In this experimental study, six post-tensioned light weight concrete (LWC) continuous one-way slabs were tested in the following manner: the flexural behaviors of the members were compared with the calculations from the existing standards. The test also examined the effect of prestressing in tendons and proper prestress conditions to reduce the deflection and crack width, and to enhance the flexural capacity and ductility of LWC members. Flexural capacity and stress increments in unbonded tendons of the specimens were compared with those of the simply supported normal and the lightweight concrete members. The suggested safety limit from the American Concrete Institute (ACI) regulation on the maximum capacity and the stress incremental in unbonded tendons were also compared with the test results under simple and continuous supporting conditions.
1 Introduction
Due to many well-known advantageous aspects, researchers have investigated the possibility of light weight concrete (LWC) as a replacement for normal weight concrete (NWC) for structural components. A comparative study on the fracture properties of high-strength concrete with normal aggregate and lightweight aggregate was conducted (Tang et al. 2008). Through the study, the critical stress intensity factor and critical crack tip opening displacement for the double-parameters model and the fracture energy for a fictitious crack model were examined. Since LWC possesses thermal insulation capacity, it can enhance energy consumption efficiency for commercial and residential heating and cooling systems (Chandra and Berntsson 2003; Kayali 2008). For example, using LWC as a structural material may reduce the overall energy consumption of buildings (Yang 2010). Consequently, LWC has been gathering attention as a potential construction material to minimize long-term carbon dioxide (CO2) emissions. On one hand, LWC has shown disadvantages in structural performance due to its relatively low Young’s modulus and tensile resistance capacity causing larger deformations and crack width in concrete. By the way, prestressing is highly effective in minimizing cracks and controlling deflections of concrete flexural members (Collins and Mitchell 1991). Introducing a prestressing force to the LWC flexural members can compensate for the reduced serviceability of the members, producing considerable synergistic advantages in structural and environmental aspects. Therefore, a prestressed concrete system with LWC is recognized as a decent solution for creating a suitable structure that can decrease the consumption of the natural resources and reduction in the enormous amount of CO2 emitted from construction and residual environments (Chandra and Berntsson 2003; Oh and Choi 2004).
Most of the research using prestressed concrete flexural members has been conducted with normal weight concrete (NWC) (Warwaruk et al. 1962; Harajli and Kanj 1990; Campbell and Chouinard, 1991; Chakrabrti 1995; Mainsekar and Senthil 2006; Lou and Xiang 2007; Ellobody and Bailey 2008; Cai et al. 2009). Yang and Mun (2013) initiated experimental studies on the flexural capacity of post-tensioned LWC beams. They found the stress increase in the unbonded strands (Δfps) at the ultimate strength of the post-tensioned LWC beam was higher than that of the post-tensioned NWC beams under same reinforcing index values. This indicates that the ACI 318-11 provisions for Δfps would be unconservative for post-tensioned LWC members.
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Currently, most codes and recommendations, including American Concrete Institute standards (ACI Committee 318 2011), evaluate the flexural behaviors of the post-tensioned concrete members based on studies with NWC; therefore, there could be a question about how to evaluate the flexural behavior of post-tensioned LWC members. As it is well known, LWC has lower stiffness than NWC. LWC also shows many different material properties from NWC including creep and drying shrinkage deformation. The flexural behaviors of post-tensioned LWC members are distinguished from those of NWC in bending strength, ductility and stress in unbonded strands.
One of the most important factors in the design of post-tensioned flexural members is to evaluate the stress incremental in unbonded tendons to which the sectional strain compatibility condition is not applicable. The stress increase in unbonded tendons is suggested by the member compatibility condition based upon the test results using simply supported NWC beams (ACI Committee 318 2011; Yang et al. 2013). However, when it comes to the LWC, insufficient data have been provided to assure the safety of the existing models and current design standards. For safe design of post-tensioned LWC beams, the effects of variables on the stress incremental in unbonded tendons must be studied under both simple and continuous support conditions. Therefore, the bond reduction coefficients of plastic hinge length proposed to evaluate stress increase in unbonded tendon need to be adjusted in LWC members because the proposed equations are empirically derived using limited test data from the NWC members. However, available test results and information are very rare for LWC flexural members.
