Paper ACI

765ACI Structural Journal/July-August 2014

ACI STRUCTURAL JOURNAL TECHNICAL PAPER

Relatively little research has been reported on the time-dependent in-service behavior of composite concrete slabs with profiled steel decking as permanent formwork, and little guidance is available for calculating long-term deflections. The drying shrinkage profile through the thickness of a composite slab is greatly affected by the impermeable steel deck at the slab soffit, but this has not yet been quantified satisfactorily. This paper presents the results of long-term laboratory tests on composite slabs subjected to both drying shrinkage and sustained loads. Based on laboratory measurements, a design model for the shrinkage strain profile through the thick-ness of a slab is proposed. In addition, an existing analytical model developed by the authors to calculate the time-dependent deflection of composite slabs is used to calculate the final deflection of the test slabs. The calculated deflections are shown to be in good agree-ment with the experimental measurements.

Keywords: composite slabs; creep; deflection; profiled steel decking; serviceability; shrinkage; time-dependent.

INTRODUCTIONComposite one-way concrete floor slabs with profiled

steel decking as permanent formwork are commonly used in the construction of floors in buildings (Fig. 1(a)). The steel decking supports the wet concrete of a cast-in-place rein-forced or post-tensioned concrete slab and, after the concrete sets, acts as external reinforcement. Embossments on the profiled sheeting provide the necessary shear connection to ensure composite action between the concrete and the steel deck (Fig. 1(b)).

Despite their common usage, relatively little research has been reported on the in-service behavior of composite slabs. In particular, the drying shrinkage profile through the slab thickness (which is greatly affected by the imper-meable steel deck) and the restraint to shrinkage provided by the deck have only recently been quantified.1-4 In their research, Gilbert et al.1 measured the nonlinear variation of shrinkage strain through the thickness of several slab speci-mens, with and without steel decking at the soffit, and sealed on all exposed concrete surfaces except for the top surface. Carrier et al.5 measured the moisture contents of two bridge decks; one was a composite slab with profiled steel decking, and the other was a conventional reinforced concrete slab permitted to dry from the top and bottom surfaces after the timber forms were removed. The moisture loss was signifi-cant only in the top 50 mm (2 in.) of the slab with profiled steel decking and in the top and bottom 50 mm (2 in.) of the conventionally reinforced slab.

As a consequence of the dearth of published research, little design guidance is available to structural engineers for predicting the in-service deformation of composite slabs. The techniques used to predict deflection and the onset of

cracking in conventionally reinforced concrete slabs6-8 are often applied inappropriately. Although techniques are avail-able for the time-dependent analysis of composite slabs,8 due to lack of guidance in codes of practice, structural designers often specify the decking as sacrificial formwork, instead of timber formwork, and ignore the structural benefits afforded by the composite action. This provides a conservative

Title No. 111-S63

Time-Dependent Deflection of Composite Concrete Slabsby Alireza Gholamhoseini, R. Ian Gilbert, Mark Bradford, and Zhen-Tian Chang

ACI Structural Journal, V. 111, No. 4, July-August 2014.MS No. S-2012-335.R2, doi: 10.14359/51686629, was received April 1, 2013, and

reviewed under Institute publication policies. Copyright © 2014, American Concrete Institute. All rights reserved, including the making of copies unless permission is obtained from the copyright proprietors. Pertinent discussion including author’s closure, if any, will be published ten months from this journal’s date if the discussion is received within four months of the paper’s print publication.

Fig. 1—Profiled steel decks (Fielders Australia).

766 ACI Structural Journal/July-August 2014

estimate of strength. The non-uniform shrinkage caused by the steel decking at the bottom surface of the slab, however, may lead to significant deflection, and this should not be ignored.

In this paper, the results of an experimental study of the long-term deflection of composite concrete slabs due to sustained service loads and shrinkage are presented. Deflections caused by creep of the concrete and the effects of drying shrinkage are reported and discussed. Based on the experimental results, a shrinkage profile is proposed for design purposes, and an analytical technique is proposed for determining the time-varying deflections of composite floor slabs with profiled steel decking.

