of this drift series was 9.6% and 12.3% in the positive and negative directions, respectively. The measured 3rd floor drift capacities corresponded to analytically-determined roof (i.e., 8th floor) drift capacities of Δr=+3.25% and -3.22% in the positive and negative directions, respectively, which are greater than and reasonably close to the 3.0% roof drift demand used in design; thus, supporting the design approach, assumptions, and approximations. The reasonable comparison between the DRAIN-2DX model prediction (dashed line) and the measured behavior (solid line) in Fig. 6.5(b) justifies the analytical extension of the 3rd floor measured drifts to the roof drifts for the full 8-story structure.

(a) (b) Figure 6.5 Overall behavior of Specimen 2: (a) average 3rd floor drift; (b) total base

shear force versus 3rd floor drift Failure of the structure ultimately occurred after the completion of a single full

cycle to Δ3=+3.68% and -3.35% (8-story roof drifts of +4.35% and -4.10%, respectively) in the west and east directions, respectively. During this cycle, an additional drop in lateral resistance (13.5% and 14.5% in the positive and negative directions, respectively) was observed due to the low-cycle fatigue fracture (preceded by buckling) of the extreme (outer) vertical (i.e., flexural) mild steel bars in the wall pier flange regions at the base of the structure. Significant strength loss (i.e., failure) ultimately occurred during the subsequent half cycle in the positive direction due to the fracture (preceded by buckling) of the vertical mild steel bars in the toe regions of the west wall pier. This ultimate failure mechanism was also observed in the wall pier toes of Specimen 1, but was delayed in Specimen 2 due to the deliberate unbonding of the vertical bars in these regions. Despite the significantly greater number of loading cycles prior to failure, the largest full drift cycle that was achieved by the structure was about 62% greater than the maximum drift reached (but not repeated due to failure) in the conventional coupled wall specimen tested by Lehman et al. (2013). This comparison again demonstrates the high performance of the structures designed and tested in this research project.

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The lateral shear forces, axial forces, and overturning moments applied on the load block at the top of each wall pier in Specimen 2 are shown in Figs. 6.6(a-c), respectively. Much like Specimen 1, the applied lateral shear forces, Vlb in Specimen 2 were weighted more towards the tension-side pier, which was likely due to the unsymmetrical C-shaped cross-section of the wall piers. Similarly, there was an uneven distribution of the overturning moments between the compression-side and tension-side wall piers as shown in Fig. 6.6(c). Note that the shear forces, Vlb, and the axial forces, Nlb, applied at the top of each load block in Specimen 2 were larger than the applied forces in Specimen 1. This can be attributed, in part, to the larger lateral strength of Specimen 2.

(a) (b)

(c) Figure 6.6 Specimen 2 applied load block forces: (a) shear forces; (b) axial forces;

(c) overturning moments

As would be expected, the relative energy dissipation of Specimen 2 at a given drift level was smaller than that of Specimen 1 due to the elimination of the ED bars in the coupling beams. Figs. 6.7(a) and 6.7(b) show the 3rd hysteresis cycle from the drift series to Δ3=+2.68% and -2.53% (which exceeded the validation-level 8-story roof drift of 3.0%) and the calculated third-cycle relative energy dissipation ratios, βh with increasing 3rd floor drift, respectively, for Specimen 2. It can be seen that the relative energy dissipation in the system was significantly greater than the minimum required by ACI ITG-5.1 during the later drift cycles and continued to increase almost linearly up

43

through the final completed drift cycle of the test. These results demonstrate that the yielding of the vertical mild steel reinforcement at the wall pier bases provided an adequate amount of energy dissipation to the structure.

(a) (b) Figure 6.7 Specimen 2 energy dissipation: (a) third hysteresis loop from the drift

series to Δ3=+2.68% and -2.53%; (b) relative energy dissipation ratio, βh

6.3.2 Damage at Completion of Test

Fig. 6.8 shows the damage states of various components of Specimen 2 at the completion of the test. For comparison purposes, the photographs in Fig. 6.8 were selected for similar locations to those provided in Fig. 5.8 for Specimen 1. Fig. 6.8(a) shows the post-test state of the north toe region of the east wall pier base after removal of the spalled concrete debris. It can be seen that the confined concrete core remained mostly intact with damage limited to the spalling of the cover concrete. The deliberate unbonding of the vertical mild steel bars below the toe resulted in significantly less degradation of the concrete at the top of the foundation when compared to Fig. 5.8(a) for Specimen 1. As discussed in the previous section, failure of the structure was ultimately due to the low-cycle fatigue fracture (preceded by buckling) of the vertical mild steel bars in the toes of the west wall pier [pictured in Fig. 6.8(b)] during the final, positive (i.e., west) half cycle of the test to a maximum 3rd floor drift of 3.68%. As such, the vertical bars in the toes of the east wall pier [Fig 6.8(a)] would have likely fractured in a similar manner if the test had continued to the negative (i.e., east) peak upon returning to Δ3=0%. The superior performance of Specimen 2 was due, in large part, to the improved detailing of the vertical reinforcement in the wall pier toe regions.

The buckling and subsequent low-cycle fatigue fracture of the extreme (outer) vertical mild steel bars in the wall pier flange regions at the base of the structure initiated earlier during the 1st cycle to Δ3=+3.68% and -3.35% [e.g., see Fig. 6.8(c) for the southeast corner of the structure after removal of the spalled concrete debris]. Unlike the vertical bars at the toes, the bars in the flanges were not deliberately unbonded from the concrete. The placement of additional closely-spaced U-bars at the outside corners of the wall pier bases resulted in less spalling of the pier concrete above the foundation. Furthermore, the buckling of the vertical mild steel bars occurred at the wall-to-

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foundation interface rather than in between the U-shaped bars as observed in Specimen 1 [see Fig. 5.8(b)]. The large base rotations that developed at the wall-to-foundation interface resulted in the eventual degradation of the foundation surface concrete (particularly at the outside corners of the wall piers) leading to the buckling and subsequent fracture of the outer vertical mild steel bars in the wall pier flanges. This indicates that structural performance could be improved further by applying the detailing for the unbonding of the vertical mild steel bars at the wall pier toes to the outer bars in the flanges as well. Much like Specimen 1, additional damage was observed through well-distributed diagonal shear cracks and horizontal flexural cracks in the wall pier webs and flanges, respectively.

