Seismic Performance of Reinforced Concrete Columns Under Biaxial Excitation

Tiffany McCarthy, REU StudentLaskar, Graduate Mentor

Padmanabha Rao Tadepalli, Graduate MentorDr. Y. L. Mo, Faculty Mentor

Final ReportDepartment of Civil and Environmental Engineering

University of HoustonHouston, TX

Sponsored by The National Science FoundationAugust 2007

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Abstract

Response of reinforced concrete (RC) structures to seismic forces varying randomly in direction and magnitude result from a complex interaction of properties of the concrete and the steel. Hence, it is essential to study the behavior of RC structures under biaxial loading. Six RC column specimens having a height to width ratio of 2.0 were tested under biaxial loads on a shake table at the National Center for Research on Earthquake Engineering in Taiwan. The parameters that were varied in the six specimens are the ratio of the biaxial loads and the amount of lateral ties in the column specimens. This paper describes the details of the experimental results. The failure modes of the specimens are discussed. The behavior of the specimens with changes in the ratio of biaxial loads and the amount of lateral ties is also studied.

Introduction

Considering the devastating earthquakes in recent years, particularly in Southeast Asia, this report investigates the performance of concrete reinforced with steel bars. The damage incurred by various reinforced concrete (RC) structures as a result of earthquakes around the world is often severe. Though much research and experimentation has been conducted in order to develop more reliable concrete structures, there are many questions which remain unanswered. Within the last century numerous earthquakes have occurred, taking many lives and leaving many others injured, destitute, jobless and homeless. Therefore, it is of great importance to develop better design guidelines for structures to resist earthquakes. No progress can be made towards achieving this goal unless more research is conducted to simulate the effects of seismic loads on various types of reinforced concrete structures. Observations made from such tests need to be critically analyzed to completely understand the seismic behavior of RC structures and to cultivate creative solutions to the issue of structures damaged by powerful natural causes.

While many studies have been conducted on RC columns under uniaxial loads, few studies have been conducted under biaxial loads. The biaxial loads, unlike uniaxial loads, account for the fact that earthquakes forces can act on structures in any direction. Forces in any direction on a given plane could be considered to be equivalent to biaxial loads acting along two perpendicular directions. Thus, columns tested under biaxial loads are subjected to a more realistic form of earthquake loads in comparison to columns under uniaxial loads.

This paper addresses the performance of reinforced concrete columns subjected to biaxial loads. These loads are time-dependent as they simulate seismic activity. The parameters that were varied in the six specimens are the ratio of the biaxial loads and the amount of lateral ties in the column specimens.

Previous Studies

A research study was conducted to develop a numerical model which closely predicted the response of reinforced concrete members to seismic excitation [Dönmez, Sözen 2007]. This model was intended to better predict the absolute maxima of earthquake response and to generate a reliable model of a complete response waveform of RC structures showing all ranges of response. This model is an effective tool for estimating the maximum force and displacement responses, as

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well as for estimating all ranges of response of biaxially loaded reinforced concrete members [Dönmez, Sözen 2007].

Another study focused on the behavior of RC columns under sustained axial loads and seismic forces [Rey, Schultz, and Welton 2004]. This study identified a pattern of characteristic changes in the thirteen columns which were analyzed. It was found that RC columns which have sustained axial loads for longer durations tend to have reduced flexural strength, stiffness, and energy dissipation capacity, but increased deformation capacity. Considering the decrease in flexural strength was relatively small while the increase in drift capacity was significant, this study suggests that more research and experimentation should be conducted about the long-term effects on RC members and that there may be some positive effects of long-sustained loads on such members.

