ABSTRACT. From past research post-tensioned concrete masonry walls have performed well

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1 ABSTRACT ROSENBOOM, OWEN ARTHUR. Post-Tensioned Clay Brick Masonry Walls for Modular Housing in Seismic Regions. (Under the direction of Dr. Mervyn Kowalsky.) From past research post-tensioned concrete masonry walls have performed well due to in-plane loading, yet despite the advantage of being more aesthetically pleasing, post-tensioned clay brick masonry walls have not been investigated under this loading. Five half scale structural specimens using this system were constructed and tested, and the results from these tests plus a proposed force-displacement analysis procedure are included herein. The results show that post-tensioned clay brick masonry walls are well suited for seismic regions when the walls are grouted and unbonded, and the presence of confinement plates in the compression region greatly enhances the overall performance of the wall. In addition, the force-displacement analysis shows that in order to account for the overall behavior of the wall, cyclic degradation characteristics must be included.

2 POST-TENSIONED CLAY BRICK MASONRY WALLS FOR MODULAR HOUSING IN SEISMIC REGIONS by OWEN ARTHUR ROSENBOOM A thesis submitted to the Graduate Faculty of North Carolina State University in partial fulfillment of the requirements for the Degree of Masters of Science CIVIL ENGINEERING Raleigh 2002 APPROVED BY: Chair of Advisory Committee

3 BIOGRAPHY Born and raised in Denver, CO, Owen Arthur Rosenboom received his undergraduate degree from Oklahoma State University in December After graduating from North Carolina State University with a Master s of Science in Structural Engineering he plans to travel to South America. ii

4 ACKNOWLEDGEMENTS The research described herein was funded by the National Science Foundation (Grant # ) under the auspices of the PATH (Partnership for Advancing Technology in Housing) Program. See for more information. Material support was given by AmeriSteel, General Shale Masonry, and Pinnacle Masonry, all from Raleigh, NC. In addition, none of this would have been possible without the technical guidance of Jerry Atkinson in the Constructed Facilities Laboratory (where this research took place). iii

5 Table of Contents List of Figures...vi List of Tables...x 1 Introduction Objective and Methods PATH Program Literature Review Page & Huizer, Larsen, Ingham, et al, PT Masonry Behavioral Mechanisms Origin Oriented Sliding Rocking Compression Strut Base Crack Formation Wall, Footing and Stub Beam Design Clay Masonry Units Wall Aspect Ratio and Width Post-Tensioning System Confinement Plates Design of PH Steel Design of Footing, Stub Beam Material Properties Design for Post-Tensioning Force Wall Design Procedure Laursen Ingham Equation Post-Tensioning Force Determination Problems with Design Procedure Instrumentation Linear Potentiometers Strain Guages String Potentiometers Load Cells Construction and Test Setup Construction of Specimen Preliminaries Placement Attachment Stressing Operation Bonding Operation Test 1 - Unbonded Loading History Observations Test Results Test 2 PH Steel Observations Test Results Test 3 - Confined Observations Test Results Test 4 - Ungrouted Observations Test Results Test 5 - Bonded...91 iv

6 12.1 Observations Test Results Analysis ACI 530 Method Laterally Unrestrained Prestressing Tendons Laterally Restrained Prestressing Tendons Proposed Force-Displacement Analysis Procedure F- Analysis Unbonded Initial Conditions Cracking After Cracking F- Analysis PH Steel F- Analysis Confined F- Analysis - Bonded F- Analysis - Ungrouted Problems with Force-Displacement Analysis Neutral Axis Degradation Cyclic Behavior of PT Steel Cyclic Behavior of Masonry Analysis Using Known Bar Forces Limit States Discussion Limit States Determination Base Crack, Lateral Force Ratio, Residual Drift Ratio Average Masonry Compression Strain Secant Stiffness Post-Tensioning Force Relationships Strain from PH Steel Damping Conclusion / Recommendations Implications for Housing Structures Recommendations REFERENCES Appendix 1 Pictures A1.2 Test 1 Unbonded A1.2 Test 2 PH Steel A1.3 Test 3 Confined A1.4 Test 4 Ungrouted A1.5 Test 5 Bonded Appendix 2 Example Spreadsheet from Proposed Force-Displacement Analysis v

7 List of Figures Figure 1.1 Plan View of a Typical Structure...2 Figure 2.1 Drawing of Test Setup (Laursen, Ingham)...6 Figure 2.2 Photo of Test Setup (Laursen, Ingham)...6 Figure 2.3 Force-Displacement Hysteresis (Laursen, Ingham)...8 Figure 2.4 Total Force History (Laursen, Ingham)...9 Figure 3.1 Rocking Schematic...12 Figure 3.2 Diagram of Compression Strut...13 Figure 3.3 Base Crack from Top Displacement...15 Figure 4.1 Standard Clay Brick...17 Figure 4.2 Typical Cross-Section and Elevation of Test Specimens...18 Figure mm Dywidag Bars...19 Figure 4.4 Photo of Anchorage System...20 Figure 4.5 Drawings of Anchorage System...21 Figure 4.6 Drawing of Confinement Plate...23 Figure 4.7 Picture of Confinement Plate...23 Figure 4.8 Cross Section and Elevation of Confined Wall...24 Figure 4.9 Cross Section and Elevation of PH Steel Wall...26 Figure 4.10 Stress-Strain Curve of A706 Steel...27 Figure 4.11 Design Loads on Footing...28 Figure 4.12 Footing Cross Section...29 Figure 4.13 Stub Beam Cross Section...30 Figure 5.1 Displacement Design Spectra...34 Figure 5.2 PTR v. Drift Ratio...36 Figure 6.1 Linear Potentiometers at end of Wall...39 Figure 6.2 Linear Potentiometers along Wall/Footing Interface...39 Figure 6.3 Example of Base Crack Profile...41 Figure 6.5 Location of Strain Gauges on Plastic Hinge Steel...43 Figure 6.6 Picture of String Potentiometer...44 Figure 6.7 Types of Load Cells and Location...45 Figure 6.8 Picture of Load Cells...45 Figure 7.1 Drawing of Test Setup...46 Figure 7.2 Picture of Test Setup...47 Figure 7.3 Load Cell on top of Stub Beam...52 Figure 8.1 Loading History for All Tests...55 Figure 8.2 Force-Displacement History Test 1 Unbonded...60 Figure 8.3 Total Bar Force Test 1 Unbonded...61 Figure 8.4 Base Crack Profile Push Direction Test 1 Unbonded...62 Figure 8.5 Base Crack Profile Pull Direction Test 1 Unbonded...63 Figure 8.6 Base Crack Profile at Zero Displacement Test 1 Unbonded...64 Figure 8.7 Wall Curvature Test 1 Unbonded...65 Figure 9.1 Force-Displacement History Test 2 PH Steel...69 Figure 9.2 Total Bar Force Test 2 PH Steel...70 Figure 9.3 Base Crack Profile Push Direction Wall 2 PH Steel...71 Figure 9.4 Base Crack Profile Pull Direction Wall 2 PH Steel...71 Figure 9.5 Base Crack Profile at Zero Displacement Test 2 PH Steel...72 Figure 9.6 Wall Curvature Test 2 PH Steel...73 Figure 9.7 Strain Gauge History of PH1T...74 Figure 9.8 Strain Gauge History of PH2T...74 Figure 9.9 Strain Gauge History of PH3T...75 Figure 9.10 Strain Gauge History of PH4T...75 Figure 10.1 Force Displacement History Test 3 Confined...79 Figure 10.2 Total Bar Force Test 3 Confined...80 Figure 10.3 Base Crack Profile Push Direction Test 3 Confined...81 vi

8 Figure 10.4 Base Crack Profile Pull Direction Test 3 Confined...81 Figure 10.5 Wall Curvature Test 3 Confined...82 Figure 10.6 Base Crack Profile at Zero Displacement Test 3 Confined...83 Figure 11.1 Force Displacement History Test 4 Ungrouted...86 Figure 11.2 Total Bar Force Test 4 Ungrouted...87 Figure 11.3 Base Crack Profile Push Direction Test 4 Ungrouted...88 Figure 11.4 Base Crack Profile Pull Direction Test 4 Ungrouted...88 Figure 11.5 Wall Curvature Test 4 Ungrouted...89 Figure 11.6 Base Crack Profile at Zero Displacement Test 4 - Ungrouted...90 Figure 12.1 Force Displacement History Test 5 Bonded...94 Figure 12.2 Total Bar Force Test 5 Bonded...95 Figure 12.3 Base Crack Profile Push Direction Test 5 Bonded...96 Figure 12.4 Base Crack Profile Pull Direction Test 5 Bonded...96 Figure 12.5 Wall Curvature Test 5 Bonded...97 Figure 12.6 Base Crack Profile at Zero Displacement Test 5 Bonded...98 Figure 13.1 Force Displacement Envelope Test 1 Unbonded...99 Figure 13.2 Force Displacement Envelope Test 2 PH Steel Figure 13.3 Force Displacement Envelope Test 3 Confined Figure 13.4 Force Displacement Envelope Test 4 Ungrouted Figure 13.5 Force Displacement Envelope Test 5 Ungrouted Figure 13.6 d determination Figure 13.7 Masonry Strain Profile at Cracking Figure 13.8 Steel Strain Profile over the Cross-Section at Cracking Figure 13.9 Wall Free Body Diagram Figure Stress-Strain Curve for Dywidag PT Bar Figure Unconfined Masonry Stress-Strain Curve Figure Masonry Strain Profile Figure Stress-Strain Curve for Mild Steel Figure Stress-Strain Curve for Confined Masonry Figure Ungrouted Effective Width Figure Bar Force 1 Test 1 Unbonded Figure Bar Force 2 Test 1 Unbonded Figure Bar Force 3 Test 1 Unbonded Figure Bar Force 1 Test 2 PH Steel Figure Bar Force 2 Test 2 PH Steel Figure Bar Force 3 Test 2 PH Steel Figure Bar Force 1 Test 3 Confined Figure Bar Force 2 Test 3 Confined Figure Bar Force 3 Test 3 Confined Figure Bar Force 1 Test 4 - Ungrouted Figure Bar Force 2 Test 4 Ungrouted Figure Bar Force 3 Test 4 Ungrouted Figure Total Bar Force v. Cm Test 1 Unbonded Figure Total Bar Force v. Cm Test 2 PH Steel Figure Total Bar Force v. Cm Test 3 Confined Figure Total Bar Force v. Cm Test 4 Ungrouted Figure Analysis with Known Forces v. Test Test 1 Unbonded Figure Analysis with Known Forces v. Test Test 2 Ph Steel Figure Analysis with Known Forces v. Test Test 3 Confined Figure Analysis with Known Forces v. Test Test 4 Ungrouted Figure 14.1 Establishment of Base Crack Size Figure 14.2 Maximum Size of Base Crack Test 1 Unbonded Figure 14.3 Maximum Size of Base Crack Test 2 PH Steel Figure 14.4 Maximum Size of Base Crack Test 3 Confined Figure 14.5 Maximum Size of Base Crack Test 4 Ungrouted Figure 14.6 Maximum Size of Base Crack Test 5 Bonded vii

9 Figure 14.7 Lateral Force Ratio Test 1 Unbonded Figure 14.8 Lateral Force Ratio Test 2 PH Steel Figure 14.9 Lateral Force Ratio Test 3 Confined Figure Lateral Force Ratio Test 4 Ungrouted Figure Lateral Force Ratio Test 5 Bonded Figure Residual Drift Ratio Test 1 Unbonded Figure Residual Drift Ratio Test 2 PH Steel Figure Residual Drift Ratio Test 3 Confined Figure Residual Drift Ratio Test 4 Ungrouted Figure Residual Drift Ratio Test 5 Bonded Figure Adjusted Average Masonry Compression Strain Profile Figure Average Masonry Compression Strain Test 1 Unbonded Figure Average Masonry Compression Strain Test 2 PH Steel Figure Average Masonry Compression Strain Test 3 Confined Figure Average Masonry Compression Strain Test 4 Ungrouted Figure Average Masonry Compression Strain Test 5 Bonded Figure Secant Stiffness Ratio Test 1 Unbonded Figure Secant Stiffness Ratio Test 2 PH Steel Figure Secant Stiffness Ratio Test 3 Confined Figure Secant Stiffness Ratio Test 4 Ungrouted Figure Secant Stiffness Ratio Test 5 Bonded Figure Post-Tensioning Force Ratio Test 1 Unbonded Figure Post-Tensioning Force Ratio Test 2 PH Steel Figure Post-Tensioning Force Ratio Test 3 Confined Figure Post-Tensioning Force Ratio Test 4 Ungrouted Figure Post-Tensioning Force Ratio Test 5 Bonded Figure Residual Post-Tensioning Force Ratio Test 1 Unbonded Figure Residual Post-Tensioning Force Ratio Test 2 PH Steel Figure Residual Post-Tensioning Force Ratio Test 3 Confined Figure Residual Post-Tensioning Force Ratio Test 4 Ungrouted Figure Residual Post-Tensioning Force Ratio Test 5 Bonded Figure Limit State Strains in PH1T and PH2T Figure Limit State Strains in PH3T and PH4T Figure Damping from Hysteretic Loops Figure Damping v DR for All Walls Figure A1.1 Note on Pictures Figure A1.2 E side at DR=0.75% Figure A1.3 N side at DR=1.75% Figure A1.4 S side at DR=2.25% Figure A1.5 W side at DR=5.0% Figure A1.6 N end at DR=6.5% Figure A1.7 W side after DR=6.5% (end of test) Figure A1.8 W side at DR=0.5% Figure A1.9 N end at DR=1.0% Figure A1.10 N end at DR= Figure A1.11 E side at DR=5.0% Figure A1.12 E side at DR=6.5% cycle one pull Figure A1.13 E side during wall demolition Figure A1.14 S end at DR=0.5% Figure A1.15 S end at DR=1.75% Figure A1.16 S end at DR=2.25% Figure A1.17 N end at DR=5.0% Figure A1.18 E side at DR=6.5% Figure A1.19 S end at DR=8.0% Figure A1.20 W side at DR=10.0% Figure A1.21 W side at DR=11.3% first cycle push (end of test) viii

10 Figure A1.22 S end at DR=11.3% first cycle push (end of test) Figure A1.23 N end at DR=11.3% first cycle push (end of test) Figure A1.24 E side at DR=0.5% Figure A1.25 W side at DR=0.75% cycle one push Figure A1.26 E side at DR=0.75% cycle two push Figure A1.27 E side at DR=1.0% cycle one push (end of test) Figure A1.28 W side at DR=1.25% Figure A1.29 N end at DR=1.75% Figure A1.30 W side at DR=3.0% Figure A1.31 W side at DR=3.75% cycle one pull (end of test) Figure A1.32 W side at DR=3.75% cycle one pull (end of test) ix

11 List of Tables Table 2.1 Page Huizer Experimental Results...5 Table 2.2 Laursen Ingham Test Results (Walls with Aspect Ratio=2)...7 Table 4.1 Material Properties from Laboratory Tests...31 Table 4.2 Results from Grouted Prism Tests...31 Table 13.1 Results from Code Analysis Table 14.1 Limit States Test 1 Unbonded Table 14.2 Limit States Test 2 PH Steel Table 14.3 Limit States Test 3 Confined Table 14.4 Limit States Test 4 Ungrouted Table 14.5 Limit States Test 5 Bonded Table 14.6 Limit State Strain in Supplemental Mild Steel x

12 1 Introduction Due to poor past behavior, the use of clay masonry in earthquake regions is largely used to provide façade elements. The structural properties of the masonry are not taken into consideration when designing the building. But the walls which failed in a brittle manner due to these past seismic events were largely unreinforced. One type of clay masonry system which shows promise in seismic regions, and has not been extensively investigated, is a post-tensioned configuration. Using standard clay bricks, two wythes are constructed, and in the cavity readily available high strength threaded post-tensioning bars are placed. The cavity can be left ungrouted or grouted, and the bars may be bonded or unbonded. In any case, once the wall is constructed the bars are stressed using a hydraulic jack. It is this type of wall system under seismic (or cyclic in-plane) loading that is currently under investigation at North Carolina State University, and the results from the first set of tests are presented herein. The motivation for the research program on post-tensioned clay brick masonry is two-fold: First, clay brick is readily available throughout the world and is a familiar material that can be utilized as both the structural and architectural elements in a structure. Second, post-tensioned wall systems subject to seismic forces have been shown to provide several benefits, one of which is the self-correcting nature of such a system (9). This will be discussed in greater detail later. 1.1 Objective and Methods Described herein is traditional research aimed at evaluating the effect of different design details on the performance of post-tensioned clay brick masonry. Specifically, the 1

13 influence of grout, confinement, regular reinforcing in the plastic hinge region and bond between the grouted cavity and the post-tensioning steel are considered. The end product of identifying a sound post-tensioned masonry system is to apply such a system in a modular housing or a light industrial application. The largescale tests conducted in this research only deal with the structural performance of such a system, and future tests must be performed to evaluate how a post-tensioned masonry wall can be tied into an overall system, and how different variables such as door and window cutouts will influence design. However, the simple structural wall tested in this research had its basis from isolating an element in a simple structure such as a house (see Figure 1.1). Masonry Wall Figure 1.1 Plan View of a Typical Structure Some momentum in studying post-tensioned masonry walls also comes from the fact that they may be well suited for off-site construction. Once constructed, they could be transported to the job site, where the post-tensioning bars could be added and stressed. 2

14 This could provide a way to construct an economical modular structure in a seismic region. The research involves the following components: (1) Review of past research on post-tensioned masonry. (2) Discussion of the major behavioral characteristics of posttensioned masonry walls. (3) Design for post-tensioning force based upon a displacement based design approach. (4) Design, construction and testing of five large scale walls. (5) Assessment of limit state design parameters such as drift levels, damping and strength. (6) Comparison between a proposed force-displacement analysis and existing analysis procedures. (6) Identification of aspects of non-linear cyclic response that require further research. Each of these items will be discussed in subsequent chapters. 1.2 PATH Program The funding for this research comes from the National Science Foundation under the auspices of the PATH Program (Partnership for Advancing Technology in Housing). The goals of the program are: * 1. Develop new housing technology 2. Disseminate information about new and existing housing technologies 3. Study and establish mechanisms for sustained housing technology development and market acceptance * Obtained from the PATH Program website: 3