The damage pattern for the bottom of the 1st floor slab is shown in Fig. 6.8(d).

Despite the modifications to the post-tensioned floor slab construction and detailing, significant cracking and concrete spalling was still observed propagating outward from the beam ends to the terminated slab edges outside of the core, similar to the behavior shown in Fig. 5.8(d) for Specimen 1. Inside the core, where the slab was continuous between the wall piers, cracking was better distributed and less spalling was observed. This may indicate that the greater slab damage that occurred outside of the core wall could be a result of the slab discontinuity along the outer edges of the test specimen. In an actual building, the continuation of the floor slabs further out from the core wall would eliminate this discontinuity and likely improve the performance of the slabs.

Overall, the fully post-tensioned coupling beams performed well during the test

and demonstrated the advantages of the new system. As representative examples, Figs. 6.8(e-f) show the post-test damage states of the 1st and 3rd floor south coupling beams, respectively. Much like in Specimen 1, concentrated cracks formed at the beam ends while minimal cracking was observed in the span. Concrete crushing was mostly limited to the spalling of the cover near the beam ends and in the adjacent wall pier regions. The confined concrete at the beam ends remained mostly undamaged despite the larger beam rotations (see next section) in Specimen 2. The concrete damage in the wall pier regions adjacent to the coupling beams was similar to the damage observed in Specimen 1, indicating that the additional horizontal mild steel bars provided in the wall pier regions did not have a significant effect on the performance of these regions in Specimen 2.

6.3.3 Coupling Beam Behavior

The measured absolute end rotations, |θb|, for the coupling beams in Specimen 2 are shown in Fig. 6.9. Because Specimen 2 was subjected to greater lateral drifts than Specimen 1, the maximum beam end rotations were also significantly greater. The largest beam rotations occurred in the 3rd floor of the structure, reaching a maximum of |θb|=11.0%. This was nearly 30% greater than the largest measured beam end rotation in Specimen 1 (|θb|=8.5%), which was also in the 3rd floor. Overall, the coupling beams in both test specimens demonstrated similar behavior with rotations increasing from the 1st to the 3rd floor.

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(a) (b)

(c) (d)

(e) (f) Figure 6.8 Damage at completion of test (Specimen 2): (a) north toe of east wall pier base; (b) north toe of west wall pier base; (c) south corner of east wall pier base; (d)

bottom of 1st floor slab; (e) 1st floor south beam; (f) 3rd floor south beam

Fig. 6.10 shows the measured average PT strand stresses in the coupling beams of Specimen 2, calculated as the total beam PT force, Fp (sum of the strand forces) divided by the total design ultimate strength of the strands, Fpu=ΣApfpu. Despite the larger beam rotations and greater beam depth in Specimen 2, the measured PT forces were not significantly greater than those measured in Specimen 1. The largest average strand

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stresses during the test were slightly greater than 0.90fpu, which occurred in the 2nd and 3rd floor south coupling beams because of slightly greater initial strand stresses in these beams prior to testing. These maximum stresses exceeded the limit of proportionality, fpl=0.85fpu, of the steel by a small amount. The average strand stresses in the other four coupling beams were all less than the proportionality limit.

Figure 6.9 Absolute beam end rotation versus 3rd floor drift (Specimen 2): (a) 3rd floor south; (b) 3rd floor north; (c) 2nd floor south; (d) 2rd floor north; (e) 1st floor

south; (f) 1st floor north

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Figure 6.10 Total beam PT force versus 3rd floor drift (Specimen 2): (a) 3rd floor

south; (b) 3rd floor north; (c) 2nd floor south; (d) 2rd floor north; (e) 1st floor south; (f) 1st floor north

Similar to Fig. 5.11(a) for Specimen 1, Fig. 6.11(a) shows the maximum measured horizontal separation between the pier flanges (along the same line as the coupling beams) at the first peak of the 1st cycle in each drift series from the testing of Specimen 2. Note that some of the data is missing from Fig. 6.11(a) due to the loss of displacement transducers during the test. The increases in the beam PT strand forces, Fp illustrated in Fig. 6.10 occurred as the horizontal distance between the wall piers increased with increased lateral displacements. Because of the greater coupling beam

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depth, the maximum wall pier separations in Specimen 2 were generally greater than those in Specimen 1 at the same drift level. However, it can be seen that the maximum pier separations in Specimen 2 no longer increased and actually decreased during the final drift series due to increased concrete crushing at the coupling beam ends under larger rotations than those for Specimen 1. This is consistent with the measured beam PT forces in Fig. 6.10. For example, Fig. 6.10(b) shows a large drop in the 3rd floor north coupling beam PT forces during the final drift series. A similar drop in maximum wall pier separation is shown in Fig. 6.11(a) for the same location in the structure.