Experimental Program

Six RC column specimens having dimensions of 600 mm x 300 mm were fabricated and tested at the National Earthquake Engineering Research Center, Taiwan. Three of the specimens, namely SH1, SH2, and SH3 had a stirrup spacing of about 100 mm c/c, while in the other three specimens SH4, SH5, and SH6 the stirrup spacing was increased to 200 mm c/c. The orientations of the different specimens were varied in order to subject them to changing amounts of biaxial loads about their major and minor axes. While specimens SH1 and SH4 were oriented along the direction of vibration of the shake table, specimens SH2 and SH5 were oriented at an angle of 22.5° to the direction of vibration of the shake table, and specimens SH3 and SH6 had an orientation of 45°. Other reinforcement detailing was the same for all specimens. The stirrup steel had a yield stress of 371 MPa. The 28-days concrete compressive strength of the specimens was 34.0 MPa. The location of the reinforcements, and the dimensions and details of the reinforcements are shown in Figures 1 and 2, respectively.

The reinforcement cages for the specimens were first assembled as shown in Figure 3. They were then placed into formworks (Figure 4) and concrete mix was poured into each formwork. The formwork was removed one day after the casting of the specimens when the concrete had developed sufficient strength. A concrete mass block was made using the same procedure as described above. This block was mounted on top of each of the specimens during testing.

The specimens were tested on a 5000 mm by 5000 mm shake table having six degrees of freedom as shown in Figures 5 and 6. During the tests, a mass block (Figure 5) of 12,696 kg was mounted above each column specimen to develop inertial forces acting on the specimens. The block was supported by four separate steel columns so that its weight was not carried by the RC specimen being tested. The model for the system was an inverted pendulum as shown in Figure 7. The shake table was vibrated laterally during testing as shown in Figure 2. The seismograms obtained during the 1999 Taiwan Earthquake served as the ground motion accelerator for these tests. Loads of 0.05 PGA, 0.2 PGA, 0.4 PGA, 0.6 PGA, 0.8 PGA, 1.2 PGA, and 1.5 PGA or 1.6 PGA were applied to each of the six specimens individually. Linear Voltage Displacement Transducers (LVDTs) and accelerometers were used to measure the displacements and accelerations of the specimens.

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The columns were secured to the shake table so that no slipping would occur during the tests. Two load cells supported each column specimen and were connected to a data acquisition system to allow collection of data about loads acting on each specimen. Two steel columns flanked each side of the column specimen being tested at a given time in order to support the concrete mass block above the specimen.

LVDTs, accelerometers, and strain gages were used for all the tests conducted. The LVDTs and accelerometers were located as shown in Figure 8. Three displacement sensors (D01, D02, D03) and two accelerometers, one underneath the mass at the top of the column (A49) and the other at the top of the mass (A50) are shown. Two load cells were also installed at the bottom of the foundation (L01, L02). All data was collected at intervals of 0.005 seconds for a total of approximately 80 seconds for each test. This increment and total time were sufficient to facilitate observation and analysis of the displacement and acceleration responses for each excitation. The results of this experimental program are presented in the following section and subsequently analyzed.

Experimental Results

Cracking and YieldingEach specimen exhibited a unique response to the accelerations to which it was subjected. While all of the specimens first showed cracking at 800 Gal, they each failed at different Gals. For SH1, between 800 Gal and 1200 Gal crack widths increased, varying in length and direction. By 1500 Gal the specimen failed showing huge cracks. For SH2, between 800 Gal and 1500 Gal crack widths extended and many more cracks developed intersecting previous cracks. At 1500 Gal SH2 showed signs of failure. By 1800 Gal, when SH2 failed, the shell spalled off leaving the majority of the steel frame exposed. For SH3, between 800 Gal and 1500 Gal cracks also increased. At 1800 Gal SH3 failed. SH4 sustained cracks until 1600 Gal, and failed by 2000 Gal, while SH5 also sustained cracks until 1600 Gal and failed sometime thereafter. SH6 developed the most cracks of all the specimens, showing some flaking at the top of the column at 1600 Gal, but not failing until 2000 Gal. At 2000 Gal not only had the shell spalled off, but also numerous steel bars of the internal frame had snapped.