15 2 Literature Review The first instance of post-tensioned masonry in the literature is from F.J. Samuely in the United Kingdom who noted in 1953 that it was used to construct brickwork piers in a school (20). Since then, post-tensioned masonry has been researched and used for outof-plane designs such as basement and retaining walls, mainly in Europe. The literature researching the seismic, or in-plane, response of post-tensioned masonry has dealt with concrete block masonry, not the clay brick systems used in this research. Nevertheless, the behavior of a clay brick post-tensioned system is similar to a post-tensioned concrete block system, and the two sets of research dealing with concrete masonry will be presented. 2.1 Page & Huizer, 1988 Using Monarch hollow clay units (400mm long x 100mm high x 200mm thick, approximately twice the size of the units used in the research discussed herein) three walls were tested monotonically to failure in the in-plane direction by Page and Huizer in 1988 (16). The walls were 2950mm tall by 2425 high. Descriptions of each wall show the purpose of their research: to compare fully grouted regularly reinforced walls to ungrouted post-tensioned walls. Wall A. Wall B. Wall C. Ungrouted, post-tensioned vertically and horizontally Ungrouted, post-tensioned vertically Grouted, regularly reinforced of each wall. Table 2.1 gives major values obtained during their testing, and the mode of failure 4

16 Table 2.1 Page Huizer Experimental Results Wall Wall-Base Separation Load kn Maximum Load kn Ult Displ mm A Failure Mode Premature local web splitting near point of load application B Diagonal tension failure C Diagonal tension failure The results of this research show that ungrouted post-tensioned masonry walls have higher capacity than grouted regularly reinforced walls. Although Wall A had a premature failure, the potential for horizontal post-tensioning (to close the diagonal cracks in the wall) seems high. 2.2 Larsen, Ingham, et al, 2000 An extensive investigation of the cyclic in-plane response of prestressed concrete masonry walls (note that in this case prestressed is used interchangeably with posttensioned) is ongoing at the University of Auckland, New Zealand under the supervision of Peter Laursen and Jason Ingham (7,9,10,11,21). Phase I of their testing involved eight walls, of varying dimensions, grout infill, and prestress level. In all eight walls the prestressing tendons were left unbonded. A picture and sketch of their test setup is shown in Figures 2.1 and

17 Figure 2.1 Drawing of Test Setup (9) Figure 2.2 Photo of Test Setup (9) 6

18 Out of the eight walls tested in Phase I, five had an aspect ratio of approximately one, and the others had an aspect ratio of about two. Aspect ratio is defined as: h w = (Eqn 2.1) l w where h w is the height of the wall, and l w is the length of the wall. The results from all of the tests will be discussed, but here the concentration will be on the walls with an aspect ratio of two since this is closest to the NCSU configuration. All three walls had the same dimensions: 2800mm high x 1800mm long x 150mm wide (the height is defined as the distance from the wall/footing interface to the center of the load), but one wall had a thickness of 90mm (UG:L1.8-W10-P2). Some results from these tests are presented in Table 2.2. Table 2.2 Laursen Ingham Test Results (Walls with Aspect Ratio=2) Wall Maximum Ult Prestress Failure Mode Load kn Displ mm Ratio f m /f m FG:L1.8-W15-P Rocking, compression toe crushing FG:L1.8-W15-P Rocking, inclined diagonal shear crack, shear failure UG:L1.8-W10-P Inclined shear crack, shear failure Drastically different behavior was found in each of these three tests, with only small changes in the design. The first wall had two prestressing tendons, the second and third had three. The first two walls were fully grouted, the last one left ungrouted. But these changes led to different failure modes and surprising results. Of all eight walls tested, only the last two in Table 2.2 experienced shear failures. For FG:L1.8-W15-P3 the high prestress ratio is most likely to blame for the shear failure, and in UG:L1.8-W10-7

19 P2 the high prestress ratio along with the ungrouted cavity most likely led to early shear failure. The first wall, FG:L1.8-W15-P2, is the wall most similar to the ones tested at NCSU, and a wall which exhibited good behavior, meaning a high force capacity and high levels of ultimate displacement. A force-displacement history of this test is shown below in Figure 2.3, along with a plot of the total post-tensioning force versus drift ratio in Figure 2.4. Figure 2.3 Force-Displacement Hysteresis (9) 8

20 Figure 2.4 Total Force History (9) Some results concluded from the Laursen-Ingham research (9) include the following: 1. Prestressed concrete masonry exhibit a nearly non-linear elastic behavior dominated by a rocking response 2. Even after tendon yielding, self-centering behavior is present. 3. Little hysteretic energy dissipation was measured during the tests 4. A sliding mechanism exists only in walls with low aspect ratios (see Chapter 3 for a discussion of sliding) 9

21 3 PT Masonry Behavioral Mechanisms There are several behavioral mechanisms for unbonded post-tensioned masonry walls which have been noted in earlier research. These mechanisms will be explained to give a preview of the expected behavior of the tests, and give a background on the behavior of post-tensioned masonry. 3.1 Origin Oriented Self-centering or origin oriented behavior is a quality noted in previous research on unbonded post-tensioned structures (4,19). Most of the post-tensioned concrete masonry walls tested by Laursen-Ingham showed this behavior as well. Characterized by small amounts of residual deformation in a return cycle of loading, it can mainly be attributed to the unbonded post-tensioning which, even after yielding, presents little damage in the wall while supporting large residual displacement in the bars themselves. This is of special importance in seismic zones, where large events usually result in permanent deformation of structural wall systems, an undesirable attribute. In one of the walls tested at NCSU (Test 3 Confined), there was a large region of zero-stiffness where the post-tensioning bars had no force. In order to have self-centering behavior in this case, the post-tensioning bars need to be designed to ensure that they remain elastic up to a design level of displacement. This is discussed more in Chapter Sliding In the research done by Laursen-Ingham a sliding mechanism was noted for some of the walls with low aspect ratios of around one. Although not expected for the NCSU 10

22 tests since the aspect ratio of the walls tested was higher, sliding is a major concern for other post-tensioned masonry walls and needs to be considered. Sliding is defined as displacement the wall undergoes in the horizontal direction with respect to the foundation. In the one Laursen-Ingham test that showed sliding, it was significant, with 45% of the maximum displacement in the pull direction attributed to sliding, which caused a large residual displacement. One reason this behavior occurs is because the wall-foundation interface is smooth. They recommend to roughen the surface to an amplitude of 2mm in future tests to entirely eliminate this issue and receive good bond between the mortar in the bottom course and the foundation. Although this was not done for the tests conducted in this research, it is recommended for wall systems with low aspect ratios. 3.3 Rocking Rocking behavior is associated with flexural failure in an unbonded posttensioned wall. If there is sufficient shear reinforcement, axial load, or shear resistance by the masonry, this type of failure will occur, as long as there is a stable compression strut (see Section 3.4). Rocking occurs due to the formation of large zones of degradation in the compression toe region at either end of the wall, but little damage elsewhere. As the wall is cycled at high drift levels the masonry crushes in the extreme fibers, and the compression area is reduced. This results in slight strength degradation in the wall, and leads to a rocking type mechanism where large displacements are possible (see Figure 3.1). This mechanism is one of the main reasons that unbonded post-tensioned walls have low energy dissipation. 11

23 F act Post-Tensioned Wall Displaced configuration Damaged Compression Toe Figure 3.1 Rocking Schematic In the large scale tests conducted for this research, rocking behavior was most present in the unbonded, grouted and confined configurations (Test 1 and 3). 3.4 Compression Strut In order to achieve rocking type behavior there must be a stable compression strut in the post-tensioned wall. The compression strut can be defined as a diagonal region across the length of the wall (X-shaped for cyclic motion) in which the force from the actuator is transmitted to the footing (see Figure 3.2). 12

24 F act F act Compression Strut Figure 3.2 Diagram of Compression Strut Stability of the compression strut is obtained when there is no damage to the wall outside the toe compression region and the wall/footing interface (the base crack). Items that could cause damage to the compression strut include: 1. Permanent deformation due to yielding of regular reinforcing or bonded post-tensioning steel. 2. Debonding of regular reinforcing or bonded post-tensioning in the grouted cavity. 3. Flexural and/or shear cracking within the compression strut. 13

25 This last item involves the most uncertainty, but could be caused by a high posttensioning ratio (forcing flexural and shear cracking), or a small compression area (caused by an ungrouted cavity or narrow wall). When the compression strut becomes unstable due to introduced strains as shown above, the ability to transfer force from the top to the bottom of the wall becomes compromised, and large inclined cracks or buckling of the wall could occur. In the tests conducted for this research, the bonded and ungrouted configurations (Tests 4 and 5) exhibited behaviors associated with an unstable compression strut. 3.5 Base Crack Formation One of the most basic properties of an unbonded post-tensioned wall is the formation of a base crack at the wall/foundation interface. Before explaining its properties and why this occurs, some items that must be mentioned: 1. The foundation system used in this research did not rotate; actual foundation systems on soil need to be designed with this in mind. 2. Other non-structural components of the structure must be able to facilitate the opening of a base crack during an average seismic event. The opening of a base crack in an unbonded post-tensioned wall is a result of the semi-rigid behavior of the wall. With the rocking mechanism discussed above, and little flexural deformation of the wall, a base crack forms. Due to the large in-plane deformations that can occur in an unbonded post-tensioned wall, the base crack can be substantial in size and cause little damage to the wall at high drift ratios. Assuming the wall rotates about a point at the edge of the compression zone, from geometry this in- 14

26 plane deformation can be related to the base crack in the following manner (see Figure 3.3): BC DR = 100 ( l c) w (Eq 3.1) An equation for drift ratio (DR) is shown in Equation 8.1. F act Unbonded Post- Tensioned Wall BC c l w TOP Figure 3.3 Base Crack from Top Displacement Base cracks formed on all walls tested in this research. The largest was that of the confined wall, which reached a maximum value of almost 80mm. 15

27 4 Wall, Footing and Stub Beam Design Five post-tensioned clay masonry walls were constructed for this research. Each wall was identical in dimensions, but had different characteristics. Each was designed to be easy to construct, cost-effective, and practical to the laboratory environment as well as to real applications. Brief descriptions of the walls tested are given below: 1. Unbonded Wall the control specimen, with a grouted cavity and unbonded post-tensioning. 2. Plastic Hinge Steel Wall identical to the control specimen, but possessing mild steel in the plastic hinge region to raise energy dissipation. 3. Confined Wall identical to the control specimen except for the placement of confinement plates between the mortar joints in the compression zone to increase masonry compression strain capacity. 4. Bonded Wall grouted cavity and bonded post-tensioning. 5. Ungrouted Wall ungrouted cavity and unbonded post-tensioning. 4.1 Clay Masonry Units The most common type and size of clay brick was used in this research. According to the Brick Association of the Carolinas, the most commonly used brick in terms of sales in 1999 was a Modular type brick with dimensions 194mm by 92mm by 57mm. The average width of the mortar joint can be assumed to be 10mm. There are also three approximately 38mm diameter holes in the brick. These cooling holes help induce uniform cooling after the brick has been fired. A picture of a typical brick is shown in Figure

28 Figure 4.1 Standard Clay Brick 4.2 Wall Aspect Ratio and Width The size of the walls tested were 1.22m by 2.44m by 0.305m. The space in the laboratory dictated this design as did the goals of the research. The footing used in this project was 0.457m high, and the actuator which applied the load was 2.44m above this, so 2.44m was chosen as the height of the wall. With masonry units that are 57mm high, with a mortar joint of approximately 10mm, this yields a wall 31 courses high. The goal to find a system that could be used for modular housing or light industrial buildings yielded an aspect ratio of two: a reasonable value to assume for a structural wall in such a building. So the length of the wall was taken as 1.22m. This gave us a wall dimension that is approximately ½ the size of what would go into an actual building. 17

29 The width of the walls tested was 0.305m. This dimension was determined as a result of two factors. One is the size of the post-tensioning sleeves. Whereas the regular reinforcing was 19mm in diameter, the sleeve used in this research was 64mm in diameter. In order to have sufficient cover on either side of the sleeve in the cavity, it needed to be widened. The second reason was the length of the bricks. It was noticed during construction of the previous research that the bricks had to be broken off in order to fit at the ends of a wall 0.254m in width. Making the width would eliminate this and make the width of the wall approximately equal to the length of one unit plus the width of another plus the mortar joint. A typical cross-section and elevation is shown in Figure 4.2. Figure 4.2 Typical Cross-Section and Elevation of Test Specimens 4.3 Post-Tensioning System The unbonded post-tensioning system was used in four of the walls, and a bonded configuration in one wall. The anchorage systems used were similar in all walls, as was 18

30 the length and diameter of the bars. In each wall, three bars were placed in the cavity. One each at a location 152mm from edge of wall, and one in the center of the cavity. The bars used were 25.4mm Dywidag high-strength threaded post-tensioning bars. This size was chosen because of the design post-tensioning force (see Chapter 5 for design) and the width of the cavity. Dywidag bars were used because of their wide availability around the United States, and the familiarity they possess in the laboratory. Each was shipped as 4.115m long. The extra length at the top of the wall was used to accommodate the stressing operation. A picture of a post-tensioning bar is shown in Figure 4.3. Figure mm Dywidag Bars A drawing and picture of the anchorage system used in the footing is shown in Figure 4.4 and 4.5. It consists of a standard square 25.4mm Dywidag plate, and a steel pipe with the dimensions shown. The purpose of the steel pipe was to provide a void in 19

31 the footing, so that after casting the post-tensioning bars could be inserted into it. In the first wall tested (the unbonded wall), a standard Dywidag nut was welded to the plate in order to simplify the construction process. In subsequent walls this was abandoned and the nut was free until stressing. This was to allow for the possibility to reuse the footings, but this was never done. The anchorage system at the top of the stub beam can be seen with the load cell instrumentation in Figure 7.3. Figure 4.4 Photo of Anchorage System 20

32 Figure 4.5 Drawings of Anchorage System The post-tensioning ducts, or sleeves, were different for the unbonded and bonded post-tensioning bars. For the unbonded bars, 38mm ID diameter PVC was used. This was chosen because of its wide availability, low cost, and the fact that it was not necessary to bond the bar to the grout in the cavity, only to create a void. For the bonded bars, 51mm ID diameter corrugated sheathing was used (provided by Dywidag), along with the associated tubes and nozzles for the bonding operation (for bonding operation see Section 7.6) 4.4 Confinement Plates Earlier work has shown that the performance of brick masonry shear-wall test units was greatly enhanced by the inclusion of confinement plates in the compression zone at each end of the wall. (18) Masonry strength values (f m ) and ultimate strain values (value of strain at a stress of 0.2f m ) can be dramatically increased by the inclusion of this simple plate placed in the mortar joint during construction. (Stress-strain curves 21

33 for confined and unconfined masonry used in the force-displacement analysis can be found in Chapter 13) Previous research with confinement plates used concrete block masonry, so there were considerable changes to the design of the confinement plate to work in a clay brick system. Whereas in a concrete block system the confinement plate is confining grout placed inside the masonry unit, in a clay brick system the plate is confining grout placed in the cavity created by the masonry units. Other design considerations include: 1. The plate is not as wide as the wall in order to allow for mortar joint pointing, continuity of mortar, and aesthetics (no visible signs of plates after construction). 2. Holes were placed in the plate to allow for mortar continuity and bonding between the mortar and the plate. 3. The plate extends a short distance (6mm) into the grouted cavity to allow for some bonding between the plate and the grout. A drawing and picture of a typical 3.2mm galvanized steel confinement plate that was used in this research are shown in Figure 4.6 and

34 Figure 4.6 Drawing of Confinement Plate Figure 4.7 Picture of Confinement Plate 23

35 The confinement plate described above was used in one wall (the confined wall), and placed in the compression zone at each end of the wall for the first five courses (including below the bottom course at the wall/footing interface). A cross section and elevation of the confined wall is shown in Figure 4.8. Figure 4.8 Cross Section and Elevation of Confined Wall 4.5 Design of PH Steel One expected characteristic of unbonded post-tensioned clay masonry is low energy dissipation (see Chapter 3). Whereas another characteristic of unbonded posttensioning, self-centering behavior, is advantageous to structures in seismic zones, low energy dissipation is not necessarily a good characteristic to possess. In designing the walls, obtaining a system with higher energy dissipation was considered for one of the specimens, and mild supplemental steel was placed in the plastic hinge region of this wall. 24

36 The impetus for placing this steel came from a 1999 University of California at San Diego research project which involved a pre-cast post-tensioned test building (17). They recognized the low-energy dissipation qualities of their structure and added mild steel between the post-tensioned frames and post-tensioned slabs. The yielding of this supplemental steel at high displacements provided higher energy dissipation in the system. In the tests conducted for this research, similar behavior occurs at the wall/footing interface, and the addition of mild steel in this region could exhibit the same qualities of higher energy dissipation. The placement of the mild steel within the cross section is shown in Figure 4.9. In order to increase the effectiveness of the mild steel it must be placed as far towards the edge of the wall as possible. Not wanting to change the location of the post-tensioning bars, the mild steel was placed as close to the post-tensioning ducts as possible on either end. The length of the mild steel was determined by two factors: the footing size and the plastic hinge region of the wall. In the footing, the mild steel extended to the depth of the bottom mesh of reinforcing, and then outward at a 90º angle towards the edge of the footing. This last bend was staggered for the four bars. Above the footing, the mild steel extended into the wall a length approximately equal to the unbonded length (see below) plus the development length. Reinforcing suitable for earthquake regions, ASTM A706 bars, were used. A cross section and elevation of the plastic hinge steel wall is shown in Figure

