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Steel strap confined high strength concrete under uniaxial cyclic compression
Construction and Building Materials 72 (2014) 48–55
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Steel strap confined high strength concrete under uniaxial cyclic compression Hoong-Pin Lee, Abdullah Zawawi Awang ⇑, Wahid Omar Faculty of Civil Engineering, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia
h i g h l i g h t s Laterally pre-tensioned and steel strapped concrete was cyclically tested. Examination of the effect of confining ratio on cyclic stress–strain behaviour. Effect of monotonic and cyclic loading patterns is systematically examined. Evaluation the response of envelope curve, plastic strain, loading history effect. A plastic strain model is proposed and assessed with existing models.
a r t i c l e
i n f o
Article history: Received 10 December 2013 Received in revised form 5 August 2014 Accepted 7 August 2014 Available online 27 September 2014 Keywords: Lateral confinement Steel straps Confining ratio Uniaxial cyclic loading Stress–strain behaviour
a b s t r a c t This paper discusses an affordable and effective lateral confinement technique to enhance concrete’s compressive strength and ductility – the steel strapping tensioning technique (SSTT). Considerable studies have been done on the characteristics of SSTT-confined concrete under uniaxial monotonic compression loading, but none has addressed its uniaxial cyclic response. In this paper, 21 high-strength concrete specimens having diameter of 150 mm and height of 300 mm had been cast, laterally pre-tensioned with steel straps in different confining ratios, and tested to failure under uniaxial cyclic and monotonic compression loadings. Results indicated that the basic hypothesis of envelope curve is valid for SSTT-confined high-strength concrete specimens for uniaxial monotonic and cyclic loadings. The development of plastic strain is independent of the confining ratio when the envelope unloading strain exceeds 0.0025. Moreover, SSTT-confinement has the lowest plastic strain compared to several related existing plastic strain models. The stress deterioration ratio is independent of confining ratio and loading patterns. Lastly, the concept which neglects the effect of loading history on the permanent axial strain of the unloading and reloading paths of concrete is invalid because repeated unloading/reloading cycles have demonstrated a cumulative effect on the permanent strain and stress deterioration. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction Steel strapping tensioning technique or SSTT is a type of lateral confining technique used to enhance the capacity and ductility of new and existing concrete structures by confining the steel straps with prescribed lateral pre-tensioning stress in layers. The remarkable enhancement of the confined concrete structures’ mechanical properties, ease to operate as well as the time and cost saved allow lesser interrupted structure serviceability and reduce dependence on experienced workers. As such, SSTT has become one of the most affordable confining techniques for concrete confinement, especially for high-strength concrete that is naturally brittle and ⇑ Corresponding author. Tel.: +60 19 7107185. E-mail address: [email protected] (A.Z. Awang). http://dx.doi.org/10.1016/j.conbuildmat.2014.08.007 0950-0618/Ó 2014 Elsevier Ltd. All rights reserved.
experiences low lateral dilation when loaded [1–10]. One of the effective parameters that govern the stress-strain behaviour of SSTT-confined concrete is the confining ratio, which is most commonly studied under uniaxial monotonic loading [1–7]. For instance, Moghaddam et al. [1–5] studied the effect of confining ratio of steel straps on the stress-strain behaviour of SSTT-confined concrete. The confining ratio takes into account the number of steel strap layers and the spacing between the steel straps. As proposed in EC8, the effective mechanical volumetric ratio has also been adopted to allow comparison with confining ratio. Moghaddam and his co-workers concluded that a strong relationship exists between the effective mechanical volumetric ratio of steel straps and the compressive strength as well as ductility of the confined specimens. The study also proposed empirical models in the function of effective mechanical volumetric ratio for design purpose.
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The results indicated that the higher the effective mechanical volumetric ratio, the higher the compressive strength and ductility performance of SSTT-confined specimens. Frangou et al. [6] in their investigation found an inverted relationship between the spacing between the steel straps and the compressive strength of SSTTconfined specimens, i.e., the smaller the spacing between steel straps, the higher the compressive strength. Awang et al. [7] also indicated a close and increasing linear relationship between the effective mechanical volumetric ratio and the compressive strength of SSTT-confined high-strength concrete specimens. A simple strength model for SSTT confinement was proposed and compared with several existing models. The result showed very promising compressive strength enhancement compared to other confinement methods. In short, a great quantity of existing studies have demonstrated the performance of SSTT confinement on different aspects under the action of uniaxial monotonic compressive loading [1–10], but no study has been carried out on the uniaxial cyclic stress–strain behaviour of the confined concrete, especially high-strength concrete. The lacking of test data for these confinements thus calls for more quantitative experimental investigations on the influence of confining ratios, especially under uniaxial cyclic compression, for the development of theoretical models. In this paper, the results of uniaxial cyclic and monotonic compression loading tests on 21 SSTT-confined high-strength concrete specimens with different confining ratios are presented and the quantified behaviour of these confined specimens shall be discussed through several aspects of cyclic behaviour. 2. Experimental work 2.1. Specimen preparation A set of 21 high-strength concrete specimens having diameter of 150 mm in circular section and height of 300 mm had been prepared. The testing parameters primarily dealt with the number of steel strap layers (confining ratio) externally confined on the high-strength concrete specimens and the loading patterns (uniaxial monotonic and cyclic compression). Uniaxial cyclic compression load test was carried out to validate the performance of these confinement methods under different loading patterns. Each of the high-strength concrete specimens were not reinforced longitudinally with steel bar. For all SSTT-confined concrete specimens, the clear distance between each steel straps along the concrete specimens was fixed at 15 mm in the middle of the specimen and 7.5 mm in the two quarter end regions to provide sufficient confinement (see Figs. 1 and 2) to reduce the possibility of failure at the two end sections of the specimens. The properties of high-strength concrete specimens including number of steel strap layers and type of loading are shown in Table 1.
