DESIGN, VERIFICATION, AND CALIBRATION OF DIGITAL IMAGE CORRELATION SYSTEM IN APPLICATIONS TO LARGE SCALE STRUCTURAL TESTING

Transcription

1 NEES REU SUMMER PROGRAM 2014 DESIGN, VERIFICATION, AND CALIBRATION OF DIGITAL IMAGE CORRELATION SYSTEM IN APPLICATIONS TO LARGE SCALE STRUCTURAL TESTING Marissa Shea Home Institution: University of Massachusetts Amherst REU Institution: University of California, Los Angeles REU Mentor: Christopher Segura REU Principal Investigator: John Wallace, Ph.D., P.E. Project: NEESR: Performance of Conventional and Innovative Special Structural Walls August 22, 2014

2 ABSTRACT The use of traditional sensors, such as linear variable differential transformers (LVDTs) and strain gauges, for large-scale structural testing may be time consuming and require large equipment costs. Alternatively, digital image correlation (DIC) is a non-contact technique that measures displacements of a specimen by processing images before and after deformation; a much faster and cheaper method. This project was performed at the George E. Brown, Jr., Network for Earthquake Engineering Simulation facility at the University of California, Los Angeles (NEES@UCLA). The project focuses on the design, verification, and calibration of the DIC system using NCorr: an open source 2D DIC MATLAB program. Three concrete columns and three reinforced concrete (RC) beams were designed and decorated with speckle patterns to verify the accuracy of the DIC results. The first two columns were tested in the lab until failure; displacement and strain results proved to be positive for the validation of DIC, but further testing is required to fully verify accuracy. The strategy and results of this paper are being used to facilitate a UCLA NEESR project conducted by PhD candidate Christopher Segura exploring the seismic performance of slender RC shear walls. i

3 TABLE OF CONTENTS LIST OF FIGURES... iii 1 INTRODUCTION LITERATURE REVIEW Shear Wall Research Shear Wall Theory DIC Research METHODS AND CONTRIBUTIONS Camera Equipment Experimental Testing Contributions to Shear Wall Project RESULTS DISCUSSION OF RESULTS FUTURE WORK Application to NEESR Shear Wall Project CONTACT INFORMATION ACKNOWLEDGEMENTS REFERENCES APPENDIX A BEAM DESIGN CALCULATIONS... A-1 ii

4 LIST OF FIGURES Figure 1. Sketch of a rectangular isolated cantilever RC shear wall with applied lateral forces (the right shows an exaggerated deformation)... 1 Figure 2. Concrete crushing and spalling and buckling of vertical reinforcement from the 2010 Chile Earthquake (Wallace, 2011)... 2 Figure 3. Test setup for isolated cantilever wall specimen (Source: Chris Segura)... 2 Figure 4. LVDT setup on Wall One (left) and strain gauges attached to the shear wall boundaries (right)... 3 Figure 5. Photos taken throughout the strain gauge application process... 4 Figure 6. Example of a speckle pattern created with black spray paint... 5 Figure 7. Strain data fit to model for compressive stress at onset of buckling in cyclic tests where the effective length factor, K, is 0.75 (Rodriguez et al., 1999)... Error! Bookmark not defined. Figure 8. Sketch of steel rebar buckling in compression after an inelastic tensile strain... Error! Bookmark not defined. Figure 9. Lateral pressure of a rectangular column cross-section in compression (Saatcioglu and Razvi, 1992)... Error! Bookmark not defined. Figure 10. Proposed stress-strain behavior comparison for confined and unconfined concrete compressive behavior (Saatcioglu and Razvi, 1992)... Error! Bookmark not defined. Figure 11. Cross-section of a boundary element in a 6" thick RC shear wall Figure 12. Computer-generated random patterns used for image analysis with subset size in red (Stoilov et al., 2012) Figure 13. Canon EOS 6D with 35mm Lens, Planar T* Lens, 88mm Lens, and Zoom Lens Figure 14. Wireless transmitters (left) and studio light with umbrella (right) Figure 15. Two cameras and one studio light set up for DIC testing Figure 16. Column One photos chosen for the DIC Figure 17. Column Two photos chosen for the DIC Figure 18. High resolution displacement results in the y-direction (inches) from the DIC and MTS machine for Columns One and Two Figure 19. Strain and displacement (inches) DIC results for Column One using low resolution and high resolution cameras Figure 20. Strain and displacement (inches) DIC results from Column Two using the high resolution camera Figure 21. Displacement and strain variance along the length of a fixed member with a point load axial force Figure 22. The three beams designed for the DIC testing Figure 23. Current state of the first four RC shear wall specimens (courtesy of Chris Segura) iii