37 Figure 4.9 Cross Section and Elevation of PH Steel Wall Additional design considerations for the plastic hinge steel involved two potential problems: 1. Would the plastic hinge steel rupture at the footing/wall interface, where the displacement was expected to be large? 2. Could the post-tensioning force in the wall eliminate residual deformation in the bars between cycles? At the footing/wall interface, the base crack was expected to be 50mm or more (see force-displacement analysis in Chapter 13). With the mild steel bonded to the surrounding grout in this region, rupture or massive debonding would most definitely occur at an early stage in the testing. To ameliorate this, the bar was unbonded by way of a 20mm PVC pipe in this region. The length of the unbonded region (l ub ) was determined from: 26

38 l ub bc = (Eq 4.2) ε u where bc is the expected size of the base crack and ε u is the ultimate or desired strain in the mild reinforcing. With a desired strain in the mild reinforcing of 0.08, and an expected base crack of 50mm, an unbonded length of 610mm was chosen, of which 460mm was placed above the footing/wall interface and 150mm was placed in the footing. The second design consideration was to provide adequate post-tensioning force to eliminate residual deformation in the mild steel. The residual deformation in the mild steel was determined from the unloading curve of the stress-strain relationship (see Figure 4.10) Stress (ksi) f sreq d Strain Figure 4.10 Stress-Strain Curve of A706 Steel 27

39 The force required to eliminate residual deformation at high levels of drift (F req d ) is therefore: F ( N )( A ) req' d = f sreq' d s (Eq 4.3) where N is the number of mild steel bars in the tension zone (assumed to be all of the bars, four) and A s is the area of steel. Given a 13mm diameter bar and f sreq d of approximately 620MPa, the required force is 320kN; less than the initial force applied to one bar (see Chapter 5). 4.6 Design of Footing, Stub Beam Using wall analysis procedures outlined in Chapter 13, a fairly good estimate of the ultimate loads placed on the system were obtained. From this, the footing and stub beam were designed to remain elastic over the loads prescribed. The design loads applied on the footing are shown in Figure The stub beam had very small loads acting upon it during testing, and was designed using a minimum amount of reinforcing, mainly to resist lifting stresses after testing was complete kn 350 kn 854 kn-m Figure 4.11 Design Loads on Footing 28

40 The footing was 2440mm long x 1220mm wide x 457mm deep and had mm bars top and bottom main reinforcing, along with 14 13mm bars top and bottom in a direction perpendicular to loading. To attach the two cages were 10mm C-hooks placed at 305mm along each side. These hooks were erroneously omitted in the PH Steel test specimen and led to heavy damage in the footing at the conclusion of testing. In the center of the footing, above the anchorage system and around the post-tensioning ducts in the footing were three cages made of 6 13mm bars in a 254mm square. This provided a way to disseminate the loads around the post-tensioning bars and to control cracking around the anchorage system. In addition to the reinforcement, the footing had an applied post-tensioning load of 890kN applied longitudinally distributed through four 25.4mm Dywidag bars; this provided additional strength to the footing. A cross section of the footing is shown in Figure Figure 4.12 Footing Cross Section The stub beam was 1981mm long x 483mm wide x 610mm deep and had 3 layers of 16mm U bars as main reinforcing on each side. In the vertical direction on each side 29

41 there were 13mm bars at 175mm. A cross section of the stub beam is shown in Figure Figure 4.13 Stub Beam Cross Section A section analysis of the footing showed that under the predicted ultimate load in the wall, the footing would remain elastic. Within this elastic range there can be said to be virtually no deformation or rotation coming from the footing during testing. 4.7 Material Properties Tests were performed on all materials used in this research. Table 4.1 shows compression tests of all materials from the specimen along with a tension test of the galvanized steel from the confinement plate. For the stress-strain curve obtained from a tension test performed on the mild supplemental steel see Figure Table 4.2 has compression test results from a series of masonry prisms constructed with a grouted cavity, one which was left unconfined, one which was confined. All concrete and masonry tests were performed between days of casting. Further information is available on these results (6). 30

42 Table 4.1 Material Properties from Laboratory Tests Clay Brick f c (MPa) 34.0 Mortar f j (MPa) 15.7 Grout f g (MPa) 23.6 Confinement Steel f y (MPa) 266 Footing Concrete f c (MPa) 34.2 Stub Beam Concrete f c (MPa) 32.0 Masonry Prism (Wall 1) f m (MPa) 22.2 Masonry Prism (Walls 2-5) f m (MPa) 25.9 Table 4.2 Results from Grouted Prism Tests Prism Type f m (MPa) ε ult ε 50% ε 20% Unconfined Confined

43 5 Design for Post-Tensioning Force Once the dimensions of the wall system and the types and properties of the materials to be used were determined, it became necessary to find the amount of posttensioning force to apply to each wall. To accomplish this, displacement-based design methodology was used in order to obtain a design base shear. From this, an equation developed by Laursen & Ingham was manipulated to find the post-tensioning force (7,9,10,11). Changes to the design procedure are suggested at the end of the chapter. 5.1 Wall Design Procedure Developed by Priestley and Kowalsky (13) in 2000, the displacement based design procedure (DBD) allows a designer to specify a particular level of drift and appropriate seismic event, and receive a design moment. The first step in a DBD is to specify a level of drift desired. For this design, different levels of drift were used in order to obtain a relationship between design drift level and post-tensioning force. Next, estimates for the ultimate displacement and yield displacement of the wall were calculated. In the absence of an equation to estimate the yield curvature (φ y ) of a post-tensioned clay brick masonry wall, an equation derived by Ayers (3) was used that estimates yield curvature for a regularly reinforced clay brick masonry wall. This equation gives only a rough estimate, however, since in a post-tensioned masonry wall there is virtually no wall curvature. φ y 2.13ε y = (Eq 5.1) l w where ε y is the reinforcement yield strain, and l w is the length of the wall. 32

44 ε y was determined from the yield stress of the Dywidag post-tensioning bars, which can be taken as 80% of the ultimate stress (f pu ), divided by the modulus of elasticity of steel, E s f pu ε y = (Eq 5.2) E s Using a linear approximation of the curvature relationship, the yield displacement ( y ) can be estimated as: 2 φ ylw y = (Eq 5.3) 3 The ultimate displacement ( u ) at each specified level of drift is found by: DR u = * h w (Eq 5.4) 100 The next step also involved uncertainty: a damping-ductility relationship must be found that adequately describes the behavior of post-tensioned clay brick masonry. In the Laursen & Ingham research (see Section 2.2) no damping behavior was quantified, but lower energy dissipation was expected in the post-tensioned masonry walls compared to other reinforced concrete structures. As a result, the damping-ductility relationship was taken as the Takeda Model (which adequately describes reinforced concrete) divided by two µ µ ζ = + Takeda 0.05 (Eq 5.5) π where the first term of 0.05 is an estimate for elastic damping, and µ is the displacement ductility 33

45 u µ = (Eq 5.6) y u and y being the ultimate and yield displacement. Once the damping and ultimate displacement values for each drift ratio were found they were entered into a response spectrum and T eff, a structure s effective period, was obtained. The response spectrum that defined the design seismic event was constructed from specifications in the 2000 International Building Code (8) for the Charleston, SC area. An example of obtaining T n is presented in Figure 5.1. The different lines represent various damping values. 2% Displacement (mm) u T eff 5% 10% 20% Period (seconds) Figure 5.1 Displacement Design Spectra With the effective period obtained, you can obtain a design moment if you know the mass (M) and height (h w ) of the structure. A mass value was obtained by taking the self-weight of the wall system and a hypothetical dead and live load estimation. Given that the practical uses desired for a post-tensioned masonry wall include housing and 34

46 light industrial applications, a dead and live load combination of 9600kN/m 2 was used on an effective area of 465 m 2. The effective stiffness (K eff ) of the structure can now be determined as well as the design moment (M u ). K eff 2 4π M = (Eq 5.7) T eff M u = K h (Eq 5.8) eff u w 5.2 Laursen Ingham Equation Once the moment at different levels of drift from the displacement based design procedure is obtained, one can find the post-tensioning force required to achieve this value from an equation derived by Laursen and Ingham (7): lw a lw a M u = ( Ti + T ) + et + N (Eq 5.9) where a T + T + N i = (Eq 5.10) 0.85 f ' m b w e t lw T = (Eq 5.11) 6 ( T + T ) i f m is the masonry compressive strength, b w is the width of the wall, T i is the initial posttensioning force and T is the change in post-tensioning force due to deformation. T is the value that is hardest to quantify, and was taken as 50kN per the suggestion of the authors of the equation. The equation can now be solved for the initial post-tensioning force at different levels of drift. This post-tensioning force was divided by the area of the masonry wall and in turn the masonry compressive strength to get the applied posttensioning ratio (PTR) 35

47 PTR T i b w w = (Eq 5.12) f ' m l A graph of drift ratio versus PTR for the wall system and response spectrum used is shown in Figure Drift Ratio ( % ) f ps /f' m ( % ) Figure 5.2 PTR v. Drift Ratio 5.3 Post-Tensioning Force Determination From previous research and design specifications a post-tensioning force ratio between 5% and 15% was desired. Using a drift ratio of 1.5%, a post-tensioning force ratio of 11.5% was chosen. This yielded an approximate post-tensioning force of 36

48 1000kN, or 333kN for each of the three 25.4mm Dywidag bars used. This is below the limit of stress set by Dywidag for the design of post-tensioning (0.60f pu ). 5.4 Problems with Design Procedure As mentioned earlier in the chapter, there are a few problems with this design procedure which need to be mentioned. The behavior of a post-tensioned clay brick masonry wall needs to be further developed to identify important limit states point such as the yield and ultimate displacement, and find a suitable damping-ductility relationship. Identifying these behaviors further beyond what is done in this chapter is important in obtaining a design post-tensioning force ratio. In addition, while the post-tensioning force ratio may be adequate to resist the design loads, it is important to design the post-tensioning in such a way so that at a certain design drift ratio, all the bars remain elastic. When residual displacement occurs in the PT bars, there is a loss of prestress which results in a region of low stiffness as the structure cycles. Keeping the bars in the elastic range could eliminate or reduce the region of low stiffness. A region of low or zero stiffness occurred most notably in the confined wall, whose force-displacement history is shown in Figure

49 6 Instrumentation A total of three different types of gauges were used to measure behavior of the walls during testing: linear potentiometers, strain gauges, string potentiometers and load cells. The linear potentiometers were used to measure the curvature of the wall and the displacement at the footing/wall interface (the base crack profile). Strain gauges were used to measure strain on the mild reinforcing placed in the lower region of the plastic hinge steel wall. The string potentiometers measured the overall in-plane and out-ofplane displacement of the walls during testing. Load cells were an invaluable data collection tool used to measure the force in the post-tensioning bars. 6.1 Linear Potentiometers A linear potentiometer measures straight line displacement over a certain gauge length. There were twelve of these potentiometers on each test specimen. At each end of the wall, vertically spaced approximately 250mm apart, were four linear potentiometers. At the footing/wall interface, horizontally across the wall, two linear potentiometers were placed on each side 320mm from the edge of the wall and 250mm from the top of the footing. These were attached to the wall in the following manner: 1. 6mm threaded rods were placed during construction, in the mortar joint between the bricks, at the appropriate locations. 2. Each linear potentiometer is placed on an aluminum angle piece which is in turn fastened on the two threaded rods. Pictures showing the placement of the linear potentiometers on the wall are shown in Figures 6.1 to

50 Figure 6.1 Linear Potentiometers at end of Wall Figure 6.2 Linear Potentiometers along Wall/Footing Interface 39

51 There were two types of linear potentiometers used in the test: long and short stroke. The long stroke potentiometers (stroke of 152mm) were used on all of the gauges at the footing/wall interface (6 per specimen). The other six gauges used were short stroke potentiometers (stroke of 38mm). This was not the case for the first wall tested, which used short stroke potentiometers exclusively. The high displacement demand in the base area led to the increase in stroke for subsequent tests. The linear potentiometers were used for two purposes: to quantify the base crack profile, and to obtain values for wall curvature. The base crack profile is simply the displacement at four points at the footing wall interface. At each end of the wall there is one reading, and at two points along the base there are two readings (one for each side). The values at each end are taken, along with the average of the two values from each side to produce a base crack profile. From the base crack profile, one can get a fairly accurate measure of the neutral axis depth. The neutral axis depth can be considered the distance on the base crack profile which is in compression. An example is given in Figure

52 Length of wall NA Depth Average readings at these points Readings at end gauges Figure 6.3 Example of Base Crack Profile The curvature of the wall was calculated from the data obtained from the linear potentiometers at each end of the wall. Equations to calculate rotation (θ) and curvature (φ) of the wall are given below: δ S + δ N θ = (Eq 6.1) D where δ S and δ N are the measured displacements in the linear potentiometers on the North and South side of the wall at each level, and D is the horizontal distance between them. θ φ = (Eq 6.2) G where G is the gauge length. This is further explained in Figure

53 δ N δ S G D Figure 6.4 Curvature Determination The average masonry compression strain was also calculated using data from the linear potentiometers. This is covered in some detail in Section Strain Guages Strain gauges were not used very extensively in this research. Strain gauges were not used on the post-tensioning steel for two reasons: 1. Four of the walls used unbonded post-tensioning, so the strain in each bar can easily be found from load cell data. 2. The grinding involved for application of strain gauges was deemed to be too damaging to the bars. Strain gauges were only used, therefore, on the mild steel that was placed in the plastic hinge region of one of the walls. Two gauges were placed on each bar, one in the unbonded region, and one in a bonded region (see Section 4.5). A diagram of these locations is shown in Figure

54 Strain Gauge Locations 610mm Unbonded Region 457mm 152mm 305mm Top of Footing PH Steel Figure 6.5 Location of Strain Gauges on Plastic Hinge Steel The strain gauges used were identical in type to ones used in previous research, and information on the type of gauge and application procedure can be found there (15). 6.3 String Potentiometers A string potentiometer with a stroke of 1016mm was used to measure the displacement in the in-plane direction (the direction of loading). The instrument was attached to the loading frame system, and the string was attached to the center face of the stub beam of the specimen. This gave a measure of displacement which was independent of the displacement values from the actuator, which were not very accurate. In earlier research a string potentiometer was used to measure out-of-plane displacement and was used in this research as well. A shorter stroke string potentiometer was used (635mm of stroke). The instrument was attached to a stationary column, and the string was attached similarly to the center face of the stub beam. A picture of a typical string potentiometer used in this research is shown in Figure

55 Figure 6.6 Picture of String Potentiometer 6.4 Load Cells The most valuable data obtained in this research was from the load cells which measured the force in the post-tensioning bars. Knowing significant forces in the system is very crucial to determining the behavior of post-tensioned clay masonry, and the load cells accomplished this. There were two different types of load cells that were used. For the bars on the outside a 890kN load cell from Interface was used, and for the center bar a 445kN load cell from StrainSert was used. Locations of the loads cells on the test specimen can be seen in Figure 6.7, and a picture of the load cells used in Figure

56 StrainSert Load Cell Stub Beam Interface Load Cells Figure 6.7 Types of Load Cells and Location StrainSert Load Cell Interface Load Cell Figure 6.8 Picture of Load Cells 45

57 7 Construction and Test Setup Once the masonry walls systems were constructed, they were setup for testing (see Figure 7.1 and 7.2 for a drawing and picture of the test setup). Four different steps led to a complete test setup: construction of the specimen, preliminaries, placement, attachment, stressing operation and (if applicable) bonding operation. Figure 7.1 Drawing of Test Setup 46

58 Figure 7.2 Picture of Test Setup 7.1 Construction of Specimen In the Constructed Facilities Laboratory at North Carolina State University all five walls were constructed and tested. There were three distinct segments in the construction process: footing construction, wall erection and stub beam construction. The first step was to construct five footings as shown in Figure There were differences in the footings due to the differences in the walls: the footings for the plastic hinge steel wall and bonded wall differing from the others. Once this was completed professional masons were brought in to brick up the walls to half their final height. At this intermediate stage, the walls were grouted (except one which was left ungrouted). The grout had the following proportions: 1 part cement, 1.5 parts sand, 2 parts aggregate, and 1 part water. The cement was standard Type I, and the aggregate had a maximum 47

59 size of 9.5mm. The masons then returned to brick up the remaining portion of the wall, and they were again grouted. This two stage process ensured the grout was evenly distributed throughout the wall height. Once the wall and footing were constructed, scaffolding was erected around the specimen and the stub beam was cast-in-place on top of the wall to the specifications in Figure After allowing the wall time to cure, the preliminary items in setting up the test were performed. 7.2 Preliminaries Before placing the wall in the test area, important steps had to be completed including curvature potentiometer attachment, low friction surface attachment between loading frame and stub beam, post-tensioning of the footing, and sealing of a hydrostone dam. As mentioned earlier in the instrumentation chapter, the linear potentiometers extended from the wall by the way of 6mm threaded rods placed during masonry wall construction in the mortar joints. These threaded rods had to be cleaned with a wire brush and/or threaded with a die device in order to accept the nuts and washers that are used to attach the aluminum angle pieces. Once the angle pieces with the linear potentiometers were attached to the threaded rods, they were leveled and their precise location was measured. From the previous research at NCSU involving reinforced clay masonry walls, a guidance frame was assembled to control out-of-plane displacement of the wall during testing. Although no out-of-plane problems were predicted to occur with these posttensioned walls (due to the applied axial force from post-tensioning), the guidance frame 48

60 was kept to control any uncertainties. In the preliminary phase of the test setup, a low friction surface attachment between loading frame and stub beam of the size 1829mm x 102mm x 19mm was attached lengthwise on the stub beam using rawl plugs. This attachment was placed snug between the bottom flange of the guidance beam and the stub beam, in order to reduce friction between the two members. The next step was to post-tension the footing (this was made easier outside of the crowded test area). There were four 51mm diameter lengthwise voids in the footing created using PVC piping, and it was into these holes that four 25mm Dywidag highstrength threaded bars were tensioned each to 222kN to give a total post-tensioning force in the footing as 890kN (see Section 4.6 for design). The final step in the preliminary test setup was to seal a hydrostone dam which fit around the outside of the footing in the testing area. This dam was made of 38mm x 89mm wood approximately 2.75m x 1.8m in dimension. This dam was placed on the lab floor and would be filled with Hydrocal cement (hydrostone) in order to provide friction resistance and bond between the footing and the floor during testing. This dam was sealed to the floor by caulking silicon between all interfaces to prevent leaks. A similar dam was made and sealed on top of the stub beam to insure leveling of the vertical inwall post-tensioning plates to the stub beam. Finally, hydrostone was also utilized for the interface between the vertical post-tensioning plates (that go through the footing to the lab floor) and the top of the footing. The dam around these plates was made by applying successive beads of silicon. 49