2.2. Material and pre-tension technique The mixture proportions for the high-strength concrete are as given in Table 2. All specimens and cubes were removed from the formworks and moulds right after 24 h after casting and went through wet curing for 28 days. The cubes of size
49
100 mm 100 mm 100 mm were compressively tested after 7 days, 28 days, and on the day of testing and the cube compressive strength of the high-strength 0 concrete, f c , were recorded. The achieved concrete compressive strength and strain at ultimate were 61.4 MPa and 0.0021 mm/mm, respectively. After 28 days, the specimens were removed from curing tank and laterally pre-tensioned with prescribed layers of steel straps as illustrated in Table 1, except for unconfined specimens. All the confining materials in this study were using 15.85 mm 0.55 mm steel straps. Tensile tests for confining materials were carried out using 250 kN Universal Testing Machine, in compliance with BS EN 10 002-1:1990. The tensile strength was averagely about 916 N/mm2, as illustrated in Fig. 3. The confinement method fully followed the SSTT confinement method designed by Awang et al. and Hoong-Pin et al. [7–10] where the tensioner used in packaging industry was utilized to confine the specimens. Moghaddam et al. recommended a confinement of about 30% of the steel strap’s tensile yield strength to effectively mobilize the lateral confining stress of steel straps from the initial state of loading application [1]. Tensioning work for both layers of confinement needed to be performed in slow and steady pace and should be stopped once the steel straps had tightened up. Then, the surplus steel strap was bended across the connection clips and tied up to lock the applied pre-tensioning stress onto the concrete specimen. The detailing for SSTT confinement on concrete specimen is as shown in Fig. 2. The specially designed connection clip used in these method is able to self-distribute the pretensioning stress among the layers of steel strapping to achieve a uniform pretensioning stress in different layers [11]. The actual lateral pre-tensioning stress applied by steel strap layers onto the concrete core was measured using two semi-circular steel frameworks [1,8]. The measured pre-tensioned stress applied by two and four layers of steel straps using the tensioner was 286.78 ± 20 MPa, which was 29.12–33.5% of the steel strap’s tensile yield strength. This indicated that these confinement had satisfied the recommended pre-tensioned stress in literature [1]. During the study, the 21 high-strength concrete specimens were assigned into seven groups with the notation of C60-C for control column as well as C60S15-2FTM and C60S15-4FT-M for specimens pre-tensioned with two and four layers of steel straps respectively. ‘‘M’’ meant that the specimens were tested under uniaxial monotonic compression loading. C60S15-2FT-1C and C60S15-4FT-1C were assigned to specimens pre-tensioned with two and four layers of steel straps respectively and tested under uniaxial single cyclic compression loading. Meanwhile, C60S152FT-3C and C60S15-4FT-3C meant that the specimens had been pre-tensioned with two and four layers of steel straps respectively and tested under uniaxial three cyclic compression loadings. The notation of ‘‘15’’ was for the clear distance between the straps along the specimen. To ensure that the specimens were uniformly loaded during testing, the top and bottom surface of the specimens had to be parallel. So, the specimens had to be cast horizontally on a levelled surface. 2.3. Test setup and strain measuring instrumentations The load tests have been conducted using TINIUS OLSEN Super ‘‘L’’ Universal Testing Machine which has the capacity of 3 MN in the Faculty of Civil Engineering Laboratory, Universiti Teknologi Malaysia. The load tests are based on displacement-controlled loading with a constant loading rate of 0.4 mm/min. The overall view of the specimen set up and diagram for the loading machine and measuring equipment are as shown in Fig. 4. The overall longitudinal axial deformations of the specimens were obtained using the three linear variable differential transducers (LVDTs) which had a gauge length of 50 mm located at the machine platen and three other LVDTs of 25 mm gauge length attached to the centre of the specimens to measure the relative axial displacement over the 100 mm height of the specimens. The transverse deformations of the specimens were obtained using two LVDTs (gauge length of 25 mm) located at the centre of the specimens, diametrically wrapped with a steel ties around the specimen (see Fig. 5). The overall concrete longitudinal strains were presented as the average value of LVDTs divided by the particular measured length. The transverse deformations of the concrete and steel strapping were measured using two sets of strain gauges (gauge length of 60 mm and 10 mm for concrete and steel strapping, respectively) installed at the centre of the specimen in a diametrically direction. All the strains were measured using the data logger, which also recorded the values of loads and displacement. Any cracking pattern, buckling, deformation, and etc., were recorded during testing as well. The compressive strength of specimens was tested according to ASTM C39/C39M-11. In this paper, the method of obtaining the actual stress-strain curve for confined concrete specimen from the above-mentioned instrumentations followed the method implemented by Mansur et al. [12]. A correction factor which including end-zone effect and machine flexibility which has been validated for the Universal Testing Machine in Universiti Teknologi Malaysia, has also been included in the initial stress–strain curve plotting for correction purpose. 2.4. Loading patterns
Fig. 1. SSTT-confined high-strength concrete specimens.
The loading patterns are shown in Fig. 6. For loading pattern notated as ‘‘M’’, monotonically increasing displacement at a rate of 0.4 mm/min had been performed until erratic deformation (i.e., failure) was observed. For the loading
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Fig. 2. Detailing of confined concrete specimen with SSTT confinement.
Table 1 Properties of the unconfined and SSTT-confined specimens. Specimen notation
Number of steel strap layers
Loading patterns
C60-C C60S15-2FT C60S15-2FT C60S15-2FT C60S15-4FT C60S15-4FT C60S15-4FT
– 2 2 2 4 4 4
M M 1C 3C M 1C 3C
Table 2 High-strength concrete mix design. Materials
Type
Quantity
Cement (kg/m3) Sand (kg/m3) Aggregate (kg/m3) Superplasticizer (mL) Water (kg/m3) Water/cement ratio
Type I OPC River sand Maximum size 12 mm Glenium ACE388 (RM) Pipe water –
550 885 957 0.75% of 100 kg cement 190 0.35
1000
Fig. 4. The strain measuring equipment and the loading device (TINIUS OLSEN Super ‘‘L’’ Universal Testing Machine).
specimen was loaded to the next prescribed load value for cyclic loading until the specimen failed. Three unloading and reloading cycles at each prescribed unloading load level had been designed for loading pattern ‘‘3C’’. For the case of uniaxial cyclic compression load, the target load level at which unloading was terminated and reloading was started was about 1–3 kN; this is equivalent to an uniaxial stress of about 0.057–0.170 MPa in this case of study.
Tensile stress (MPa)
900 800
3. Test results
700 600
3.1. Envelope curve
500 400 300 200 100 0 0.00
Steel Strapping 0.50
1.00
1.50
2.00
2.50
3.00
Elongation (%) Fig. 3. Tensile test result for steel strapping. pattern notated as ‘‘1C’’, uniaxial single cyclic compression involving unloading and reloading cycles with similar displacement control rate had been implemented at several prescribed unloading load values until failure. In other words, the specimen was loaded by increasing the uniaxial load to a prescribed load value, and it was next unloaded by reducing the uniaxial load to a target load level. Then, the
The concept of an envelope curve for unconfined and confined concrete refers to the curve joining the resultant broken curves or the loading branches between each cycle and the monotonic stress–strain curve, which tends to fall within the envelope curves under constantly increasing strain [13]. Envelope curve can also be considered as an upper boundary response of unconfined and confined concrete that has been subjected to any loading history in the stress–strain domain [14]. However, the crossing point of envelope curve and monotonic stress–strain curve for confined concrete is still a debated issue among researchers where some suggested that the monotonic stress–strain curve for confined concrete may stay below the envelope curve [15,16] while other suggested a coincidence of both monotonic and envelope curves [14,17,18]. Rousakis in his experimental studies also discovered that the variation of
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Stress
Stress
Stress
Fig. 5. LVDT holder rig and strain gauges position [9].
Strain
Strain
Strain
“M”
“1C”
“3C”
Fig. 6. Loading patterns: ‘‘M’’: uniaxial monotonic loading; ‘‘1C’’: uniaxial single cycle loading at each prescribed load level; ‘‘3C’’: uniaxial three cycles loading at each prescribed load level.