RESEARCH SIGNIFICANCEThe paper provides experimental evidence of the dominant

role played by drying shrinkage in the long-term deflection of composite concrete slabs with steel decking as permanent formwork. Based on the experimental results, the shrinkage model proposed by ACI Committee 2099 is adapted to provide a shrinkage strain profile through the slab thickness suitable for use in structural design. An analytical method proposed by the authors1 is also shown to accurately predict final long-term deflections. The study provides previously unavailable guidance for determining long-term deforma-tions in composite slabs and for designing such slabs at the serviceability limit states.

EXPERIMENTAL PROGRAM

OverviewThe experimental program involved the testing of 10 large-

scale simple-span composite one-way slabs under different sustained, uniformly distributed service load histories for periods of up to 240 days. Two different decking profiles were considered (KF40 and KF70,10 as shown in Fig. 1(c)).

The creep coefficient and drying shrinkage strain for the concrete were measured on companion specimens cast with the slabs and cured similarly. Additionally, the compres-sive strength and the elastic modulus of concrete at the age of first loading and at the end of the sustained load period were measured on standard 100 mm (4 in.) diameter cylin-ders, while the concrete flexural tensile strength (modulus of rupture) was measured on 100 x 100 x 500 mm (4 x 4 x 20 in.) concrete prisms. The elastic modulus Es and the yield stress fy of the steel decking were also measured on coupons cut from the decking.

Crack locations and crack widths on the side surfaces of the slabs were recorded throughout the long-term test, together with the time-dependent change in concrete and steel strains, midspan deflection, and the slip between the steel decking and the concrete at each end of the specimen.

The objectives of the experimental program were to obtain benchmark, laboratory-controlled data on the long-term structural response of composite slabs under different sustained service loads, particularly the time-varying deflec-tion, and to analyze the effect of creep and shrinkage on the long-term behavior of composite slabs. The laboratory data was then used to validate analytical models for the predic-

tion of time-dependent behavior1,8 and to assist in the devel-opment of design-oriented procedures to assess the service-ability of composite slabs.

Test specimens and instrumentationEach slab was 3300 mm (130 in.) long, with a cross

section 150 mm (5.9 in.) deep and 1200 mm (47 in.) wide, and contained no reinforcement (other than the external steel decking). Each slab was tested as a single, simply supported span. The center-to-center distance between the two end supports (one hinge and one roller) was 3100 mm (122 in.). Five identical slabs with KF70 decking were cast at the same time from the same batch of concrete. An additional five identical slabs with KF40 decking were cast at a different time from a different batch of concrete (but to the same spec-ification and from the same supplier). The thickness of the steel sheeting in both types of decking was ts = 0.75 mm (0.03 in.). The cross section of each of the five slabs with KF70 decking is shown in Fig. 2. The choice of specimen variables was made to examine the effects of shrinkage and sustained load levels on long-term deflections for slabs with two different deck profiles, while keeping slab thick-ness and concrete properties the same for each specimen. Further testing will be necessary to consider the effects of varying the concrete properties and slab thickness on long-term deflection.

Each slab was covered with wet hessian and plastic sheets within 4 hours of casting and kept moist for 6 days to delay the commencement of drying. At an age of 7 days, the side forms were removed, and the slabs were lifted onto the supports. Subsequently, the slabs were subjected to different levels of sustained loading provided by means of differ-ent-sized concrete blocks. A photograph of the five KF70 slabs showing the different loading arrangements and the slab designations are also shown in Fig. 2. The first digit in the designation of each slab is the specimen number (1 to 10), and the following two letters indicate the nature of the test, with LT for long-term. The next two numbers indicate the type of decking (with 70 and 40 for KF70 and KF40, respectively). The final digit indicates the approximate value of the maximum superimposed sustained loading in kPa (1 kPa = 20.9 lb/ft2).

The section properties of the steel decking profiles are provided in Table 1, and the self-weight and cross-sectional properties of the composite slabs are given in Table 2.