61 7.3 Placement Once the preliminary steps for the test setup had been completed the wall systems were placed in the testing area. In the footing there were four 51mm diameter holes in the vertical direction whose dimension matched that of the holes in the laboratory floor which were 76mm in diameter. On top of each of the four holes in the lab floor, a 300mm square piece of 13mm thick fiber sheathing was placed in order to compensate for small discrepancies in the bottom of the footing and the lab floor. On top of this sheathing the wall system was placed, paying careful detail so that the center of the wall lined up with the center of the actuator. This alignment was checked using the other holes in the lab floor as guidance. Once the proper alignment of the wall was obtained, hydrostone was mixed with water in a 1:1 ratio and poured into the dam around the footing, the dam around the vertical post-tensioning plates at each corner of the footing, and the dam on top of the stub beam for the wall post-tensioning. 7.4 Attachment Once the hydrostone was allowed to cure overnight, the attachment of the wall system proceeded. First the vertical post-tensioning bars (35mm Dywidag high-strength threaded bars) were placed in the four holes in the footing, extending to a depth of at least 300mm beneath the lab floor, and each tensioned to 333kN. The actuator used to test the specimens was of the type MTS T, with a 980kN load capacity and a 1.0m stroke. This was attached to the specimen using 4 38mm diameter threaded rods, which extended throughout the length of the stub beam. On the south side of the specimen, four standard rectangular plates for 35mm Dywidag 50

62 bars were placed between the stub beam and the bolts in order to evenly spread the load from each bar to the stub beam. The last step in the attachment phase of the test setup involved the hookup of the gauges. An Optim Megadac 3108AC data acquisition system with a Windows based TCS system was used to collect data from all of the tests. During each test, and during each stressing operation (see Section 7.4) a reading of all the gauges was taken every second. The strain gauges in the plastic hinge steel were wired using a three wire half bridge and an excitation voltage of 5 volts. The linear potentiometers, string potentiometers, and load cells were wired using a full bridge and an excitation voltage of 10 volts. The load and displacement readings from the MTS actuator were wired using an excitation voltage of 10 volts. An analog X-Y recorder was utilized for visual aid during testing; this was connected to the load reading from the actuator, and the in-plane string potentiometer. Each linear and string potentiometer was balanced at an approximate stroke of 45% of maximum except the linear potentiometers used to measure the base crack which had an available extension of 75% of maximum. 7.5 Stressing Operation Once the specimen was attached to the lab floor and the actuator, the post tensioning bars inside the wall were stressed. On top of the stub beam the following items were placed around each post-tensioning bar (from the bottom): a standard rectangular 35mm Dywidag plate, the load cell, a washer, a standard square 25mm Dywidag plate and nut (see Figure 7.3). The Dywidag plate was needed to elevate the load cell above the level of the hydrostone dam. 51

63 Figure 7.3 Load Cell on top of Stub Beam From the design of the post-tensioning force (see Chapter 5), each bar should be stressed to 333kN. This process was done in step levels, with 111kN applied first to the center bar and then each edge bar, repeated three times until the desired force reached. Of note: the target force was read from each of the load cells, not from the stressing jack, so the target force of 333kN for each bar is minus the seating loss. 7.6 Bonding Operation One of the walls tested had bonded post-tensioning and the bonding operation for this wall began after the bars were stressed. The bonding agent used had the proportions: 1 part water, 2.26 parts cement. Type III high early strength concrete was used so that the specimen could be tested soon after bonding. A hand pump was used to transfer the bonding agent after being mixed into the bonding tubes. Due to Hydrostone dripping from the top of the stub beam down the 52

64 bonding tube into the footing, the center tube became clogged and couldn t be pumped from the footing level. The operation was performed from the top of the specimen with no overall problems noticed later. 53

65 8 Test 1 - Unbonded The first specimen tested used unbonded post-tensioning bars in a grouted configuration (for cross section and elevation, see Figure 4.2). This chapter will give the loading history of the specimen, observations made during the test, and test results. A proposed force-displacement analysis of the wall is discussed in Chapter Loading History The loading history described here is identical for all of the tests. Usually a specimen being tested under a cyclic loading history is tested by force control until a yield point, and then at displacement control after this. In the absence of a readily defined yield point, all the wall specimens were tested using displacement control (see Figure 8.1). The displacement levels were specified as drift ratios, defined as: DR = 100 (Eq 8.1) h w 54

66 Drift Ratio Cycle Figure 8.1 Loading History for All Tests The methodology for this testing was taken from ACI ITG/T Acceptance Criteria for Moment Frames Based on Structural Testing (1). They specify that for each level of drift three reversed cycles shall be applied (7.2) and the sequence is intended to insure that the displacements are increased gradually in steps that are neither too large nor too small. If steps are too large, the drift capacity of the system may not be determined with sufficient accuracy. If the steps are too small, the system may be unrealistically softened by loading repitions, resulting in artificially low maximum lateral resistances and artificially high drift ratios (R7.0). 55

67 From this criteria, the step levels were taken as approximately 40% higher than the previous level until a drift ratio of 1.0%, and then as 20-30% higher for the subsequent drift ratios: similar to their example test sequence. 8.2 Observations What follows are step-by-step observations at each significant point in the testing of the first wall. Pictures of this test can be found in Appendix 1 (Figures A1.2 to A1.7). Force and displacement values will be given, along with information on crack size and locations, crushing in masonry compression zone, and other findings/problems during testing. These are visual observations, and the more accurate data on wall curvature and base crack profiles can be found in the Test Results section later in this chapter. In addition, a limit states discussion occurs in Chapter 14. Before the first test had begun, the actuator applied a force of approximately 260kN on the wall resulting in a displacement of 5mm. This was the result of the hydraulics in the laboratory being turned on while the hydraulics to the MTS machine were turned to high. The base crack opened, but no other damage to the wall was noticed. At the first drift ratio of 0.2%, a crack at the base of the wall (between the wall and the footing, at the extreme opposite end of the wall from the compression zone) opened up to an approximate size of.6mm. The force at this initial cycling was 215kN and the displacement approximately 5mm. During cycle 2 in the push direction, the bolts on the threaded rods attaching the actuator to the stub beam were tightened to eliminate slippage in the pull direction due to small strains in the rods. 56

68 At the next two levels of drift, 0.25 and 0.35%, the behavior was similar with the base crack opening to 1.5mm and 2mm respectively. The wall force response was around 230kN for DR = 0.25 and 250kN for DR = At a drift ratio of 0.5% (12mm) the force response had reached 275kN. The base crack was approximately 3mm. In the first cycle, a small amount of spalling was noticed in the masonry joint in the extreme compression fiber, this can be assumed at the drift ratio where crushing first occurred. In the subsequent cycles at this drift ratio more spalling occurred, but only in the described mortar joint. At a drift ratio of 0.75% (18mm) the force in the actuator was up to 300kN. The base crack was approximately 4mm, and crushing in the first mortar joint was expanding. A picture of this crushing is in Figure A1.2. At this level the force in the edge posttensioning bar had gone above 450kN. At a drift ratio of 1.0% (24mm), the crushing in the compression zone mortar joints had now extended to the second course. The wall was resisting a force of 320kN, and the base crack was enlarging at a fast pace to almost 10mm. At drift ratio 1.25% (30mm), the force in the wall was 325kN (near the maximum force observed in the wall), and the base crack was 13mm. On the sides of the masonry compression zone, vertical splitting cracks in the brick could be seen stretching from the footing interface up into the second course of masonry. Just after the first cycle in the push direction at this drift ratio and going in the pull direction, the hydraulic system for the lab shut itself down. The test continued without incident once the hydraulics were turned back on. 57

69 Due to the vertical splitting cracks in the previous drift ratio, at 1.75% (42mm) in the first cycle the face shell (defined as the piece from the edge of the brick to the cooling holes ) in the bottom course came off (see Figure A1.3). By the end of the third cycle the face shell in the bottom two courses had come off. But this is the only damage in the wall. Everything above the second course is crack-free. This drift ratio could also be assumed as the point where the wall achieved its maximum force value of 330kN. The base crack at this level was about 17mm. At a drift ratio of 2.25% (53mm) it was first noticed that the force in the compression side post-tensioning bar had reduced to zero at the maximum point in each cycle. The force applied on the wall hovered at around 330kN, and the base crack was at approximately 22mm. The face shell on the second course of masonry was coming off (see Figure A1.4). At a drift ratio of 3.0% (71mm) there was a small amount of force degradation to 310kN (about 94% of ultimate force). At this point the base crack by observation is becoming hard to determine because of the loss of masonry in the first two courses, but is estimated at 25mm. At drift ratio 3.75% (89mm) during the first cycle, large vertical splitting cracks are observed extending into the third course. The applied force in the wall is about 95% of ultimate and the base crack 33mm during the first cycle, but by the third cycle the base crack is 40mm and the force is 75% of ultimate. It is at this point that the linear potentiometers are taken off the specimen. As mentioned in Chapter 6, for the first test 51mm potentiometers were used on the base, and these were deemed to have too low a 58

70 stroke to adequately measure the base crack, and were replaced by larger stroke potentiometers on subsequent tests. By drift ratio 5.0% (119mm), the damage due to vertical splitting cracks had extended up to the fourth course of the wall, and all the masonry in the compression zone was gone, and the grouted core was quickly degrading (see Figure A1.5). The base crack remained approximately 40mm, and the force had degraded to 62% of ultimate during the first course, and 48% after the third course. After the drift ratio 6.5% (153mm) the test was stopped. The force in the wall was at 34% of ultimate (150kN). Since all the brick and grout extending at least 200mm from the edge of the wall was gone, it was behaving in a rocking fashion taking displacement but not holding much load. This rocking type behavior can be implied from Figures A1.6 and A1.7. The test could have continued to further drift ratios, but this amount of strength degradation was deemed sufficient to analyze all reasonable limit states for which a wall would be typically designed to achieve. 8.3 Test Results From the data obtained during the test, the dimensions of the wall, and locations of the gauges, relationships can be formed as to the behavior of the wall. The figures shown in this section will include overall performance of the wall, profiles of the base crack, and post-tensioning bar force relationships. The force-displacement hysteresis of the first test is shown in Figure 8.2. The small amount of degradation at the top of each curve is a result of the displacement reading from the actuator being dissimilar to the displacement reading from the string potentiometer. This problem was corrected in subsequent tests. At the drift ratios 3.75% 59

71 and 5.0% it can be noticed that there is some residual deformation in the wall, this can be shown further in the base crack profiles at zero displacement discussed below. At the last three drift ratios there is an area on the descending curves where the stiffness in the wall is virtually zero. This occurs until the displacement becomes large enough for the bar on tension edge to engage and increase the wall strength and stiffness. Also notice that the area inside the force-displacement loops is, as expected, very small, which means the wall has low levels of energy dissipation, an item that should be improved by the addition of mild steel in the plastic hinge region, as was done in Test Force (kn) Displacement (mm) Figure 8.2 Force-Displacement History Test 1 Unbonded Shown in Figure 8.3 is the total post-tensioning bar force, as defined as: F T = F F2 F3 60

72 As mentioned earlier, around a drift ratio 2.25% the force in the compression bar was reduced to zero. This is a result of yielding of the post-tensioning bar due to cyclic loading and possibly a small reduction in height due to softening of the wall. As the wall was cycled, during the point of zero stiffness, the two edge bars do not have any force in them, and the center bar is sustaining a small amount of load Total Bar Force (kn) total initial bar force Wall Displacement (mm) Figure 8.3 Total Bar Force Test 1 Unbonded Figure 8.4 represents the base crack profile in the push direction and Figure 8.5 is the same in the pull direction. The base crack profile is taken from the linear potentiometers along the base of the wall at the maximum value in the first cycle at each drift ratio (see Chapter 6). A good estimate of the neutral axis depth of the masonry compression zone can be obtained by locating the point along the line that crosses the x- axis. The base crack can be determined by finding the point which the line crosses the 61

73 wall edges in the positive y-direction. The profiles are shown only to a drift ratio of 2.25% due to the stroke problems in the linear potentiometers mentioned earlier. A few items that should be noticed in these plots are: The initial deformation due to the application of post-tensioning force on the wall The linear nature of the profile The stability of the neutral axis depth at around 190mm. If the profiles were shown to the maximum drift ratio of 6% in the test, the neutral axis depth would have migrated away from the extreme compression fiber due to the degradation in the masonry at these levels. 30 Wall Edges Base Displacement (mm) DR =.2 DR =.25 DR =.35 DR =.5 DR =.75 DR = 1.0 DR = 1.25 DR = 1.75 DR = 2.25 initial Wall Length (mm) Figure 8.4 Base Crack Profile Push Direction Test 1 Unbonded 62

74 Base Displacement (mm) DR =.2 DR =.25 DR =.35 DR =.5 DR =.75 DR = 1.0 DR = 1.25 DR = 1.75 DR = 2.25 initial Wall Edges -10 Figure 8.5 Base Crack Profile Pull Direction Test 1 Unbonded Figure 8.6 shows the base crack profile at zero displacement. This is obtained in a similar manner to the base crack profiles above, but the values in the linear potentiometers were taken after the third cycle was completed, as the wall moves through an in-plane string potentiometer displacement of zero. Although the values are small for these low drift ratios (maximum of 0.5mm), at higher ones more residual displacement is bound to occur Wall Length (mm) 63

75 Residual Base Displacement (mm) Wall Edges DR =.2 DR =.25 DR =.35 DR =.5 DR =.75 DR = 1.0 DR = 1.25 DR = 1.75 DR = 2.25 initial Wall Length (mm) Figure 8.6 Base Crack Profile at Zero Displacement Test 1 Unbonded In Figure 8.7 the average wall curvature is shown for the push and pull directions. Virtually all of the curvature in the wall is contained in the lowest level, due to the base crack. 64

76 Wall Height (mm) DR =.2 DR =.25 DR =.35 DR =.5 DR =.75 DR = 1.0 DR = 1.25 DR = 1.75 DR = 2.25 DR = 3.0 DR = Average Wall Curvature (1/mm) Figure 8.7 Wall Curvature Test 1 Unbonded 65

77 9 Test 2 PH Steel The second test performed was identical to the first except for the addition of mild steel in the plastic hinge region (for cross section and elevation, see Figure 4.9). In this chapter observations made during the test will be presented, along with results from the test. A proposed force-displacement analysis of the wall is discussed in Chapter 13. The loading history was identical to the first test, see Section Observations What follows are step-by-step observations at each significant point in the testing of the second wall. Pictures of this test can be found in Appendix 1 (Figures A1.8 to A1.13). Force and displacement values will be given, along with information on crack size and locations, crushing in masonry compression zone, and other findings/problems during testing. These are visual observations, and the more accurate data on wall curvature and base crack profiles can be found in the Test Results section later in this chapter. In addition, a limit states discussion occurs in Chapter 14. At the first drift ratio of 0.2%, a base crack opened up to an approximate size of.6mm. The force at this initial cycling was 242kN and the displacement approximately 5mm. At the next two levels of drift, 0.25 and 0.35%, the behavior was similar with the base crack opening to.8mm and 2mm respectively. The wall force response was around 230kN for DR = 0.25 and 250kN for DR = At a drift ratio of 0.35%, minor spalling and crushing was observed in the extreme compression side mortar joint. 66

78 The following two levels of drift, 0.5% (12mm) and 0.75% (18mm) the applied forces were 312kN and 340kN and the base crack enlarged from 3mm (0.5%) to 5mm (0.75%). Some crushing in the mortar joint can be noticed in Figure A1.8. At a drift ratio of 1.0% (24mm) the force was 350kN and the base crack 6mm. In the compression zone on either side of the wall during the first cycle, large vertical splitting cracks extended into the second course. By the third cycle, the face shell was lost on the north side (see Figure A1.9). Drift ratios 1.25% (30mm) and 1.75% (42mm) saw an increase in base crack size (8mm for 1.25% and 10mm for 1.75%) and saw the maximum force in 1.75% at 361kN. The face shells continued to degrade, with the south side finally falling off at 1.75% cycle three (see Figure A1.10). It was also during these drift ratios that large cracks were forming in the footing. It was determined that the C-hooks for this footing (13mm diameter bars connecting the top and bottom meshes of steel) had erroneously been omitted. At a drift ratio of 2.25% (54mm) the force was 97% of ultimate, and the base crack 15mm. On the north end of the specimen, the damage to the face shell extended into the third course, whereas on the south side the face shell was only partially lost in the first course. The next drift ratio, 3.0% (73mm), the force was 95% of ultimate and the base crack 27mm, and the trend of higher damage in the north side continued. By drift ratio 3.75% (91mm), a large degradation in force was noticed between the first (96% of ultimate) and third (68% of ultimate) cycle. Cracks extended up into the tenth course of the wall. The base crack was approximately 31mm. 67

79 At a drift ratio of 5% (121mm) further strength degradation occurred from 83% of ultimate at the first cycle to 54% by the last cycle. The masonry in the compression zone was gone and the grout core was exposed (see Figure A1.11). For the first time, cracks extended from the edge of the compression zone up 45 degrees toward the other end of the wall. This only occurred on the south end of the wall on the east side. It seemed the south side of the wall was buckling due to the residual displacement of the plastic hinge steel. The wall was taken through the first cycle of drift ratio 6.5% (157mm) and the test was stopped. At this point the post-tensioning bar PVC was exposed, and the compression zone heavily damaged to a length of 250mm (see Figure A1.12). The force degradation of the wall was 32% of ultimate at the end. The supplemental mild steel was also buckling towards the end of testing as can be noted from Figure A1.13 which was taken during wall demolition. The footing was also performing badly: large cracks now were on the top along the edge of the wall, as well as on the side where some cover was lost. The test could have been continued through at least the third cycle of this drift ratio, but the poor state of the footing prevented this. 9.2 Test Results From the data obtained during the test, the dimensions of the wall, and locations of the gauges, relationships can be formed as to the behavior of the wall. The figures shown in this section will include overall performance of the wall, profiles of the base crack, post-tensioning bar force relationships, and data from the strain gauges in the plastic hinge steel. 68