Similar to Specimen 1, a permanent (residual) increase in Fp in Fig. 6.10 from the initial PT force occurred in all six coupling beams as Specimen 2 was returned to Δ3=0% from increasing nonlinear lateral displacements. This increase in Fp was caused by the permanent separation of the wall piers as shown in Fig. 6.11(b) by plotting the increase in the horizontal distance between the pier flanges upon returning the structure to Δ3=0% after the completion of the 1st half cycle in each drift series. It can be seen that there was an almost linear increase in the permanent wall pier separation until the final drift series when the permanent separation essentially remained constant (except for the 3rd floor south beam location). This can likely be attributed to the fracture of numerous vertical bars at the wall pier bases, which greatly reduced the continued accumulation of plastic strains in the structure. The reason for the increased permanent wall pier separation at the 3rd floor south beam location during the final drift series is not known; however, one possibility is concrete debris filling the large cracks at the beam ends and preventing the cracks from closing. Because the permanent separation of the wall piers at a given drift level was similar in magnitude between the two specimens (i.e., pier separation in Specimen 1 was not greater than that in Specimen 2), which had the same amount of mild steel reinforcement at the wall pier bases, it can be concluded that the yielding of the ED mild steel bars in the coupling beams of Specimen 1 did not contribute significantly to the permanent horizontal separation between the piers.

Figure 6.11 Measured separation between east and west wall piers (Specimen 2): (a) maximum; (b) residual

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6.3.4 DIC Results Fig. 6.12 shows the processed DIC images [from sensor 3D9 (see Fig. 6.4)] for the horizontal strains at the west end of the 3rd floor north coupling beam during loading of the structure in the west (positive) direction. These strains were calculated using a gauge length of 16.575 mm (0.65 in.) from the displacements taken at the west peak of the 1st cycle for each drift series. The corresponding measured 3rd floor drift, Δ3, and beam end rotation, θb, are provided beneath each image. The bright red colors in the figures represent the largest positive (tension) horizontal strains and indicate where concrete cracks likely formed (note that the widths of the red shaded regions are not indicative of the crack widths). For example, a crack at the top of the beam end (below the slab) is shown in the image for Δ3=+0.09%. Due to the location of DIC sensor 3D9, the strains at the top of the slab could not be captured and, therefore, it can be assumed that the crack actually initiated earlier during the test at the top of the slab. The downward propagation of this crack is illustrated in the subsequent images as the beam end rotations increased significantly. This resulted in the degradation of the DIC pattern painted on the concrete surface and the loss of data along the crack in the later images. Another important observation is the large compression (negative) strains at the bottom corner of the beam end and the adjacent wall pier region (i.e., dark blue colors in the later images). The development of these large compression strains validates the coupling beam behavior and the need for significant confinement reinforcement in the beam web.

Similarly, Fig. 6.13 shows the horizontal strains at the 3rd floor beam west end when the structure was loaded in the east (negative) direction. It can be seen that tensile strains in the concrete began to develop at the bottom of the beam-to-wall interface during the first drift series of the test. The upward propagation of the crack occurred during the Δ3=-0.07% drift series before extending into the bottom of the floor slab in the following drift increments. Again, due to the location of DIC sensor 3D9, the strains at the top of the slab could not be measured. As such, the compression strains that developed at the top of the slab when the structure was loaded in the east direction cannot be seen.

Similar to Fig. 5.12(a) for Specimen 1, Fig. 6.14(a) shows the concentrated crack

widths measured near the west end bottom corners of the 1st and 3rd floor coupling beams using DIC sensors 3D8 and 3D9 in Specimen 2 (see Fig. 6.4). The crack widths were determined as the horizontal displacement over the cracked zone between the end of each beam and the adjacent wall pier when the peak drift was reached during the 1st cycle of each wall drift increment in the east (negative) direction. Similar to Specimen 1, the crack widths for Specimen 2 increased from the 1st to the 3rd floor beams. However, because of the greater beam depth, the measured crack widths for Specimen 2 were greater than those for Specimen 1 at the same drift levels.

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Δ3 = +0.01% θb = +0.04%

Δ3 = +0.02% θb = +0.06%

Δ3 = +0.05% θb = +0.17%

Δ3 = +0.09% θb = +0.26%

Δ3 = +0.14% θb = +0.40%

Δ3 = +0.20% θb = +0.68%

Δ3 = +0.30% θb = +1.04%

Δ3 = +0.46% θb = +1.61%

Δ3 = +0.73% θb = +2.42%

Δ3 = +1.15% θb = +3.61%

Δ3 = +1.65% θb = +5.03%

Δ3 = +2.65% θb = +8.07%

Figure 6.12 Specimen 2 DIC images – 3rd floor beam west end horizontal strains (loading west)

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Δ3 = -0.02% θb = -0.04%

Δ3 = -0.03% θb = -0.08%

Δ3 = -0.07% θb = -0.12%

Δ3 = -0.10% θb = -0.34%

Δ3 = -0.14% θb = -0.50%

Δ3 = -0.21% θb = -0.75%

Δ3 = -0.30% θb = -1.16%

Δ3 = -0.43% θb = -1.75%

Δ3 = -0.67% θb = -2.58%

Δ3 = -1.01 % θb = -3.69%

Δ3 = -1.62% θb = -5.73%

Δ3 = -2.50% θb = -8.76%

Figure 6.13 Specimen 2 DIC images – 3rd floor beam west end horizontal strains (loading east)

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(a) (b)

(c) Figure 6.14 Specimen 2 DIC results: (a) beam end concentrated crack widths;

(b) contributions to 1st floor drift; (c) relative contributions to 1st floor drift

Similar to Fig 5.12(b) for Specimen 1, Fig. 6.14(b) shows the contributions of four deformation mechanisms to the 1st floor drift, Δ1 of Specimen 2 (using the measurements from DIC sensors 3D2 and 3D3) plotted against the 3rd floor drift, Δ3. The drift contributions were calculated (and averaged) for the east and west wall piers at the positive and negative peaks during the 1st cycle for each drift increment, except for the validation-level drift series when the contributions were calculated for the 1st and 3rd cycles. Fig. 6.14(c) normalizes these drift contributions with respect to the total 1st floor drift, Δ1 (such that the sum of the four relative contributions is equal to 100%). Unlike the trends observed for Specimen 1 [see Fig. 5.12(c)], the wall pier shear deformations in Specimen 2 were greater than the pier axial-flexural deformations throughout the test. This behavior may be attributed to the larger stiffness of the deeper coupling beams in Specimen 2. During the larger Δ3 levels, the two specimens behaved similarly, with the lateral displacements governed by the concentrated rotations of the wall piers with respect to the foundation. Additionally, the contributions from the shear deformations of

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the wall piers (around 10-30%) and slip at the base joint (around 5-10%) for Specimen 2 were similar to those for Specimen 1 during the larger Δ3 levels.