In this experimental study, six post-tensioned LWC continuous one-way slabs were tested. For each test parameter, the crack developments, failure modes, load–displacement relation, and load-tendon stress relationship were measured. The ultimate stress and stress incremental of the tendons were compared to the calculation results using the existing standards; ACI 318-11, AASHTO (1998) and CAN3-A23-M94. The stress increments of the tendons were also compared to the previous NWC test data generated by Lim et al. (1999). The flexural behaviors of the members were compared using calculations derived from the existing standards (ACI, AASHTO, and CAN3). The tests also examined the effect of prestressing in tendons and proper prestress procedures to reduce the deflection and crack width, and to enhance the flexural capacity and ductility of LWC members. Flexural capacity and stress increment in unbonded tendons of the specimens were compared to those of the simply supported normal and the LWC members. The suggested safety limit from the ACI regulation on the maximum capacity and the stress incremental in unbonded tendons were also compared to the test results under simple and continuous supporting conditions.
1.1 Significance of Research
This research provides meaningful test results on the behaviors of the post-tensioned continuous lightweight slabs. Here, the applicability of the stress incremental equations for unbonded tendons suggested by design standards was evaluated. The stress increments in unbonded tendons were also reviewed under simple and continuous support conditions. Authors believe the results can provide basic data for development of a future design manual of post-tensioned continuous lightweight concrete slabs.
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2 Experimental Program
2.1 Specimens
Six LWC one-way continuous slab specimens post-tensioned with unbonded tendons were prepared for flexural tests, as shown in Table 1. The nomenclature for each specimen is shown in Fig. 1. Each specimen had three supports with two spans. Two critical parameters affecting the stress increase in unbonded tendons were considered in experiments: span-to-effective tendon depth ratio (L/dp) in Group 1; and steel ratio in member section (ρs) in Group 2.
Table 1
Specimen details (unit: mm).
Group
Specimen
Load Type
b
h
L (one span)
L/dp
PPR
ρs
ρp
fpe/fpu
e
1
S-L/dp-25
Uniform
600
125
2400
25
0.792
0.00247
0.00206
0.6
33.1
S-L/dp-35
3400
35
S-L/dp-45
4300
45
2
S-PPR-0.5
0.884
0.00123
33.2
S-PPR-1.0
0.792
0.00247
33.1
S-PPR-1.5
0.718
0.00370
32.9
b member width, h member height, e eccentricity of prestressing strands, ρs ratio of steel, ρp ratio of tendon, dp effective depth of prestressing strands.
PPR (partial prestressing ratio) = Apfpe/(Apfpe + Asfy), where fpe effective prestress, Ap sectional area of prestressing steel, fy yield stress of steel, As sectional area of steel.
Fig. 1
Specimen nomenclature.
×
As known well from the study by Mojtahedi and Gamble (1978), L/dp of the concrete member can affect the stress in tendons. ACI 318 equation (18-4) overestimates Δfps in NWC members when L/dp is greater than 35. In this study, L/dp varies from 25, 35, and 45 to evaluate the stress changes in tendons. It was Warwaruk et al. (1962) who conducted an experiment about the loading pattern for the first time. Harajli and Kanj (1990) found the length of the plastic hinges of beams, as well as the stress in tendons, can be changed according to the loading patterns. When it comes to continuous slabs, a uniform loading method has been suggested for ideal member behaviors (Burns et al. 1978), so the use of uniformly distributed loading was applied in this test.
