Journal of Building Engineering 7 (2016) 133–142
`
`Contents lists available at ScienceDirect
`
`Journal of Building Engineering
`
`journal homepage: www.elsevier.com/locate/jobe
`
`Prestress losses of double-tee girders cast with lightweight self-
`consolidating concrete
`Dustin B. Ward a, Canh N. Dang b, Royce W. Floyd c, W. Micah Hale b,n
`a B & F Engineering, 928 Airport Rd, Hot Springs, AR 71913, USA
`b University of Arkansas, Department of Civil Engineering, 4190 Bell Engineering Center Fayetteville, AR 72701, USA
`c University of Oklahoma, School of Civil Engineering and Environmental Science, 202 W. Boyd St., Norman, OK 73019, USA
`
`a r t i c l e i n f o
`
`a b s t r a c t
`
`Article history:
`Received 30 July 2015
`Received in revised form
`6 June 2016
`Accepted 6 June 2016
`Available online 7 June 2016
`
`Keywords:
`Pretensioned concrete
`Prestress loss
`Creep
`Shrinkage
`Elastic shortening
`Lightweight concrete
`Self-consolidating concrete
`
`1.
`
`Introduction
`
`Prestress loss estimation is a necessary and important procedure in design of pretensioned concrete
`girders. The current specifications were developed from the experimental results of normal-weight
`concrete that are possibly inaccurate in estimating prestress losses for members cast with lightweight
`self-consolidating concrete (SCC). This study measures prestress losses for two full-scale double-tee
`girders cast with sand-lightweight SCC. Expanded clay, which had a specific gravity of 1.25 and an ab-
`sorption capacity of 15%, was used as the lightweight coarse aggregate for the designed concrete mixture.
`The prestress losses were measured for 26 days and at 83 days using vibrating wire strain gauges at-
`tached to prestressing strands, after which the tested girders were then used in the construction of a
`parking garage. The experimental results indicated that the modulus of elasticity of lightweight SCC can
`be predicted using a correction factor of 0.99. The measured elastic-shortening loss was slightly lower
`than the predicted values. The predicted time-dependent losses, however, significantly over-estimated
`the measured results, which yielded the over-estimation of total prestress losses that varied from 86% to
`153%.
`
`& 2016 Elsevier Ltd. All rights reserved.
`
`Pretensioned concrete members are widely used in the con-
`struction of buildings, parking garages, and bridges. Prestress
`losses occur throughout the life of pretensioned concrete mem-
`bers, and have significant impact on the design for long-term ef-
`fects [1–4]. In the design period, structural engineers rely on the
`existing empirical
`formulas to calculate prestress losses. The
`variability in predicting prestress losses directly causes the in-
`accuracy in estimating the camber and long-term deflection of
`pretensioned concrete members. At erection, the under- or over-
`estimation of camber increases the possibility of construction-re-
`lated problems, which increases the construction cost, delays the
`project, or affects the structural performance. The inaccuracy in
`predicting the long-term deflection reduces the riding quality if
`the deflection is over-estimated, or rises the public concern and
`affects the structural durability if
`the deflection is under-
`estimated.
`The use of self-consolidating concrete (SCC) for pretensioned
`concrete members
`is
`advantageous when compared to
`
`n Corresponding author.
`E-mail address: micah@uark.edu (W.M. Hale).
`
`http://dx.doi.org/10.1016/j.jobe.2016.06.004
`2352-7102/& 2016 Elsevier Ltd. All rights reserved.
`
`conventional or vibrated concrete. The fresh SCC has high flow-
`ability and deformability, so it can flow through narrow regions
`and fill the formwork by its self-weight without segregation or
`bleeding. This feature particularly benefits at the anchorage zone
`of pretensioned concrete members that normally contain con-
`gested reinforcement, or thin elements like double-tee girders that
`are widely used in the United States [5]. The use of lightweight
`aggregates in SCC offers further advantages for the concrete
`technology [6–8]. First, the use of lightweight concrete can reduce
`the self-weight of structures up to 20%, which decreases the di-
`mensions of concrete members and vertical load on foundations
`[6,9]. Second, internal curing techniques can be employed for
`lightweight concrete to enhance the durability and resilience of
`concrete structures [10–14]. In summary, the use of lightweight
`SCC not only furthers the advantages of SCC but also improves the
`long-term performance for pretensioned concrete members.