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CHAPTER 7: SUMMARY OF RESULTS AND REMAINING WORK

This research report presents the findings from the large-scale experimental evaluation and the associated design and analytical studies of two multi-story RC coupled shear wall test specimens with post-tensioned coupling beams. The results from both of these structures are in conformance with and support the original project objectives of: (1) demonstrating the performance benefits of the new system as compared to conventional RC coupled wall structures; (2) developing a validated seismic design procedure and practical design guidelines/recommendations; (3) developing validated analytical models and design tools that can accurately predict performance; and (4) providing experimental and analytical evidence that support the classification of these structures as “special” RC shear walls per ACI 318 (2011) and ACI ITG-5.1 (2007). These results constitute a necessary step towards the practical implementation of post-tensioned coupled shear wall structures in moderate and high seismic regions of the U.S. 7.1 Comparisons with ACI ITG-5.1 Validation Requirements Table 7.1 evaluates the measured performance of the two test specimens according to the ACI ITG-5.1 (2007) validation requirements up to the 3rd cycle of the largest sustained drift series. In reviewing these results, it should be kept in mind that both structures were intentionally designed with little over-capacity in force or displacement so as to critically assess the limits of the design procedure, assumptions, and approximations. The strength loss of Specimen 2 from the overall peak strength to the peak load during the 3rd cycle of the last fully-completed drift series (with 8-story roof drift of Δr=+3.25% and -3.22%) was 9.6% and 12.3% in the positive and negative directions, respectively. Thus, this specimen satisfied the main validation criterion of sustaining three loading cycles at or above the validation-level 8-story roof drift of Δwm=±3.0% with no more than 20% loss in peak lateral resistance. While the strength losses in Specimen 1 (20.7% and 22.2% loss in the positive and negative loading directions, respectively) slightly exceeded the maximum 20% loss permitted by ACI ITG-5.1, these losses occurred during displacements of the structure (Δr=+3.10% and -3.18%) that exceeded the validation-level roof drift. Important design and detailing considerations were learned from the performance of Specimen 1, which contributed to the improved performance of Specimen 2 (in particular, the deliberate unbonding of the vertical mild steel bars in the wall pier toes at the base of Specimen 2).

Both structures satisfied all of the other ACI ITG-5.1 validation requirements, with the exception of the minimum secant stiffness ratio and maximum shear slip limits (the measured shear slips for Specimen 1 would have been greater than the ACI ITG-5.1 limit during the validation-level drift series). The secant stiffness and shear slip in both structures did not result in any undesirable performance, indicating that the current limits in ACI ITG-5.1 may be too conservative for RC coupled shear wall structures with post-tensioned coupling beams. Note that the secant stiffnesses were originally calculated using the measured 3rd floor drift rather than the 8-story roof drift for the full structure as prescribed by ACI ITG-5.1, leading to an artificial reduction in the secant stiffness ratio,

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Ksec/Ks. As such, the secant stiffness ratios in Table 7.1 were scaled up by a factor of about 30% (determined using the analytical models) to account for this effect. Note also that although the secant stiffnesses for both test specimens did not satisfy the minimum requirement per ACI ITG-5.1, these stiffnesses would satisfy the acceptance criterion in ACI ITG-1.1 (2001) for moment frames, which requires that the secant stiffness, Ksec≥0.05Ks.

Table 7.1 – Comparisons with ACI ITG-5.1 Validation Requirements Validation Criterion Performance Requirement Specimen 1 Specimen 2

largest sustained roof drift series

Δwm = ±3.0% +loading (west) +3.10%1 +3.25%1

-loading (east) -3.18%1 -3.22%1

base shear strength loss ≤ 20% +loading (west) 20.7% 9.6% -loading (east) 22.2% 12.3%

2design/measured base shear strength

0.90-1.20 (range) +loading (west) 1.00 0.93 -loading (east) 0.97 0.94

relative energy dissipation ratio, βh

≥ 0.125 n/a 0.314 0.277

3secant stiffness, Ksec ≥ 40.10Ks +loading (west) 0.07Ks 0.09Ks -loading (east) 0.10Ks 0.05Ks

beam PT stress at 0.5Δwm ≤ [email protected]

1st floor beams 0.77 0.73

2nd floor beams 0.76 0.86

3rd floor beams 0.85 0.87

6shear slip at base ≤ 1.5 mm +loading (west) 1.55 mm 4.29 mm -loading (east) 1.34 mm 3.15 mm

Notes: 1Δr=analytically-determined 8-story roof drift corresponding to the measured 3rd floor drift, Δ3; 2ratio taken at the design-level drift, Δwd using the predicted base shear strength from the design procedure; 3Ksec=measured secant stiffness during the 3rd cycle of the largest sustained drift series [ACI ITG-5.1 (2007)]; 4Ks=measured initial secant stiffness at 75% of Ent, where Ent is the design base shear strength of the structure using measured material properties [ACI ITG-5.1 (2007)]; [email protected]=stress in PT steel at 0.01 mm/mm strain based on monotonic material testing [1719.5 MPa and 1705.0 MPa for 15.2 mm and 12.7 mm diameter strands, respectively]; 6Specimen 1 shear slip values are for the drift series prior to the validation-level drift, because of lack of data (removal of sensors) beyond this point in the test.