Group 1 consists of three continuous one-way slabs receiving uniformly distributed load whose L/dp ranges from 25, 35 and 45. The ACI 318-11 requires at least 0.4 % reinforcement of the cross section between the flexural tension face and center of gravity of gross section (Act). Three slabs in Group 2 receiving uniformly distributed load have three different ρs’s with the same span and the L/dp; half of the ACI requirement (S-PPR-0.5), same with the requirement (S-PPR-1.0), and 50 % more than the requirement (SPPR-1.5). In all specimens, identical three-strand tendons with 2050 MPa tensile strength were used. D10 and D6 rebars were used as reinforcing steel. The effective prestress of tendon (fpe) was 60 % of its ultimate stress (fpu). The concrete compressive strength was 35 MPa. See Figs. 2 and 3 for their configurations.
Fig. 2
Test setup a actuator and specimen b loading points and support c load cell and LVDT.
Fig. 3
Loading points and supports of a specimen S-L/dp-25, b specimen S-L/dp-35, c specimen S-L/dp-45 and specimen S-PPR.
×
×
The mixtures of LWC for the test are listed in Table 2, and the material properties of lightweight aggregates are listed in Table 3. Test results of lightweight concrete mixture are shown in Table 4. The designed compressive strength of the ready-mixed concrete using lightweight aggregates was 35 MPa for all specimens. Artificially expanded clay granules with maximum sizes of 20 and 5 mm were used for lightweight coarse and lightweight fine aggregates, respectively. The lightweight fine aggregates were replaced with local natural sand by as much as 30 % by volume in order to control the continuous grading. The average dry density of the mixed LWC was approximately 1770 kg/m3. The mechanical properties of the steel reinforcing bars are listed in Table 5. The tensile strength and equivalent yield strength (fpy) of the low relaxation three-wire mono-strand were 2050 and 1852 MPa, respectively. The equivalent yield strength of the strand was calculated using measured nonlinear stress–strain curves according to ASTM A 416 (American Society for Testing and Materials 1996). The yield strengths of the mild reinforcing bars with diameters of 10 and 6 mm were 446 and 475 MPa, respectively.
Table 2
Mixture proportions of lightweight concrete.
W/C (%)
VG
Unit weight (kg/m3)
Water
Cement
Light fine aggregate
Sand
Light coarse aggregate
37
0.573
181
542
311
230
554
W/C water-cement ratio, VG apparent density ratio of coarse aggregate.
Table 3
Material properties of lightweight aggregates.
Aggregates
Max. size (mm)
Specific gravity
Unit weight (kg/m3)
Fineness modulus
Absorption (%)
Void ratio (%)
1 day
14 days
Coarse
19
1.80
931
3.365
11.8
14.29
48
Fine
4
1.80
1105
1.838
15.9
18.53
39
2
1.30
978
2.458
19.1
24.3
25
Table 4
Lightweight concrete mixture test results.
No.
Slump (mm)
Compressive strength (MPa)
Splitting tensile strength
Modulus of rupture
Modulus of elasticity (MPa)
1 day
3 days
7 days
28 days
56 days
92 days
\( f_{sp} \)
(MPa)
\( \frac{{f_{sp} }}{{\sqrt {f_{ck} } }} \)
\( f_{r} \)
(MPa)
\( \frac{{f_{r} }}{{\sqrt {f_{ck} } }} \)
\( E_{c} \)
1
220
4.9
15.1
30.4
36.7
38.7
39.3
3.19
0.53
2.81
0.46
11,614
2
230
4.7
13.5
24.1
29.2
30.5
31.9
2.62
0.49
3.15
0.58
13,442
3
242
5.2
16.7
29.4
35.2
38.5
39.3
2.53
0.47
2.91
0.49
11,280
Table 5
Material properties of steels.