`The use of lightweight SCC in pretensioned concrete members
`may present several challenges. First, lightweight SCC contains a
`high volume of paste, which may increase concrete shrinkage and
`affect time-dependent losses [15]. The high flowability of light-
`weight SCC may also reduce the concrete stiffness at the interface
`of prestressing strands and concrete, which consequently weakens
`the bond between the two materials [15–23]. Second, the reduced
`stiffness of lightweight aggregates decreases concrete stiffness,
`
`Metromont Ex-1013, p.1
`
`

`

`134
`
`D.B. Ward et al. / Journal of Building Engineering 7 (2016) 133–142
`
`which affects instantaneous and time-dependent losses [24]. Fi-
`nally, the absorption capacity of lightweight aggregates is greater
`than normal-weight aggregates, which can reduce concrete
`shrinkage due to the effect of internal curing. The contribution of
`these factors can affect the prediction of prestressed losses for
`pretensioned concrete members cast with lightweight SCC.
`
`2. Literature review
`
`A trend in over-estimating prestress losses for pretensioned
`concrete girders cast with high performance lightweight concrete
`has been recognized. Cousins and Nassar [40] measured prestress
`losses for two AASHTO Type IV girders for 9 months. The experi-
`mental results indicated the total predicted loss using the PCI [34]
`and the ACI 209 [36] specification over-estimates the measured
`values by 9% and 51%, respectively. Lopez and Kahn [41] stated that
`AASHTO-Refined method [26] over-estimates the measured pres-
`tress losses by 40% and 80% for two AASHTO Type II girders, which
`are measured for 4 months. The over-estimation was about 20%
`and 40% when the ACI 209 [36] is used for predicting prestress
`losses.
`In summary, a number of concerns regarding the use of light-
`weight SCC for pretensioned concrete members have been de-
`termined. The current specifications, in fact, were primarily de-
`veloped for normal-weight concrete. Researchers and engineers
`generally extend these specifications for lightweight concrete. This
`practice leads to a high variability in estimating prestress losses for
`pretensioned concrete members. This project examines the ap-
`plicability of using the existing specifications in predicting pres-
`tress losses for two full-scale double-tee girders cast with light-
`weight SCC. In the experimental investigation, the prestress losses
`were measured continuously for 26 days and at 83 days, while the
`girders were stored at the precast facility. The measured in-
`stantaneous and time-dependent prestress losses were compared
`to the predicted values in the analytical
`investigation, and a
`number of assessments and recommendations regarding predict-
`ing the prestress losses were provided in the remaining sections of
`the paper.
`
`3. Experimental investigation
`
`3.1. Girder fabrication
`
`This project monitored prestress losses for two out of several
`full-scale double-tee girders, which were cast at the Coreslab
`Structures, Arkansas, USA. The girders were used to construct a
`parking garage. Both girders had an identical depth of 660 mm.
`These girders were identified as DT-A and DT-B, which had a
`length of 9.72 m and 17.85 m, respectively. Girder DT-A consisted
`of ten fully bonded, 12.7-mm, Grade 1860, low-relaxation pre-
`stressing strands that were tensioned to 0.65fpu (where fpu is the
`ultimate strand strength) or 1212 MPa. All the prestressing strands
`were straight, and Fig. 1 shows the strand pattern of girder DT-A.
`Girder DT-B used an identical number of prestressing strands and
`the prestress level as girder DT-A, but the prestressing strands
`were depressed in the midspan. Figs. 2 and 3 show the strand
`pattern at the ends and midspan of girder DT-B, respectively.
`These girders were two of several girders cast in the 152-m pre-
`stressing bed.
`Vibrating wire strain gauges (VWSGs) were embedded in the
`girders to measure strains caused by prestress losses. Each girder
`included four VWSGs in which two VWSGs were placed at or near
`the center of gravity of the prestressing strands, and the other
`VWSGs were placed at the location where the stems meet the
`flange for each girder. For girder DT-A, two VWSGs were placed at
`the center of gravity of the prestressing strands of 175 mm, and
`the others were placed at a distance of 655 mm from the bottom
`fiber of the girder. Fig. 1 illustrates the placement of these VWSGs.