strength and ductility of FRP confined concrete tested under loadunload cycles was the same for the monotonic mode of loading, regardless of concrete strength [19]. In order to compare both uniaxial monotonic and cyclic stress– strain curves of SSTT-confined specimens, the envelope curves as shown in Figs. 7(a1), (b1) and 8(a1), (b1) (longitudinal deformation for specimens pre-tensioned with two and four layers of steel strapping, respectively) had been obtained by connecting all initial unloading points on the stress–strain curve within the uniaxial cyclic loading history for both single cycle and three cycles of loading under the prescribed load level. It has been clearly observed that, for SSTT confined specimens, the unloading/reloading cycles at each prescribed axial load coincided with the corresponding monotonic stress–strain curve before ultimate regardless of confining ratios and loading patterns. After the ultimate compressive stress, the envelope curves stayed below the monotonic stress– strain curves. Hence, this observation proved that the basic hypothesis of envelope curve is valid for SSTT-confined high-strength concrete – the envelope curve coincided with the monotonic stress–strain curve for the initial unloading points until the ultimate compressive load, while the subsequent envelope curve stayed below the monotonic curve. Besides, the variation of confining ratios and loading patterns does not have any effect on this hypothesis, thus indicates the independency of the envelope curve’s validity to the confining ratios and loading patterns. The concrete’s stress–strain curves in lateral direction for two and four layers of SSTT confinement are shown in Figs. 7(a2), (b2) and 8(a2), (b2) respectively. Similar to the longitudinal deformation, it is concluded that the envelop curve for unloading/ reloading cycles coincided with the corresponding monotonic stress–strain curve until ultimate loading, regardless also of the effect of confining ratio and loading history. Hence, the results
for both longitudinal and lateral deformations again validated the basic hypothesis of envelop curve for SSTT confinement. 3.2. Plastic strain The definition for plastic strain is the residual axial strain of concrete after being unloaded to zero stress [14]. It can also be defined as the non-recoverable ‘‘residual’’ longitudinal strain at the end of each unloading cycle and which increases each time a load cycle is being taken beyond the maximum load of the preceding cycle [15]. Fig. 9 shows the relationship of plastic strain, epl, versus envelope unloading strain, eun;env , of SSTT-confined specimen pre-tensioned with two layers and four layers of steel strap under uniaxial cyclic compression loading test respectively. A number of existing studies [14,20] clarified that a linear relationship exists between the plastic strains of unconfined or steel confined concrete and the axial strain at the starting point of unloading. Lam et al.’s study showed that the plastic strain of FRP-confined concrete under cyclic load is linearly related to the envelope unloading strain and is independent of the amount of confinement since both trend lines have coincided [14]. In Fig. 9, a linear relationship between the plastic strain and the envelope unloading strain is observed for SSTT-confined specimens when eun;env > 0:0025. Moreover, the linear trend lines for the two series of SSTT-confined specimens pre-tensioned with two and four layers of steel strap coincided with each other. This demonstrated that the plastic strain of SSTT-confined specimen is independent of the amount of confinement. Hence, a relationship of plastic strainenvelope unloading strain can be developed (with correlation coefficient, R2, equals to 0.77) as follows:
epl ¼ 0:46eun;env þ 0:00015; eun;env > 0:0025
ð1Þ
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120.0
120.0 Monotonic (2-layers) Single Cyclic (2-layers) Monotonic (Unconfined)
100.0
80.0
stress (Mpa)
stress (Mpa)
100.0
60.0 40.0
80.0 60.0 Monotonic (2-layers)
40.0
Single cyclic (2-layers) Monotonic (unconfined)
20.0
Longitudinal deformation 0.0 0.000
0.005
0.010
0.015
-0.007 -0.006 -0.005 -0.004 -0.003 -0.002 -0.001
axial strain (mm/mm)
axial strain (mm/mm)
(a1)
(a2)
0.0 0.000
120.0
120.0 Monotonic (2-layers) Three Cyclics (2-layers) Monotonic (Unconfined)
100.0 80.0
100.0 80.0
stress (Mpa)
stress (Mpa)
20.0
Lateral deformation
60.0 40.0
60.0 Monotonic (2-layers)
40.0
Three cyclic (2-layers)
20.0
Monotonic (unconfined)
Longitudinal deformation 0.0 0.000
0.005
0.010
20.0
Lateral deformation 0.015
-0.007 -0.006 -0.005 -0.004 -0.003 -0.002 -0.001
axial strain (mm/mm)
axial strain (mm/mm)
(b1)
(b2)
0.0 0.000
Fig. 7. Uniaxial cyclic stress–strain curves of concrete confined with two layers of steel strapping in comparison with monotonic stress–strain curves of corresponding confined concrete: (a1) longitudinal deformation for single cyclic loading; (a2) lateral deformation for single cyclic loading; (b1) longitudinal deformation for three cyclic loadings; and (b2) lateral deformation for three cyclic loadings.
To evaluate the unrecoverable strain (plastic strain) level of the current study with existing confining methods, several existing plastic strain model equations have been selected (see Table 3). Sakai and Kawashima’s model focused on the internal confinement that utilizes tie reinforcement while other studies have focused on FRP-type confinements. Fig. 10 shows the comparison graph between existing plastic strain model equations and present study’s plastic strain model equation according to Eq. (1). Result indicated that the lowest level of plastic strain of the current study was at eun;env > 0:007. Compared to the existing model equations, this shows a small strain deterioration when SSTT confinement is practiced. The active and passive lateral confinement of steel straps with lateral pre-tensioning stress has slowed down the plastic strain of the confined concrete specimen, especially for highstrength concrete that naturally shows low lateral dilation when loaded. 3.3. Stress deterioration The discussions from several researches on stress deterioration of uniaxial cyclic compression [17,21,22] has shown that the new stress, fnew,1, of a reloading branch is less than the envelope unloading stress, eun;env , at the point of intersection at its corresponding maximum unloading axial strain, eun;env , in the envelope unloading path (see Fig. 11). The ratio between those stresses, defined as stress deterioration ratio, bl, is:
bl ¼
f new;1 f un;env
ð2Þ
Fig. 12 shows the comparison graph of stress deterioration ratio versus envelope unloading strain for different confining ratios for single cycle of uniaxial cyclic compression. Results showed that, when the unloading axial strains eun;env 6 0:005, the stress deterioration ratio was quite low and negligible. After that, the ratio continued to decrease when the unloading axial strain increased (eun;env P 0:005) and became fixed around 0.97. There was no significant effect on the stress deterioration ratio when the confining ratio changed. Fig. 13 depicts the comparison graph of stress deterioration ratio versus envelope unloading strain for different confining ratios and three cycles of uniaxial cyclic compression. The repeating loading cycles had caused the stress to deteriorate within the range of 1.05–0.95 along the unloading axial strains. This was attributed to an increase in the exerted lateral pre-tensioning stress by the steel straps and the lateral dilation of concrete core which had subsequently reduced stress deterioration of the confined specimen. The stress deterioration rate, which had remained almost constant at 0.95 for different confining ratios, was less than that for single cyclic loading test (i.e., 0.97). Nevertheless, it can still be concluded that the confining ratio does not affect the stress deterioration rate for three cycles of uniaxial cyclic compression. 3.4. Effect of loading history In a loading history, the reloading path of an unloading/reloading cycle that crosses the unloading path is called the ‘locus of common points’ [23]. This is the stability limit because stresses applied at or below the locus of common point has the same
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H.-P. Lee et al. / Construction and Building Materials 72 (2014) 48–55
120.0
120.0
100.0
100.0
stress (Mpa)
140.0
stress (Mpa)
140.0
80.0 60.0
80.0 60.0 Monotonic (4-layers)
Monotonic (4-layers) Single Cyclic (4-layers) Monotonic (Unconfined)
40.0 20.0
Monotonic (Unconfined)
Longitudinal deformation 0.0 0.000
40.0
Single cyclic (4-layers)
20.0
Lateral deformation 0.0
0.005
0.010
0.015
-0.007
-0.005
axial strain (mm/mm)
-0.003
-0.001
axial strain (mm/mm)
(a1)
(a2)
120.0
120.0
100.0
100.0
80.0 60.0 Monotonic (4-layers) Three Cyclic (4-layers) Monotonic (Unconfined)
40.0
stress (Mpa)
140.0
stress (Mpa)
140.0
80.0 60.0 Monotonic (4-layers) Monotonic (Unconfined)
20.0
Longitudinal deformation 0.0 0.000
40.0
Three cyclic (4-layers)
20.0
Lateral deformation 0.0
0.005
0.010
0.015
-0.007
-0.005
-0.003
-0.001
axial strain (mm/mm)
axial strain (mm/mm)
(b1)
(b2)
Fig. 8. Uniaxial cyclic stress–strain curves of concrete confined with four layers of steel strapping in comparison with monotonic stress–strain curves of corresponding confined concrete: (a1) longitudinal deformation for single cyclic loading; (a2) lateral deformation for single cyclic loading; (b1) longitudinal deformation for three cyclic loadings; and (b2) lateral deformation for three cyclic loadings.
0.025 0.020
0.0050
Plastic Strain
0.0045
Plastic Strain
0.0040 0.0035 0.0030 0.0025
Current Study Abbasnia et al (2012) Wang et al (2012) Lam et al (2006) Sakai and Kawashima (2000)
0.015 0.010 0.005
0.0020
0.000 0.000
0.0015
0.005
0.010
0.015
0.020
0.025
0.030
0.0010 0.0005
2layers
-0.005
4layers
Envelope Unloading Strain
0.0000 0
0.002
0.004
0.006
0.008
0.01
Fig. 10. Comparison of existing plastic strain models with current study.
Envelope Unloading Strain Fig. 9. Plastic strain (epl ) versus envelope unloading strain (eun;env ).