The midspan deflection of each slab was measured throughout the sustained load period, with dial gauges at the soffit of the specimen. Dial gauges were also used to measure the slip between concrete and steel deck at the ends of the slab at both roller and hinge supports in all slabs. At the midspan of each slab, the concrete strains were measured on the top and bottom surfaces using 60 mm (2.4 in.) long strain gauges. The strain gauges were glued onto the concrete surface and steel sheeting after removing the wet hessian at an age of 7 days. Internal embedded wire strain gauges were used to measure the concrete strains at different depths through the thickness of Slabs 2LT-70-3, 5LT-70-8, 7LT-40-3 and 9LT-40-6, with locations shown on the cross section in Fig. 2.


The location, height, and width of the cracks were measured on the side faces of each specimen and recorded throughout the test. Of particular interest was the time- dependent development of cracking and the increase in crack widths with time. Crack widths were measured using a microscope with a magnification factor of 40. The average relative humidity in the laboratory throughout the period of testing was 67 and 72% for the KF70 and KF40 test speci-mens, respectively.

Loading procedureEach of the KF70 slabs was placed onto its supports at an

age of 7 days, and remained unloaded (except for its self-weight, see Table 2) until an age of 64 days. At 64 days, with the exception of 1LT-70-0, each slab was subjected to superimposed sustained loads in the form of concrete blocks. Each concrete block was placed on 60 mm (2.4 in.) high timber blocks to ensure a largely uninterrupted air flow over the top surface of the slabs and allow the concrete to shrink freely on the top surface. The block layouts are illustrated in Fig. 3 (and are also shown in the photograph of Fig. 2(c)). Slab 1LT-70-0 carried only self-weight for the full test duration of 240 days. Slabs 2LT-70-3 and 3LT-70-3 were identical, carrying a constant superimposed sustained load of 3.4 kPa (71.0 lb/ft2) from 64 to 247 days—that is, a total sustained load of 6.4 kPa (134 lb/ft2). Slab 4LT-70-6 carried a constant superimposed sustained load of 6.0 kPa (125 lb/ft2) from 64 to 247 days, that is, a total sustained load of 9.0 kPa (188 lb/ft2). Slab 5LT-70-8 carried a constant superimposed sustained load of 6.1 kPa (127 lb/ft2) from 64 to 197 days, that is, a total sustained load of 9.1 kPa (190 lb/ft2); from 197 to 247 days, the superimposed sustained load

was 7.9 kPa (165 lb/ft2)—that is, a total sustained load of 10.9 kPa (228 lb/ft2).

Each of the KF40 slabs was placed onto the supports at an age of 7 days and remained unloaded except for its self-weight—that is, 3.2 kPa (66.8 lb/ft2)—until 28 days. At 28 days (after 21 days of drying), with the exception of 6LT-40-0, each slab was subjected to superimposed sustained loads with the block layouts similar to that used for the KF70 slabs and shown in Fig. 3. Slab 6LT-40-0 carried only self-weight for the full test duration of 244 days. Slabs 7LT-40-3 and 8LT-40-3 were identical, carrying a constant superimposed sustained load of 3.4 kPa (71.0 lb/ft2) from 28 to 251 days, that is, a total sustained load of 6.6 kPa (138 lb/ft2). Slabs 9LT-40-6 and 10LT-40-6 were also identical and carried a constant superimposed sustained load of 6.4 kPa (134 lb/ft2) from 28 to 251 days, that is, a total sustained load of 9.6 kPa (201 lb/ft2). The loading history for each slab is summarized in Table 3.

EXPERIMENTAL RESULTS

Material propertiesThe measured compressive strength, modulus of elasticity,

and flexural tensile strength are presented in Table 4. The measured creep coefficient versus time curve for concrete cylinders cast with the KF70 slabs and first loaded at an age of 64 days is shown in Fig. 4(a). The creep coefficient at the end of test was jcc = 1.62. For the KF40 slabs, the creep coefficient at the end of the test (251 days) for the concrete first loaded at 28 days was jcc = 1.50.