Failure ModesOne of the main reasons for the degradation of the structural properties of the members subjected to cyclic loading is the gradual increase of the influence of shear deformations [Costa, 2003]. As the crack propagates due to unloading and reloading of the member the strength and stiffness of concrete gradually decreases. Another factor that affects the strength degradation is the bond deterioration.

For all specimens, the initial cracks were horizontal. For those specimens oriented along the direction of the applied excitation (SH1 and SH4), inclined cracks became predominant as the loads increased. The widths of these cracks increased at higher loads. Finally, both specimens failed when the shear reinforcements yielded. At failure, these inclined cracks overlapped with each other. Due to this overlapping of cracks the failed specimens appear to have developed vertical cracks along their lengths as shown in Figure 9.

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For the specimens oriented at 22.5° to the applied excitation (SH2 and SH5), inclined cracks developed as the loads were increased. The cracks intersected each other and had greater widths compared to those in specimens SH1 and SH4. The cracks which developed at higher loads tended to be less inclined to the longitudinal axis of the specimens. The crack patterns of these specimens are shown in Figure 10. For the specimens oriented at 45° to the applied excitation (SH3 and SH6), inclined cracking predominated throughout the testing. Both failed at high excitations when each specimen’s shell crushed and slid off of the steel reinforcement cage. Typical cracking patterns of SH3 and SH6 are shown in Figure 11. Ultimate ForcesThe ultimate forces corresponding to each specimen are shown in Table 1. It is clear from the table that as the stirrup spacing decreased the column became stronger and better able to sustain force. Columns with cross-sections symmetrical about the applied excitation showed higher capacities to take load than columns which are asymmetrical.

Steel YieldingTable 2 gives the yield point of the steel for each specimen. The yield point is reported as the point where the strain value in steel reached a value of 0.002.

Energy DissipationTable 3 shows the energy dissipation values for each specimen at various excitations. The energy dissipation values are calculated by finding the area of the force-displacement curves shown in Figures 12 to 29, and the units of the reported energy are N-mm. As can be seen from Table 3, at lower excitation stirrup spacing has no effect on the energy dissipation at a given excitation for a given orientation. At higher excitation the energy dissipated by the column with larger stirrup spacing is greater. Also, Table 4 gives the percentage of decrease in energy dissipation as the orientation of column is changed. It is clear that as the angle of orientation increased energy dissipated by the column decreased. It is probable that as the angle of orientation increases it causes reduction in the effectiveness of the shear reinforcement. This suggests that orientation of the column with respect to the earthquake forces plays a very important role in the performance of the column.

Hysteretic ResponseWhen concrete cracks from one edge to another the concrete becomes ineffective, leaving the steel alone to resist moment. Cracks in the compression face gradually close after the steel bars yield in compression. This leads to a reactivation of the concrete and consequent stiffening of the reloading branch of the hysteretic curve. The succession of the stiffening of the unloading branches moves the hysteresis curve toward the origin, an effect known as pinching. This is because the reinforcing bars are not in the direction of the principal stress [Mansour and Hsu, 2005]. Members exhibiting the pinching effect fail in shear, known as brittle failure, and absorb less energy than those not exhibiting this effect. Steel bars in the concrete, yield in compression after the concrete cracks. Thus, steel bars cannot take the same tensile force as they could before yielding. Consequently, the hysterisis curve softens. This effect is referred to as Bauschinger effect, which is typically observed in steel. Members with this effect perform better compared to members exhibiting pinching effect.

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The force versus displacement relationships were obtained for all the six specimens. From the graphs below (see Figures 12 to 31) it is clear that the first set of specimens SH1, SH2 and SH3 show similar types of behavior when compared with the second set of specimens SH4 and SH5. Pinching effect has been observed in the specimens SH2, SH3, SH5 and Bauschinger effect in specimens SH1, SH4. The effect of pinching is more dominant in specimens oriented with some angle to the applied excitation than the specimens which are parallel to it.