7.2 Comparisons with Design Predictions Table 7.2 compares key aspects of the measured behavior in the initial loading direction (east for Specimen 1 and west for Specimen 2) of the test specimens with the design predictions at the design-level drift, Δwd3 for the 3rd floor. The design-level drift differed slightly between the two test specimens because of the different material properties (i.e., actual compression strength, f’c of the concrete) in each specimen as well as differences in the depths and assumed effective linear-elastic stiffnesses of the coupling beams (see Table 3.1). The measured material properties for the concrete and for the PT and mild steel (see Figs. 5.3 and 6.4), as well as the measured initial stresses in the PT strands, were used in the design predictions. It can be seen from Table 7.2 that the design predictions at the design-level drift compared reasonably well with the measured behaviors of the test specimens. The predicted design-level base shear strengths, Vwd were about 2.9% and 7.3% lower than the measured strengths for Specimens 1 and 2, respectively, indicating that the design procedure provided conservative and close strength predictions. Overall, the design procedure also provided reasonable predictions for the measured beam rotations at the design-level drift. The predictions for the PT strand stresses, unbonded mild steel bar strains, and concentrated crack widths at the bottom of the beam ends compared well with the measured values as well. Some of the

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discrepancies could be attributed to the inability of the effective linear-elastic coupled shear wall models to accurately predict the deformation distributions within the structure.

Table 7.2 – Comparisons with Design Predictions at Design-Level Drift

Design Parameter Specimen 1 (Δwd3=0.52%) Specimen 2 (Δwd3=0.53%)

Design Measured Design Measured

base shear strength, Vwd

1512 kN 1557 kN 1650 kN 1779 kN

beam end rotation, θbd

1st floor (south) 1.21% 1.02% 1.19% 1.08%

1st floor (north) 1.21% 1.05% 1.19% 1.00%

2nd floor (south) 1.60% 1.53% 1.57% 1.55%

2nd floor (north) 1.60% 1.49% 1.57% 1.44%

3rd floor (south) 1.90% 1.84% 1.87% 1.96%

3rd floor (north) 1.90% 1.92% 1.87% 1.82%

average beam PT

stresses, fpd

1st floor (south) 0.61fpu 0.61fpu 0.62fpu 0.59fpu

1st floor (north) 0.61fpu 0.61fpu 0.58fpu 0.56fpu

2nd floor (south) 0.64fpu 0.62fpu 0.67fpu 0.65fpu

2nd floor (north) 0.61fpu 0.59fpu 0.59fpu 0.57fpu

3rd floor (south) 0.63fpu 0.61fpu 0.72fpu 0.70fpu

3rd floor (north) 0.68fpu 0.68fpu 0.63fpu 0.61fpu

1average unbonded mild steel strains, εsd

1st floor (south) 0.77% 0.66% 0.19% 0.16%

1st floor (north) 0.77% 0.53% 0.20% 0.16%

2nd floor (south) 1.12% 1.25% 0.27% 0.25%

2nd floor (north) 1.13% 1.01% 0.28% 0.22%

3rd floor (south) 1.35% 1.24% 0.33% 0.30%

3rd floor (north) 1.30% 1.29% 0.32% 0.28%

2beam end concentrated crack width,

δbd

1st floor (south) 2.67 mm 2.53 mm 3.57 mm 3.29 mm

1st floor (north) 2.67 mm 2.47 mm 3.59 mm 3.25 mm

2nd floor (south) 3.62 mm 3.71 mm 4.75 mm 5.11 mm

2nd floor (north) 3.63 mm 3.75 mm 4.79 mm 5.20 mm

3rd floor (south) 4.30 mm 4.82 mm 5.67 mm n/a

3rd floor (north) 4.27 mm 5.13 mm 5.66 mm 5.99 mm Notes: n/a = not available. 1strains given for Specimens 1 and 2 are for the unbonded ED bars and the unbonded slab reinforcement (see Fig. 6.3), respectively; 2horizontal displacement between the bottom of the beam end and the adjacent wall pier.

7.3 Main Findings and Conclusions

The main findings and conclusions from this research are listed below. (1) Overall, both test specimens performed as predicted and validated the design

approach. The structures demonstrated ductile behavior up to 3rd floor drifts that analytically translated to drift levels greater than 3.0% at the roof of the full 8-story structure, which was the maximum drift used in design according to the validation requirements prescribed by ACI ITG-5.1 (2007). Despite the significantly greater number

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of loading cycles, both structures showed greater ductility and better performance than that observed in the recent testing of a conventional RC coupled shear wall structure.

(2) The predicted behavior from the fiber-element numerical models generally

matched the measured behavior of the test specimens well, demonstrating the validity of the modeling approach.

(3) The high-fidelity measured performance of both structures as well as

favorable comparisons with the design and analytical predictions support the classification of unbonded post-tensioned coupled wall structures as “special” RC shear walls per ACI 318 (2011) and ACI ITG-5.1

(4) Results from the digital image correlation (DIC) monitoring showed that the

nonlinear lateral drift response of both structures was dominated by concentrated rotations at the wall pier bases, while contributions due to shear and axial-flexural deformations of the wall piers were much smaller.

(5) Consistent with the large base rotations of the wall piers, the ultimate failure

in both structures was largely caused by the low-cycle fatigue fracture (preceded by buckling) of the vertical (flexural) reinforcing bars crossing the pier-to-foundation joints at the wall pier toes. This behavior was significantly delayed in Specimen 2 due to the deliberate unbonding of the vertical bars from the foundation concrete below the wall pier toes, resulting in greater ductility of the structure. The superior performance that was achieved by unbonding the vertical bars below the wall pier toes would be possible in conventional RC coupled walls and isolated walls as well. Thus, it is recommended that this improved detailing be implemented in ACI 318 as a required specification for the vertical bars in the boundary regions of special RC shear walls.