5 1 INTRODUCTION Shear walls are one of the most widely used structural elements for the resistance of lateral forces, i.e. earthquake loads and high winds, because of their low-cost and extraordinary strength capabilities (Wallace, 2011). The forces acting parallel to floor levels and in-plane with the wall (lateral forces) cause the wall to deflect and deform in that same plane. Figure 1 shows a view looking straight onto a reinforced concrete (RC) shear wall. The image on the right shows how the structure deforms when subjected to lateral loads. When the load is applied in one lateral direction, one boundary is in tension while the other is in compression, as seen in Figure 1. Figure 1. Sketch of a rectangular isolated cantilever RC shear wall with applied lateral forces (the right shows an exaggerated deformation) Over the years, engineers have pushed the limits of shear wall design to save time and money, producing walls more slender than any wall that has been verified in lab or field experiments. High-magnitude earthquakes in Chile and New Zealand caused unfavorable compression failure modes: rebar buckling, global buckling, concrete spalling and crushing, etc. (Wallace, 2011). Examples of these failures can be seen in Figure 2. The 2011 magnitude (M w ) 6.2 earthquake in Christchurch, New Zealand, in particular, led to 185 deaths and an estimated total loss of NZ$20 billion (Elwood, 2013; Deam & Dhaka, 2011). Chile s 2010 M w 8.8 earthquake took the lives of 251 people, and was estimated to total about $30 billion in damage (Moehle & Riddell, 2010). Chile and New Zealand have very similar building codes to the United States, and the walls that were damaged, as thin as 6 inches, were all designed according to their respective codes. Current research at the University of California Los Angeles (UCLA) focuses on assessing code provisions (i.e. ACI ) to identify potential sources of unfavorable failure modes in RC shear walls. A-1

6 Figure 2. Concrete crushing and spalling and buckling of vertical reinforcement from the 2010 Chile Earthquake (Wallace, 2011) A Network for Earthquake Engineering Simulation Research (NEESR) project, Performance of Special and Innovative Structural Walls, being performed by PhD student Christopher Segura, investigates the seismic response of thin reinforced concrete shear walls. This project is taking place at UCLA under Principal Investigator, John W. Wallace. Twelve half-scale RC shear wall panels with different boundary detailing are being subjected to cyclic loading (Figure 3) representative of the shear and bending demands expected at the base of an isolated cantilever shear wall. The goals for this project include defining practical limits for structural wall boundary zones of conventional RC shear walls. In particular, the project aims to identify minimum confinement provisions necessary to promote ductile compression failures and to define critical cross-section geometry provisions (slenderness ratio, hoop spacing, clear cover, flexural reinforcement layout, etc.) necessary to limit buckling failures and fracture of flexural reinforcement. The intension is to recommend provisions that can be implemented in the new building code (ACI ), and to ultimately assist in the design of more resilient special structural walls that result in improved social and economic outcomes. Figure 3. Test setup for isolated cantilever wall specimen (Source: Chris Segura) 2

7 Each of the twelve shear wall specimens will be instrumented with approximately 60 linear variable differential transformers (LVDTs) and 40 strain gauges to collect stress-strain data throughout testing. Figure 4 shows the first wall specimen, tested in August 2014, with the LVDT setup and the strain gauges attached to the inner boundary elements. Figure 4. LVDT setup on Wall One (left) and strain gauges attached to the shear wall boundaries (right) Instrumenting traditional sensors like LVDTs and strain gauges is an excessively lengthy, tedious, and costly task because of the numerous steps involved in the application process. The steps to installing strain gauges, pictured in Figure 5, include grinding and sanding rebar to get a smooth surface for the strain gauges (a, b, c), applying the gauges to the bars (e, f, g), connecting lead wires to the attached strain gauges (i, j, k), and producing connections for the strain gauges to be hooked up to computer systems (l). LVDT installation includes calibrating each sensor, making connections to a computer, and mounting them on the specimen. 3