Conclusions

The following conclusions were made about the behavior of reinforced concrete columns under biaxial excitation:

1) As the stirrup spacing decreased, the column became stiffer, enabling the column to sustain greater loads. However, this was observed only for columns with stirrups arranged symmetrically to the direction of the shake table excitation.

2) Columns with uni-axial excitation showed higher energy dissipation than columns with biaxial excitation.

3) Stiffness of the columns decreased when the PGA increased which can be attributed to cracking of the concrete and yielding of steel reinforcements at higher PGA.

4) At lower excitation, stiffness of the column or stirrup spacing had negligible effect on the energy dissipation at a given excitation for a given orientation. However, at higher excitation the energy dissipated by the column with more stirrup spacing was greater.

Acknowledgments

The research study described herein was sponsored by the National Science Foundation under the Award No. EEC-0649163. The opinions expressed in this study are those of the authors and do not necessarily reflect the views of the sponsor.

References

Costa, J.L.D. (2003), “Reinforced Concrete Under Large Seismic Action”, Denmarks Tekniske Universitet, Report BYG DTU R-076, ISSN 1601-2917, ISBN 87-7877-139-0.

Dönmez, C. and Sözen., M.A. (2007), “Numerical Model for Biaxial Earthquake Response of Reinforced Concrete,” Computer-Aided Civil and Infrastructure Engineering, Vol. 22, pp. 238-253.

Mansour, M. and Hsu, T. T. C., (2005). “Behavior of Reinforced Concrete Elements underCyclic Shear: Part I—Experiments,” Journal of Structural Engineering, ASCE, Vol.131, No. 1, January, pp. 44-53.

Rey, L. E., Schultz ,A. E., and Welton, S. S., (2004) “Long-Term Effects on Response of Reinforced Concrete Columns to Cyclic Loading,” Journal of Structural Engineering, ASCE, Vol. 130, No. 9, pp. 1320-1332.

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Appendix-1 Table 1. Ultimate Force Of Each Specimen

Specimen Ultimate Force (N)SH1 1.9 x 105

SH2 1.78 x 105

SH3 1.81 x 105

SH4 2.18 x 105

SH5 2.06 x 105

SH6 2.46 x 105

Table 2. Yield Point Of Steel Reinforcements In Each SpecimenSpecimen Yield Point (Gal)

SH1 1200SH2 1200SH3 800SH4 1600SH5 1200SH6 800

Table 3. Energy Dissipations For Each Specimen In N-Mm

Specimen @400 gal @800 gal @1200 gal@1500/1600*

gal

SH1 5.64E+06 2.13E+07 4.25E+07 4.11E+07

SH2 3.64E+06 1.87E+07 3.98E+07 4.95E+07

SH3 3.10E+06 1.81E+07 2.98E+07 2.04E+07

SH4* 5.96E+06 1.94E+07 3.24E+07 3.31E+07

SH5* 3.37E+06 1.41E+07 3.07E+07 4.20E+07

SH6* 6.06E+06 2.03E+07 4.12E+07 5.86E+07

Table 4. Percentage Decrease In Energy Dissipations

Specimens Compared

@400 gal @800 gal @1200 gal

SH1- SH2 35.4% 12.2% 6.35%SH2- SH3 14.5% 3.2% 25.1%SH4- SH5 43.4% 27.3% 5.24%

Appendix-2

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Figure 1. Shake Table Diagrams For Setup Used For SH1-SH3 (Left) And Setup Used For SH4-SH6 (Right), Including Location Of Reinforcement Cross-Sections

SH1 SH2 SH3

SH4 SH5 SH6

Figure 2. B-B Cross-Sections For All Specimens Showing Dimensions Of Column And Reinforcement Bars

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Figure 3. Steel Reinforcement Cage

Figure 4. Formwork

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Figure 5. Front-View Of Entire Setup Of Shake Table With Dimensions Given (in cm)