80 The force-displacement hysteresis of the first second is shown in Figure 9.1. As a result of adding the plastic hinge steel, the following differences can be noted in this plot as opposed to the force-displacement hysteresis of the first test: The loops are wider more energy dissipation There is no region of zero stiffness in the wall There is a larger amount of residual displacement in the wall at the high drift ratios The initial stiffness, and the maximum force in the wall are similar to the first test Force (kn) Displacement (mm) Figure 9.1 Force-Displacement History Test 2 PH Steel Shown in Figure 9.2 is the total post-tensioning bar force. This plot looks very similar to the plot from the first test. 69

81 1400 Total Bar Force (kn) total initial bar force Figure 9.2 Total Bar Force Test 2 PH Steel In Figures 9.3 and 9.4 the base crack profiles in the push and pull direction are shown for the maximum points in the first cycle. Notice the slight non-linearity of the profile at high drift ratios from the yielding of the plastic hinge steel, and the difference in values at high drift ratios between the push and pull directions. As mentioned in Chapter 8, the neutral axis depth from these plots gets larger after a drift ratio of 2.25% due to the degradation of the compression zone. This phenomena is more pronounced in the pull direction, where the compression zone was damaged earlier than in the push direction Wall Displacement (mm) 70

82 Base Displacement (mm) Wall Edges DR =.2 DR =.25 DR =.35 DR =.5 DR =.75 DR = 1.0 DR = 1.25 DR = 1.75 DR = 2.25 DR = 3.0 DR = 3.75 initial Wall Length (mm) Figure 9.3 Base Crack Profile Push Direction Wall 2 PH Steel Base Displacement (mm) DR =.2 DR =.25 DR =.35 DR =.5 DR =.75 DR = 1.0 DR = 1.25 DR = 1.75 DR = 2.25 DR = 3.0 DR = 3.75 initial Wall Edges Wall Length (mm) Figure 9.4 Base Crack Profile Pull Direction Wall 2 PH Steel 71

83 Figure 9.5 shows the base crack profile at zero displacement. As one would expect, the residual displacement in the wall is higher for this test than for the previous one due to the yielding and buckling of the plastic hinge steel. On the right side of the plot (the compression side in the pull direction) the values for residual displacement are much higher. Residual Base Displacement (mm) DR =.2 DR =.25 DR =.35 DR =.5 DR =.75 DR = 1.0 DR = 1.25 DR = 1.75 DR = 2.25 DR = 3.0 DR = 3.75 DR = 5.0 initial Wall Edges Wall Length (mm) Figure 9.5 Base Crack Profile at Zero Displacement Test 2 PH Steel In Figure 9.6 the average wall curvature is represented for the push and pull directions. Similar to the first wall, virtually all of the curvature in the wall is contained in the lowest level, due to the base crack. But at the highest drift ratio achieved during the test (6.5%), the wall curvature starts to increase above the base crack. 72

84 Wall Height (mm) DR =.2 DR =.25 DR =.35 DR =.5 DR =.75 DR = 1.0 DR = 1.25 DR = 1.75 DR = 2.25 DR = 3.0 DR = 3.75 DR = 5.0 DR = Average Wall Curvature (1/mm) Figure 9.6 Wall Curvature Test 2 PH Steel In Figures 9.7 through 9.10 the hysteresis data from the strain gauges is presented. As mentioned in Chapter 6, there were originally eight gauges affixed to the plastic hinge steel. One of these (PH1B) was damaged during casting of the footing, and no data was obtained. Of the seven remaining, three of these did not perform very well. All three are in the bottom unbonded region of the steel, and it is possible the PVC pipe used to unbond the steel moved in a different direction than the surrounding grout, pinching the wires. But the top gauges provide important insights into the behavior of the steel during cycling. The loops are very large after the yield point, which on the plot is around 500uE. Also, as was mentioned in the observation section of this chapter, the compression zone on the push side was damaged heavily around a drift ratio of 5.0% due to buckling of the plastic hinge steel. This behavior can be noted in the high values of strain for PH3T and PH4T towards the end of testing. 73

85 top Micro-Strain (ue) Wall Displ (mm) Figure 9.7 Strain Gauge History of PH1T top Micro-Strain (ue) Wall Displ (mm) Figure 9.8 Strain Gauge History of PH2T 74

86 top Micro-Strain (ue) Wall Displ (mm) Figure 9.9 Strain Gauge History of PH3T top Micro-Strain (ue) Wall Displ (mm) Figure 9.10 Strain Gauge History of PH4T 75

87 10 Test 3 - Confined The third test performed was identical to the first except for the addition of confinement plates in the compression zones on either end of the wall (for design see Section 4.4, for cross section and elevation, see Figure 4.8). In this chapter observations made during the test will be presented, along with results from the test. A proposed force-displacement analysis of the wall is discussed in Chapter 13. The loading history was identical to the first test, see Section Observations What follows are step-by-step observations at each significant point in the testing of the third wall. Pictures of this test can be found in Appendix 1 (Figures A1.14 to A1.23). Force and displacement values will be given, along with information on crack size and locations, crushing in masonry compression zone, and other findings/problems during testing. These are visual observations, and the more accurate data on wall curvature and base crack profiles can be found in the Test Results section later in this chapter. In addition, a limit states discussion occurs in Chapter 14. The first three drift levels this wall was taken to (0.2%, 0.25%, 0.35%) showed the force increase to 260kN and the base crack become 3mm. Similar to the first two tests, spalling in the extreme masonry joint occurred at a drift ratio of 0.5% (12mm) in the first cycle (see Figure A1.14). The applied force during this cycle was approximately 285kN, and the base crack 5mm. At a drift ratio of 0.75% (18mm) small vertical splitting cracks were noticed in the compression zones, the force was around 310kN and the base crack 8mm. The drift ratio level of 1.0% (24mm) saw similar behavior with the force reaching 330kN and the 76

88 base crack 13mm. At the next level of cycling, 1.25% (30mm), crushing in the mortar joints was noticed in the second course above the footing. The applied force and the size of the base crack were approximately the same as the previous level. The splitting cracks in the compression zone continued at a drift ratio of 1.75% (43mm), and small pieces of the face shell on either end were lost during cycle three (see Figure A1.15). The base crack was approximately 17mm. During the next two drift ratio levels, 2.25% (55mm) and 3.0% (73mm), the bottom face shells on both ends were lost and the base crack enlarged to 30mm (see Figure A1.16). In the second drift ratio, the maximum applied force to the wall was achieved (350kN). The next drift ratio, 3.75% (91mm), saw the first major damage to the second course, with some face shell lost. The base crack here was approximately 32mm. At drift ratio levels of 5.0% (122mm) and 6.5% (158mm) the force dropped very little (approximately 95% of maximum). The first two courses were the only ones with face shell lost, and the base crack kept getting larger to over 50mm (see Figure A1.17 and A1.18). At a drift ratio level of 8.0% (194mm) the base crack was around 80mm. The push and pull cycles at this drift ratio were noticed to have different values of applied force, where the push direction was much lower than the pull direction (for the first cycle: push was 290kN and pull was 350kN). The confinement plates on the compression end were almost touching each other at this level (see Figure A1.19). Also around a drift ratio of 8%, it was noticed that upon reversal of the cycle there is a large region where none of the post-tensioning bars have any force in them. This results in a low or zero stiffness region, where the wall is holding virtually no force, yet 77

89 displacing. A possible reason this occurred is because the post-tensioning bars were not designed to be elastic up to this drift ratio (see the end of Chapter 5). The next drift ratio of 10% (243mm) saw this trend of unequal forces continue because the push side compression zone was damaged into the third course, with the first course damaged over 50mm into the grout cavity (see Figure A1.20). The pull side, however, only was damaged in the first course, with the second course missing some face shell. The third specimen failed as it was brought to a drift ratio of 12%, at a drift ratio of 11.3% (276mm). The force at failure was 185kN. Failure occurred when a large crack (average size 6mm) extended from the compression zone approximately 350mm from edge of wall up a 45 degree angle until it reached the opposite side of the wall (this can be seen in Figures A1.21 to A1.23). A possible reason this occurred was that the neutral axis wanted to extend beyond the boundaries of the region confined by the confinement plate Test Results From the data obtained during the test, the dimensions of the wall, and locations of the gauges, relationships can be formed as to the behavior of the wall. The figures shown in this section will include overall performance of the wall, profiles of the base crack, and post-tensioning bar force relationships. The force-displacement hysteresis of the third test is shown in Figure As a result of adding confinement plates, the following differences can be noted in this plot as opposed to the force-displacement hysteresis of the first test: 78

90 Large drift ratio capacity with little loss in applied force (especially on the pull side where the applied force at the last drift ratio is still close to the maximum) Self-centering behavior with little residual deformation Better energy dissipation at high drift ratios A zero-stiffness region as the wall moves through zero after the drift ratio 3.75% Force (kn) Figure 10.1 Force Displacement History Test 3 Confined Shown in Figure 10.2 is the total post-tensioning bar force. After a drift ratio of 3.75%, when the wall has zero-stiffness, the total bar force has been reduced to zero. But even after this level the total bar force still exceeds the initial bar force at the maximum displacement level Displacement (mm) 79

91 total initial bar force Total Bar Force (kn) Wall Displacement (mm) Figure 10.2 Total Bar Force Test 3 Confined In Figures 10.3 and 10.4 the base crack profiles in the push and pull direction for the maximum points in the first cycle are shown. As noted for the second test, the depth of the neutral axis is migrating in at the high drift ratios due to the degradation in the compression zone. Also notice the high values for the size of the base crack; the maximum measured size was 80mm at a drift ratio of 8.0%. 80

92 Base Displacement (mm) Wall Edges DR =.2 DR =.25 DR =.35 DR =.5 DR =.75 DR = 1.0 DR = 1.25 DR = 1.75 DR = 2.25 DR = 3.0 DR = 3.75 DR = 5.0 DR = 6.5 DR = 8.0 initial Wall Length (mm) Figure 10.3 Base Crack Profile Push Direction Test 3 Confined Base Displacement (mm) DR =.2 DR =.25 DR =.35 DR =.5 DR =.75 DR = 1.0 DR = 1.25 DR = 1.75 DR = 2.25 DR = 3.0 DR = 3.75 DR = 5.0 DR = 6.5 DR = 8.0 initial Wall Edges Wall Length (mm) Figure 10.4 Base Crack Profile Pull Direction Test 3 Confined 81

93 In Figure 10.5 the average wall curvature for the push and pull directions is shown. As in previous tests, virtually all of the curvature in the wall is contained in the lowest level, due to the base crack. Wall Height (mm) DR =.2 DR =.25 DR =.35 DR =.5 DR =.75 DR = 1.0 DR = 1.25 DR = 1.75 DR = 2.25 DR = 3.0 DR = 3.75 DR = 5.0 DR = 6.5 DR = 8.0 DR = Average Wall Curvature (1/mm) Figure 10.5 Wall Curvature Test 3 Confined The Figure 10.6 shows the base crack profile at zero displacement. Although the lower drift ratios show little residual displacement, once the higher levels are reached (in the region of zero stiffness), this increases until a maximum of around 10mm was recorded. This shows that possibly a higher post-tensioning level is needed in order to close the base crack at these high displacements. 82

94 Residual Base Displacement (mm) DR =.2 DR =.25 DR =.35 DR =.5 DR =.75 DR = 1.0 DR = 1.25 DR = 1.75 DR = 2.25 DR = 3.0 DR = 3.75 DR = 5.0 DR = 6.5 DR = 8.0 initial Wall Edges Wall Length (mm) Figure 10.6 Base Crack Profile at Zero Displacement Test 3 Confined 83

95 11 Test 4 - Ungrouted The fourth test performed was identical to the first except the cavity inside the wall was left ungrouted (cross section and elevation shown in Figure 4.2). In this chapter observations made during the test will be presented, along with results from the test. A proposed force-displacement analysis of the wall is discussed in Chapter 13. The loading history was identical to the first test, see Section Observations What follows are step-by-step observations at each significant point in the testing of the fourth wall. Pictures of this tests can be found in Appendix 1 (Figures A1.24 to A1.27). Force and displacement values will be given, along with information on crack size and locations, crushing in masonry compression zone, and other findings/problems during testing. These are visual observations, and the more accurate data on wall curvature and base crack profiles can be found in the Test Results section later in this chapter. In addition, a limit states discussion occurs in Chapter 14. Before testing, an accident occurred when the actuator was lifted by the crane while attached to the wall. The wall was of yet untensioned, so the wall itself was broken as the stub beam lifted up. The result was a crack all the way around the wall. On the north side the crack was in the first course below the stub beam, on the south side it was in the second course. It was determined to continue without repairing the wall since the moment demand on the top section of the wall is very low, and the applied posttensioning force would close the crack. After post-tensioning, virtually no visual signs of the crack were present. No problems occurred as a result of this during the test. 84

96 The first three drift ratios saw similar behavior to the other walls tested. At drift ratio 0.35% (9mm), the applied force on the wall was 230kN and the base crack was about 2.5mm. At drift ratio 0.5% (12mm) the applied force was 240kN and the base crack 4mm. This was the highest force achieved by the specimen. During the second cycle at this level, mortar joint crushing and small vertical splitting cracks were noticed in the compression zone. By the third cycle, extensive vertical cracks were propagating up the wall to a height 1200mm above the footing as can be seen in Figure A1.24. The next drift ratio of 0.75% (18mm) saw the face shell being lost in the compression zone during the first cycle (see Figure A1.25). The force at this level had dropped to 200kN. During the second cycle, the base crack constricted and the wall began to have large diagonal cracks in an X shaped fashion (see Figure A1.26). In the third cycle, the face shell was lost on both sides, and the diagonal cracks extended all the way to the top of the wall. As the wall was close to a 1.0% (24mm) drift ratio in the first push cycle failure occurred. This happened when a large crack (approximately 10mm) swiftly propagated from the outside edge of the compression zone up to the top edge of the wall on the opposite end (see Figure A1.27). The applied force after failure was 55kN Test Results From the data obtained during the test, the dimensions of the wall, and locations of the gauges, relationships can be formed as to the behavior of the wall. The figures shown in this section will include overall performance of the wall, profiles of the base crack, and post-tensioning bar force relationships. 85

97 The force-displacement hysteresis of the fourth test is shown in Figure 11.1, in the same scale as previous tests. The fourth specimen performed much worse than the first test, with the only difference being a grouted cavity. The total post-tensioning bar force is presented in Figure 11.2, also on the same scale as earlier tests. The potential of the post-tensioning bars were not realized in this test Force (kn) Displacement (mm) Figure 11.1 Force Displacement History Test 4 Ungrouted 86

98 1400 Total Bar Force (kn) total initial bar force Wall Displacement (mm) Figure 11.2 Total Bar Force Test 4 Ungrouted In Figures 11.3 and 11.4 the base crack profiles in the push and pull direction for the maximum points in the first cycle are shown. Notice the migration of the neutral axis very early due to the loss of the face shell, which was a significant contributor to the overall compression zone. 87

99 Base Displacement (mm) Wall Edges DR =.2 DR =.25 DR =.35 DR =.5 DR =.75 initial Wall Length (mm) Figure 11.3 Base Crack Profile Push Direction Test 4 Ungrouted Base Displacement (mm) DR =.2 DR =.25 DR =.35 DR =.5 DR =.75 initial Wall Edges Wall Length (mm) Figure 11.4 Base Crack Profile Pull Direction Test 4 Ungrouted 88

100 In Figure 11.5 the average wall curvature for the push and pull directions is shown. Due to the small amount of curvature achieved, values above the footing level can be seen to be greater than zero When the base crack all but disappeared during the third cycle of drift level 0.75%, this must have been the result of the bottom two courses (underneath the first gauge above the footing) detaching from the rest of the wall because of the absence of the grout which provides continuity between the courses. Wall Height (mm) DR =.2 DR =.25 DR =.35 DR =.5 DR =.75 DR = Average Wall Curvature (1/mm) Figure 11.5 Wall Curvature Test 4 Ungrouted The Figure 11.6 shows the base crack profile at zero displacement. There was very little residual displacement until a drift ratio of 0.75% where the softening of the wall has shown a reduction in height of the wall. 89

101 Residual Base Displacement (mm) Wall Edges Wall Length (mm) DR =.2 DR =.25 DR =.35 DR =.5 DR =.75 initial Figure 11.6 Base Crack Profile at Zero Displacement Test 4 - Ungrouted 90

102 12 Test 5 - Bonded The fifth test performed was identical to the first except the post-tensioning bars were bonded to the grouted cavity (for cross section and elevation see Figure 4.2). In this chapter observations made during the test will be presented, along with results from the test. A proposed force-displacement analysis of the wall is discussed in Chapter 13. The loading history was identical to the first test, see Section Observations What follows are step-by-step observations at each significant point in the testing of the fifth wall. Pictures of this test can be found in Appendix 1 (Figures A1.28 to A1.32). Force and displacement values will be given, along with information on crack size and locations, crushing in masonry compression zone, and other findings/problems during testing. These are visual observations, and the more accurate data on wall curvature and base crack profiles can be found in the Test Results section later in this chapter. In addition, a limit states discussion occurs in Chapter 14. During the bonding of the post-tensioning ducts, the center duct became clogged. This was later found to be a result of hydrostone leaking from the top of the wall where the post-tensioning plates were bonded to the stub beam. Instead of pumping from the bottom, as was done on the two edge bars, the bonding agent was pumped from the top. Inspection after the test revealed the hydrostone at the very bottom of the duct, but the rest of the duct was well bonded with the bonding agent. At the first drift ratio cycle of 0.2% (5mm) the base crack opened. By the third cycle, horizontal cracks formed around the fifth course in the mortar joint at the ends of the wall. The wall resistance was 244kN. The next drift ratio 0.25% (6mm) saw the 91