The development of the drying shrinkage strain for the concrete in the KF70 slabs is shown in Fig. 4(b). The curve represents the average of the measured shrinkage on two standard shrinkage prisms, 75 x 75 x 275 mm (3 x 3 x 10.8 in.), from the day after removing the wet hessian until the end of the test. The average measured shrinkage strain at the end of test was εsh = 512 με. Similarly, for the KF40 slabs, the average measured shrinkage strain at the end of tests was εsh = 630 με.

The average of the measured values of yield stress and elastic modulus taken from three test samples of the KF70

Fig. 2—Cross sections and view of KF70 slabs under load.

Table 1—Properties of profiled steel decking

Deck profile type

Deck thickness ts,

mm (in.)

Section area As, mm2/m

(in.2/ft)

Centroid height ys, mm (in.)

Mass, kg/m2 (lb/ft2)

Ixx, mm4/m(in.4/ft)

KF70 0.75 (0.03) 1100 (0.520)27.7

(1.09)9.17

(1.88)584,000 (0.428)

KF40 0.75 (0.03) 1040 (0.491)14.0

(0.55)8.67

(1.78)269,000 (0.197)

Table 2—Properties of composite slabs

Slab deck profile

Specimen self-weight, kPa (lb/ft2)

Gross section (Ixx)gross, mm4

(in.4)

Cracked section (Ixx)cr, mm4

(in.4)

KF70 3.0 (63) 278 × 106 (668) 102 × 106 (245)

KF40 3.2 (67) 310 × 106 (745) 111 × 106 (267)


decking were fy = 544 MPa (78.9 ksi) and Es = 212 GPa (30,740 ksi), respectively. Similarly, from three test samples of the KF40 decking, average values were fy = 475 MPa (68.9 ksi) and Es = 193 GPa (27,990 ksi), respectively.

Midspan deflection and end slipThe variations of midspan deflection with time for the

KF70 and KF40 slabs are shown in Fig. 5 and 6, respec-tively. Key deflection values are summarized in Table 5. The measured deflection includes that caused by shrinkage, the creep-induced deflection due to the sustained load (including self-weight), the short-term deflection caused by the super-imposed loads (blocks), and the deflection caused by the loss of stiffness resulting from time-dependent cracking (if any). It does not include the initial deflection of the uncracked slab at an age of 7 days due to self-weight (which has been calculated to be approximately 0.5 mm [0.02 in.] for both the KF70 and KF40 slabs).

The measured end slips were very small, with maximum values of approximately 0.1 and 0.12 mm (0.0039 and

Fig. 3—Sustained load configuration for KF70 slabs.

Table 3—Equivalent uniformly distributed load history for each slab specimen, kPa (lb/ft2)

SlabFrom age 7 to

64 daysFrom age 64 to

197 daysFrom age 197 to

247 days

1LT-70-0 3.0 (63) 3.0 (63) 3.0 (63)

2LT-70-3 3.0 (63) 6.4 (134) 6.4 (134)

3LT-70-3 3.0 (63) 6.4 (134) 6.4 (134)

4LT-70-6 3.0 (63) 9.0 (188) 9.0 (188)

5LT-70-8 3.0 (63) 9.1 (190) 10.9 (228)

SlabFrom age 7 to 28

days From age 28 to 251 days

6LT-40-0 3.2 (67) 3.2 (67)

7LT-40-3 3.2 (67) 6.6 (138)

8LT-40-3 3.2 (67) 6.6 (138)

9LT-40-6 3.2 (67) 9.6 (201)

10LT-40-6 3.2 (67) 9.6 (201)


0.0047 in.) at the supports in 3LT-70-3 and 4LT-70-6, respectively. The end slips were negligible in the other slabs.

Time-dependent strainsThe measured strain variations with time through the

thickness of Slabs 2LT-70-3 and 5LT-70-8 at midspan and through the thickness of Slabs 7LT-40-3 and 9LT-40-6 at midspan are shown in Fig. 7 and 8, respectively, and the measured curvatures κ at midspan at selected times for each of these slabs are given in Table 6.