8 Figure 5. Photos taken throughout the strain gauge application process Because of the inconvenience of the traditional sensors, the NEESR shear wall project is studying the use of digital image correlation (DIC) as a replacement for the LVDT s and strain gauges simultaneously with the testing of the walls. DIC is an alternative method for measuring surface deformation of specimens subjected to mechanical loading. It is a non-invasive technique that measures planar surface displacements through processing images before and after deformation (Pan et al., 2009). In addition to the traditional instrumentation on the 12 half-scale shear walls, the specimens will also be decorated with speckle patterns to perform the DIC using NCorr: an open source two dimensional (2D) DIC MATLAB program (Blaber, 2014). The NEESR shear wall project is scheduled to be completed by May of To calculate displacements, DIC software compares the locations of reference subsets to targeted subsets on the images of specimens before and after deformation. Greyscale images, also known as speckle patterns, are captured and processed through software to achieve stress-strain relationships for mechanical experimentation (Pan et al., 2008). A speckle pattern is a randomized arrangement of black dots on a white background, as seen in Figure 6. 4

9 Figure 6. Example of a speckle pattern created with black spray paint For all versions of DIC, the user must input a reference image (prior to any deformation), as well as deformed pictures into the DIC software, and the system calculates displacements by tracking the movement of the speckles. Some research in the recent years has examined the creation of speckle patterns to optimize DIC results, but more is needed to continue the study (Pan et al., 2009). As a subset of the NEESR shear wall project, this particular NEES@UCLA 2014 summer research project explored the feasibility and accuracy of DIC analysis for applications of largescale RC structural testing. The objectives of the study were as follows: design an experiment to test the accuracy and limitations of DIC, work with different speckle patterns and resolutions to optimize DIC results, and prepare the system for larger-scale structural testing. 2 LITERATURE REVIEW 2.1 Shear Wall Research In 1992, a study, conducted by Saatcioglu and Razi (1992), looking at a comparison of the stressstrain behavior of confined and non-confined RC boundaries produced a model that yields results similar to ones found in experimental lab tests. This model is capable of representing multiple cross-sectional shapes and rectangular sections confined by different hoops and tie directions. Concrete behavior under in-plane and out-of-plane loading is displayed accurately through this model. During compression, the concrete and longitudinal bars apply outward forces on the hoops, putting the hoops in tension (Figure 7). 5

10 Figure 7. Lateral pressure of a rectangular column cross-section in compression (Saatcioglu and Razvi, 1992) Boundaries that are confined by seismic hoops and ties are capable of resisting greater compressive forces. Confinement increases ultimate strength, and allows for greater strains prior to failure (Saatcioglu and Razvi, 1992). This relationship can be seen in Figure 8. Figure 8. Proposed stress-strain behavior comparison for confined and unconfined concrete compressive behavior (Saatcioglu and Razvi, 1992) In 1999, the model was improved to include the stress-strain behavior of high-strength concrete as well as normal strength concrete. This newer analysis, encompassing concrete strengths from 30-MPa to 130-MPa, was made as a user-friendly approach to modeling different shaped sections with any arrangement of lateral confinement detailing (Saatcioglu and Razvi, 1999). Paulay and Priestly (1993) studied the response of thin rectangular walls subjected to intense earthquake simulation loading to determine the cause of global buckling. They suggested that out-of-plane buckling during cyclic loading occurs when the longitudinal bars are loaded in 6

11 compression after undergoing irreversible tensile strains. When the strain in rebar surpasses the elastic range, the cross-sectional area decreases and thus becomes much weaker when loaded back in compression; the result is global instability and ultimately, global buckling. Figure 9 shows an isolated longitudinal steel bar permanently deforming in tension, elongating, losing strength, and buckling when it is being loaded in compression. Figure 9. Sketch of steel rebar buckling in compression after an inelastic tensile strain Chai and Elayer (1999) used strain and out-of-plane displacement data from an experimental axial cyclic test on an RC column to produce a model capable of predicting maximum tensile strains. In the study, the columns represented boundary elements from shear walls. Tests have proven that the model is conservative with respect to the predictions of the maximum tensile strains. Additionally, the equation used in the model can be incorporated to existing design procedures to determine a limit to wall thickness. In 2010, Earth-Defense (E-Defense) Lab, at Hyogo Earthquake Engineering Research Center located in Miko, Japan, performed full scale tests on four-story buildings with high ductility structural walls to collect new data (Wallace, 2012). Even though these buildings were designed to their code, many of the thin wall boundaries failed to result in ductile failure during compression loading (Wallace, 2012). Studies have proven that smaller spacing between the transverse reinforcement may be required to suppress rebar buckling in the longitudinal bars (Wallace, 2012). Although this relation has been proven, further evidence from the 2010 Chile earthquake suggest that the failures under the seismic loading may not have been a result of the lack of boundary confinement (Wallace, 2011). Additional research is required to study this phenomenon and the driving force to undesired failure (Wallace, 2011). The damage from the New Zealand earthquake suggests that confinement may be required in boundary areas where there are many narrow longitudinal bars and in areas where the height exceeds the assumed plastic hinge length (Elwood, 2013). Tests conducted at the National University of Mexico, by Rodriguez et al. (1999) have proven longitudinal steel bars to buckle in the inelastic range when subjected to repeated tensile and compressive axial loading. Rodriguez 7