Table 3 The plastic strain models. Source
Plastic strain model
Abbasnia et al. [17] Wang et al. [24] Lam et al. [14] Sakai and Kawashima [20]
epl = 0.4309eun,env - 0.0003 epl = 0.815eun,env - 0.0020 epl = 0.7160eun,env - 0.0016 epl = 0.9600eun,env - 0.0023
stress-strain responses and follows the same path of unloading/ reloading cycle without causing any further permanent axial strains. This concept neglects the effect of loading history on the permanent axial strain of the unloading and reloading paths of concrete. However, such is not entirely supported by some researchers like [14,17]. The results of the present study showed that the concept of locus of common point is invalid for SSTT-confined specimen. When the confined specimens were subjected to repeated cycles at each prescribed load level, the axial stress–axial strain response of the subsequent unloading/reloading cycle did not coincide with previous unloading/reloading cycle, but shifted to the higher or
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1.2 C60S15-2FT-1C
Axial stress
Increasing strain ratio
1.1
C60S15-4FT-1C
1 0.9 0.8 0.7 0.6 0.5
Axial strain
1.05
1.40
Increasing strain ratio
stress deterioration ratio
1.60
1.00 0.95 0.90
SSTT-2MT-1C
0.85
SSTT-4MT-1C 0.0020
0.0040
0.0060
0.0080
0.0100
5
1.20 1.00 0.80 0.60
1
2
3
4
Number of cycles, n
1.20
stress deterioration ratio
4
C60S15-2FT-3C C60S15-4FT-3C
0
Fig. 12. Stress deterioration versus envelope loading strain for SSTT confinement for single cycle of uniaxial cyclic compression.
Fig. 15. Increasing strain ratio, cn, versus number of cycles, n, for SSTT-confined specimens tested under uniaxial three cycles of compression load.
had undergone three repeated cyclic loadings under a prescribed load, the increase in lateral dilation of concrete core due to loading did increase the pre-tensioning stress of confined steel straps, making the strain ratio to lie between +1.20 and 0.80 (see Fig. 15). For confined specimens that had undergone single cyclic loading, the continuously increasing reloading and unloading cyclic loading results had increased the strain ratio (see Fig. 14).
1.15 1.10 1.05 1.00 0.95 0.90
4. Conclusion
SSTT-2MT-3C
0.85
SSTT-4MT-3C 0.0020
0.0040
0.0060
0.0080
0.0100
envelope unloading strain Fig. 13. Stress deterioration versus envelope loading strain for SSTT confinement for three cycles of uniaxial cyclic compression.
lower axial strain side. This is indicative of the cumulative effect of loading history on the permanent strain (plastic strain) and stress deterioration of SSTT-confined high strength concrete (see Figs. 7-b and 8-b). To illustrate this phenomenon, two graphs of increasing strain ratio (cn) versus number of cycles, n, have been plotted and shown in Figs. 14 and 15 for different loading patterns. The increasing strain ratio is defined as:
eun epl;n eun epl;n1
3
0.40
0.0120
envelope unloading strain
0.80 0.0000
2
Fig. 14. Increasing strain ratio, cn versus number of cycles, n, for SSTT-confined specimens tested under uniaxial single cycles compression load.
1.10
0.80 0.0000
1
Number of cycles, n
Fig. 11. Stress–strain curve for a cycle of unloading-reloading.
cn ¼
0
ð3Þ
where epl;n and epl;n1 are the plastic strains of the nth and (n 1)th unloading/reloading cycle respectively. In Figs. 14 and 15, the increment (less than 1.0) and decrement (more than 1.0) of plastic strain with the number of cycles again do not support the above-mentioned concept with SSTT-confinement. For confined specimens that
In this study, a total of 21 SSTT-confined high-strength concrete specimens with different confining ratios were tested and evaluated under three different loading patterns: uniaxial compression load, uniaxial single cycle compression load, and three cycles of uniaxial compression load. Based on the test results, several conclusions have been drawn: 1. For SSTT confinement with different confining ratios, the basic hypothesis of envelope curve is valid for SSTT-confined highstrength concrete specimens. The stress–strain curve under uniaxial monotonic loading has coincided with the corresponding stress–strain curve under all tested loadings at prescribed load levels. 2. The relationship between eun;env and epl is linear for eun;env > 0:0025 and the confining ratio does not have any significant effect on the plastic strain. SSTT-confinement also possesses the lowest plastic strain compared to several related existing plastic strain models. 3. The stress deterioration ratio is independent of variations in confining ratio and loading patterns. The highest stress deterioration ratio is about 3% of the uniaxial single cycle compression
H.-P. Lee et al. / Construction and Building Materials 72 (2014) 48–55
load and about 5% of the three cycles of uniaxial compression load. 4. Repeated unloading/reloading cycles have a cumulative effect on the permanent strain and stress deterioration. The concept which neglects the effect of loading history on the permanent axial strain of the unloading and reloading paths of concrete is thus invalid. It should be noted that the above conclusions have been reached only in regard to the basis of laboratory tests conducted on standard scaled high-strength concrete specimens. Dimension and size variability may impose different effects and results. Acknowledgements The work described in this paper was fully supported by the GUP Grant (Tier 2) of Universiti Teknologi Malaysia (Project Vote No.: QJ130000.2622.06J91). Besides, the authors are also grateful to Mybrains 15 from Ministry of Higher Education of Malaysia for sponsoring this research study through the MyPhD scholarship. References [1] Moghaddam H, Samadi M, Pilakoutas K, Mohebbi S. Axial compressive behavior of concrete actively confined by metal strips; Part A: experimental study. Mater Struct 2010;43:1369–81. [2] Moghaddam H, Samadi M, Pilakoutas K. Compressive behavior of concrete actively confined by metal strips, Part B: analysis. Mater Struct 2010;43:1383–96. [3] Moghaddam H, Samadi M, Mohebbi S. RC members strengthening by lateral post-tensioning of external metal strips. In: Int. Earthq. Symp. KOCAEU 2007, 1995. p. 454–62. [4] Moghaddam H, Pilakoutas K, Samadi M, Mohebbi S. Behavior and modeling of concrete columns confined by external post-tensioned strips. Struct Congr 2008:1–10. [5] Saadatmanesh H, Ehsani MR, Li MW. Strength and ductility of concrete members confined by external post-tensioned strips. In: 4th Natl. Conf. Civ. Eng., 2008. [6] Frangou M, Pilakoutas K, Dritsos S. Structural repair/strengthening of RC columns. Constr Build Mater 1995;9:259–66.