CrackingBecause of the steel decking at the slab soffit, it was diffi-

cult to inspect for flexural cracking in these simply supported slabs. None of the slabs exhibited any signs of cracking at first loading. Time-dependent flexural cracking, however, was observed on the side surfaces of all KF40 slabs in the tensile zone in the middle third of the span, but these cracks remained fine and well controlled for the duration of the test and less than 0.15 mm (0.006 in.) in width throughout. The average crack spacing in the KF40 slabs was 180 mm (7.1 in.).

No cracking was observed in any of the KF70 slabs at any stage of loading, except for Slab 5LT-70-8, in which three flexural cracks were detected in the bottom of the slab in the middle 0.5 m (20 in.) of the span at an age of 210 days (14 days after the second layer of blocks was placed on the slab and the superimposed load was increased to 7.9 kPa). The average spacing between the three cracks was 167 mm (6.6 in.). Typical crack patterns are illustrated in Fig. 9.

DISCUSSION OF TEST RESULTSShrinkage clearly has a dominant effect on the final

deflection of these composite slabs. With a sustained load of 3.2 kPa (67.7 lb/ft2) (self-weight), the final deflection of 6LT-40-0 was 4.99 mm (0.197 in.). When the sustained load was increased by a factor of approximately 3 to 9.6 kPa (201 lb/ft2), the slabs suffered additional cracking and yet the final deflection only increased by a factor of approximately 1.4 to 6.94 mm (0.273 in.) (9LT-40-6), and by a factor of approximately 1.7 to 8.26 mm (0.325 in.) (10T-40-6). A similarly dominant effect of shrinkage over load was observed in the KF70 slabs.

Fig. 3—Sustained load configuration for KF70 slabs.

Table 4—Concrete properties

Slab type fc′, MPa (psi) Ec, MPa (ksi) fct.f, MPa (psi)

KF7064 days 28.0 (4060) 64 days 30,725 (4455) 64 days 3.50 (508)

247 days 29.8 (4320) 247 days 31,650 (4590) 247 days 4.54 (658)

KF4028 days 35.5 (5150) 28 days 28,200 (4090) 28 days 3.80 (551)

251days 42.70 (6190) 251 days 31,600 (4580) 251 days 5.05 (732)

Fig. 4—Creep coefficient and shrinkage strain versus time curves for KF70 slabs.

Fig. 5—Midspan deflection versus time for KF70 slabs.


Before the application of any load other than self-weight, the slabs deflected significantly, mainly due to the shrink-age-induced curvature. For the five KF70 slabs, after 57 days of drying (when εsh = 400 με), the deflection varied from 2.18 mm (0.086 in.) for 4LT-70-6 to 3.54 mm (0.139 in.) for 2LT-70-3. Although this was mainly due to early shrinkage, it included the creep deflection resulting from self-weight, which was estimated at approximately 0.4 mm (0.016 in.). At this stage, all KF70 slabs were identical (in terms of materials, geometry, and load history), yet the deflection varied significantly. This highlights the large degree of variability when considering the service load behavior of concrete slabs, with deflection being highly dependent on the nonlinear and time-dependent behavior of the concrete. For the five KF40 slabs, after 21 days of drying (when εsh = 390 με), the deflection varied from 2.72 mm (0.107 in.) for 8LT-40-3 to 3.33 mm (0.131 in.) for 7LT-40-3.

The difference in the extent of time-dependent cracking between the KF70 slabs and the KF40 slabs was somewhat

unexpected. With the centroid of the KF40 steel decking being only 14 mm (0.55 in.) above the bottom of the slab (and that of the KF70 decking being 27.7 mm [1.09 in.] above the bottom), the tensile force that developed with time

Table 5—Measured midspan deflections

Slab

Time-dependent deflection, mm (in.)