12 et al. proposed a relationship between the length of unsupported steel rod and the amount of plastic strain that is needed for it to buckle. Through experimentation, plastic strain at onset of buckling was related to the spacing of the hoops divided by the diameter of the longitudinal bar. They tested rebar not confined by concrete and fit a graph to data to create a relation for the plastic strain for buckling given the ratio of seismic hoop spacing (S h ) to diameter of the longitudinal bars (D). One conclusion of this testing was that more compressive strain is needed to make the rebar buckle when the spacing between the hoops is smaller. Prevention of bar buckling plays a large role in producing favorable failure modes. Figure 10 shows an example of a graph displaying the strain for compressive stress at onset of buckling (ε p * ) during a cyclic test versus the S h to D ratio. Figure 10. Strain data fit to model for compressive stress at onset of buckling in cyclic tests where effective factor, K, is 0.75 (Rodriguez et al., 1999) Recent tests indicate that the ACI building code may lead to brittle compression failures for thin special boundary element compression zones (Moehle and Riddell, 2010). Additional research is required to improve upon the code specifications for thin shear walls. Thin walls have been proven to perform poorly under continued cyclic tension and compression loading. Paulay and Priestly (1993) suggested that spalling of cover concrete exposes an even thinner wall section that is vulnerable. Evidence from the 2010 Chile earthquake suggests that instability is driven by global buckling of slender core concrete sections after spalling, as opposed to the previously believed tension crack propagation (Paulay and Priestly, 1993). Simulation and computer modeling for reinforced concrete walls have been created to study the inelastic behavior of these thin shear walls. The models by Paulay and Priestly (1993) and Chai and Elayer (1999) were both created under the assumption that thin walls fail due to cracks formed in tension. Evidence from the 2010 Chile earthquake, this may not be the case; therefore, models must be updated to account for the new research. 8

13 Field observation of structural performance after large magnitude earthquakes has proven to be a great way of studying material behavior under repeated ground excitation (Deam & Dhaka, 2011). For the purpose of research studies like the NEESR@UCLA shear wall project, engineers have analyzed the behavior of and damage to shear walls in RC structures in significant earthquakes. In particular, studying the failure modes of RC shear walls from buildings affected by the 2010 M w 8.8 Chile earthquake and the 2011 M w 6.2 New Zealand earthquake has been greatly advantageous for the progress of research in the earthquake engineering field (Deam & Dhaka, 2011). Striking similarities between the wall destruction from these two quakes suggest particular design and construction practices that are causing these undesired failures (Deam & Dhaka, 2011). According to Wallace (2011), buildings in the 1985 M w 7.8 Chile earthquake performed so well that Chilean engineers pushed the limits of shear wall design to be less stringent than their previous code. In 1996, shortly after the creation of ACI , Chile implemented a building code very similar to the U.S. One significant difference between the two codes was that Chile omitted the provisions requiring special transverse reinforcement at wall boundaries to confine the concrete and restrain rebar buckling. Consequently, over the course of years, a substantial number of thin RC shear walls were constructed with limited seismic ties and boundary confinement (Wallace, 2011). Wallace (2011) found that the devastating failures from the 2010 M w 8.8 Chile earthquake were located within the buildings erected after 1985, under the less stringent codes. Reviewing floor plans created before and after 1985 led to the discovery that the successful (older) buildings had a higher ratio of wall cross-sectional area to floor area; global stability was therefore greater. For example, typical ratios were 3% before and 1.5% after Additionally, the newer buildings were designed with more stories and much thinner walls, subjecting them to higher probabilities of out-of-plane buckling (Wallace, 2011). 2.2 Shear Wall Theory Building codes are put in place to ensure that structures succeed, resulting in favorable failures under extreme loading. When an earthquake or other disaster occurs, the building codes are supposed to promote safety for the humans inside and around the structures. An example of a favorable failure would be a ductile failure mode where the steel undergoes a large amount of plastic deformation prior to failure. In contrast, brittle failures occur rapidly without much plastic deformation or visible warning beforehand. RC shear walls are constructed with steel reinforced boundary elements at both ends of the wall. Each boundary contains a rectangular perimeter of longitudinal rebar confined by steel hoops and ties, also known as boundary confinement, which is arranged horizontally along the height of the wall. The cross-sectional area of steel, vertical spacing of the hoops, and number of ties required is defined by the building code (ACI ). Figure 11 shows an example of boundary confinement cross-section with the seismic hoop and cross tie to hold the steel rebar in place. Boundary confinement requirements are intended to prevent unstable compression failures that lead to rebar buckling and buckling of entire sections, by promoting ductile compression failures. ACI Equation 21-4 is intended to protect the post-spalled core of compression members from buckling once the cover concrete has spalled, while from ACI is intended to protect the longitudinal rebar from buckling 9