Area (mm2)
Yield strain
Yield strength (MPa)
Tensile strength (MPa)
Young’s modulus (MPa)
Elongation (%)
Anchoring plate
–
–
402
480
–
–
Tendon (3 strands)
19.89
0.01000
1852
2050
201,319
5.7
Mild bar
D10
71.00
0.00279
446
639
214,976
18.4
D6
31.60
0.00282
475
500
171,121
3.9
2.2 Test Procedure and Measurement
Each continuous one-way slab specimen was supported on hinges at both ends and on a roller at the center. The uniform load was applied by universal testing machine (UTM) at a rate of 2.5 mm per minute. Linear variable differential transducers (LVDTs) were installed beneath the specimens at the loading points to measure the vertical deflection (Fig. 2). The 200 kN capacity load cells were installed on both ends of specimens to trace the stress incremental in unbonded tendons. The loading points and supports of each specimen are described in Fig. 3 and the section details are shown in Fig. 4. The crack width was measured from where the first cracks appeared until the reinforcing steels yielded. Electrical resistance strain gages were attached to the surface of the concrete and the steel to check how the strain changes, especially when concrete reached its ultimate strain (0.003). Concrete strain gages were installed on both compressive and tensile area of the center and the edges of specimens. Wire strain gages were installed on rebars at intervals of d/2. All data from the UTM, load cells, and gages were collected into a data logger and saved in a computer. Through the process, the following information was obtained: crack development pattern and failure mode; load–displacement relationship; load-reaction relationship; load-tendon stress; flexural capacity; flexural ductility; and curvature-prestress loss.
Fig. 4
Section details and arrangement of reinforcing bars in specimens.
×
3 Test Results
3.1 Crack Propagation and Failure Mode
Crack propagation patterns were marked in Fig. 5. No diagonal crack was found; that means in this test, that flexural behavior was dominant. The maximum moment occurred at the center supports of the slabs; therefore, cracks were initiated at the upper parts of the center supports (negative moment region) and then developed at the lower parts of mid-spans (positive moment region). Due to the reinforcing steels, the cracks maintained the same intervals to each other, propagating towards the middle of the spans. Upon reaching maximum loading, cracks also achieved their maximum width at the center of the spans, while cracks at the supporting areas stopped developing prior to that stage. When the simultaneous compressive fracture and dramatic flexural strength reduction was achieved the test was terminated. The crack happened at the same position of the members regardless of the L/dp. The major cracks propagated until the peak loading was reached and then compressive fractures were triggered. With the higher L/dp, the cracks distributed more broadly. In all specimens, only a little more crack propagations were observed after the peak loading. In Group 2, specimen S-PPR-0.5 reinforced less than S-PPR-1.5 showed fewer number of cracks although their width were bigger. That means specimens with more reinforcing steels are advantageous in control of crack width, although more fine cracks are expected.
Fig. 5
Crack development of each group.
×
3.2 Load–Deflection Relationship
In Group 1, as the L/dp increased from 25 to 45, the ultimate load was reduced by 44 %, while the deflection at the ultimate loads was increased (Table 6). Initial crack strength (Pcr) and yield strength (Py) also dropped as the L/dp increased. As shown in Fig. 6a, as L/dp increased, the maximum flexural strength of the slabs decreased and the ductility increased. In Group 2, as shown in Fig. 6b, specimen S-PPR-1.0 showed excellent ductility while specimen S-PPR-0.5 reinforced with the least number of reinforcement among Group 2 specimens showed compressive fracture after the reinforcement yielding. Specimen S-PPR-1.5 which is reinforced with 50 % more steel than required was less ductile than S-PPR-1.0 with 17 % higher ultimate load.
Table 6
Test results.