57 days of drying 190 days of drying 240 days of drying

Before After Before After Before After

1LT-70-0 2.92 (0.115) 2.92 (0.115) 4.24 (0.167) 4.24 (0.167) 4.04 (0.159) 4.04 (0.159)

2LT-70-3 3.54 (0.139) 4.29 (0.169) 6.74 (0.265) 6.74 (0.265) 6.72 (0.265) 6.01 (0.237)

3LT-70-3 2.97 (0.117) 3.63 (0.143) 5.80 (0.228) 5.80 (0.228) 5.84 (0.230) 5.16 (0.203)

4LT-70-6 2.18 (0.086) 3.38 (0.133) 6.37 (0.251) 6.37 (0.251) 6.40 (0.252) 5.31 (0.209)

5LT-70-8 2.94 (0.116) 4.23 (0.167) 6.56 (0.258) 6.96 (0.274) 7.23 (0.285) 5.78 (0.228)

Slab


21 days of drying

28 days of drying 56 days of drying

244 days of drying

Before After Before After

6LT-40-0 2.83 (0.111) 2.83 (0.111) 3.15 (0.124) 3.87 (0.152) 4.99 (0.197) 4.99 (0.197)

7LT-40-3 3.33 (0.131) 4.14 (0.163) 4.72 (0.186) 5.68 (0.224) 7.30 (0.287) 6.62 (0.261)

8LT-40-3 2.72 (0.107) 4.12 (0.162) 4.70 (0.185) 5.38 (0.212) 6.57 (0.259) 5.53 (0.218)

9LT-40-6 2.95 (0.116) 4.35 (0.171) 4.60 (0.181) 5.90 (0.232) 6.94 (0.273) 5.68 (0.224)

10LT-40-6 3.30 (0.130) 5.10 (0.201) 5.52 (0.217) 6.72 (0.265) 8.26 (0.325) 7.81 (0.308)

Fig. 6—Midspan deflection versus time for KF40 slabs.

Fig. 7—Strain profiles at midspan of 2LT-70-3 and 5LT-70-8.


on the concrete, due to the restraint provided by the KF40 decking to drying shrinkage, is significantly more eccen-tric to the centroid of the concrete than that provided by the KF70 decking. This will increase the concrete tensile stress in the bottom fibers of the concrete, and may have contrib-uted to the observed differences in crack patterns.

ANALYTICAL MODELINGAn analytical procedure for the time-dependent analysis

of composite concrete cross sections with uniform shrinkage through the thickness of the concrete slab and with full interaction was presented by Gilbert and Ranzi8 using the age-adjusted effective modulus method.11,12 Gilbert et

al.1 extended the method to calculate the effects of a non- uniform shrinkage gradient by layering the concrete cross section, with the shrinkage strain specified in each concrete layer depending on its position within the cross section and with the assumption of full shear interaction at service load levels. This method is adopted herein.

To calculate the time-dependent deformation of a composite concrete cross section, the shrinkage strain profile and the creep coefficient for the concrete slab are needed. In the following, a shrinkage strain profile is proposed for concrete slabs on profiled steel decking that is suitable for use in structural design, and a modification to the provisions of ACI 209.2R-089 for estimating the shrinkage strain and creep coefficient for composite slabs is also proposed. The proposals have been developed empirically from experi-mental measurements of shrinkage-induced strain distribu-tions in composite slabs.1

According to ACI 209.2R-08,9 the shrinkage strain εsh(t, tc) and creep coefficient j(t, t0) can be estimated using Eq. (1) and (2)

ε ε

α

αsh cc

cshut t

t t

f t t( , )

( )

( )=

−+ −

(1)

ϕ ϕ

ψ

ψ( , )( )

( )t t

t t

d t t u00

0

=−

+ − (2)

where εshu is the ultimate (final) shrinkage strain; ju is the final creep coefficient; (t – tc) is the time from the end of initial curing (in days); and (t – t0) is the time since the appli-cation of load, respectively. The suggested values for the constants within these equations under standard conditions are: α = 1; f = 35 for 7 days of moist curing, εshu = 780 με, ψ = 0.6, d = 10, and ju = 2.35.