14 (Rodriguez et al., 1999). Compression failures occur when the bars are too stressed and buckle or the core is too stressed and global buckling occurs (Rodriguez et al., 1999). Global buckling occurs when an eccentricity develops in the structure because the line of action is off of the line of resistance as a result of a permanent deformation in the steel. This causes a moment, and the entire structure fails. (6) #6 #3 hoop Optional Cross-Tie 6" 1" 15" 2.3 DIC Research Figure 11. Cross-section of a boundary element in a 6" thick RC shear wall A study on the subset size selection in DIC for speckle patterns (Pan et al., 2008) concluded that the accuracy of the measured displacements is directly dependent on the size of the reference subset chosen by the user through experience and intuition. For all DIC software, the user must choose a subset size varying from several pixels to even more than a hundred pixels prior to the analysis. The subset size is defined as the area being tracked by the DIC to determine the movements in the speckles between the reference and target subsets, where each speckle is at least a few pixels in size (Hild and Roux, 2006). It should be large enough to contain a distinctive speckle pattern, but the smaller, the more accurate (Pan et al., 2008). Figure 12 shows examples of chosen subset sizes for different speckle patterns. Figure 12. Computer-generated random patterns used for image analysis with subset size in red (Stoilov et al., 2012) All of the factors that affect the accuracy of the DIC include the sub-pixel optimization algorithm, subset shape function, subset size, sub-pixel intensity interpolation scheme, image noise, and camera lens distortion (Pan et al., 2008). In general, DIC analysis programs are developed using either subset-based cross-correlation (CC) or sum-squared difference (SSD) correlation criteria (Pan et al., 2008). Based on these criteria, in addition to the use of a low 10

15 image noise gradient, Pan et al. (2008) derived a theoretical model that the displacement measurement accuracy of DIC can be accurately predicted based on the variance of image noise and Sum of Square of Subset Intensity Gradients (SSSIG). This model allowed for a simpler criterion for choosing a proper subset size, and illuminated the relation that a smaller subset size can be used for images with greater contrast. Because DIC is still a relatively new approach to collecting displacements and strains, more research and testing is needed to further the growing knowledge of DIC. 3 METHODS AND CONTRIBUTIONS 3.1 Camera Equipment In 2014 NEES@UCLA purchased high quality camera equipment for the use of DIC analysis. Images captured for this project were taken with a Canon EOS 6D (Figure 13) that is capable of taking pictures with 5472x3648 pixels. Figure 13. Canon EOS 6D with 35mm Lens, Planar T* Lens, 88mm Lens, and Zoom Lens Two studio lights and four wireless transmitters (Figure 14) were purchased so that the cameras could be synced to take pictures at the same time as the flash from the lights by receiving a signal from the wireless transmitter. Figure 15 shows an example of the equipment setup for testing. Figure 14. Wireless transmitters (left) and studio light with umbrella (right) 11