`For girder DT-B, the first two VWSG were offset 0.61 m from the
`midspan to avoid damage from the depression equipment. These
`VWSGs were placed at the center of gravity of the prestressing
`strands of 75 mm. The others VWSGs were placed at a distance of
`655 mm and 665 mm from the bottom fiber of the girder as shown
`in Fig. 3.
`
`The modulus of elasticity (MOE) of concrete is necessary for
`estimating the instantaneous loss or elastic-shortening loss. The
`MOE of lightweight concrete may be lower than that of compar-
`able, normal-weight concrete since the stiffness of lightweight
`aggregates is generally lower than that of normal-weight ag-
`gregates [25]. The MOE of normal-weight concrete can be pre-
`dicted using Eq. (1). The American Concrete Institute – Building
`Code Requirements for Structural Concrete and Commentary (herein
`referred as ACI 318-14) [1] incorporates a modification factor of
`0.85 for sand-lightweight concrete and 0.75 for all-lightweight
`concrete. AASHTO LRFD Bridge Design Specifications (herein re-
`ferred as AASHTO) [26], however, uses a correction factor K1 to
`consider the effect of aggregate stiffness on the MOE of concrete.
`Cousins et al. [6] determined that a factor K1 of 1.0 is appropriate
`for predicting the MOE of sand-lightweight concrete. In other
`words, the use of lightweight coarse aggregates has minimal effect
`on the MOE.
`=
`
`
`fand ’ in MPa
`c
`
`)
`
`( )
`1
`
`E
`c
`
`0.043
`
`1.5
`w f
`c
`
`′
`c
`
`(
`
`w
`c
`
`in
`
`3
`
`kg m/
`
`where Ec is the modulus of elasticity of concrete; wc is the concrete
`unit weight; f’c is concrete compressive strength.
`Concrete creep and shrinkage are important factors affecting
`the time-dependent losses [27,28]. Creep and shrinkage of light-
`weight concrete are different from those of comparable, normal-
`weight concrete because of the difference in aggregate stiffness
`and absorption capacity [29–31]. The aggregate stiffness is a main
`factor affecting concrete creep, while the aggregate absorption
`capacity and amount of paste affect concrete shrinkage [32,33].
`Technically, concrete creep and shrinkage of normal-weight con-
`crete can be predicted by empirical models proposed by Precast/
`Prestressed Concrete Institute (PCI) [34], Model Code 2010 [35],
`ACI 209 [36], and AASHTO [26]. However, there is little to no re-
`commendation regarding a suitable model to predict creep and
`shrinkage for lightweight SCC [6]. Therefore, more research is
`needed to evaluate the applicability of using existing empirical
`formulas, which were developed based on the experimental re-
`sults of normal-weight concrete, to predict the instantaneous and
`time-dependent prestress losses for pretensioned concrete mem-
`bers cast with lightweight SCC.
`A number of studies have been conducted to evaluate prestress
`losses of pretensioned concrete girders using lightweight concrete.
`Different conclusions have been made regarding the accuracy of
`using existing formulas in predicting prestress losses of preten-
`sioned concrete members. Holste et al. [30] measured prestress
`losses for inverted-tee beams cast with lightweight SCC for one
`year. The total measured loss is 490 MPa which is 20% greater than
`the predicted value of 407 MPa using AASHTO specifications [37].
`Dymond [38], however, presented a contrary conclusion when
`evaluating prestress losses over a 4-month period for a full-scale
`19.8-m long PCBT-53 girder. The total measured loss is 179 MPa,
`which is 30% lower than the total predicted value of 255 MPa
`using AASHTO-Refined method [26]. Ziehl et al. [39] had a similar
`conclusion to Dymond when measuring prestress losses of thee
`AASHTO Type III girders. The total measured loss is 207 MPa,
`which is 21% lower than the predicted value of 262 MPa.
`
`Metromont Ex-1013, p.2
`
`

`

`D.B. Ward et al. / Journal of Building Engineering 7 (2016) 133–142
`
`135
`
`Fig. 1. DT-A cross section at midspan* and at ends. (Note: *¼vibrating strain gauges were only attached in the midspan).
`
`Fig. 2. DT-B cross section at ends.
`
`Fig. 3. DT-B cross section at midspan*. (Note: *¼vibrating strain gauges were offset 0.61 m from the midspan).