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[7] Awang AZ, Omar W, Hoong-Pin L, Ma CK. Behaviour of externally-confined high strength concrete column under uniaxial compression load. In: APSECICCER 2012, 2012: p. 1–9. [8] Hoong-Pin L, Awang AZ, Omar W. Behaviour of steel strapping tensioning technique (SSTT) confined high-strength concrete with different lateral pretensioning stresses. In: IGCESH 2013, 2013. [9] Hoong-Pin L, Awang AZ, Omar W. Short term durability studies on high strength concrete columns confined with steel strapping tensioning technique (SSTT). In: GEOCON 2013, Johor, 2013. [10] Awang AZ, Omar W, Hoong-Pin L. The effectiveness of metal straps strengthening in layers at high strength concrete column. In: APSEC-ICCER 2012, Surabaya, Indonesia, 2012. [11] Awang AZ. In: Stress–strain behaviour of high-strength concrete with lateral pre-tensioning confinement. Universiti Teknologi Malaysia; 2013. [12] Mansur MA, Wee TH, Chin MS. Derivation of the complete stress–strain curves for concrete in compression. Mag Concr Res 1995;47:285–90. [13] Shah SP, Fafitis A, Arnold R. Cyclic loading of spirally reinforced concrete. J Struct Eng 1983;7:1695–710. [14] Lam L, Teng JG, Cheung CH, Xiao Y. FRP-confined concrete under axial cyclic compression. Cem Concr Compos 2006;28:949–58. [15] Cheong HK, Perry SH. Cyclic loading of laterally confined concrete columns. Mater Struct 1993;26:557–62. [16] Rodrigues C, Silva MG. Experimental investigation of CFRP reinforced concrete columns under uniaxial cyclic compression. In: Fifth Int. Conf. FibreReinforced Plast. Reinf. Concr. Struct., London, UK, 2001. p. 783–92. [17] Abbasnia R, Hosseinpour F, Rostamian M, Ziaadiny H. Effect of corner radius on stress–strain behavior of FRP confined prisms under axial cyclic compression. Eng Struct 2012;40:529–35. [18] Ilki A, Kumbasar N. Compressive behaviour of carbon fiber composite jacketed concrete with circular and non-circular cross sections. J Earthq Eng 2003;3:381–406. [19] Rousakis TC. Experimental investigation of concrete cylinders confined by carbon FRP sheets. In: Under monotonic and cyclic axial compressive load. Demokritus University of Thrace; 2001. [20] Sakai J, Kawashima K. An unloading and reloading stress–strain model for concrete confined by tie reinforcements. In: 12WCEE 2000, 2006. p. 1–8. [21] Lam L, Teng JG. Stress–strain model for FRP-confined concrete under cyclic axial compression. Eng Struct 2009;31:308–21. [22] Shao Y, Zhu Z, Mirmiran A. Cyclic modeling of FRP-confined concrete with improved ductility. Cem Concr Compos 2006;28:959–68. [23] Sinha BP, Gerstle KH, Tulin LG. Stress–strain relations for concrete under cyclic loading. ACI J 1964;61:195–211. [24] Wang Z, Wang D, Smith ST, Lu D. Experimental testing and analytical modeling of CFRP-confined large circular RC columns subjected to cyclic axial compression. Eng Struct 2012;40:64–74.
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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Steel strap confined high strength concrete under uniaxial cyclic compression Hoong-Pin Lee, Abdullah Zawawi Awang ⇑, Wahid Omar Faculty of Civil Engineering, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia
h i g h l i g h t s Laterally pre-tensioned and steel strapped concrete was cyclically tested. Examination of the effect of confining ratio on cyclic stress–strain behaviour. Effect of monotonic and cyclic loading patterns is systematically examined. Evaluation the response of envelope curve, plastic strain, loading history effect. A plastic strain model is proposed and assessed with existing models.
a r t i c l e
i n f o
Article history: Received 10 December 2013 Received in revised form 5 August 2014 Accepted 7 August 2014 Available online 27 September 2014 Keywords: Lateral confinement Steel straps Confining ratio Uniaxial cyclic loading Stress–strain behaviour
a b s t r a c t This paper discusses an affordable and effective lateral confinement technique to enhance concrete’s compressive strength and ductility – the steel strapping tensioning technique (SSTT). Considerable studies have been done on the characteristics of SSTT-confined concrete under uniaxial monotonic compression loading, but none has addressed its uniaxial cyclic response. In this paper, 21 high-strength concrete specimens having diameter of 150 mm and height of 300 mm had been cast, laterally pre-tensioned with steel straps in different confining ratios, and tested to failure under uniaxial cyclic and monotonic compression loadings. Results indicated that the basic hypothesis of envelope curve is valid for SSTT-confined high-strength concrete specimens for uniaxial monotonic and cyclic loadings. The development of plastic strain is independent of the confining ratio when the envelope unloading strain exceeds 0.0025. Moreover, SSTT-confinement has the lowest plastic strain compared to several related existing plastic strain models. The stress deterioration ratio is independent of confining ratio and loading patterns. Lastly, the concept which neglects the effect of loading history on the permanent axial strain of the unloading and reloading paths of concrete is invalid because repeated unloading/reloading cycles have demonstrated a cumulative effect on the permanent strain and stress deterioration. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction Steel strapping tensioning technique or SSTT is a type of lateral confining technique used to enhance the capacity and ductility of new and existing concrete structures by confining the steel straps with prescribed lateral pre-tensioning stress in layers. The remarkable enhancement of the confined concrete structures’ mechanical properties, ease to operate as well as the time and cost saved allow lesser interrupted structure serviceability and reduce dependence on experienced workers. As such, SSTT has become one of the most affordable confining techniques for concrete confinement, especially for high-strength concrete that is naturally brittle and ⇑ Corresponding author. Tel.: +60 19 7107185. E-mail address: [email protected] (A.Z. Awang). http://dx.doi.org/10.1016/j.conbuildmat.2014.08.007 0950-0618/Ó 2014 Elsevier Ltd. All rights reserved.
experiences low lateral dilation when loaded [1–10]. One of the effective parameters that govern the stress-strain behaviour of SSTT-confined concrete is the confining ratio, which is most commonly studied under uniaxial monotonic loading [1–7]. For instance, Moghaddam et al. [1–5] studied the effect of confining ratio of steel straps on the stress-strain behaviour of SSTT-confined concrete. The confining ratio takes into account the number of steel strap layers and the spacing between the steel straps. As proposed in EC8, the effective mechanical volumetric ratio has also been adopted to allow comparison with confining ratio. Moghaddam and his co-workers concluded that a strong relationship exists between the effective mechanical volumetric ratio of steel straps and the compressive strength as well as ductility of the confined specimens. The study also proposed empirical models in the function of effective mechanical volumetric ratio for design purpose.
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The results indicated that the higher the effective mechanical volumetric ratio, the higher the compressive strength and ductility performance of SSTT-confined specimens. Frangou et al. [6] in their investigation found an inverted relationship between the spacing between the steel straps and the compressive strength of SSTTconfined specimens, i.e., the smaller the spacing between steel straps, the higher the compressive strength. Awang et al. [7] also indicated a close and increasing linear relationship between the effective mechanical volumetric ratio and the compressive strength of SSTT-confined high-strength concrete specimens. A simple strength model for SSTT confinement was proposed and compared with several existing models. The result showed very promising compressive strength enhancement compared to other confinement methods. In short, a great quantity of existing studies have demonstrated the performance of SSTT confinement on different aspects under the action of uniaxial monotonic compressive loading [1–10], but no study has been carried out on the uniaxial cyclic stress–strain behaviour of the confined concrete, especially high-strength concrete. The lacking of test data for these confinements thus calls for more quantitative experimental investigations on the influence of confining ratios, especially under uniaxial cyclic compression, for the development of theoretical models. In this paper, the results of uniaxial cyclic and monotonic compression loading tests on 21 SSTT-confined high-strength concrete specimens with different confining ratios are presented and the quantified behaviour of these confined specimens shall be discussed through several aspects of cyclic behaviour. 2. Experimental work 2.1. Specimen preparation A set of 21 high-strength concrete specimens having diameter of 150 mm in circular section and height of 300 mm had been prepared. The testing parameters primarily dealt with the number of steel strap layers (confining ratio) externally confined on the high-strength concrete specimens and the loading patterns (uniaxial monotonic and cyclic compression). Uniaxial cyclic compression load test was carried out to validate the performance of these confinement methods under different loading patterns. Each of the high-strength concrete specimens were not reinforced longitudinally with steel bar. For all SSTT-confined concrete specimens, the clear distance between each steel straps along the concrete specimens was fixed at 15 mm in the middle of the specimen and 7.5 mm in the two quarter end regions to provide sufficient confinement (see Figs. 1 and 2) to reduce the possibility of failure at the two end sections of the specimens. The properties of high-strength concrete specimens including number of steel strap layers and type of loading are shown in Table 1.