Specimen
Pcr (kN)
Py (kN)
Pn (kN)
Vn (kN)
Δcr (mm)
Δy (mm)
Δn (mm)
fps (MPa)
Δ fps (MPa)
Δ fps−ACI (MPa)
Δ fps−EXP/Δ fps−ACI
Pn−ACI (kN m)
Pn−EXP/Pn−ACI
Mcr (kN m)
ηcr
ω
Mn (kN m)
ηn
Mn−EXP/Mn−ACI
Mid
Edge
Mid
Edge
Mid
Edge
Group 1
S-L/dp-25
61.7
65.7
80.9
89.8
254.5
77.2
50.1
5.6
13.0
48.8
1613
358
256
1.40
214.5
1.19
14.77
0.0401
0.114
26.98
0.0732
1.35
S-L/dp-35
23.5
46.1
37.8
64.2
155.5
48.3
29.4
11.8
31.1
85.3
1788
505
256
1.97
155.9
1.00
14.68
0.0398
0.123
26.29
0.0713
1.32
S-L/dp-45
14.7
30.4
46.6
43.3
111.1
33.2
22.3
11.6
36.8
165.8
1669
430
132
3.25
120.7
0.92
12.25
0.0332
0.116
21.68
0.0588
1.22
Group 2
S-PPR-0.5
14.7
28.4
25.7
24.4
75.9
23.9
14.1
29.1
14.0
95.8
1540
285
132
2.16
97.5
0.78
11.46
0.0311
0.095
14.68
0.0398
0.97
S-PPR-1.0
14.7
30.4
46.6
43.3
111.1
33.2
22.3
11.6
36.8
165.8
1669
430
132
3.25
120.7
0.92
12.25
0.0332
0.116
21.68
0.0588
1.22
S-PPR-1.5
25.5
33.3
34.1
55.0
129.9
40.9
24.0
16.7
57.5
113.6
1655
400
132
3.03
131.8
0.99
13.43
0.0365
0.130
26.82
0.0728
1.32
Pcr cracking load, Py yielding load, Pn ultimate load, Vn force at failed span, Δcr, Δy, Δn deflection at the first flexural crack, at yielding of mild longitudinal tensile reinforcement, and at the ultimate state, respectively, fps, Δ fps stress of prestressing strands and its increase, Pn−ACI ultimate load predicted by ACI, Pn(ExP) ultimate load by experiment, ηcr cracking moment capcity (=Mcr/f′c·bw·h2), ηn ultimate moment capcity (=Mn/f′c·bw·h2), ω reinforcing index \( \left( { = \frac{{A_{p} f_{ps} + A_{s} f_{y} }}{{bd_{e} f_{c} '}}} \right) \).
Fig. 6
Load-deflection relationship for each group.
×
3.3 Stress of Unbonded Prestressing Tendons
The relationship of the load and the unbonded prestressing tendon stress was almost identical to that of the load–deflection. Even after reaching the ultimate loading, the tendon stresses increased continuously to bear the tension stress until the member failure. Figure 7a shows the effect of the L/dp on the load-tendon stress relationship. As the L/dp increased, the ultimate stress in tendons decreased. Figure 7b shows the effects of the ρs on the load-tendon stress relationship. All specimens in Group 2 showed similar stress increments until the initial crack happened. The maximum stress of S-PPR-1.0 was higher than S-PPR-0.5, even higher than S-PPR-1.5. The measured stress increase in unbonded tendons was higher than that from ACI and AASHTO (Table 7).
Fig. 7
Load-tendon stress relationship for each group.
Table 7
Comparison of experiments and standards for ultimate stress increment of unbonded tendons.
The normalized cracking capacities, \( \eta_{cr} \) =Mcr/(f′c·bw·h2) and the ultimate moment capacities, \( \eta_{n} \) =Mn/(f′c·bw·h2) of the specimens are listed in Table 6. The \( \eta_{cr} \) decreased as the L/dp ratio increased in Group 1, and a higher \( \eta_{n} \) was developed with an L/dp ratio of 25 than those with an L/dp ratio of 35 or 45. In Group 2, \( \eta_{n} \) increased in proportion to the ρs.
In Fig. 7, the ultimate moment of the specimens, (Mn)Exp is compared with the corresponding value predicted by the ACI 318-11 design procedure, (Mn)Pre. The safety of the ACI 318-11 provision is significantly dependent on the reinforcing index (ω) and the loading type, but it is independent of the L/dp ratio. However, a moment capacity reduction was observed in the S-L/dp-45 of Group 1 (Fig. 8a). When ρs is half of the requirement, the (Mn)Exp/(Mn)Pre is less than unit (Fig. 8b).