`
`All VWSGs were connected to a data-acquisition system. The
`strain and temperature of each VWSG were continuously mon-
`itored at 3-min intervals after transfer and at 15-min intervals
`when the girders were placed in storage location. The VWSG
`readings require temperature correction. The results presented in
`the following sections were the corrected data, which were cal-
`culated from the calibration temperature provided by the manu-
`facturer and the measured temperature of each VWSG.
`
`3.2. Concrete mixture proportion, placement, and testing
`
`The girders DT-A and DT-B were cast using the same light-
`weight SCC mixture. A Type I portland cement and normal weight
`river sand were used in the concrete. The lightweight coarse ag-
`gregate consisted of expanded clay aggregate that had a specific
`gravity of 1.25 and an absorption capacity of 15%. Table 1 shows
`the concrete mixture proportion. The fresh concrete properties
`
`Metromont Ex-1013, p.3
`
`

`

`136
`
`D.B. Ward et al. / Journal of Building Engineering 7 (2016) 133–142
`
`Table 1
`Concrete mixture proportion and fresh concrete
`properties.
`
`Material
`
`Parameter
`
`Cement (kg/m3)
`469
`Normal weight, fine aggregate (kg/m3) 762
`Lightweight, coarse aggregate (kg/m3)
`438
`Water (kg/m3)
`178
`Water/Cement ratio
`0.38
`
`Concrete properties
`Slump flow (mm)
`Visual Stability Index
`Unit weight (kg/m3)
`Air content (%)
`
`780
`1.5
`1922
`0.5
`
`were measured from a sample taken prior to casting the double-
`tee girders. Table 1 also summarizes the measured slump flow and
`Visual Stability Index [42], unit weight [43], and air content [44].
`The slump flow and Visual Stability Index were slightly greater
`than the recommended thresholds of 730 mm and 1.0, respectively
`[45]. However, there were no signs of segregation in the girders
`during casting or in the cylinders after measuring compressive
`strength.
`The concrete was batched in a central batch plant at the precast
`facility and transported to the formwork in ready-mix trucks. The
`concrete was first placed in stems of the girders and then the
`flanges. After placement, a tarp was placed over the girders to
`prevent rapid moisture loss. The strands were detensioned 16 h
`after casting. In the detensioning process, each strand was flame
`cut simultaneously at the ends of the prestressing bed. After the
`ten strands were cut at the bed ends, individual girders were then
`detensioned using the same procedure. The girders were then
`removed from the bed, inspected, and moved to the storage yard
`at the precast facility until transported to the construction site.
`
`4. Analytical investigation
`
`An in-house computer program was used to calculate prestress
`losses according to three methods: Zia et al. [46] study, AASHTO-
`Approximate method [26], and AASHTO-Refined method [26]. The
`AASHTO-Approximate and the AASHTO-Refined methods have the
`same procedures to estimate elastic shortening loss, but the pro-
`cedures used to estimate term-dependent losses are different. The
`program includes three parts for: (1) input, (2) calculation, and (3)
`results. Table 2 shows parameters necessary for the input part. The
`calculation part computes related equations of the mentioned
`methods. The results part presents intermediate parameters as
`summarized in Table 3 and results of prestress losses. This com-
`puter program has been verified by several studies [9,47–49].
`
`5. Experimental results and discussion
`
`5.1. Concrete properties
`
`The hardened concrete properties were measured from a
`sample taken from a diverted stream of concrete during the pla-
`cement of each double-tee girder. The specimens were cured with
`the double-tee girders until testing. Compressive strength [50] and
`modulus of elasticity [51] were measured at strand release (16 h),
`and at 7, 28, and 90 days of age. Three specimens were tested for
`each concrete property at a specific age.
`Table 4 shows the concrete compressive strengths. At release,
`
`Table 2
`Properties of girders DT-A and DT-B.