2.2. Material and pre-tension technique The mixture proportions for the high-strength concrete are as given in Table 2. All specimens and cubes were removed from the formworks and moulds right after 24 h after casting and went through wet curing for 28 days. The cubes of size
49
100 mm 100 mm 100 mm were compressively tested after 7 days, 28 days, and on the day of testing and the cube compressive strength of the high-strength 0 concrete, f c , were recorded. The achieved concrete compressive strength and strain at ultimate were 61.4 MPa and 0.0021 mm/mm, respectively. After 28 days, the specimens were removed from curing tank and laterally pre-tensioned with prescribed layers of steel straps as illustrated in Table 1, except for unconfined specimens. All the confining materials in this study were using 15.85 mm 0.55 mm steel straps. Tensile tests for confining materials were carried out using 250 kN Universal Testing Machine, in compliance with BS EN 10 002-1:1990. The tensile strength was averagely about 916 N/mm2, as illustrated in Fig. 3. The confinement method fully followed the SSTT confinement method designed by Awang et al. and Hoong-Pin et al. [7–10] where the tensioner used in packaging industry was utilized to confine the specimens. Moghaddam et al. recommended a confinement of about 30% of the steel strap’s tensile yield strength to effectively mobilize the lateral confining stress of steel straps from the initial state of loading application [1]. Tensioning work for both layers of confinement needed to be performed in slow and steady pace and should be stopped once the steel straps had tightened up. Then, the surplus steel strap was bended across the connection clips and tied up to lock the applied pre-tensioning stress onto the concrete specimen. The detailing for SSTT confinement on concrete specimen is as shown in Fig. 2. The specially designed connection clip used in these method is able to self-distribute the pretensioning stress among the layers of steel strapping to achieve a uniform pretensioning stress in different layers [11]. The actual lateral pre-tensioning stress applied by steel strap layers onto the concrete core was measured using two semi-circular steel frameworks [1,8]. The measured pre-tensioned stress applied by two and four layers of steel straps using the tensioner was 286.78 ± 20 MPa, which was 29.12–33.5% of the steel strap’s tensile yield strength. This indicated that these confinement had satisfied the recommended pre-tensioned stress in literature [1]. During the study, the 21 high-strength concrete specimens were assigned into seven groups with the notation of C60-C for control column as well as C60S15-2FTM and C60S15-4FT-M for specimens pre-tensioned with two and four layers of steel straps respectively. ‘‘M’’ meant that the specimens were tested under uniaxial monotonic compression loading. C60S15-2FT-1C and C60S15-4FT-1C were assigned to specimens pre-tensioned with two and four layers of steel straps respectively and tested under uniaxial single cyclic compression loading. Meanwhile, C60S152FT-3C and C60S15-4FT-3C meant that the specimens had been pre-tensioned with two and four layers of steel straps respectively and tested under uniaxial three cyclic compression loadings. The notation of ‘‘15’’ was for the clear distance between the straps along the specimen. To ensure that the specimens were uniformly loaded during testing, the top and bottom surface of the specimens had to be parallel. So, the specimens had to be cast horizontally on a levelled surface. 2.3. Test setup and strain measuring instrumentations The load tests have been conducted using TINIUS OLSEN Super ‘‘L’’ Universal Testing Machine which has the capacity of 3 MN in the Faculty of Civil Engineering Laboratory, Universiti Teknologi Malaysia. The load tests are based on displacement-controlled loading with a constant loading rate of 0.4 mm/min. The overall view of the specimen set up and diagram for the loading machine and measuring equipment are as shown in Fig. 4. The overall longitudinal axial deformations of the specimens were obtained using the three linear variable differential transducers (LVDTs) which had a gauge length of 50 mm located at the machine platen and three other LVDTs of 25 mm gauge length attached to the centre of the specimens to measure the relative axial displacement over the 100 mm height of the specimens. The transverse deformations of the specimens were obtained using two LVDTs (gauge length of 25 mm) located at the centre of the specimens, diametrically wrapped with a steel ties around the specimen (see Fig. 5). The overall concrete longitudinal strains were presented as the average value of LVDTs divided by the particular measured length. The transverse deformations of the concrete and steel strapping were measured using two sets of strain gauges (gauge length of 60 mm and 10 mm for concrete and steel strapping, respectively) installed at the centre of the specimen in a diametrically direction. All the strains were measured using the data logger, which also recorded the values of loads and displacement. Any cracking pattern, buckling, deformation, and etc., were recorded during testing as well. The compressive strength of specimens was tested according to ASTM C39/C39M-11. In this paper, the method of obtaining the actual stress-strain curve for confined concrete specimen from the above-mentioned instrumentations followed the method implemented by Mansur et al. [12]. A correction factor which including end-zone effect and machine flexibility which has been validated for the Universal Testing Machine in Universiti Teknologi Malaysia, has also been included in the initial stress–strain curve plotting for correction purpose. 2.4. Loading patterns
Fig. 1. SSTT-confined high-strength concrete specimens.
The loading patterns are shown in Fig. 6. For loading pattern notated as ‘‘M’’, monotonically increasing displacement at a rate of 0.4 mm/min had been performed until erratic deformation (i.e., failure) was observed. For the loading
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Fig. 2. Detailing of confined concrete specimen with SSTT confinement.
Table 1 Properties of the unconfined and SSTT-confined specimens. Specimen notation
Number of steel strap layers
Loading patterns
C60-C C60S15-2FT C60S15-2FT C60S15-2FT C60S15-4FT C60S15-4FT C60S15-4FT
– 2 2 2 4 4 4
M M 1C 3C M 1C 3C
Table 2 High-strength concrete mix design. Materials
Type
Quantity
Cement (kg/m3) Sand (kg/m3) Aggregate (kg/m3) Superplasticizer (mL) Water (kg/m3) Water/cement ratio
Type I OPC River sand Maximum size 12 mm Glenium ACE388 (RM) Pipe water –
550 885 957 0.75% of 100 kg cement 190 0.35
1000
Fig. 4. The strain measuring equipment and the loading device (TINIUS OLSEN Super ‘‘L’’ Universal Testing Machine).
specimen was loaded to the next prescribed load value for cyclic loading until the specimen failed. Three unloading and reloading cycles at each prescribed unloading load level had been designed for loading pattern ‘‘3C’’. For the case of uniaxial cyclic compression load, the target load level at which unloading was terminated and reloading was started was about 1–3 kN; this is equivalent to an uniaxial stress of about 0.057–0.170 MPa in this case of study.
Tensile stress (MPa)
900 800
3. Test results
700 600
3.1. Envelope curve
500 400 300 200 100 0 0.00
Steel Strapping 0.50
1.00
1.50
2.00
2.50
3.00
Elongation (%) Fig. 3. Tensile test result for steel strapping. pattern notated as ‘‘1C’’, uniaxial single cyclic compression involving unloading and reloading cycles with similar displacement control rate had been implemented at several prescribed unloading load values until failure. In other words, the specimen was loaded by increasing the uniaxial load to a prescribed load value, and it was next unloaded by reducing the uniaxial load to a target load level. Then, the
The concept of an envelope curve for unconfined and confined concrete refers to the curve joining the resultant broken curves or the loading branches between each cycle and the monotonic stress–strain curve, which tends to fall within the envelope curves under constantly increasing strain [13]. Envelope curve can also be considered as an upper boundary response of unconfined and confined concrete that has been subjected to any loading history in the stress–strain domain [14]. However, the crossing point of envelope curve and monotonic stress–strain curve for confined concrete is still a debated issue among researchers where some suggested that the monotonic stress–strain curve for confined concrete may stay below the envelope curve [15,16] while other suggested a coincidence of both monotonic and envelope curves [14,17,18]. Rousakis in his experimental studies also discovered that the variation of
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Stress
Stress
Stress
Fig. 5. LVDT holder rig and strain gauges position [9].