103 same cracks extend, and by the third cycle there was also a horizontal crack at the ninth course. The wall resistance increased to 260kN. At drift ratio 0.35% (8mm) the same cracks extended, and new ones were formed at the eighth and 15 th course. By the third cycle, these cracks started to migrate downward into other courses through the mortar joints. The force from the actuator was around 290kN for this level of drift. At drift ratio 0.5% (12mm) the force from the actuator was 311kN. At this point most of the cracks mentioned above had migrated to other courses, some going through the brick instead of the mortar joint. By the third cycle, the base crack was measured to be 3mm. Similar behavior occurred at the next drift ratio of 0.75% (18mm), with cracks observed on the second, fourth, eighth, tenth, and 15 th course. The base crack was 7mm by the third cycle, and the force from the actuator at 340kN. The next level of drift, 1.0% (24mm), the first spalling of masonry was observed in the first cycle. Vertical splitting cracks in the compression zone, similar to other tests, also formed at this drift ratio. The force from the actuator was about 340kN. The maximum force achieved during the test (350kN) occurred at drift ratio 1.25% (30mm). The base crack was observed to be 9mm at this level. The first course in the compression zone was also becoming damaged at both ends; the face shell was spalling off as can be seen in Figure A1.28. At a drift of 1.75% (42mm) the force in the wall decreased slightly to 335kN. The base crack was observed to be 14mm and further deterioration of the first course in the compression zone occurred. By the third cycle, large vertical cracks were noticed at 92

104 each end of the wall and at the center, extending almost halfway up the wall (see Figure A1.29). They were approximately at the location of the post-tensioning ducts. Drift ratio level 2.25% (55mm) saw another slight decrease in force to 320kN. The compression zone was now damaged in the second course, and the vertical cracks at the post-tensioning extended farther up the wall. At a level of drift of 3.0% (73mm) the wall resistance was around 290kN. The same vertical cracks enlarged at this level, and the formation of a second base crack was identified around the third course, where there was a large opening between courses (see Figure A1.30). By the third cycle, rapid deterioration of the wall led to the wall resistance being only 43% of the maximum By drift ratio 3.75% (91mm) the wall resistance was only 25% of the maximum. The ends of the wall, between the cracks at the end post-tensioning and the edge, were buckling away from the rest of the wall (see Figures A1.31 and A1.32). After the first cycle the test was stopped Test Results From the data obtained during the test, the dimensions of the wall, and locations of the gauges, relationships can be formed as to the behavior of the wall. The figures shown in this section will include overall performance of the wall, profiles of the base crack, and post-tensioning bar force relationships. The force-displacement hysteresis of the fifth test is shown in Figure 12.1, in the same scale as previous tests. The bonded wall performed similarly to the unbonded wall until a drift ratio of 3.0%, when damage in the compression strut due to yielding and 93

105 buckling of the post-tensioning bars led to fast degradation after the first cycle. Energy dissipation was the highest of all the tests, as was the residual deformation. Force (kn) Displacement (mm) Figure 12.1 Force Displacement History Test 5 Bonded The total post-tensioning bar force is presented in Figure 12.2, also on the same scale as earlier tests. As one would expect, the force remained constant throughout the test because of the bonding of the bars. 94

106 Total Bar Force (kn) Wall Displacement (mm) Figure 12.2 Total Bar Force Test 5 Bonded In Figures 12.3 and 12.4 the base crack profiles in the push and pull direction for the maximum points in the first cycle are shown. The base crack was smaller in this test than any of the others, but the same migration behavior can be seen after a drift ratio of 2.25%. The behavior of the bonded tendons probably contributed to the slight nonlinearity seen at drift ratio 3.0%. 95

107 Base Displacement (mm) Wall Edges DR =.2 DR =.25 DR =.35 DR =.5 DR =.75 DR = 1.0 DR = 1.25 DR = 1.75 DR = 2.25 DR = 3.0 initial Wall Length (mm) Figure 12.3 Base Crack Profile Push Direction Test 5 Bonded Base Displacement (mm) DR =.2 DR =.25 DR =.35 DR =.5 DR =.75 DR = 1.0 DR = 1.25 DR = 1.75 DR = 2.25 DR = 3.0 initial Wall Edges Wall Length (mm) Figure 12.4 Base Crack Profile Pull Direction Test 5 Bonded 96

108 In Figure 12.5 the average wall curvature is shown for the push and pull directions. The curvature in the wall is confined to the lower 300mm of the wall, until the drift ratios of 3.0% and 3.75% where the buckling of the wall can be seen. Wall Height (mm) DR =.2 DR =.25 DR =.35 DR =.5 DR =.75 DR = 1.0 DR = 1.25 DR = 1.75 DR = 2.25 DR = 3.0 DR = Average Wall Curvature (1/mm) Figure 12.5 Wall Curvature Test 5 Bonded The Figure 12.6 shows the base crack profile at zero displacement. From the early drift ratios there is residual displacement, and although the confined wall achieved higher values of residual displacement, these were at much higher drift ratios than those shown for this wall. 97

109 Residual Base Displacement (mm) Wall Edges DR =.2 DR =.25 DR =.35 DR =.5 DR =.75 DR = 1.0 DR = 1.25 DR = 1.75 DR = 2.25 initial Wall Length (mm) Figure 12.6 Base Crack Profile at Zero Displacement Test 5 Bonded 98

110 13 Analysis Presented in this chapter is a comparison of three different analysis methods and their ability to predict the performance of the walls tested in this research. The methods considered are: (1) ACI 530 method (2) Laursen and Ingham (see Chapter 5) and (3) A monotonic procedure developed as part of this research. Force-Displacement Envelopes for all the wall configurations are shown in Figures 13.1 to These include: (1) The force-displacement envelope from test data. (2) The force-displacement from the proposed analysis procedure. (3) Two horizontal lines representing the ACI 530 method and the results from the Laursen-Ingham equation (see Equations 5.9 to 5.11) Force (kn) Test F-Displ Anal Laursen-Ingham Masonry Code Displacement (mm) Figure 13.1 Force Displacement Envelope Test 1 Unbonded 99

111 Force (kn) Test F-Displ from Anal Laursen-Ingham Masonry Code Displacement (mm) Figure 13.2 Force Displacement Envelope Test 2 PH Steel Force (kn) Test F-Displ from Anal Laursen-Ingham Masonry Code Displacement (mm) Figure 13.3 Force Displacement Envelope Test 3 Confined 100

112 Force (kn) Test F-Displ from Anal Laursen-Ingham Displacement (mm) Figure 13.4 Force Displacement Envelope Test 4 Ungrouted Force (kn) Test F-Displ from Anal Lausen-Ingham Masonry Code Displacement (mm) Figure 13.5 Force Displacement Envelope Test 5 Bonded 101

113 As will be shown in this chapter, it is clear from analysis results that it is important to include the effects of cyclic degradation on the loss of prestress in the wall in order to obtain an accurate prediction of the force-displacement response ACI 530 Method Post-tensioned (or prestressed) masonry was codified in the United States in The most recent code is ACI / ASCE 6-02 / TMS (2); a joint document produced by the American Concrete Institute, the American Society of Civil Engineers, and the Masonry Society in This code was used to analyze the five walls tested in this research in axial compression and flexure. Note: the effective prestress was taken as the value read from load cells at the beginning of testing (approx 323kN per bar), which includes such effects such as elastic shortening of masonry, anchorage seating loss and other effects discussed in Section 4.4 of the code document Laterally Unrestrained Prestressing Tendons Section in the code prescribes a procedure to analyze laterally unrestrained prestressing tendons; of which there is one: the ungrouted wall (Test 4). The procedure is identical to that of analyzing unreinforced masonry with an axial load (with minor changes). There are two equations which must be satisfied (Eqns 2.10 and 2.11 in the code): f F a a f + F b b 1 (Eq 13.1) 1 P Pe 4 (Eq 13.2) where f a and f b are the calculated stresses due to axial compression and compression due to flexure, and F a and F b are the allowable values of these. 102

114 For walls which have a height to radius of gyration ratio (h/r) of less than 99, the following equation is given to calculate F a (Eqn 2-12 in code): 2 1 h Fa = f ' m 1 (Eq 13.3) 4 140r But the code does not prescribe a way to calculate F b, as it does for walls with h/r greater than 99. This means a lack of flexural provisions for squat structural walls with laterally unrestrained prestressing tendons Laterally Restrained Prestressing Tendons The other four walls tested in this research have laterally restrained prestressing tendons, and fall under Section in the code. For material properties and geometry discussed in this section see Chapter 4. In determining the nominal flexural strength of a prestressed masonry section you must first calculate the stress in the prestressing tendon. This is done in Section in the code using equation 4-2 (SI): f ps = f se d f pu Aps (Eq 13.4) l p bdf ' m where f se is the effective prestress, d is the distance to the centroid of the prestressing tendons, l p is the clear span, f pu is the tensile strength of the tendon, and A ps is the area of prestressing steel. d was taken as the distance from the end of the wall to the centroid of two of the post-tensioning bars (see Figure 13.6): 103

115 Compression Zone PT bars used in Code Analysis d Figure 13.6 d determination Equation 13.4 was used to calculate f ps for the unbonded, PH steel, and confined wall. For the bonded wall, f ps was taken equal to f py (per in code). The neutral axis depth, a, is calculated from equation 4-1 in the code: f ps Aps + f y As + Pu a = (Eq 13.5) 0.85 f ' b m where f y and A s are the yield strength and area of regular reinforcing. This assumes that the centroid of the regular reinforcing is at a distance d from the edge of the wall (a good assumption for the PH steel wall when the two bars in tension are used). P u does not have to be included if the unfactored design axial load does not exceed 0.05f m A n, where A n is the net cross sectional area; which it doesn t in this case. The nominal moment strength is calculated by equation 4-3: a ( f A + f A + P ) d M n = ps ps y s u (Eq 13.6) 2 104

116 A summary of the results of the code analysis for flexure are presented in Table 4.1. By dividing these nominal moments by the height of the wall (2.44m), force values can be obtained which can be compared with the values found during testing (see Figures 13.1 to 13.5). The code analysis yields values for predicted strength that are on the conservative side of the values obtained during testing. To compare with the Laursen- Ingham analysis a strength reduction factor of 0.8 was not included. Table 13.1 Results from Code Analysis Wall M n kn-m Ungrouted No Provisions Unbonded PH Steel Confined Bonded Proposed Force-Displacement Analysis Procedure What follows is a step by step procedure to construct a force-displacement response for post-tensioned clay masonry walls using wall geometry, and material stressstrain relationships. A major assumption in this analysis is that planes remain plane after bending, and that the wall behaves in a semi-rigid fashion (see Chapter 3). The first wall examined is the unbonded, grouted configuration (see Figure 4.2 for cross section and 105

117 elevation); following this will be sections on this analysis for the other wall configurations. Copies of the spreadsheets developed for this research can be downloaded from www4.ncsu.edu/~kowalsky F- Analysis Unbonded There are three different states of wall stress that need to be analyzed in a forcedisplacement analysis on post-tensioned clay masonry. 1. Initial Conditions the state of stress directly following the post-tensioning operation. 2. Cracking the state when a base crack opens on the tension side of the wall. 3. After Cracking the states following cracking, at specified displacements Initial Conditions The initial strain in each post-tensioning bar (ε sp ) and the initial strain in the masonry or elastic shortening of the masonry (ε mi ) are: T bar ε sp = (Eq 13.7) APT Es 3*T bar ε mi = (Eq 13.8) Am Em where T bar is the post-tensioning force in each bar, A PT is the area of one post-tensioning bar, A m is the area of masonry, E s is the elastic modulus of steel, and E m is the elastic modulus of clay brick masonry (from Paulay and Priestley for clay brick masonry): E m = 750 f ' (Eq 13.9) m 106

118 Cracking From this the masonry compression force (Cm) can be found as a function of a variable to be iterated,ε mc, if the strain profile is considered to be linear up to cracking (see Figure 13.7). l w ε mi ε mc C m Figure 13.7 Masonry Strain Profile at Cracking In a similar manner, the strain in each post-tensioning bar can be found in terms of the same variable (ε mc ), if the distances to each of the bars are known (see Figure 13.8). 107

119 ε mi ε mc ε 1 ε 2 ε 3 ε sp l w Figure 13.8 Steel Strain Profile over the Cross-Section at Cracking Once these terms are known, statics can be used to solve for ε mc and the force from actuator (F act ) (see Figure 13.9). 108

120 l w F act W w+sb h w F f F 1 F 2 F 3 C m d cm Figure 13.9 Wall Free Body Diagram The displacement at cracking ( cr ) can be found from the curvature at cracking (φ cr ): φ cr ε + ε mi mc = (Eq 13.10) l w 2 φcrhw cr = (Eq 13.11) 3 By iterating the value of ε mc to find equilibrium, one can find the cracking displacement. 109

121 After Cracking For specified drift ratios occurring after cracking, a strain profile can be evaluated and, using the stress-strain characteristics of the materials, the force applied on the system can be solved for in an iterative process. The stress-strain characteristics of the masonry and the post-tensioning steel are crucial to the force-displacement analysis of a post-tensioning clay masonry wall. In order to find suitable relationships, existing equations relating overall behavior were modified to account for information gleaned from material tests (see Tables 4.1 and 4.2). The stress-strain relationship for the 25.4mm Dywidag post-tensioning steel was taken from a pull test performed at the University of San Diego in 1997 (14). The recorded relationship was simplified to a tri-linear plot with a yield stress (F y ) of 852MPa occurring at a strain of 0.005, and the ultimate stress (F u ) occurring at a strain of.03, with a plateau region extending until failure at a strain of A plot of the tri-linear approximation is shown in Figure

122 1200 F u 1000 F y Stress, MPa Strain Figure Stress-Strain Curve for Dywidag PT Bar The clay masonry stress-strain relationship used in the force-displacement analysis is a modified Park curve, described by Priestley and Elder for concrete masonry (18), which is further modified to account for material properties observed at specific points in the testing of grouted masonry prisms (see Table 4.2). Mainly, the Priestley and Elder curve is used up to a strain of , where it is altered due to the fact that the tests conducted showed degradation to 0.2f m at a strain of , instead of The equation for each branch of the curve is shown below, and a plot in Figure For ε m f m = f ' m ε m ε m (Eq13.12) For ε m

123 f m = f ' m ε m (Eq 13.13) For ε m > f m = 0.2 f ' (Eq 13.14) m f' m Stress 0.2f' m.0015 Strain Figure Unconfined Masonry Stress-Strain Curve After the stress-strain relationships are determined, a strain profile must be determined. Assuming that the wall behaves in a semi-rigid manner (see Chapter 3), the maximum tensile displacement in the base crack is directly related to the top displacement or drift ratio in the following manner: base DR = 100 ( l c) w (Eq 13.15) where c is the neutral axis depth (the value to be iterated) 112

124 Since the distance to the post-tensioning bars, and the initial strain in the posttensioning bars is known, the strain in the bars at a specific drift ratio is: DR ε PT = ( lw xi c) + ε i 100* l ub (Eq 13.16) where l ub is the unbonded length of the post-tensioning bars, x i is the distance from the tension edge of the wall to the center of the bar, and ε i is the initial strain in the bar. Equation gives the maximum base crack in the wall due to the top displacement, which can be utilized to obtain the compression displacement in the masonry as in equation DR c = c (Eq 13.17) 100 But some assumptions must be made in order to create a strain profile for the masonry. This compression displacement must be distributed over some height of the wall. It is proposed that that height be the plastic hinge length of the wall, which is the larger of: L = h (Eq 13.18) p1 lw + w Fy L p2 = 0.08hw (Eq 13.19) d bl Fy L p3 = (Eq 13.20) d bl where d bl is the diameter of the post-tensioning bar. Making this assumption, the maximum strain in the masonry at any drift ratio is: DR c ε m = + ε mi + ε mc (Eq 13.21) 100 L p 113

125 The masonry strain profile and an equation for the masonry strain at any point is shown in Figure c x ε m ε ( x) = m ε m c x Figure Masonry Strain Profile This equation for the masonry strain at any point can be entered into equations 12.6 to 12.8 to find the masonry compression force and its centroid. If this equation is called da, the masonry compression force, C m, and the distance from the edge of the wall to the centroid of the compression force, d cm, are: C m = da (Eq 13.22) d cm xda = lw c + (Eq 13.23) C m All of the forces acting on the system have been found in terms of the neutral axis depth, except the force in the actuator. Using the Free-Body-Diagram in Figure 12.8 this force can be found by assuming a neutral axis depth, c, and iterating until equilibrium is 114

126 reached. A graph of the force-displacement analysis for the unbonded wall can be found in Figure F- Analysis PH Steel As mentioned before, the only difference between the unbonded wall and the PH steel wall is the addition of mild steel in the plastic hinge region. In order to complete a force-displacement analysis, the strains in the mild steel must be found, which means more stress-strain assumptions. The stress-strain behavior of the mild steel was estimated using an approximation as suggested by King (12). Figure shows a stress-strain plot of the King model and a tension test performed at the laboratory Stress (MPa) Tension Test King Model Strain Figure Stress-Strain Curve for Mild Steel 115

127 As before, the strains in the plastic hinge steel must be found at initial conditions, at cracking, and at points after cracking. The initial strain in the PH steel is equal to the initial strain in the masonry. The strain at cracking is: x = (Eq13.24) ( ε ε ) i ε PHcri ε mi mi + lw where x i is the distance from the tension edge of the wall to the center of each bar. The strain in the plastic hinge steel after cracking is the displacement due to the base crack divided by the unbonded length (L PHub ) (see Design of PH Steel, Section 4.5) and the strain at cracking: PHub mc DR ε PHi = ( lw c xi ) + ε PHcr ( xi ) (Eq 13.25) 100 L Once the strains are found for a particular drift ratio as a function of the neutral axis depth, the force in each bar (F PHi ) can easily be calculated using the stress-strain relationship in Figure F = σ * A (Eq 13.26) PHi PHi PH where σ Phi is the stress from the stress-strain relationship and A PH is the area of the plastic hinge steel bar. With the forces from the deformation of the plastic hinge steel as a function of the neutral axis depth, equilibrium can be satisfied for each level of drift by iterating for c. A plot of the force-displacement analysis for the PH steel wall can be found in Figure