`
`Properties
`
`DT-A
`
`DT-B
`
`Gross Section Properties
`Ag (mm2)
`Ig (mm4)
`Exposed perimeter (mm)
`V/S (mm)
`Girder length (m)
`Weight (kN/m)
`Mg (kN-m)
`yg (mm)
`e (mm)
`n
`ni
`
`343,225
`1.579Eþ10
`9246
`37
`9.72
`6.465
`76.9
`514
`338
`8.0
`12.4
`
`320,645
`1.507Eþ10
`8357
`38
`17.85
`6.040
`244.4
`502
`432
`8.58
`12.4
`
`Transformed Section Properties at Release
`Ati (mm2)
`354,451
`331,870
`1.699Eþ10
`1.702Eþ10
`Iti (mm4)
`yti (mm)
`503
`488
`eti (mm)
`628
`417
`(Note: Ag¼gross area of section; Ig¼moment of inertia of the gross concrete section
`about the centroid axis, neglecting the reinforcement or prestressing strands; V/
`S¼volume-to-surface ratio; Mg¼midspan moment due to member self-weight;
`yg¼distance from the neutral axis to the extreme tension fiber for gross section;
`e¼eccentricity of strands with respect to centroid of girder for gross section;
`n¼modular ratio (Es /Ec); ni¼modular ratio (Es /Eci); Ati¼transformed area of sec-
`tion; Iti¼moment of inertia of the transformed concrete section about the centroid
`axis, neglecting the reinforcement or prestressing strands; yti¼distance from the
`neutral axis to the extreme tension fiber for transformed section; eti¼eccentricity
`of strands with respect to centroid of girder for transformed section)
`
`Table 3
`Inputs for AASHTO-Approximate and Refined methods.
`
`Properties
`
`DT-A
`
`AASHTO-Approximate Method
`H (%)
`70
`γst
`1.006
`γh
`1.000
`fcgp (MPa)
`9.419
`
`DT-B
`
`70
`1.006
`1.000
`9.874
`
`AASHTO-Refined Method
`26
`tf (day)
`83
`26
`83
`ti (day)
`0.667
`0.667
`0.667
`0.667
`1.260
`1.260
`1.254
`1.254
`ks
`1.001
`1.006
`1.006
`1.006
`kf
`1.000
`1.000
`1.000
`1.000
`khc
`1.020
`1.020
`1.020
`1.020
`khs
`0.359
`0.646
`0.359
`0.646
`ktd
`Ψb(tf, ti)
`0.908
`1.632
`0.904
`1.624
`0.846
`0.807
`0.791
`0.742
`Kid
`fpt (MPa)
`1095.4
`1095.4
`1089.8
`1089.8
`30
`30
`30.0
`30.0
`KL
`fpy (MPa)
`1675
`1675
`1675
`1675
`(Note: H¼relative humidity; γst¼a coefficient (AASHTO, Eq. 5.9.5.3-2); γh¼a coef-
`ficient (AASHTO-LRFD, Eq. 5.9.5.3-3); fcgp¼concrete stress at the center of gravity of
`prestressing tendons, that results from the prestressing force at either transfer or
`jacking and the self-weight of the member at sections of maximum moment;
`tf¼ final age; ti¼age of concrete when load is initially applied; ks¼factor for the
`effect of the volume-to-surface ratio; kf¼factor for the effect of concrete strength;
`khc¼humidity factor for creep; khs¼humidity factor for shrinkage; ktd¼ time de-
`velopment factor; Ψb(tf,ti)¼girder creep coefficient at final time due to loading
`introduced at transfer; Kid¼transformed section coefficient that accounts for time-
`dependent interaction between concrete and bonded steel in the section being
`considered for time period between transfer and deck placement; fpt¼stress in
`prestressing steel immediately after transfer; KL¼factor accounting for type of steel
`taken as 30 for low relaxation strands; fpy¼yield strength of prestressing steel).
`
`the precast facility used one sample from both girders to measure
`compressive strength, which is why the 16-h tests are identical.
`Separate samples were produced from diverted flows during pla-
`cement of each individual girder for compressive strength and
`modulus of elasticity testing at 7, 28, and 90 days of age. The
`
`Metromont Ex-1013, p.4
`
`

`

`D.B. Ward et al. / Journal of Building Engineering 7 (2016) 133–142
`
`137
`
`Table 4
`Concrete compressive strength.
`
`Age
`
`16 h (MPa)
`7 days (MPa)
`28 days (MPa)
`90 days (MPa)
`
`DT-A
`
`27.4
`38.5
`42.7
`47.2
`
`DT-B
`
`27.4
`37.0
`48.1
`46.6
`
`required compressive strength at release was 24.1 MPa and the
`specified 28-day compressive strength was 34.5 MPa. The de-
`signed concrete mixture achieved the required and specified
`concrete compressive strength. For girder DT-A, the concrete
`compressive strengths continued to increase up to 90 days of age.