Roller

Figure 6. Side-View Of Entire Setup Of Shake Table With Dimensions Given (in cm)

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Figure 7.Model For Shake Table Test

Figure 8. Shake Table Diagram Showing Location Of Displacement (D01, D02, And D03) And

Acceleration (A49 And A50) Sensors

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Figure 9. Mode Of Failure Of Specimens SH1 (Left) And SH4 (Right)

Figure 10. Mode Of Failure Of Specimen SH2 (Left) And Significant Diagonal Cracks On SH5 (Right) Before Failure

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Figure 11. Pictures Of Predominating Diagonal Cracks In SH3 (Left) And SH6 (Right)

SH1 @ 400gal

-1.00E+05-8.00E+04

-6.00E+04-4.00E+04-2.00E+040.00E+00

2.00E+044.00E+046.00E+04

8.00E+041.00E+05

-3.00E+00

-2.00E+00

-1.00E+00

0.00E+00 1.00E+00 2.00E+00 3.00E+00

Displacement

Fo

rce

Figure 12. Force Vs. Displacement Graph At 400 Gal For Specimen SH1

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SH1 @ 800gal

-2.00E+05

-1.50E+05

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Displacement

Fo

rce

Figure 13. Force Vs. Displacement Graph At 800 Gal For Specimen SH1

SH1 @ 1200gal

-2.00E+05

-1.50E+05

-1.00E+05

-5.00E+04

0.00E+00

5.00E+04

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0.00E+00

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1.00E+01

1.50E+01

2.00E+01

Displacement

Fo

rce

Figure 14. Force Vs Displacement Graph At 1200 Gal For Specimen SH1

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SH2 @ 400gal

-8.00E+04

-6.00E+04

-4.00E+04

-2.00E+04

0.00E+00

2.00E+04

4.00E+04

6.00E+04

8.00E+04

-3.00E+00

-2.00E+00

-1.00E+00

0.00E+00 1.00E+00 2.00E+00 3.00E+00

Displacement

Fo

rce

Figure 15. Force Vs. Displacement Graph At 400 Gal For Specimen SH2

SH2 @ 800gal

-2.00E+05

-1.50E+05

-1.00E+05

-5.00E+04

0.00E+00

5.00E+04

1.00E+05

1.50E+05

2.00E+05

-1.00E+01 -5.00E+00 0.00E+00 5.00E+00 1.00E+01 1.50E+01

Displacement

Fo

rce

Figure 16. Force Vs. Displacement Graph At 800 Gal For Specimen SH2

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SH2 @ 1200gal

-2.50E+05

-2.00E+05

-1.50E+05

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-5.00E+04

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1.50E+05

2.00E+05

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-1.00E+01

-5.00E+00

0.00E+00

5.00E+00

1.00E+01

1.50E+01

2.00E+01

Displacement

Fo

rce

Figure 17. Force Vs. Displacement Graph At 1200 Gal For Specimen SH2

SH2 @ 1500gal

-2.00E+05

-1.50E+05

-1.00E+05

-5.00E+04

0.00E+00

5.00E+04

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Displacement

Fo

rce

Figure 18. Force Vs. Displacement Graph At 1500 Gal For Specimen SH2

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SH3 @ 400gal

-1.00E+05-8.00E+04

-6.00E+04-4.00E+04

-2.00E+040.00E+00

2.00E+044.00E+046.00E+04

8.00E+04

1.00E+05

-4.00E+00

-3.00E+00

-2.00E+00

-1.00E+00

0.00E+00

1.00E+00

2.00E+00

3.00E+00

4.00E+00

Displacement

Fo

rce

Figure 19. Force Vs. Displacement Graph At 400 Gal For Specimen SH3

SH3 @ 800gal

-2.00E+05

-1.50E+05

-1.00E+05

-5.00E+04

0.00E+00