16 3.2 Experimental Testing Figure 15. Two cameras and one studio light set up for DIC testing Experimental testing with smaller specimens was designed to practice with the DIC equipment and software. Three 3x3x13 in 3 concrete columns and three 6x6x22 in 3 RC beams were decorated with speckle patterns with plans of being tested until failure using MTS mechanical equipment. All six specimens were created with Quikrete (f c = 5,500 psi). After a day of curing, two faces of each specimen were covered in silicon to fill in the holes on the surface. After drying, the faces were sprayed with white spray paint to create a flat, white surface. Finally, black spray paint was used to create a random array of black dots on the white surfaces. Each dot in the speckle pattern was intended to be between 5 and 20 pixels in size when taking a picture with the column height spanning the entire height of the frame. The three columns were designed to be tested in pure compression in an MTS machine with a fixed top and rising bottom surface. The speckle pattern on Column Two was about twice as dense as the pattern on Column One. This was designed to compare the speckle pattern results in NCorr. Two LVDTs were attached to Column Three to collect displacement data from the test and verify the accuracy of the displacements output from the DIC. Pictures were taken every 30 seconds with two Canon EOS 6Ds throughout the loading to capture the movement and displacement of the dots within the speckle pattern. The first camera was on full resolution (5472x3648 pixels) and the second camera was on half resolution (2736x1824 pixels). This was done to investigate the optimal speckle size, and to see if there was any effect on the DIC results. The photos were then input into NCorr to retrieve the displacement and strain data. 3.3 Contributions to Shear Wall Project The NEESR shear wall project progressed throughout the summer while the DIC testing was taking place. The first four RC shear wall specimens were seen from the design phase, through 12

17 construction, and up to a week prior to testing. Steel rebar was arranged in the boundary elements and webs. Seismic hoops and ties were tied into the boundaries according to the design specifications. Forty strain gauges were prepared, installed, and attached to each wall. Sixty LVDTs were calibrated and prepared for attachment to the walls after construction. Formwork was created to prepare for the concrete pouring. Concrete was poured into the four wall specimens by a construction team while concrete test cylinders were organized and made for strength testing. 4 RESULTS On August 1 st and August 6 th 2014 Columns One and Two were tested in the lab until failure. Five photos, chosen randomly throughout the 20 minutes of testing, were input into NCorr for the two columns (Figures 16 & 17). For both, the first photo was the reference photo taken before any load was applied, and the last photo was after the column had failed. For Column One, the DIC parameters chosen for both resolutions included a subset radius 10, spacing 11, and strain radius 10. The DIC parameters chosen for Column Two were subset radius 20, spacing 7, and strain radius 10. Figure 16. Column One photos chosen for the DIC Figure 17. Column Two photos chosen for the DIC Figure 18 shows the displacement results in the y-direction from the DIC and from the MTS loading machine. The top two plots are the displacement results from NCorr from the image taken after failure. The colors correspond to the displacements on the scales to the right which are in units of inches. The bottom two graphs of force vs. displacement were created from data retrieved from the MTS machine throughout the entire loading process. 13

18 Figure 18. High resolution displacement results in the y-direction (inches) from the DIC and MTS machine for Columns One and Two Figure 19 compares the strain results from NCorr from the high and low resolution cameras for the Column One test. Both graphs show the strain in the y-direction from the same point of the loading (picture 47 out of 197). It also shows the high resolution and low resolution displacement in the y-direction (inches) from an image taken after failure. 14

19 Figure 19. Strain and displacement (inches) DIC results for Column One using low resolution and high resolution cameras Figure 20 shows the DIC results for Column Two using the high resolution camera. The strain plot is from image 22 out of 43 in the loading. The displacement plot is from an image after failure. Figure 20. Strain and displacement (inches) DIC results from Column Two using the high resolution camera 15

20 5 DISCUSSION OF RESULTS The results from the displacement from Column One are the first indication that the DIC is working. As seen in Figure 18, the maximum displacement from the NCorr results as well as the MTS results are both approximately 0.6 inches. The results from Column Two, however, seem to be inaccurate (Figure 18). The maximum displacements do not match as the Ncorr indicates 0.15 inches max but the MTS results indicate 0.45 inches. To confirm the reliability of the DIC, these two values would have to match. This discrepancy can be caused by a couple of different factors. First of all, the speckle pattern could be too dense, and therefore incapable of being tracked during deformation. Also, the subset radius chosen (20) could be inaccurate, resulting in false displacements. Another cause for error could be sourced from inaccuracies from the MTS system. The top platform rotates, and therefore could have caused a discrepancy in the results. The displacement and strain distributions from the two tests are consistent with theory, suggesting that the DIC captures the displacement and strain patterns on the specimen. For a point load axial force on a member that is fixed on one end, the displacement is supposed to vary with x while the strain is constant (Figure 21). Figure 21. Displacement and strain variance along the length of a fixed member with a point load axial force Strain for a point load axial force can be determined from deriving Hooke s Law: σ = Eε (Eq. 1) σ = F A (Eq. 2) F A = Eε (Eq. 3) ε = F EA (Eq. 4) 16