128 F- Analysis Confined The only difference between the unbonded wall and the confined wall is the addition of confinement plates in the plastic hinge region (see Section 4.4). Therefore, the only item to change in the force-displacement analysis is the stress-strain relationship. Priestley and Elder (18) examined the effects of confinement on the stress-strain relationship, and proposed equations using the geometrical and material properties of the confinement. Like the unconfined case, these equations are modified to include the values obtained from tests on confined masonry prisms. Curve equations are listed below, and a plot of the stress v. strain is given in Figure For ε m 0.002K f m = 1.067Kf ' m 2ε m 0.002K ε m 0.002K 2 (Eq 13.27) For 0.002K ε m ( 1 Z (. K )) f m = Kf ' m m ε m 002 (Eq 13.28) For ε m > f m = 0.2Kf ' (Eq 13.29) m where K and Z m are: K f yh = 1+ ρ s (Eq 13.30) f ' m Z m 0.5 = f ' m 3 + s 145 f ' m 1000 ρ 4 h'' 0.002K s h (Eq 13.31) 117

129 ρ s is the volumetric ratio of confining steel, f yh is the yield strength of the confinement plate, h is the lateral dimension of the confined core, and s h is the longitudinal spacing of the confinement plates. Kf' m Stress 0.2Kf' m 0.002K Strain Figure Stress-Strain Curve for Confined Masonry Using the above equations to solve for the masonry compression force is the only change to the force-displacement analysis for the confined wall. A plot of the force-displacement analysis for the confined wall is shown in Figure F- Analysis - Bonded One of the major assumptions made in the force-displacement analysis of the unbonded wall is that the wall behaves in a semi-rigid manner: the base displacement is directly related to the top displacement. This is assumption is not valid for the bonded 118

130 case because of the presence of flexural bending due to the bond between the posttensioning bars and the surrounding cavity. In fact, this wall s behavior can be assumed to be similar to a regularly reinforced masonry wall with an applied axial load. But the force-displacement analysis is similar to the unbonded case, except instead of choosing a specific drift ratio to evaluate, masonry compression strain is used. Once the forces in the system have been evaluated, the displacement at the top can be estimated using straincurvature-displacement relationships. A plot of the force-displacement analysis for the bonded wall is given in Figure F- Analysis - Ungrouted The only difference between the unbonded and ungrouted case is the presence of a grouted cavity. To account for the missing grout, an effective width is found and used to calculate C m (see Figure 13.15) c b eff b w Figure Ungrouted Effective Width 119

131 A plot of the force-displacement analysis for the ungrouted wall is given in Figure Problems with Force-Displacement Analysis The force-displacement analysis described above is for a post-tensioned clay brick masonry wall subjected to a monotonic load: it does not consider the various effects that cyclic loading has on member response. As a result, the analysis above gives good values for initial stiffness and member strength, but not for ultimate displacement or overall system behavior. Identifying the differences between the force-displacement analysis described above, and the actual tests (which were of a cyclic nature) is the purpose of this section. Major differences are: 1. Neutral Axis Degradation in the tests, the compression zone is reduced at high levels of displacement as the masonry crushes. 2. Cyclic PT Steel the cyclic nature of the tests results in cumulative tensile strains in the PT steel which in turns reduces the post tensioning force. 3. Cyclic Masonry the cyclic degradation in the masonry is not captured in the stress-strain curves which were derived from monotonic compression tests Neutral Axis Degradation The degradation of the neutral axis depth due to crushing of the masonry is not used in the force-displacement analysis. An estimate for this degradation was used in the limit states analysis of the test data to compute the adjusted average masonry compression strain (see Section 14.3), but how it is entered into a force-displacement analysis of a post-tensioned clay brick masonry wall is not clear. 120

132 In a typical force-displacement (or moment-curvature) section analysis, the depth of the section is reduced by the concrete cover at a compression strain equal to the concrete crushing strain. In this wall configuration, however, reducing the section by 152mm (the distance to the post-tensioning bar from edge of wall) at the first signs of crushing (about 0.5% drift) is not a good approximation of the degradation. In order to obtain a degradation length to be used in a force-displacement analysis, a linear relationship needs to be derived which relate degradation length to drift ratio given certain material properties Cyclic Behavior of PT Steel As the test specimen is cycled three times at each drift ratio (see Section 7.1 for loading history), the unbonded post-tensioning steel enters into the inelastic range thus resulting in residual deformation in the bar upon reversal which produces a loss of prestress. As a result of this, the forces observed in the post-tensioning bars during the tests were lower than the forces found under the force-displacement analysis. This is especially relevant for the bars on the tension side of the specimen during each cycle from the monotonic analysis these bars are assumed to have no residual displacement whereas during the tests the bars on the tension side have experienced significant strains. Plots of the bar forces from the force-displacement analysis and from the tests are shown below. Each bar from four of the tests are presented (the bonded wall did not have a change in post-tensioning force) in Figures to Note: the bar forces from the force-displacement analysis in the pull direction (negative drift ratios) are taken from the bars on the compression side of the wall. 121

133 Analysis Bar Force (MN) Test Drift Ratio (%) Figure Bar Force 1 Test 1 Unbonded Bar Force (MN) Analysis Test Drift Ratio (%) Figure Bar Force 2 Test 1 Unbonded 122

134 0.6 Bar Force (MN) Analysis Test Drift Ratio (%) Figure Bar Force 3 Test 1 Unbonded 0.6 Bar Force (MN) Analysis Test Drift Ratio (%) Figure Bar Force 1 Test 2 PH Steel 123

135 Bar Force (MN) Analysis Test Drift Ratio (%) Figure Bar Force 2 Test 2 PH Steel Bar Force (MN) Analysis Test Drift Ratio (%) Figure Bar Force 3 Test 2 PH Steel 124

136 0.7 Bar Force (MN) Analysis Test Drift Ratio (%) Figure Bar Force 1 Test 3 Confined Bar Force (MN) Analysis Test Drift Ratio (%) Figure Bar Force 2 Test 3 Confined 125

137 Bar Force (MN) Analysis Test Drift Ratio (%) Figure Bar Force 3 Test 3 Confined 0.5 Bar Force (MN) Analysis Test Drift Ratio (%) Figure Bar Force 1 Test 4 - Ungrouted 126

138 0.4 Bar Force (MN) Analysis Test Drift Ratio (%) Figure Bar Force 2 Test 4 Ungrouted 0.5 Bar Forces (MN) Analysis Test Drift Ratio (%) Figure Bar Force 3 Test 4 Ungrouted 127

139 Items that should be mentioned about the above plots are the following: 1. In the confined wall, and to a lesser extent the PH steel and unbonded walls, there is a drastic change in the post-tensioning force on the descending curve of the analysis around a drift level of 0.5%. The reason this occurs in the analysis and not in the tests is due to the masonry compression curve showing no degradation. For the forces to compensate for this, the neutral axis depth must get smaller, which raises the strain in the compression bar. 2. The drop in post-tensioning force at high levels of drift can also be attributed to degradation in the masonry; this combined with the monotonic stress-strain behavior shows why the analysis bar forces plateau or even increase at high levels of drift Cyclic Behavior of Masonry The material properties of post-tensioning steel used in the force-displacement analysis are from monotonic compression tests which do not represent the actual behavior under cyclic loading. The same can be said for the stress-strain relationship of masonry. One way to compare to the masonry compression force found during analysis (C m ) is to take the sum of the bar forces observed during the test (ΣF) plus the weight of the wall and stub beam: C ΣF + w + w (Eq 13.32) m PT w SB Figures to show C m from analysis compared to an approximation of C m from the tests. The plastic hinge steel wall is included for completeness, but equation is not valid due to the presence of the mild steel which adds extra forces into the system. 128

140 Again, the bonded wall is not included because the force recorded in the load cells was constant throughout the test Force (MN) Total Bar Force (Test) Cm from Analysis Drift Ratio (%) Figure Total Bar Force v. Cm Test 1 Unbonded 129

141 Force (MN) Total Bar Force (Test) Cm from Analysis Drift Ratio (%) Figure Total Bar Force v. Cm Test 2 PH Steel Force (MN) Total Bar Force (Test) Cm from Analysis Drift Ratio (%) Figure Total Bar Force v. Cm Test 3 Confined 130

142 Force (MN) Total Bar Force (Test) Cm from Analysis Drift Ratio (%) Figure Total Bar Force v. Cm Test 4 Ungrouted Note in the above plots that (as you would expect), on average, Cm from the analysis is higher than that observed in the tests, due to the cyclic degradation of the masonry and the reduction in the neutral axis depth Analysis Using Known Bar Forces One way to prove that the items mentioned above are causing the difference between the proposed force-displacement analysis results and the force-displacement envelopes obtained during testing is to subject the wall system to another analysis where the bar forces are known, and the force from the actuator is solved for. In other words, using static equilibrium at the limit state values (at the end of the first cycle in the push direction at prescribed levels), with the forces from the post-tensioning taken from the load cell readings, the force in the actuator can be solved for (for free body diagram, see Figure 13.9) by summing moments around the centroid of the masonry compression 131

143 force. This location was assumed to be at a distance from the compression edge of the wall equal to: 2 d c = 3 c (Eqn 13.33) where c is the neutral axis depth determined from the linear potentiometers discussed in Chapter 6. This length was taken because the stress distribution in the masonry has an approximately triangular distribution (see Figures and 13.14). The results from this analysis for all walls except the bonded wall are shown in Figures to Note: the plastic hinge steel wall in this analysis does not include any of the forces from the supplemental mild steel Analysis with Known Forces Test Force (kn) Drift Ratio (%) Figure Analysis with Known Forces v. Test Test 1 Unbonded 132

144 Analysis from Known Forces Test Force (kn) Drift Ratio (%) Figure Analysis with Known Forces v. Test Test 2 Ph Steel 400 Force (kn) Analysis from Known Forces Test Drift Ratio (%) Figure Analysis with Known Forces v. Test Test 3 Confined 133

145 300.0 Force (kn) Analysis with Known Forces Test Drift Ratio (%) Figure Analysis with Known Forces v. Test Test 4 Ungrouted The results from the analysis with known bar forces show good agreement with the force-displacement envelopes observed during the test, and show that if the cyclic degradation characteristics of the post-tensioning steel can be included in a forcedisplacement analysis procedure, good results will be obtained. 134

146 14 Limit States Discussion The behavior of a structure is increasingly being scrutinized under limit states criteria. As put by Paulay and Priestley, these relate to preservation of functionality, different degrees of efforts to minimize damage that may be caused by a significant seismic event, and the prevention of loss of life. The different limit states degrees include: 1. Serviceability Limit State The level obtained during a small seismic event that involves cracking of masonry and some yielding of reinforcement, but requires no repair for good future performance. 2. Damage Control Limit State The level at which the structure can be repaired and still have good performance. Any point beyond this the structure is irreparable. 3. Survival Limit State The point during a large seismic event where the structure obtains damage that is irreparable, but which results in no loss of life or catastrophic failure. The levels considered in this discussion are: cracking of masonry, initial crushing of masonry, maximum force, and each drift ratio after maximum force. Cracking and initial crushing are less important for seismic design, but are included nonetheless. First, these levels of drift will be found for each test and then figures presented which show trends in the performance of the specimens Limit States Determination Tables of the limit states for each test are presented below (Tables 14.1 to 14.5). These points were taken during the first cycle of each drift ratio in the push direction. 135

147 Small differences existed in the wall behavior due to construction variability and the testing procedure between the push and the pull directions, so this point was taken, as opposed to an average of the two directions, in order to provide a measure which might be considered to be independent of these variables. The residual displacement at each drift level was taken after the third cycle in that drift ratio at a zero force value. The residual post-tensioning force was taken at a wall displacement equal to zero after the third cycle. In the tables below PTF stands for post-tensioning force, RPTF stands for residual post-tensioning force, and RDR stands for residual drift ratio. 136

148 Table 14.1 Limit States Test 1 Unbonded State Drift Ratio Force Displ Resd Displ Base Crack Damping Keff ε m ε m PTF RPTF RDR % kn mm mm mm % MN/m unadj adj kn kn % Initial Cracking Spalling Max Force DR after Table 14.2 Limit States Test 2 PH Steel State Drift Ratio Force Displ Resd Displ Base Crack Damping Keff ε m ε m PTF RPTF RDR % kn mm mm mm % kn/m unadj adj kn kn % Initial Cracking Spalling Max Force DR after

149 Table 14.3 Limit States Test 3 Confined State Drift Ratio Force Displ Resd Displ Base Crack Damping Keff ε m ε m PTF RPTF RDR % kn mm mm % kn/m unadj adj kn kn % Initial Cracking Spalling Max Force DR after Table 14.4 Limit States Test 4 Ungrouted State Drift Ratio Force Displ Residual Displ Base Crack Damping Keff ε m ε m PTF RPTF RDR % kn mm mm mm % kn/m unadj adj kn kn % Initial Cracking Spalling Max Force DR after

150 Table 14.5 Limit States Test 5 Bonded State Drift Ratio Force Displ Residual Displ Damping Base Crack Keff ε m ε m PTF RPTF RDR % kn mm mm % mm kn/m unadj adj kn kn % Initial Cracking Spalling Max Force DR after

151 Cracking of the masonry, the first limit state described, occurred at 0.2% drift (the first level tested) for all of the tests. This was observed for all of the tests as being a crack at the footing/wall interface, or at the base. Crushing or spalling of masonry was observed at 0.5% drift for all the tests except the bonded case, where this occurred later at 1.0% drift due to the flexural curvature of the wall which prolonged crushing. This crushing occurred for all the tests at the extreme masonry compression fiber where the mortar joint was observed to be spalling off. The maximum force obtained during each test occurred at different drift ratios. For the unbonded and PH steel specimens the maximum force was observed at 1.75% drift. For the confined this occurred at 3.0% drift; for the ungrouted and bonded at 0.5% and 1.25% respectively Base Crack, Lateral Force Ratio, Residual Drift Ratio Graphs for the maximum size of base crack versus drift ratio are given in Figures 14.2 to This was extrapolated from the base crack profiles at the specified levels of drift, accounting for the distance from the edge of the wall to the curvature potentiometer (see Figure 14.1 below). The unbonded and PH steel walls have base crack sizes of around 25mm, and the confined wall achieved a base crack as high as 80mm. The drop in the size of the base crack at high drift levels in the PH steel and ungrouted walls is most likely due to the inaccuracies in the gauges at these levels due to a high amount of damage in the wall. 140

152 Gauge Length Base Crack Profile Displacement at Gauge Maximum Size of Base Crack at edge of wall Figure 14.1 Establishment of Base Crack Size 25 Base Crack Size (mm) Drift Ratio (%) Figure 14.2 Maximum Size of Base Crack Test 1 Unbonded 141

153 Base Crack Size (mm) Drift Ratio (%) Figure 14.3 Maximum Size of Base Crack Test 2 PH Steel Base Crack Size (mm) Drift Ratio (%) Figure 14.4 Maximum Size of Base Crack Test 3 Confined 142

154 Base Crack Size (mm) Drift Ratio (%) Figure 14.5 Maximum Size of Base Crack Test 4 Ungrouted Base Crack Size (mm) Drift Ratio (%) Figure 14.6 Maximum Size of Base Crack Test 5 Bonded 143

155 Figures 14.7 to show lateral force ratio (LFR) versus drift ratio for each test. This is defined as the maximum force obtained in each test, divided by the force at that level. Fmax LFR = (Eq 4.1) F The shapes of these curves follow closely the force-displacement relationships for each wall Lateral Force Ratio Drift Ratio (%) Figure 14.7 Lateral Force Ratio Test 1 Unbonded 144

156 1.2 1 Lateral Force Ratio Drift Ratio (%) Figure 14.8 Lateral Force Ratio Test 2 PH Steel Lateral Force Ratio Drift Ratio (%) Figure 14.9 Lateral Force Ratio Test 3 Confined 145

157 1.2 1 Lateral Force Ratio Drift Ratio (%) Figure Lateral Force Ratio Test 4 Ungrouted Lateral Force Ratio Drift Ratio (%) Figure Lateral Force Ratio Test 5 Bonded 146

158 As mentioned earlier, residual displacements ( r ) were obtained at the zero force value after the third cycle at each limit state. By comparing this to the height of each wall (h w ), a residual drift ratio or RDR was obtained and is presented in Figures to versus drift ratio for each wall. r RDR = 100 (Eq 14.2) h w The zero force value used to find the residual displacement is difficult to pinpoint at high levels of drift for some walls because of the region of zero stiffness that occurs between cycles. This is especially true of the confined wall, where the residual drift ratio chosen at high levels of wall drift is almost 8%. This was taken fairly arbitrarily since the wall is holding virtually no force for a large section of each cycle. High levels of residual displacement would most likely not occur in a real seismic event, however, because of the self-centering behavioral mechanism discussed in Chapter 3. The residual displacements were taken after the third cycle in the pull direction and are shown in these graphs to be positive, but due to the nearly symmetric nature of each wall there is residual displacement in the push direction as well. 147

159 1.2 Residual Drift Ratio (%) Drift Ratio (%) Figure Residual Drift Ratio Test 1 Unbonded Residual Drift Ratio (%) Drift Ratio (%) Figure Residual Drift Ratio Test 2 PH Steel 148

160 Residual Drift Ratio (%) Drift Ratio (%) Figure Residual Drift Ratio Test 3 Confined Residual Drift Ratio (%) Drift Ratio (%) Figure Residual Drift Ratio Test 4 Ungrouted 149