`For girder DT-B, the 90-day compressive strength was 4% less than
`the 28-day compressive strength. This deviation is possibly at-
`tributed to the slight inconsistence of the samples taken from a
`diverted stream of concrete.
`The precast facility did not have the capabilities to measure the
`MOE of concrete, therefore the 16-h MOE test was conducted on
`an identical mixture cast at the laboratory at the University of
`Arkansas. Fig. 4 shows the measured MOE values for each girder.
`Least-squares estimation method was used to determine the most
`fitting correction factor K1 of the AASHTO equation for predicting
`the MOE that based on the measured concrete unit weight and
`compressive strength. An iterative procedure was used for the
`determination of K1 factor. The trial factors were varied from 0.8 to
`1.2, and the coefficient of determination R2 was calculated for each
`iteration. For the trial factors in a range of 0.8–0.84 and 1.15–1.2,
`the values of R2 were negative, which meant the predicted and the
`measured MOE values had no correlation. For the trial factors in a
`range of 0.84–1.15, a maximum R2 of 0.722 was achieved at a K1
`factor of 0.99. This best fitting correction factor was approximately
`equal to a factor of 1.0 reported by Bymaster et al. [9]. The de-
`termined factor was also 5% less than a value of 1.035 reported by
`Noguchi and Nemati [52] for sand-lightweight concrete. The dif-
`ference in aggregate sources was the main element contributing to
`this deviation.
`Fig. 4 shows the variability in the measured MOE values in
`conjunction to the predicted values using the AASHTO equation
`with a correction factor K1 of 0.99. For girder DT-A, the AASHTO
`equation over-estimated the measured MOE values at release and
`at 7 days by 16% and 7%, respectively. At 28 days and 90 days, the
`AASHTO equation, however, under-estimated the measured MOE
`
`values by 4% and 7%, respectively. The measured MOE values of
`girder DT-B shows a trend different from that of girder DT-A. The
`measured MOE at 7 days was 2% greater than the predicted value
`while the measured MOE at 28 days was 8% lower than the pre-
`dicted value. These deviations were attributed to the variability in
`lightweight concrete mixture.
`The hatched region in Fig. 4 represents the predicted MOE
`values with 710% error. In other words, the lower and upper
`bounds of the hatched region were 90% and 110% of the predicted
`MOE values, respectively. The figure indicates that the AASHTO
`equation with a correction factor K1 of 0.99 provides a good pre-
`diction for the measured MOE values within an error of 10%. The
`predicted region only over-estimated the measured MOE values at
`release by 6% for both girders and under-estimated the measured
`MOE value at 90 days by 3% for girder DT-B.
`
`5.2. Measured prestress losses
`
`Fig. 5 shows the measured prestress losses for both girders.
`Prestress loss data were determined by multiplying the corrected
`strain gage readings, which were placed at the center of gravity of
`the prestressing steel, by the MOE of the prestressing strand. The
`prestress losses shown in Fig. 5 and in the following figures are the
`averages of the losses measured in each stem of the double-tee
`girders. Prestress losses were continuously measured for 26 days
`while the girders were stored at the precast facility. Fig. 5 indicates
`that the majority of the losses occurred at release. On average, the
`losses increased approximately 25.6 MPa over the next 26 days.
`The prestress losses over the 26-day period were 121.6 MPa for
`girder DT-A and 107.1 MPa for girder DT-B. It should be mentioned
`that these losses do not include prestress loss due to steel re-
`laxation, since the strain gages used in this study could not detect
`the changes in strains caused by relaxation in prestressing steel.
`Once the double-tee girders were erected in the parking gar-
`age, which was at 83 days of age, prestress losses were again
`measured before the topping slab was placed. During construction
`of the parking garage, the VWSG wires were accessible, and a hand
`held reader was used to measure concrete strains. At 83 days of
`age, the measured losses were 147.8 MPa and 121.7 MPa for girders
`DT-A and DT-B, respectively. When compared to the 26-day
`readings, losses increased approximately 26.2 MPa for girder DT-A
`and 14.6 MPa for girder DT-B. This increase in prestress losses
`during this period was comparable to the experimental laboratory
`study reported by Bymaster et al. [9]. The researcher stated the
`maximum increase of prestress losses for 7 months, after 28 days
`
`DT−B
`
`Measured
`Predicted
`Predicted ±10% error
`
`20
`
`60
`40
`Age (day)
`
`80
`
`100
`
`30
`
`25
`
`20
`
`15
`
`10
`
`05
`
`0
`
`Modulus of elasticity (GPa)
`
`DT−A
`
`Measured
`Predicted
`Predicted ±10% error
`
`20
`
`60
`40
`Age (day)
`
`80
`
`100
`
`30
`
`25
`
`20
`
`15
`
`10
`
`05
`
`0
`
`Modulus of elasticity (GPa)
`
`Fig. 4. Measured and predicted modulus of elasticity.