21 According to Equation 4, the strain is only affected by constants, and therefore should not change over the length of the column for any force, F. Therefore, the color distribution of strain should be fairly constant in the DIC results, which it is. For Column One, the DIC results show the strain varying between approximately 0.00 and Likewise, the DIC results for Column Two show the strain varying between approximately 0.0 and Because the integral of strain is displacement, taking the integral Equation 4 with respect to x yields Equation 5. u(x) = Fx EA (Eq. 5) Therefore, displacement (u) is a function of x (the distance along the length of the column) and it makes sense for the greatest displacements to be at the bottom of the column, farthest from the fixed top. This color distribution from least displacement to greatest is shown in the DIC results (Figure 18). A comparison between the high resolution and low resolution DIC results can be seen in Figure 19. The results yielded about the same numerical values for the strains and displacements in Column One. These results back up the idea from Hild and Roux (2006) that the size of the speckles does not affect the results, as long as the scope is at least a few pixels. In conclusion, the DIC is working properly from the results gathered from Tests One and Two. This method is much quicker and cost effective as compared to the traditional sensors. Testing Column Three with the LVDTs as well as Beams One, Two, and Three will further validate the accuracy of the DIC results. 6 FUTURE WORK Because of time restraints, the column with the LVDTs and the three RC beams were not tested before the internship ended. The next step would be to finish with the testing with these last four specimens. The beams would be simply supported with a point load mid-span. When a beam is being loaded in this manner, the top of the beam is in compression, while the bottom is in tension. This is similar to what happens to shear walls when they are loaded with lateral loads. Therefore, these beams tests will be a good precursor to testing the shear walls. The three beams were designed with different reinforcement detailing (Figure22). Using equations from the basic concepts of concrete design, the yield moment, nominal moment, and shear capacity, and failure mode were calculated for each. Beam One has no steel reinforcement, and is calculate to fail in flexure. Beam Two has four d8 bars, and is predicted to fail in a shear failure. Beam three has 5 d5 bars and number 2 stirrups spaced at 2 inches, and is calculated to fail in flexure. Appendix A contains calculations for the design of these beams. 17

22 Figure 22. The three beams designed for the DIC testing 6.1 Application to NEESR Shear Wall Project The NEESR shear wall project is currently in progress. The first four wall specimens were filled with concrete on August 9 th, and are now curing. The plan as of now is to spray paint speckle patterns onto the surface of the walls after painting them white, and using NCorr to retrieve displacement measurements. Figure 22 shows a picture of the four wall specimens in the UCLA structures laboratory. The NEESR shear wall project is projected to finish testing all of the 12 walls by May Figure 23. Current state of the first four RC shear wall specimens (courtesy of Chris Segura) 7 CONTACT INFORMATION Any and all questions or comments concerning this summer research project may be directed to my at mlshea@umass.edu. Questions about the greater NEESR shear wall project may be directed to PhD student, Christopher Segura at segurac@ucla.edu. 18

23 8 ACKNOWLEDGEMENTS This project was supported by the National Science Foundation (NSF) through the Research Experience for Undergraduates program (EEC ) and the George E. Brown Jr. Network for Earthquake Engineering Simulation (NEES) Cooperative Agreement CMMI I would like to thank Dr. John Wallace for this opportunity to assist with one of his projects. I would also like to thank my mentor, PhD student, Chris Segura for his extraordinary guidance throughout the summer. Thank you to the entire NEES@UCLA team for all of their support and contributions. I would lastly like to thank the NSF for funding this project, and giving me the chance to explore my interests in the field of earthquake engineering. 19

24 REFERENCES ACI 318, 2002, Building Code Requirements for Reinforced Concrete, American Concrete Institute, Detroit, Michigan. Blaber, J. (2014). Home. Ncorr v1.2, < (July 15, 2014). Chai, Y. H., and Elayer, D. T. (1999). Lateral stability of reinforced concrete columns under axial reversed cyclic tension and compression. ACI Structural Journal (96-S86). Deam, B., and Dhaka, R. (2011). The M 6.3 Christchurch, New Zealand, earthquake of February 22, EERI Special Earthquake Report. < web.pdf> Elwood, K. J. (2013). Performance of concrete buildings in the 22 February 2011 Christchurch earthquake and implications for Canadian codes. Canadian Journal of Civil Engineering, 40(8), Hild, F. and Roux, S., (2006). Digital image correlation: from displacement measurement to identification of elastic properties. Strain, 42(2), Moehle, J., and Riddell, R. (2010). The M w 8.8 Chile Earthquake of February 27, EERI Special Earthquake Report. < Pan B., Qian K., Xie H., and Asundi A., (2009). Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review. Measurement Science and Technology, Pan B., Xie H. M., Wang Z. Y., Qian K. M. and Wang Z. Y., (2008). Study on subset size selection in digital image correlation for speckle patterns. Optics Express, 16, Paulay, T., and Priestley, M. N. (1993). "Stability of ductile structural walls." ACI Structural Journal, 90(41), Rodriguez, M., Botero, J., and Villa J. (1999). "Cyclic stress-strain behavior of reinforcing steel including effect of buckling." Journal of Structural Engineering, 125(6), Saatcioglu, M., and Razvi, S. (1992). Strength and ductility of confined concrete. Journal of Structural Engineering, 118(6), Saatcioglu, M., and Razvi, S. (1999). Confinement model for high-strength concrete. Journal of Structural Engineering, 125(3), Stoilov, G., Kavardzhikov, V., and Pashkouleva, D. (2012). A comparative study of random 20