Strain
Strain
Strain
“M”
“1C”
“3C”
Fig. 6. Loading patterns: ‘‘M’’: uniaxial monotonic loading; ‘‘1C’’: uniaxial single cycle loading at each prescribed load level; ‘‘3C’’: uniaxial three cycles loading at each prescribed load level.
strength and ductility of FRP confined concrete tested under loadunload cycles was the same for the monotonic mode of loading, regardless of concrete strength [19]. In order to compare both uniaxial monotonic and cyclic stress– strain curves of SSTT-confined specimens, the envelope curves as shown in Figs. 7(a1), (b1) and 8(a1), (b1) (longitudinal deformation for specimens pre-tensioned with two and four layers of steel strapping, respectively) had been obtained by connecting all initial unloading points on the stress–strain curve within the uniaxial cyclic loading history for both single cycle and three cycles of loading under the prescribed load level. It has been clearly observed that, for SSTT confined specimens, the unloading/reloading cycles at each prescribed axial load coincided with the corresponding monotonic stress–strain curve before ultimate regardless of confining ratios and loading patterns. After the ultimate compressive stress, the envelope curves stayed below the monotonic stress– strain curves. Hence, this observation proved that the basic hypothesis of envelope curve is valid for SSTT-confined high-strength concrete – the envelope curve coincided with the monotonic stress–strain curve for the initial unloading points until the ultimate compressive load, while the subsequent envelope curve stayed below the monotonic curve. Besides, the variation of confining ratios and loading patterns does not have any effect on this hypothesis, thus indicates the independency of the envelope curve’s validity to the confining ratios and loading patterns. The concrete’s stress–strain curves in lateral direction for two and four layers of SSTT confinement are shown in Figs. 7(a2), (b2) and 8(a2), (b2) respectively. Similar to the longitudinal deformation, it is concluded that the envelop curve for unloading/ reloading cycles coincided with the corresponding monotonic stress–strain curve until ultimate loading, regardless also of the effect of confining ratio and loading history. Hence, the results
for both longitudinal and lateral deformations again validated the basic hypothesis of envelop curve for SSTT confinement. 3.2. Plastic strain The definition for plastic strain is the residual axial strain of concrete after being unloaded to zero stress [14]. It can also be defined as the non-recoverable ‘‘residual’’ longitudinal strain at the end of each unloading cycle and which increases each time a load cycle is being taken beyond the maximum load of the preceding cycle [15]. Fig. 9 shows the relationship of plastic strain, epl, versus envelope unloading strain, eun;env , of SSTT-confined specimen pre-tensioned with two layers and four layers of steel strap under uniaxial cyclic compression loading test respectively. A number of existing studies [14,20] clarified that a linear relationship exists between the plastic strains of unconfined or steel confined concrete and the axial strain at the starting point of unloading. Lam et al.’s study showed that the plastic strain of FRP-confined concrete under cyclic load is linearly related to the envelope unloading strain and is independent of the amount of confinement since both trend lines have coincided [14]. In Fig. 9, a linear relationship between the plastic strain and the envelope unloading strain is observed for SSTT-confined specimens when eun;env > 0:0025. Moreover, the linear trend lines for the two series of SSTT-confined specimens pre-tensioned with two and four layers of steel strap coincided with each other. This demonstrated that the plastic strain of SSTT-confined specimen is independent of the amount of confinement. Hence, a relationship of plastic strainenvelope unloading strain can be developed (with correlation coefficient, R2, equals to 0.77) as follows:
epl ¼ 0:46eun;env þ 0:00015; eun;env > 0:0025
ð1Þ
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120.0
120.0 Monotonic (2-layers) Single Cyclic (2-layers) Monotonic (Unconfined)
100.0
80.0
stress (Mpa)
stress (Mpa)
100.0
60.0 40.0
80.0 60.0 Monotonic (2-layers)
40.0
Single cyclic (2-layers) Monotonic (unconfined)
20.0
Longitudinal deformation 0.0 0.000
0.005
0.010
0.015
-0.007 -0.006 -0.005 -0.004 -0.003 -0.002 -0.001
axial strain (mm/mm)
axial strain (mm/mm)
(a1)
(a2)
0.0 0.000
120.0
120.0 Monotonic (2-layers) Three Cyclics (2-layers) Monotonic (Unconfined)
100.0 80.0
100.0 80.0
stress (Mpa)
stress (Mpa)
20.0
Lateral deformation
60.0 40.0
60.0 Monotonic (2-layers)
40.0
Three cyclic (2-layers)
20.0
Monotonic (unconfined)
Longitudinal deformation 0.0 0.000
0.005
0.010
20.0
Lateral deformation 0.015
-0.007 -0.006 -0.005 -0.004 -0.003 -0.002 -0.001
axial strain (mm/mm)
axial strain (mm/mm)
(b1)
(b2)
0.0 0.000
Fig. 7. Uniaxial cyclic stress–strain curves of concrete confined with two layers of steel strapping in comparison with monotonic stress–strain curves of corresponding confined concrete: (a1) longitudinal deformation for single cyclic loading; (a2) lateral deformation for single cyclic loading; (b1) longitudinal deformation for three cyclic loadings; and (b2) lateral deformation for three cyclic loadings.
To evaluate the unrecoverable strain (plastic strain) level of the current study with existing confining methods, several existing plastic strain model equations have been selected (see Table 3). Sakai and Kawashima’s model focused on the internal confinement that utilizes tie reinforcement while other studies have focused on FRP-type confinements. Fig. 10 shows the comparison graph between existing plastic strain model equations and present study’s plastic strain model equation according to Eq. (1). Result indicated that the lowest level of plastic strain of the current study was at eun;env > 0:007. Compared to the existing model equations, this shows a small strain deterioration when SSTT confinement is practiced. The active and passive lateral confinement of steel straps with lateral pre-tensioning stress has slowed down the plastic strain of the confined concrete specimen, especially for highstrength concrete that naturally shows low lateral dilation when loaded. 3.3. Stress deterioration The discussions from several researches on stress deterioration of uniaxial cyclic compression [17,21,22] has shown that the new stress, fnew,1, of a reloading branch is less than the envelope unloading stress, eun;env , at the point of intersection at its corresponding maximum unloading axial strain, eun;env , in the envelope unloading path (see Fig. 11). The ratio between those stresses, defined as stress deterioration ratio, bl, is:
bl ¼
f new;1 f un;env
ð2Þ
Fig. 12 shows the comparison graph of stress deterioration ratio versus envelope unloading strain for different confining ratios for single cycle of uniaxial cyclic compression. Results showed that, when the unloading axial strains eun;env 6 0:005, the stress deterioration ratio was quite low and negligible. After that, the ratio continued to decrease when the unloading axial strain increased (eun;env P 0:005) and became fixed around 0.97. There was no significant effect on the stress deterioration ratio when the confining ratio changed. Fig. 13 depicts the comparison graph of stress deterioration ratio versus envelope unloading strain for different confining ratios and three cycles of uniaxial cyclic compression. The repeating loading cycles had caused the stress to deteriorate within the range of 1.05–0.95 along the unloading axial strains. This was attributed to an increase in the exerted lateral pre-tensioning stress by the steel straps and the lateral dilation of concrete core which had subsequently reduced stress deterioration of the confined specimen. The stress deterioration rate, which had remained almost constant at 0.95 for different confining ratios, was less than that for single cyclic loading test (i.e., 0.97). Nevertheless, it can still be concluded that the confining ratio does not affect the stress deterioration rate for three cycles of uniaxial cyclic compression. 3.4. Effect of loading history In a loading history, the reloading path of an unloading/reloading cycle that crosses the unloading path is called the ‘locus of common points’ [23]. This is the stability limit because stresses applied at or below the locus of common point has the same
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H.-P. Lee et al. / Construction and Building Materials 72 (2014) 48–55
120.0
120.0
100.0
100.0
stress (Mpa)
140.0
stress (Mpa)
140.0
80.0 60.0
80.0 60.0 Monotonic (4-layers)
Monotonic (4-layers) Single Cyclic (4-layers) Monotonic (Unconfined)
40.0 20.0
Monotonic (Unconfined)
Longitudinal deformation 0.0 0.000
40.0
Single cyclic (4-layers)
20.0
Lateral deformation 0.0
0.005
0.010
0.015
-0.007
-0.005
axial strain (mm/mm)
-0.003
-0.001
axial strain (mm/mm)
(a1)
(a2)
120.0
120.0
100.0
100.0
80.0 60.0 Monotonic (4-layers) Three Cyclic (4-layers) Monotonic (Unconfined)
40.0
stress (Mpa)
140.0
stress (Mpa)
140.0
80.0 60.0 Monotonic (4-layers) Monotonic (Unconfined)
20.0
Longitudinal deformation 0.0 0.000
40.0
Three cyclic (4-layers)
20.0
Lateral deformation 0.0
0.005
0.010
0.015
-0.007
-0.005
-0.003
-0.001
axial strain (mm/mm)
axial strain (mm/mm)
(b1)
(b2)
Fig. 8. Uniaxial cyclic stress–strain curves of concrete confined with four layers of steel strapping in comparison with monotonic stress–strain curves of corresponding confined concrete: (a1) longitudinal deformation for single cyclic loading; (a2) lateral deformation for single cyclic loading; (b1) longitudinal deformation for three cyclic loadings; and (b2) lateral deformation for three cyclic loadings.