(6) In Specimen 1, spalling of the cover concrete and buckling of the vertical bars

in between the U-shaped bars at the outer corners of the wall pier bases were also observed. The use of additional U-shaped bars in these regions delayed the buckling of the vertical bars in Specimen 2. However, buckling and subsequent fracture of numerous extreme vertical mild steel bars along the outer edges of the flanges occurred at the wall-to-foundation interface (rather than in between the U-shaped bars above the interface, as was observed in Specimen 1). This indicates that structural performance could be improved further by applying the detailing for the unbonding of the vertical mild steel bars at the wall pier bases to the extreme (outer) bars in the flanges as well.

(7) The PT steel in the coupling beams was designed to create a large diagonal

compression strut over the beam length, which also resulted in large compression stresses at the beam-to-wall joint regions. In addition to the spalling of cover concrete at the beam ends, these large compression stresses caused spalling of the cover concrete in the wall pier regions adjacent to the coupling beam webs in both structures. In Specimen 2, the placement of additional horizontal wall pier reinforcement across from the beam confined concrete regions had no significant effect on the spalling of the wall pier cover concrete.

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(8) The coupling beams performed well during both tests, demonstrating the advantages of the new system and validating the overall design philosophy. The damage was mostly limited to localized cover concrete spalling at the beam ends, indicating that the confinement hoops were adequate. Concentrated cracks at the beam ends allowed large nonlinear rotations (up to 8.5% in Specimen 1 and 11.0% in Specimen 2) with minimal cracking in the rest of the span. The rectilinear orientation of the beam reinforcement and localization of damage under large nonlinear rotations represent significant benefits of the new system over conventional diagonally-reinforced beams.

(9) The results from both tests showed that the beam end rotations increased from

the 1st to the 3rd floor of the specimen. This behavior, which was also evident in the numerical models, occurred due to the larger restraining effect of the wall piers at the base and the nonlinear deflected shape of the structure over the height.

(10) In Specimen 1, buckling of a single ED bar was observed in one of the

partially post-tensioned coupling beams (with additional concrete spalling and splitting adjacent to the buckled bar). This can be prevented by extending the closely-spaced confinement hoops over the entire unbonded length of the ED bars.

(11) The elimination of the ED bars in Specimen 2 resulted in a fully post-

tensioned coupling beam design that further simplified the proposed system. Despite this major simplification, the coupling beams provided adequate coupling to the structure. Furthermore, the energy dissipation in the system was still significantly above the minimum level prescribed by ACI ITG-5.1 (2007). These results indicate that the fully post-tensioned coupling beam is the preferred design.

(12) In both structures, significant concrete cracking and spalling were observed

in the post-tensioned slabs outside of the core wall. Inside the core, where the slab was continuous between the wall piers, cracking was better distributed and less spalling was observed. Modifications to the post-tensioned floor slab construction and reinforcement detailing in Specimen 2 had minimal effect, indicating that the slab damage that occurred outside of the core wall could be a result of the slab discontinuity along the outer edges of the test specimens.

(13) As each structure was displaced laterally, the deformed shape of the coupling

beams (i.e., large rotations and development of concentrated cracks at the beam ends) caused the two wall piers to separate horizontally. Despite the elongation of the beam PT strands due to this wall pier separation, the PT steel in both structures remained mostly linear-elastic with maximum stresses below or slightly exceeding the limit of proportionality of the strands. Consistent with the increased beam end rotations, the strands with the largest stresses during the test were in the 3rd floor beams.

(14) With increased lateral displacements of the structure, crushing of concrete in

the beam-to-wall joint regions resulted in the eventual reduction in the rate of increase in maximum wall pier separation. This caused an eventual reduction in the rate of increase in the PT steel stresses at larger drift values.

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(15) In both tests, the accumulation of plastic strains in the vertical (flexural) mild steel bars at the wall pier bases resulted in permanent (residual) horizontal separation of the wall piers upon returning the structure to zero 3rd floor drift (i.e., Δ3=0%) from increasing lateral drift in the nonlinear range. This permanent wall pier separation caused permanent increases in the PT strand stresses in all of the coupling beams when the structure was returned to Δ3=0%. Because the permanent horizontal separation of the wall piers was similar in magnitude between the two specimens (which had the same amount of mild steel reinforcement at the wall pier bases), it is concluded that the yielding of the ED mild steel bars in the coupling beams of Specimen 1 did not contribute significantly to the permanent wall pier separation. The strain gauge data for the ED bars showed little accumulation of plastic strains, supporting this conclusion.

(16) The permanent horizontal separation between the wall piers increased almost

linearly with increased lateral displacement throughout both tests; however, in Specimen 2, the permanent separation essentially remained constant between the final two drift increments (except for the separation of the structure along the 3rd floor south coupling beam) after a large number of vertical mild steel bars at the wall pier bases fractured.

(17) DIC was a valuable contributor to accomplishing the overall project

objectives. As examples, strains in critical regions, concentrated cracking, contributions of various deformation mechanisms (e.g., base rotation, shear) to overall drift were all measured. It is believed that this project deployed the largest number of DIC sensors (14 on Specimen 1) and the largest number of 3D DIC sensors (9 on Specimen 2) ever for a structural building evaluation. It was demonstrated that structural response monitoring using multiple DIC sensors can be done successfully with a reasonably simple protocol. 7.4 Remaining Work As part of the design of the two test specimens, a number of analytical models were built to simulate the expected structural behavior under reversed-cyclic lateral loading. Although these initial numerical models provided an accurate representation of the test specimens, they can be improved upon by using the full measured data. The continued analysis of the experimental data will assist in developing a more refined analytical model. Currently, the post-processing and study of the results from the test specimens have been limited to a subset of the available measured data. A detailed evaluation of the full sensor data will be conducted. Specifically, the continued processing of hundreds of DIC images that were obtained during the tests represents a significant undertaking. This will be conducted by Prof. Michael McGinnis at the University of Texas at Tyler. One of the most important remaining tasks is the organization of the validated seismic design procedures, approximations, assumptions, and tools into a final Design Procedure Document for post-tensioned coupled shear wall systems that can be used by structural engineering practitioners. This document will include a step-by-step description of the design, demonstrated by a full-scale numerical example. The completion of the

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Design Procedure Document is an important and vital step towards the eventual implementation of the new system in practice.