Fig. 8
Comparisons of measured and ACI318-11 predicted ultimate moment capacities.
×
4 Comparison with Standards
In Table 7, the stress in prestressing steel (fps) and its increment (Δfps) of each specimen are listed. Also, the experimental results were compared to the standards.
The mean and standard deviation of the ratios of the measured and predicted moment capacities of the post-tensioned NWC beams are 1.05 and 0.22, respectively (Yang et al. 2013). Hence, the ACI 318-11 procedure for predicting the Mn value of post-tensioned flexural members can be considered conservative for LWC. In other words, the ACI 318 design equations generally underestimated Δfps. The Δfps predictions from ACI 318 are as conservative as in NWC. In addition the predictions obtained from the AASHTO 1998 were in better agreement with the test results than ACI 318-11, showing that the mean, standard deviation, and coefficient of variation of the ratios between measured and predicted stress increases (Δfps) are 1.70, 0.53, and 0.31, respectively. The predictions obtained from CAN 3 were the least conservative among three standards showing that the mean, standard deviation, and coefficient of variation of the ratios between measured and predicted stress increases (Δfps) are 1.10, 0.23, and 0.21, respectively. The ratios of measured to predicted incremental stresses are plotted against ω accompanying with the NWC test results by Lim et al. (1999) in Fig. 9.
Fig. 9
Comparisons of measured and predictions for Δfps.
×
In all cases, \( {{\left( {\Delta f_{ps} } \right)_{exp } } \mathord{\left/ {\vphantom {{\left( {\Delta f_{ps} } \right)_{\exp } } {\left( {\Delta f_{ps} } \right)_{pre} }}} \right. \kern-0pt} {\left( {\Delta f_{ps} } \right)_{pre} }} \) for LWC is less than that for NWC. Note that \( {{\left( {\Delta f_{ps} } \right)_{exp } } \mathord{\left/ {\vphantom {{\left( {\Delta f_{ps} } \right)_{\exp } } {\left( {\Delta f_{ps} } \right)_{pre} }}} \right. \kern-0pt} {\left( {\Delta f_{ps} } \right)_{pre} }} \) of specimen S-L/dp = 25, S-L/dp = 45, and S-PPR-0.5 in CAN 3 are less than one, while all NWC data are more than one.
5 Conclusions
To evaluate the flexural capacity and the ductility of post-tensioned LWC continuous slabs, six specimens were tested and compared with the design standards. Through the test the followings have been found: (1) The initial crack happened at the center of negative moment and then developed at the positive moment areas on both sides simultaneously; (2) As the steel ratio in member section (ρs) increased, the width of the crack decreased while the number of micro cracks increased. Also the maximum capacity increased while the ductility decreased; (3) As the span-to-effective tendon depth ratio (L/dp) increased, the maximum strength (Pu) decreased. The initial crack load (Pcr) and the yielding capacity (Py) also decreased while the deflection increased with L/dp growth; (4) As the quantity of minimum required rebars increased, the initial crack load, yielding capacity, and maximum strength increased; (5) Even after reaching the ultimate stress of flexural members, the stress in the tendons continuously increased sharing the tensile stresses. The stress increases stopped when the flexural member finally ruptured; (6) As the L/dp increased, the stresses in tendons decreased. That means L/dp is a critical factor affecting the tendon stresses; (7) In all specimens, before the initial crack, no stress change was observed in the tendons. After initial crack happened, the tendon stresses increased gradually as the applied load was increased; (8) With fewer rebars, the stress-increasing rate in the tendons was relatively high. The ACI standard evaluated the stress increment conservatively.
The expected stress increase in unbonded tendon especially by ACI and AASHTO were less than the test results in all specimens. In other words, the normalized flexural capacity of the post-tensioned LWC slabs was higher than the predictions based on the ACI code provision. The differences were not negligible quantity so it may cause overdesign.
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