`
`Metromont Ex-1013, p.5
`
`

`

`138
`
`D.B. Ward et al. / Journal of Building Engineering 7 (2016) 133–142
`
`Fig. 5. Measured prestress losses of DT-A and DT-B.
`
`Gross section
`Transformed section
`Zia et al.
`Iterative
`Alternative
`
`DT−A
`
`DT−B
`
`DT−A
`
`DT−B
`
`DT−A
`
`DT−B
`
`Girder
`
`2
`
`1.5
`
`1
`
`0.5
`
`0
`
`Predicted loss / Measured loss
`
`Fig. 6. Ratios of predicted elastic-shortening loss using Zia et al. study, AASHTO
`iterative procedure, and AASHTO alternative procedure to the measured elastic-
`shortening loss.
`
`prior to transfer (fpj). This procedure resulted in elastic-shortening
`loss of 114.8 MPa for girder DT-A and 120.1 MPa for girder DT-B,
`which over-estimated the measured results by 19% and 35%.
`
`of age, ranged from 21.7 MPa to 27.0 MPa. This comparability was
`attributed to the use of similar lightweight SCC in both studies.
`Prestress losses of pretensioned concrete members may be
`significant for first several months or the first year after casting
`[24]. In this study, however, prestress losses were unable to be
`measured after 83 days of age since the tested girders were used
`for construction of a parking garage. This duration may not long
`enough to evaluate the time-dependent losses in comparison with
`the members’ service life. When quantifying prestress losses for
`pretensioned concrete beams cast with lightweight SCC, Bymaster
`et al. [9] found that the prestress losses show little changes after
`75 days of age. As shown in Fig. 5, prestress losses may occur after
`83 days, possibly at a slow rate. When the topping slab is placed,
`the girders can gain elastic shortening prestress that can com-
`pensate for the time-dependent losses occurring after 83 days of
`age.
`
`5.3. Elastic-shortening loss
`
`An increase in elastic-shortening loss was observed when the
`strands were cut at the ends of each girder, and after the girders
`were removed from the prestressing bed (5 h after strands were
`cut). After the strands were cut at girder ends, the elastic-short-
`ening loss was 73.6 MPa and 28.0 MPa for DT-A and DT-B, re-
`spectively. After the girders were removed from prestressing bed,
`the elastic-shortening loss increased to 96.2 MPa and 88.8 MPa for
`girders DT-A and DT-B, respectively. A possible explanation of the
`increase in prestress losses is the large frictional force of a long
`prestressing bed acting on the concrete, reducing elastic short-
`ening of the concrete. If friction reduces the ability for the concrete
`to shorten under transfer, then elastic shortening may not fully
`occur until the frictional restraint is removed. Cook et al. [53] re-
`ported that they observed a significant increase in camber after
`the girders in their study were removed from the bed, likely be-
`cause of the frictional force present between the bed liner and the
`girder. They also reported this effect would be more pronounced
`on longer girders. A large frictional force could lead to less than
`expected values in both elastic prestress losses and initial camber.
`Fig. 6 shows the ratios of the predicted prestress losses using
`Zia et al. study [46] and AASHTO specifications [26] to the mea-
`sured elastic-shortening loss when the girders were removed from
`prestressing bed. The basic mechanism of elastic-shortening loss
`shown in Eq. (2) is to relate the concrete stress at the centroid of
`the prestressing strands (fcpg) at prestress transfer to the elastic-
`shortening loss through the modular ratio (Ep/Eci). Zia et al. pro-
`posed to calculate fcpg using gross-section properties, and the
`prestress after transfer (fpt) is assumed to be 90% of the prestress
`
`Δ
`f
`
`pES
`
`f
`cgp
`
`p c
`E E
`
`i
`
`=
`
`( )
`2
`where ΔfpES is elastic-shortening loss; Ep is modulus of elasticity of
`prestressing strands (196.5 GPa); Eci is the modulus of elasticity of
`concrete at release; fcpg is the concrete stress at the centroid of the
`prestressing strands at prestress transfer.