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REFERENCES

ACI, “ACI 318-11 Building Code Requirements for Structural Concrete (ACI 318-11) and Commentary,” Committee 318, American Concrete Institute, 2011.

ACI, “ACI ITG-1.1-01 Acceptance Criteria for Moment Frames Based on Structural Testing,” ACI Innovation Task Group 1, American Concrete Institute, 2001.

ACI, “ACI ITG-5.1-07 Acceptance Criteria for Special Unbonded Post-Tensioned Precast Structural Walls Based on Validation Testing and Commentary,” ACI Innovation Task Group 5, American Concrete Institute, 2007.

ACI, “ACI ITG-5.2-09 Design of a Special Unbonded Post-Tensioned Precast Shear Wall Satisfying ACI ITG-5.1 Requirements,” ACI Innovation Task Group 5, American Concrete Institute, 2009.

Adebar, P., Hindi, R., and Gonzalez, E., “Seismic Behavior of a Full-Scale Diagonally Reinforced Slender Coupling Beam,” Technical Report, Dept. of Civil Engineering, The University of British Columbia, Vancouver, Canada, 2001.

Aktan, A.E., Bertero, V.V., “Seismic Responses of R/C Frame-Wall Structures,” J. of Structural Engineering, 110(8), 1984, 1803-1821.

ASCE/SEI 7-10, “Minimum Design Loads for Buildings and Other Structures,” American Society of Civil Engineers, Reston, Virginia, 2010.

ASTM, Annual Book of ASTM Standards, ASTM Intern., 2013, West Conshohocken, PA.

Barney, G., Shiu, K., Rabbat, B., Fiorato, A., Russell, H., Corley, W., “Earthquake Resistant Structural Walls – Tests of Coupling Beams,” Construction Tech. Lab. Report, Portland Cement Assoc., January 1978.

Bristowe, S., “Seismic Response of Normal and High Strength Concrete Members,” Ph.D. Dissertation. Civil Engineering and Applied Mechanics, McGill U., Montreal, Canada, 2000.

Canbolat, B., Parra-Montesinos, G., Wight, J., “Experimental Study on Seismic Behavior of High-Performance Fiber-Reinforced Cement Composite Coupling Beams,” ACI Structural J., 102(1), 2005, 159-166.

CSI, “CSI Analysis Reference Manual for SAP2000, ETABS, and SAFE,” Computers and Structures, Inc., Berkeley, California, October 2005.

Fortney, P., Rassati, G., Shahrooz, B., “Investigation on Effect of Transverse Reinforcement on Performance of Diagonally Reinforced Coupling Beams,” ACI Str. J., 105(6), 2008, 781-788.

Galano, L., Vignoli, A., “Seismic Behavior of Short Coupling Beams with Different Reinforcement Layouts,” ACI Structural J., 97(6), 2000, 876-885.

Kwan, A. and Zhao, Z., “Cyclic Behaviour of Deep Reinforced Concrete Coupling Beams,” Structures & Buildings, 152(3), 2002, 283-293.

Kurama, Y., Weldon, B., Shen, Q., “Experimental Evaluation of Post-Tensioned Hybrid Coupled Wall Subassemblages,” J. of Structural Engineering, Vol. 132, No. 7, July 2006, pp. 1017-1029.

Lehman, D., Turgeon, J., Birely, A., Hart, C., Marley, K., Kuchma, D., Lowes, L., “Seismic Behavior of a Modern Concrete Coupled Wall,” J. of Structural Engineering, 139, SPECIAL ISSUE: NEES 2: Advances in Earthquake Eng., 2013, 1371-1381.

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Lequesne, R., Parra-Montesinos, G., Wight, J., “Seismic Behavior and Detailing of High-Performance Fiber-Reinforced Concrete Coupling Beams and Coupled Wall Systems,” J. of Structural Engineering, 139, SPECIAL ISSUE: NEES 2: Advances in Earthquake Eng., 2013, 1362-1370.

McGinnis, M., Barbachyn, S., Holloman, M., Kurama, Y., “Experimental Evaluation of a Multi-Story Post-Tensioned Coupled Shear Wall Structure,” ASCE Structures Congr., Pittsburgh, PA, May 2-4, 2013, 12 pp.

McGinnis, M., Barbachyn, B., Kurama, Y., “Application of Multiple Digital Image Correlation Sensors in Earthquake Engineering,” 10th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014, 10 pp.

Oesterle, R. G., Fiorato, A. E., Johal, L. S., Carpenter, J. E., Russell, H. G., Corley, W. G., “Earthquake Resistant Structural Walls – Tests of Isolated Walls,” Report to National Science Foundation, PCA Construction Technology Laboratories, Skokie, IL, 1976, 317 pp.

Ozselcuk, A. R., “Experimental and analytical studies of coupled wall structures.” Ph.D. dissertation, Univ. of California, Berkeley, CA, 1989.

Peterson, K., Pakzad, S., Shahidi, S., Barbachyn, S., Kurama, Y., “Advanced Sensing Techniques for Damage Detection in Reinforced Concrete Structures,” ASCE Structures Congr., Boston, MA, April 3-5, 2014, 12 pp.