25 patterns for digital image correlation. Journal of Theoretical and Applied Mechanics, 42(2), Wallace, J. W. (2011). "February 27, 2010 Chile earthquake: Preliminary observations on structural performance and implications for U.S. building codes and standards." ASCE Structures Congress, Las Vegas, NV Wallace, J. W. (2012). "Behavior, design, and modeling of structural walls and coupling beams." International Journal of Concrete Structures and Materials, 6(1),

26 APPENDIX A BEAM DESIGN CALCULATIONS Calculations for Beam Design All three beams are simply supported with a point load (P) at the center of an 18 inch span. Factored moment: M u = 9in 2 P Factored shear: V u = P 2 Note: In calculating the nominal moments and shear capacities, the safety factor, phi (φ), is ignored because these beams are being tested until failure. The compression steel in Beams Two and Three is also being ignored for simplification. Beam One Given: f c = 5,500 psi f r = 7.5 f c = psi = 556 psi I = 1 12 bh3 = in 6in3 = 108 in 4 A-1

27 Nominal Moment: M cr = f ri y = 0.557ksi 108in4 3in = 20 kip in M n M u Shear Capacity: 20kip in 9in 2 P P 4. 4 kips V c = 2 f c b w d = psi 6in 6in = 5.34 kips V n V u 5.34kips P 2 P kips The load capacity from the nominal moment is smaller, and therefore governs. Beam One will fail in flexure. Beam Two Given: f c = 5,500 psi fy = 80 ksi 4 d8 bars (d b = in) c c = 0.5 in d = 6in 0.5in in = in 2 A s = in 2 = 0.32 in 2 A-2

28 a = Nominal Moment: A s f y 0.85 f c b = 0.32in 2 80ksi = 0.91 in ksi 6in M n = A s f y d a 2 = 0.32in2 80ksi in 0.91in = 125 kip in 2 M n M u Strain Check: 125kip in 9in 2 P P kips β 1 = f c c = a β 1 = 0.91in = in = = d c in 1.174in ε t = = = c 1.174in The strain is greater than 0.005, therefore the steel has yielded. Shear Capacity: V c = 2 f c b w d = psi 6in in = 4.75 kips V n V u 4.75kips 9in 2 P P 9. 5 kips The load capacity from the shear is smaller, and therefore governs. Beam Two will result in a shear failure. A-3

29 Beam Three Given: f c = 5,500 psi fy = 40 ksi 5 d5 bars (d b = in) #2 2 in c c = 0.5 in d = 6in 0.5in in in = in 2 A s = in 2 = 0.25 in 2 a = Nominal Moment: A s f y = 0.25in2 40ksi = in 0.85 f c b ksi 6in M n = A s f y d a = in2 40ksi 5.124in 0.357in = 49.5 kip in M n M u Strain Check: β 1 = kip in 9in 2 P P kips c = a β 1 = 0.357in ε t = d c c = in = in 0.461in = in The strain is greater than 0.005, therefore the steel has yielded. 2 A-4

30 Shear Capacity: V c = 2 f c b w d = psi 6in 5.124in = 4.56 kips A v = 2(stirrup area) = 2(0.05in 2 ) = 0.1 in 2 V s = A vf y d s = 0.1in2 40ksi 5.124in 2in = 10.3 kips V n = V s + V c = 10.3kips kips = 14.8 kips V n V u 14.8 kips P 2 P kips The load capacity from the nominal moment is smaller, and therefore governs. Beam three will fail in flexure. A-5