0.025 0.020
0.0050
Plastic Strain
0.0045
Plastic Strain
0.0040 0.0035 0.0030 0.0025
Current Study Abbasnia et al (2012) Wang et al (2012) Lam et al (2006) Sakai and Kawashima (2000)
0.015 0.010 0.005
0.0020
0.000 0.000
0.0015
0.005
0.010
0.015
0.020
0.025
0.030
0.0010 0.0005
2layers
-0.005
4layers
Envelope Unloading Strain
0.0000 0
0.002
0.004
0.006
0.008
0.01
Fig. 10. Comparison of existing plastic strain models with current study.
Envelope Unloading Strain Fig. 9. Plastic strain (epl ) versus envelope unloading strain (eun;env ).
Table 3 The plastic strain models. Source
Plastic strain model
Abbasnia et al. [17] Wang et al. [24] Lam et al. [14] Sakai and Kawashima [20]
epl = 0.4309eun,env - 0.0003 epl = 0.815eun,env - 0.0020 epl = 0.7160eun,env - 0.0016 epl = 0.9600eun,env - 0.0023
stress-strain responses and follows the same path of unloading/ reloading cycle without causing any further permanent axial strains. This concept neglects the effect of loading history on the permanent axial strain of the unloading and reloading paths of concrete. However, such is not entirely supported by some researchers like [14,17]. The results of the present study showed that the concept of locus of common point is invalid for SSTT-confined specimen. When the confined specimens were subjected to repeated cycles at each prescribed load level, the axial stress–axial strain response of the subsequent unloading/reloading cycle did not coincide with previous unloading/reloading cycle, but shifted to the higher or
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H.-P. Lee et al. / Construction and Building Materials 72 (2014) 48–55
1.2 C60S15-2FT-1C
Axial stress
Increasing strain ratio
1.1
C60S15-4FT-1C
1 0.9 0.8 0.7 0.6 0.5
Axial strain
1.05
1.40
Increasing strain ratio
stress deterioration ratio
1.60
1.00 0.95 0.90
SSTT-2MT-1C
0.85
SSTT-4MT-1C 0.0020
0.0040
0.0060
0.0080
0.0100
5
1.20 1.00 0.80 0.60
1
2
3
4
Number of cycles, n
1.20
stress deterioration ratio
4
C60S15-2FT-3C C60S15-4FT-3C
0
Fig. 12. Stress deterioration versus envelope loading strain for SSTT confinement for single cycle of uniaxial cyclic compression.
Fig. 15. Increasing strain ratio, cn, versus number of cycles, n, for SSTT-confined specimens tested under uniaxial three cycles of compression load.
had undergone three repeated cyclic loadings under a prescribed load, the increase in lateral dilation of concrete core due to loading did increase the pre-tensioning stress of confined steel straps, making the strain ratio to lie between +1.20 and 0.80 (see Fig. 15). For confined specimens that had undergone single cyclic loading, the continuously increasing reloading and unloading cyclic loading results had increased the strain ratio (see Fig. 14).
1.15 1.10 1.05 1.00 0.95 0.90
4. Conclusion
SSTT-2MT-3C
0.85
SSTT-4MT-3C 0.0020
0.0040
0.0060
0.0080
0.0100
envelope unloading strain Fig. 13. Stress deterioration versus envelope loading strain for SSTT confinement for three cycles of uniaxial cyclic compression.
lower axial strain side. This is indicative of the cumulative effect of loading history on the permanent strain (plastic strain) and stress deterioration of SSTT-confined high strength concrete (see Figs. 7-b and 8-b). To illustrate this phenomenon, two graphs of increasing strain ratio (cn) versus number of cycles, n, have been plotted and shown in Figs. 14 and 15 for different loading patterns. The increasing strain ratio is defined as:
eun epl;n eun epl;n1
3
0.40
0.0120
envelope unloading strain
0.80 0.0000
2
Fig. 14. Increasing strain ratio, cn versus number of cycles, n, for SSTT-confined specimens tested under uniaxial single cycles compression load.
1.10
0.80 0.0000
1
Number of cycles, n
Fig. 11. Stress–strain curve for a cycle of unloading-reloading.
cn ¼
0
ð3Þ
where epl;n and epl;n1 are the plastic strains of the nth and (n 1)th unloading/reloading cycle respectively. In Figs. 14 and 15, the increment (less than 1.0) and decrement (more than 1.0) of plastic strain with the number of cycles again do not support the above-mentioned concept with SSTT-confinement. For confined specimens that
In this study, a total of 21 SSTT-confined high-strength concrete specimens with different confining ratios were tested and evaluated under three different loading patterns: uniaxial compression load, uniaxial single cycle compression load, and three cycles of uniaxial compression load. Based on the test results, several conclusions have been drawn: 1. For SSTT confinement with different confining ratios, the basic hypothesis of envelope curve is valid for SSTT-confined highstrength concrete specimens. The stress–strain curve under uniaxial monotonic loading has coincided with the corresponding stress–strain curve under all tested loadings at prescribed load levels. 2. The relationship between eun;env and epl is linear for eun;env > 0:0025 and the confining ratio does not have any significant effect on the plastic strain. SSTT-confinement also possesses the lowest plastic strain compared to several related existing plastic strain models. 3. The stress deterioration ratio is independent of variations in confining ratio and loading patterns. The highest stress deterioration ratio is about 3% of the uniaxial single cycle compression
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load and about 5% of the three cycles of uniaxial compression load. 4. Repeated unloading/reloading cycles have a cumulative effect on the permanent strain and stress deterioration. The concept which neglects the effect of loading history on the permanent axial strain of the unloading and reloading paths of concrete is thus invalid. It should be noted that the above conclusions have been reached only in regard to the basis of laboratory tests conducted on standard scaled high-strength concrete specimens. Dimension and size variability may impose different effects and results. Acknowledgements The work described in this paper was fully supported by the GUP Grant (Tier 2) of Universiti Teknologi Malaysia (Project Vote No.: QJ130000.2622.06J91). Besides, the authors are also grateful to Mybrains 15 from Ministry of Higher Education of Malaysia for sponsoring this research study through the MyPhD scholarship. References [1] Moghaddam H, Samadi M, Pilakoutas K, Mohebbi S. Axial compressive behavior of concrete actively confined by metal strips; Part A: experimental study. Mater Struct 2010;43:1369–81. [2] Moghaddam H, Samadi M, Pilakoutas K. Compressive behavior of concrete actively confined by metal strips, Part B: analysis. Mater Struct 2010;43:1383–96. [3] Moghaddam H, Samadi M, Mohebbi S. RC members strengthening by lateral post-tensioning of external metal strips. In: Int. Earthq. Symp. KOCAEU 2007, 1995. p. 454–62. [4] Moghaddam H, Pilakoutas K, Samadi M, Mohebbi S. Behavior and modeling of concrete columns confined by external post-tensioned strips. Struct Congr 2008:1–10. [5] Saadatmanesh H, Ehsani MR, Li MW. Strength and ductility of concrete members confined by external post-tensioned strips. In: 4th Natl. Conf. Civ. Eng., 2008. [6] Frangou M, Pilakoutas K, Dritsos S. Structural repair/strengthening of RC columns. Constr Build Mater 1995;9:259–66.
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