Prakash, V., Powell, G, Campbell, S., “DRAIN-2DX Base Program Description and User Guide,” Dept. of Civil Eng., U. of California, Berkeley, California, 1993.

Santhakumar, A., “The Ductility of Coupled Shear Walls,” Ph.D. Dissertation, Univ. of Canterbury, Christchurch, New Zealand, 1974, 412 pp.

Shiu, K. N. , Aristizabal-Ochoa, J. D. , Barney, G. B. , Fiorato, A. E. , and Corley, W. G., “Earthquake resistant structural walls: Coupled wall tests.” Rep. to National Science Foundation, Construction Technology Laboratories, Portland Cement Association, Stokie, IL, 1981.

Smith, B., Kurama, Y., McGinnis, M., “Design and measured behavior of a hybrid precast concrete wall specimen for seismic regions,” J. of Structural Engineering, 137(10), 2011, 1052-1062.

Tassios, T., Moretti, M., Bezas, A., “On the Behavior and Ductility of Reinforced Concrete Coupling Beams of Shear Walls,” ACI Structural J., 93(6), 1996, 711-720.

Turgeon, J. A., “The seismic performance of coupled reinforced concrete walls.” M.S. thesis, Univ. of Washington, Seattle, WA, 2011.

Wallace, J., “Modeling Issues for Tall Core Wall Buildings,” The Structural Design of Tall and Special Buildings, 16, 2007, 615-632.

Walsh, K., Kurama, Y., “Behavior of Unbonded Post-Tensioning Monostrand Anchorage Systems Under Monotonic Tensile Loading,” PCI J., 55(1), 2010, 97-117.

Weldon, B., Kurama, Y., “Nonlinear Behavior of Precast Concrete Coupling Beams,” J. of Structural Engineering, 133(11), 2007, 1571-1581.

Weldon, B., Kurama, Y., “Experimental Evaluation of Post-Tensioned Precast Concrete Coupling Beams,” J. of Structural Engineering, 136(9), 2010, 1066-1077.

Weldon, B., Kurama, Y., “Analytical Modeling and Design Validation of Posttensioned Precast Concrete Coupling Beams for Seismic Regions,” J. of Structural Engineering, 138(2), 2012, 224-234.

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STRUCTURAL ENGINEERING RESEARCH REPORT SERIES LIST OF TECHNICAL REPORTS

NDSE-01-01 “Design of Rectangular Openings in Unbonded Post-Tensioned Precast

Concrete Walls,” by M. Allen and Y.C. Kurama, April 2001, 142 pp. (available for download at http://www.nd.edu/~concrete)

NDSE-01-02 “Capacity-Demand Index Relationships for Performance-Based Seismic Design,” by K.T. Farrow and Y.C. Kurama, November 2001, 260 pp. (available for download at http://www.nd.edu/~concrete)

NDSE-06-01 “Experimental Evaluation of Unbonded Post-Tensioned Hybrid Coupled Wall Subassemblages,” by M.A. May, Y.C. Kurama, and Q. Shen, April 2006, 212 pp. (available for download at http://www.nd.edu/~concrete)

NDSE-06-02 “Seismic Analysis, Behavior, and Design of Unbonded Post-Tensioned Hybrid Coupled Wall Structures,” by Q. Shen, Y.C. Kurama, and B.D. Weldon, December 2006, 596 pp. (available for download at http://www.nd.edu/~concrete)

NDSE-07-01 “Friction-Damped Unbonded Post-Tensioned Precast Concrete Moment Frame Structures for Seismic Regions,” by B.G. Morgen and Y.C. Kurama, March 2007, 610 pp. (available for download at http://www.nd.edu/~concrete)

NDSE-09-01 “Stress-Strain Properties of Concrete Under Elevated Temperatures,” by A.M. Knaack, Y.C. Kurama, and D.J. Kirkner, April 2009, 130 pp. (available for download at http://www.nd.edu/~concrete)

NDSE-09-02 “Behavior and Design of Unbonded Post-Tensioning Strand/Anchorage Systems for Seismic Applications,” by K.Q. Walsh and Y.C. Kurama, April 2009, 130 pp. (available for download at http://www.nd.edu/~concrete)

NDSE-11-01 “Analytical Evaluation of Diagonally-Reinforced Concrete Coupling Beams under Lateral Loads,” by S.M. Barbachyn and Y.C. Kurama, April 2011, 107 pp. (available for download at http://www.nd.edu/~concrete)

NDSE-12-01 “Hybrid Precast Wall Systems for Seismic Regions,” by B.J. Smith, Y.C. Kurama, and M.J. McGinnis, June 2012, 137 pp. (available for download at http://www.nd.edu/~concrete)

NDSE-12-02 “Seismic Design Guidelines for Special Hybrid Precast Concrete Shear Walls,” by B.J. Smith and Y.C. Kurama, June 2012, 88 pp. (available for download at http://www.nd.edu/~concrete)

NDSE-13-01 “Sustainable Concrete Structures using Recycled Concrete Aggregate: Short-Term and Long-Term Behavior Considering Material Variability,” by A.M. Knaack and Y.C. Kurama, October 2013, 566 pp. (available for download at http://www.nd.edu/~concrete)

NDSE-13-02 “Effects of Anchor Wedge Dimensional Parameters on Post-Tensioning Strand Performance,” by K.Q. Walsh, R.L. Draginis, R.M. Estes, and Y.C. Kurama, December 2013, 59 pp. (available for download at http://www.nd.edu/~concrete)

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NDSE-15-01 “Large-Scale Experimental Evaluation of Post-Tensioned Coupled Shear Wall Systems for Seismic Regions,” by S.M. Barbachyn, Y.C. Kurama, and M.J. McGinnis, January 2015, 64 pp. (available for download at http://www.nd.edu/~concrete)

Documents

Large-Scale Experimental Evaluation of Post-Tensioned