`AASHTO [26] refined the procedure proposed by Zia et al. by
`including a number of iterations to calculate fpt. Variable fpt is
`firstly assumed to be 90% of fpj, and iterated until an acceptable
`accuracy is attained. In this study, the iterations were stopped
`when fpt was 90.5% and 90.1% of fpj for girders DT-A and DT-B,
`respectively. These values were approximately equal to the as-
`sumed value by Zia et al. The predicted elastic-shortening loss
`using AASHTO was similar to that predicted by Zia et al., which
`was 115.5 MPa for girder DT-A and 120.3 MPa for girder DT-B. The
`
`Metromont Ex-1013, p.6
`
`

`

`D.B. Ward et al. / Journal of Building Engineering 7 (2016) 133–142
`
`139
`
`Steel relaxation
`
`Shrinkage
`
`1 : Measured, at 26 days
`2 : Measured, at 83 days
`3 : Zia et al. study
`4 : AASHTO−Approximate method
`5 : AASHTO−Refined method, at 26 days
`6 : AASHTO−Refined method, at 83 days
`
`Creep
`
`1 2 3 4 5 6
`DT−A
`
`1 2 3 4 5 6
`DT−B
`
`Girder
`
`Fig. 7. Measured and predicted time-dependent prestress losses.
`
`250
`
`200
`
`150
`
`100
`
`50
`
`0
`
`Time−dependent losses (MPa)
`
`girder DT-B. The AASHTO-Refined method, however, specifies the
`time-dependent losses at 26 and 83 days. The predicted losses at
`26 days using the AASHTO-Refined method were approximately
`the same as those predicted using the AASHTO-Approximate
`method for the entire life of the girders. At 83 days, the AASHTO-
`Refined method predicted prestress losses of 221.2 MPa for girder
`DT-A and 209.5 MPa for girder DT-B. Each method uses different
`coefficients in estimating prestress that were derived from ex-
`perimental results of various types of normal-weight concrete.
`Therefore, the degree of over-estimation is varied when extending
`these methods to predict prestress losses for pretensioned con-
`crete members cast with lightweight SCC.
`The use of VWSGs is a reliable technique to measure prestress
`losses. However, this technique could not separate the prestress
`losses caused by concrete creep and shrinkage, while the under-
`standing regarding the contribution of each component is im-
`portant for the design of pretensioned concrete members [54].
`Therefore, the measured shrinkage strain of lightweight SCC re-
`ported by Bymaster et al. [9] was adopted in this study, due to the
`similarities in the mix proportion, concrete properties, and relative
`humidity. In Fig. 8, the fitting line represents the trend of shrink-
`age strains for the first 112 days of age. The interpolated strains at
`26 day and 83 days were 41.27  106 and 111.31  106 that
`
`At 26 days
`
`At 83 days
`
`Expanded clay aggregate
`Fitting line
`
`0
`
`−50
`
`−100
`
`−150
`
`Shrinkage strain (10−6)
`
`−200
`
`0
`
`20
`
`40
`
`60
`Age, day
`
`80
`
`100
`
`120
`
`Fig.
`8. Concrete
`shrinkage
`[9].
`The
`equation of
`the fitting
`line
`is
`y¼4.633 10 5  x31.672  103  x21.497  x2.031; where y is the shrink-
`age strain (106), and x is the age of concrete (day). The shrinkage strains at 26
`days and 83 days are 41.27  106 and 111.31  10 6, respectively.
`
`results of this technique are shown as “Iterative” in Fig. 6. To avoid
`the iteration, AASHTO proposes an alternative procedure that uses
`transformed-section properties as stated in Eq. (C5.9.5.2.3a-1) of
`the Article 5.9.2.3 of the AASHTO specifications. The predicted
`elastic-shortening loss using the alternative procedure was
`116.7 MPa for girder DT-A and 122.1 MPa for girder DT-B, which
`over-estimated the measured values by 21% and 38%.
`To increase the accuracy in estimating