5.00E+04

1.00E+05

1.50E+05

2.00E+05

-1.00E+01 -5.00E+00 0.00E+00 5.00E+00 1.00E+01

Displacement

Fo

rce

Figure 20. Force Vs. Displacement Graph At 800 Gal For Specimen SH3

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SH3 @ 1200gal

-2.00E+05

-1.50E+05

-1.00E+05

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0.00E+00

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-5.00E+00

0.00E+00

5.00E+00

1.00E+01

1.50E+01

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Displacement

Fo

rce

Figure 21. Force Vs. Displacement Graph At 1200 Gal For Specimen SH3

SH4 @ 400 gal

-1.50E+05

-1.00E+05

-5.00E+04

0.00E+00

5.00E+04

1.00E+05

1.50E+05

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0.00E+00

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Displacement

Fo

rce

Figure 22. Force Vs. Displacement Graph At 400 Gal For Specimen SH4

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SH4 @ 800 gal

-2.50E+05-2.00E+05

-1.50E+05-1.00E+05

-5.00E+040.00E+00

5.00E+041.00E+051.50E+05

2.00E+05

2.50E+05

-8.00E+00

-6.00E+00

-4.00E+00

-2.00E+00

0.00E+00

2.00E+00

4.00E+00

6.00E+00

8.00E+00

Displacement

Fo

rce

Figure 23. Force Vs. Displacement Graph At 800 Gal For Specimen SH4

SH4 @ 1200 gal

-2.50E+05-2.00E+05-1.50E+05-1.00E+05-5.00E+040.00E+005.00E+041.00E+051.50E+052.00E+052.50E+053.00E+05

-1.00E+01 -5.00E+00 0.00E+00 5.00E+00 1.00E+01 1.50E+01

Displacement

Fo

rce

Figure 24. Force Vs. Displacement Graph At 1200 Gal For Specimen SH4

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SH4 @ 1600 gal

-3.00E+05

-2.00E+05

-1.00E+05

0.00E+00

1.00E+05

2.00E+05

3.00E+05

-1.50E+01

-1.00E+01

-5.00E+00

0.00E+00 5.00E+00 1.00E+01 1.50E+01

Displacement

Fo

rce

Figure 25. Force Vs. Displacement Graph At 1600 Gal For Specimen SH4

SH5 @ 400 gal

-8.00E+04

-6.00E+04

-4.00E+04

-2.00E+04

0.00E+00

2.00E+04

4.00E+04

6.00E+04

8.00E+04

-2.00E+00 -1.00E+00 0.00E+00 1.00E+00 2.00E+00 3.00E+00

Displacement

Fo

rce

Figure 26. Force Vs. Displacement Graph At 400 Gal For Specimen SH5

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SH5 @ 800 gal

-2.00E+05

-1.50E+05

-1.00E+05

-5.00E+04

0.00E+00

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-2.00E+00

0.00E+00

2.00E+00

4.00E+00

6.00E+00

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Displacement

Fo

rce

Figure 27. Force Vs. Displacement Graph At 400 Gal For Specimen SH5

SH5 @ 1200 gal

-2.50E+05-2.00E+05

-1.50E+05-1.00E+05-5.00E+040.00E+00

5.00E+041.00E+051.50E+05

2.00E+052.50E+05

-1.50E+01

-1.00E+01

-5.00E+00

0.00E+00 5.00E+00 1.00E+01 1.50E+01

Displacement

Fo

rce

Figure 28. Force Vs. Displacement Graph At 1200 Gal For Specimen SH5

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SH5 @ 1600 gal

-2.50E+05-2.00E+05

-1.50E+05-1.00E+05

-5.00E+040.00E+00

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2.00E+05

2.50E+05

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-1.00E+01

0.00E+00 1.00E+01 2.00E+01 3.00E+01

Displacement

Fo

rce

Figure 29. Force Vs. Displacement Graph At 1600 Gal For Specimen SH5

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