161 Residual Drift Ratio (%) Figure Residual Drift Ratio Test 5 Bonded 14.3 Average Masonry Compression Strain From the gauges located at the base on the ends of the wall estimates of the average masonry compression strain can be made (see Figures to 14.22). From damage estimates observed during testing, this value can be adjusted to account for wall degradation Drift Ratio (%) By analyzing the base crack profile for each limit state, one can find a tri-linear set of equations relating to each profile. From this, one can obtain values for the maximum compression displacement ( C ) by accounting for the distance from the edge of the wall to the gauge (as mentioned above). If you then divide by the gauge length, l g, you can obtain a value for the average masonry compression strain (ε m ) at a distance (gauge length)/2 up from the footing/wall interface. 150

162 = C ε m (Eq 14.3) lg The gauge length was taken as the distance from the wall/footing interface to the top of the aluminum angle piece used to attach the gauges to the wall (see Chapter 4). Using this value yields artificially high values of strain because the length over which the compression displacement occurs is not easily found. To adjust this strain to account for damage in the wall, a degradation length (l d ) was observed during the test (or after the test from pictures). This represents an average length over the width of the wall in which the masonry has been damaged and cannot be included in the strain computations. By adding this length to the distance from the edge of the wall to the gauge, a new compression displacement can be obtained from the trilinear equations, and from this the adjusted value of average masonry compression strain (ε ma ) (see Figure 14.17). ε ma ε m Average Masonry Compression Strain Profile l d Figure Adjusted Average Masonry Compression Strain Profile 151

163 Ave Masonry Comp Strain Unadjusted Adjusted Drift Ratio (%) Figure Average Masonry Compression Strain Test 1 Unbonded 0.09 Ave Masonry Comp Strain Unadjusted Adjusted Drift Ratio (%) Figure Average Masonry Compression Strain Test 2 PH Steel 152

164 Ave Masonry Comp Strain (m/m) Drift Ratio (%) Unadjusted Adjusted Figure Average Masonry Compression Strain Test 3 Confined Ave Masonry Comp Strain (m/m) Unadjusted Adjusted Drift Ratio (%) Figure Average Masonry Compression Strain Test 4 Ungrouted 153

165 Ave Masonry Comp Strain (m/m) Drift Ratio (%) Unadjusted Adjusted Figure Average Masonry Compression Strain Test 5 Bonded 14.4 Secant Stiffness The secant stiffness (K S ) at each limit state was calculated from the force and displacement values: K = F S (Eq 14.4) By dividing this by the initial stiffness (K i, the stiffness at cracking limit state) the secant stiffness ratio or SSR is obtained: K S SSR = (Eq 14.5) K i Graphs of SSR for all the tests are included in Figures to

166 1.2 Secant Stiffness Ratio Drift Ratio (%) Figure Secant Stiffness Ratio Test 1 Unbonded 1.2 Secant Stiffness Ratio Drift Ratio (%) Figure Secant Stiffness Ratio Test 2 PH Steel 155

167 1.2 Secant Stiffness Ratio Drift Ratio (%) Figure Secant Stiffness Ratio Test 3 Confined 1.2 Secant Stiffness Ratio Drift Ratio (%) Figure Secant Stiffness Ratio Test 4 Ungrouted 156

168 1.2 Secant Stiffness Ratio Figure Secant Stiffness Ratio Test 5 Bonded 14.5 Post-Tensioning Force Relationships At each limit state the total post-tensioning bar force (PT LS ) was found and divided by the initial total post-tensioning force PT i to get the post-tensioning force ratio (PTFR) Drift Ratio (%) PT LS PTFR = (Eq 14.6) PT i PTFR graphs for all tests are presented in Figures to

169 PT Force Ratio Drift Ratio (%) Figure Post-Tensioning Force Ratio Test 1 Unbonded PT Force Ratio Drift Ratio (%) Figure Post-Tensioning Force Ratio Test 2 PH Steel 158

170 1.2 1 PT Force Ratio Drift Ratio (%) Figure Post-Tensioning Force Ratio Test 3 Confined PT Force Ratio Drift Ratio (%) Figure Post-Tensioning Force Ratio Test 4 Ungrouted 159

171 1 PT Force Ratio Drift Ratio (%) Figure Post-Tensioning Force Ratio Test 5 Bonded As mentioned earlier, after the third cycle at each limit state, at zero displacement, the residual total post-tensioning force (PT R ) was found. By dividing this by the initial total post-tensioning force a residual post-tensioning force ratio (RPTFR) is obtained. PT PT R RPTFR = (Eq 14.7) i As can be seen in Figures to the loss of prestress occurred most rapidly in the confined wall, where for a large portion of the test there was virtually no force in the post-tensioning bars as the wall was cycled through zero. This loss of prestress leads to the presence of a zero-stiffness region in the force-displacement history (see Figure 10.1). 160

172 1.2 Residual PT Force Ratio Drift Ratio (%) Figure Residual Post-Tensioning Force Ratio Test 1 Unbonded 1.2 Residual PT Force Ratio Drift Ratio (%) Figure Residual Post-Tensioning Force Ratio Test 2 PH Steel 161

173 1.2 Residual PT Force Ratio Drift Ratio (%) Figure Residual Post-Tensioning Force Ratio Test 3 Confined 1.2 Residual PT Force Ratio Drift Ratio (%) Figure Residual Post-Tensioning Force Ratio Test 4 Ungrouted 162

174 1 Residual PT Force Ratio Drift Ratio (%) Figure Residual Post-Tensioning Force Ratio Test 5 Bonded 14.6 Strain from PH Steel The strain gauges placed on the supplemental mild steel reinforcing in the PH steel wall had limit state values given in Table 14.6 (for locations and other information, see Chapter 6). These values were taken at the maximum point in the first cycle of loading for each drift ratio in the push direction. 163

175 Table 14.6 Limit State Strain in Supplemental Mild Steel State Drift Ratio PH1T PH2T PH3T PH4T % ue ue ue ue Initial Cracking Spalling Max Force DR after four gauges. Figures and show these limit state strains versus drift ratio for the 600 Micro-Strain (ee) PH1T PH2T Drift Ratio (%) Figure Limit State Strains in PH1T and PH2T PH1T PH2T top top 164

176 PH3T PH4T Micro-Strain (ue) Figure Limit State Strains in PH3T and PH4T 14.7 Damping Drift Ratio (%) From the tests the force-displacement hysteresis was recorded. From this, the damping of the wall, ζ, can be found by numerically integrating the hysteresis loops. This is done by isolating a full cycle of response (the first cycle was used in this case), numerically integrating to find the area of the loop, and using the Equation 14.8 to find the damping (see Figure for definitions of A1 and A2). top top PH3T PH4T 2 A1 ζ = (Eq 14.8) π A2 165

177 F A1 A2 Figure Damping from Hysteretic Loops Damping for all walls during the first cycle at each drift ratio is shown in Figure 166

178 Hysteretic Damping (%) Bonded Confined PH Steel Unbonded Ungrouted Drift Ratio Figure Damping v DR for All Walls As expected, the bonded wall had the highest amount of damping, followed by the PH steel wall. For design, a damping value of 7-10% would be reasonable for the unbonded configuration without mild steel, and a slightly higher value with the presence of mild reinforcing. The estimate of damping used in the post-tensioning force determination (see Chapter 5) was the Takeda model divided by two. At a design drift ratio of 1.5%, this yields a damping value of 6.7%. This matches fairly well with the values obtained during testing for the unbonded specimen without supplemental mild steel. 167

179 15 Conclusion / Recommendations This thesis has explored the behavior of post-tensioned clay brick masonry walls under in-plane or seismic loading. The five large scale tests showed distinct advantages for certain configurations in performance, specifically: (1) the presence of a grouted cavity (2) confinement in the toe compression region (3) the presence of mild reinforcing steel in the plastic hinge region and (4) unbonded post-tensioned ducts. Placing grout in the cavity of a post-tensioned clay brick masonry wall is important to develop several of the behavioral mechanisms discussed in Chapter 3. In tests one and four, the only difference in wall layout was the presence of a grouted cavity. This resulted in an increase of maximum applied force on the system from 262kN to 320kN and an increase in maximum displacement obtained during testing from 24mm to 154mm. Grouting the cavity results in the presence of a stable compression strut; this in turn induces an advantageous rocking type behavior on the wall at high levels of drift. With the presence of a stable compression strut and rocking behavior in a posttensioned clay brick masonry wall, the only region with major damage is the toe compression region at each end of the wall. By confining the grout in the cavity in this region using steel plates (much as ties confine reinforced concrete), the maximum strains in this region can be dramatically increased. For tests one and three the only variable was confinement. This showed an increase in maximum applied force, from 320kN to 344kN, and a large increase in maximum displacement from 154mm to 276mm. Energy dissipation in post-tensioned masonry configurations is low. In order to increase this, mild supplemental reinforcing was added in the plastic hinge region of one of the wall configurations. Although the compression strut wasn t as stable as in the 168

180 unbonded, grouted configuration, the maximum displacements obtained were similar, with a modest increase in applied force. But the system with mild reinforcing did have significantly higher values of damping. For the unbonded, grouted configuration a value of approximately 7% was obtained, whereas for the wall with the additional steel a value of 10-12% was found. This supplemental mild steel needs to be designed carefully, however, to avoid high strains at the wall/footing interface. Four of the five walls tested used unbonded post-tensioning ducts. The wall with bonded post-tensioning performed similar to a reinforced masonry wall at first, with longitudinal flexural cracking; but as the test progressed inelastic residual deformation of the post-tensioning bars damaged the compression strut and led to a failure at 3% drift, much lower than the 6.5% obtained in the unbonded, grouted configuration. Due to the poor performance of the wall and added complexity in construction, bonded posttensioning is not recommended. As to the analysis of post-tensioned clay brick masonry walls, the monotonic force-displacement procedure proposed herein offers good values for maximum force response and initial stiffness values, but does not give estimates on the maximum displacement expected. This occurs mainly because (1) the cyclic inelastic deformation of the post-tensioning bars was not modeled and (2) the degradation of the masonry within the compression zone was not taken into account. In order to achieve a full forcedisplacement response in the system these two items must be accounted for in the analysis. Designing a post-tensioned clay brick masonry wall must go beyond the rough estimates used in Chapter 5. In addition to identifying key limit states such as yielding 169

181 and ultimate displacement, a damping-ductility relationship needs to be developed. Care also needs to be taken when designing the amount of post-tensioning bars, so that they remain elastic up to a certain design drift level. This could eliminate the area of low or zero stiffness which occurred most notably in the confined wall Implications for Housing Structures Assume a single story house that is 12m by 15m with four walls in each direction (two on each side) similar in size and post-tensioning ratio to the walls tested in this research. Using an unbonded, grouted configuration, the force resisted by one wall is approximately 350kN, giving a base shear resistance (V b ) for the four walls in one direction of: ( 350 kn )( 4walls) = kn V b = 1400 (Eqn 15.1) Assuming a response acceleration of 1g, this gives an inertial mass (M) of the size: 1400,000N M = = 140, 000kg (Eqn 15.2) 10 m 2 s The loads on a typical structure, however, are on the order of 475 N/m 2. This translates to an inertial mass demand (M D ) of: ( N 1kg )( 12m 15m) = kg M D = 8712 (Eqn 15.3) m 9.81N Therefore the resistance is significantly greater than the demand in a single story structure, and buildings with larger height are possible Recommendations The research performed herein should provide the impetus for further study on post-tensioned clay brick masonry walls. Such research should point in the direction of 170

182 applying such a system for use in modular housing or light industrial applications. Some areas of further structural research should be: 1. Walls with openings (window and door) * 2. L-shaped walls * 3. Shake table tests * 4. Walls with different aspect ratios In addition to structural testing, further items dealing with the analysis and design of a post-tensioned masonry system need to be explored, such as: 1. Integrating a stress-strain model for the post-tensioning bars into the forcedisplacement analysis which takes into account cyclic inelastic deformation. 2. Integrating a model of masonry degradation in the compression zone into the force-displacement analysis. 3. Further identifying limit state points used in a displacement based design procedure 4. Finding a procedure to design the amount of post-tensioning bars to keep them within the elastic range up to certain levels of drift. * Current and future topics of research at North Carolina State University 171

183 REFERENCES 1. American Concrete Institute (1999) Acceptance Criteria for Moment Frames Based on Structural Testing, ACI Provisional Standard. 2. American Concrete Institute (2002) Building Code Requirements for Masonry Structures, ACI Ayers, J. (2000). Evaluation of Parameters for Limit States Design of Masonry Walls, North Carolina State University, Department of Civil Engineering. 4. Christopoulos C., Filiatrault A., Uang C-M (2002). "Post-tensioned energy dissipating connections for steel frames". Journal of Structural Engineering, ASCE Durham, A. (2002). Influence of Confinement Plates on the Seismic Behavior of Clay Masonry Structures, North Carolina State University, Department of Civil Engineering. 6. Ewing, B., and Kowalsky, M.J. (2002). Compressive Behavior of Unconfined and Confined Clay Brick Masonry Prisms, Submitted to The Masonry Society Journal. 7. Ingham, J.M., McKinnon, R.J., and Avery, C. (1998). In-Plane Seismic Design of Unbonded Prestressed Concrete Masonry. Australasian Structural Engineering Conference, Auckland, New Zealand. 8. International Code Council (2000). "International Building Code" 9. Laursen, P., and Ingham J.M. (2000). Cyclic In-Plane Structural Testing of Prestressed Concrete Masonry Walls, Volume A: Evaluation of Wall Structural Performance. School of Engineering Report No. 599, Department of Civil and Resource Engineering, University of Auckland, New Zealand. 10. Laursen, P., and Ingham J.M. (2000). Cyclic In-Plane Structural Testing of Prestressed Concrete Masonry Walls, Volume B: Data Resource. School of Engineering Report No. 600, Department of Civil and Resource Engineering, University of Auckland, New Zealand. 11. Liddell, D., (1998). In-Plane Seismic Design of Prestressed Concrete Masonry. Year Four Project Report, Department of Civil and Resource Engineering, University of Auckland, New Zealand. 12. King, D.J., (1986). Computer Programs for Concrete Column Design, Report 86/12, University of Canterbury, Christchuch, New Zealand. 172

184 13. Kowalsky, M.J., Priestley, M.J.N., MacRae, G.A., (1995). Displacement-Based Design of RC Bridge Columns in Seismic Regions, Earthquake Engineering and Structural Dynamics, Vol. 24, Kowalsky, M.J., Priestley, N., Seible, F., (1997). Shake Table Testing of Lightweight Concrete Bridges, Structural Systems Research Report SSRP-97/10, University of California, San Diego. 15. Moyer, M.J. (2001). Influence of tension strain on buckling of reinforcement in RC Bridge columns, North Carolina State University, Department of Civil Engineering. 16. Page, A.W., and Huizer, A. (1988). Racking Tests on Reinforced and Prestressed Hollow Clay Masonry Walls. Masonry International, 2(3), Priestley M.J.N, Sritharan S., Conley J.R., Pampanin S. (1999). "Preliminary Results and Conclusions from the PRESSS Five-Story Precast Concrete Test Building", PCI Journal, Vol. 44, No. 6, pp Priestley, M.J.N., and Elder, D.M. (1983). Stress-Strain Curves for Unconfined and Confined Concrete Masonry. ACI Journal, 80(3), Ricles J.M., Sause R., Garlock M, Zhao C. (2001). "Post-tensioned seismic-resistant connections for steel frames", Journal of Structural Engineering, ASCE Vol. 127, No.2, pp Shrive, N.G. (1988). Post-Tensioned Masonry Status and Prospects, Canadian Society for Civil Engineering Annual Conference, May Tou, D.C.C., and Ingham, J.M. (1998). Analytical Strain Distribution Unbonded Prestressed Concrete Masonry Walls. Project Report, Department of Civil and Resource Engineering, University of Auckland, New Zealand. 173

185 APPENDICES 174

186 Appendix 1 Pictures Note on pictures: Side of wall shown is as shown in Figure A1.1. Unless otherwise noted, picture was taken on the third cycle in the push direction. Pull Direction Push Direction Actuator N E Wall S W Figure A1.1 Note on Pictures 175

187 A1.2 Test 1 Unbonded Figure A1.2 E side at DR=0.75% Figure A1.3 N side at DR=1.75% 176

188 Figure A1.4 S side at DR=2.25% Figure A1.5 W side at DR=5.0% 177

189 Figure A1.6 N end at DR=6.5% Figure A1.7 W side after DR=6.5% (end of test) 178

190 A1.2 Test 2 PH Steel Figure A1.8 W side at DR=0.5% Figure A1.9 N end at DR=1.0% 179

191 Figure A1.10 N end at DR=1.75 Figure A1.11 E side at DR=5.0% 180

192 Figure A1.12 E side at DR=6.5% cycle one pull Figure A1.13 E side during wall demolition 181

193 A1.3 Test 3 Confined Figure A1.14 S end at DR=0.5% Figure A1.15 S end at DR=1.75% 182

194 Figure A1.16 S end at DR=2.25% Figure A1.17 N end at DR=5.0% 183

195 Figure A1.18 E side at DR=6.5% Figure A1.19 S end at DR=8.0% 184

196 Figure A1.20 W side at DR=10.0% Figure A1.21 W side at DR=11.3% first cycle push (end of test) 185

197 Figure A1.22 S end at DR=11.3% first cycle push (end of test) Figure A1.23 N end at DR=11.3% first cycle push (end of test) 186

198 A1.4 Test 4 Ungrouted Figure A1.24 E side at DR=0.5% Figure A1.25 W side at DR=0.75% cycle one push 187

199 Figure A1.26 E side at DR=0.75% cycle two push Figure A1.27 E side at DR=1.0% cycle one push (end of test) 188

200 A1.5 Test 5 Bonded Figure A1.28 W side at DR=1.25% Figure A1.29 N end at DR=1.75% 189

201 Figure A1.30 W side at DR=3.0% Figure A1.31 W side at DR=3.75% cycle one pull (end of test) 190

202 Figure A1.32 W side at DR=3.75% cycle one pull (end of test) 191