For conditions other than standard conditions, ACI 209.2R-089 requires that εshu and ju be multiplied by applicable correction factors. The effect of relative humidity (RH, in %) on concrete shrinkage and creep can be taken into account using correction factors γsh.RH and γc.RH, respectively

γsh.RH = 1.40 – 0.0102RH (3a)

γc.RH = 1.27 – 0.0067RH (3b)

Table 6—Measured curvature at midspan

Slab

Curvature × 10–6 mm–1 (× 10–6 in.–1)

57 days (KF70); 21 days (KF40) 190 days of drying 240 days (KF70); 244 days (KF40)

Before After Before After Before After

2LT-70-3 1.80 (45.7) 2.42 (61.5) 3.83 (97.3) 3.83 (97.3) 3.51 (89.2) 2.98 (75.7)

5LT-70-8 2.07 (52.6) 2.99 (75.9) 4.55 (116) 5.66 (144) 5.88 (149) 4.42 (112)

7LT-40-3 2.52 (64.0) 3.25 (82.6) 5.70 (145) 5.70 (145) 6.34 (161) 4.69 (119)

9LT-40-6 2.83 (71.9) 4.34 (110) 8.20 (208) 8.20 (208) 9.06 (230) 7.70 (196)

Fig. 8—Strain profiles at midspan of 7LT-40-3 and 9LT-40-6.


The effect of member size on concrete shrinkage and creep are considered by employing correction coefficients γsh.vs and γc.vs defined as follows (in SI units)

γsh.vs = 1.2e{–0.00472(V/S)} (= 1.2e{–0.120(V/S)}) (4a)

γc.vs = 0.667(1 + 1.13e{–0.0213(V/S)}) (=0.667(1 + 1.13e{–0.541(V/S)})) (4b)

where V is the specimen volume in mm3 (in.3), and S is the specimen surface area in mm2 (in.2).

For a composite slab on profiled steel decking, if the average thickness of the concrete tave is defined as the area of the concrete part of the cross section Ac divided by the width of the cross section b, the following modifications to Eq. (4a) and (4b) are proposed to account for the effect of the steel decking on the drying profile through the concrete, and hence on the magnitude of creep and shrinkage.

For tave in mm (in.)

γ sh vst te eave ave

.( . ( . )) ( . ( .. ( .= =− + − +1 2 1 20 00472 25 0 25 0 120 1 0 25 ))) ) (5a)

Fig. 9—Observed crack locations in slabs. (Note: All dimensions are in mm; 1 mm = 0.0394 in.)


γ c vst te eave ave

.( . ) ( . ). ( . )= + = +− −2 0 45 2 0 450 0053 0 135

(5b)

With these values of γsh.vs and γc.vs, the creep coefficient j(t, t0) and shrinkage strain value εsh(t, tc) can be determined in accordance with ACI 209.2R-08.9

The measured shrinkage strain at any height y above the soffit of the composite slab with overall depth D, εsh(y), may be approximated by Eq. (6)

εε

α βsh

sh c

y

t t

y

D

( )

( , )= +

4

(6)

where εsh(0) = αεsh(t, tc) is the shrinkage strain at the bottom of the slab (at y = 0), and εsh(D) = (α + β)εsh(t, tc) is the shrinkage strain at the top surface of the slab (at y = D). The shrinkage profile given by Eq. (6) is shown in Fig. 10.

From the experimental results, α = 0.2 provides a reason-able estimate, but β appears to depend on the profile of the steel decking. Excellent agreement between the predicted long-term deflection and the measured values is obtained with β = 1.0 for the KF70 slabs (with 70 mm [2.75 in.] deep troughs) and β = 1.4 for the KF40 slabs (with 40 mm [1.5 in.] deep troughs), as shown in Fig. 11 and 12. For other deck

profiles considered in this study, the ratio of trough height to slab thickness (rd) was in the range 0.25 to 0.5. In this range, the following relationship for β provides good agreement with the measured shrinkage profiles

β = 2.0 – 2.25rd (7)

The analytical curves were obtained by double integration of the curvature diagram at each time instant, with the curva-ture determined at cross sections at 155 mm (6.2 in.) centers along the span using the layered cross section approach of Gilbert et al.1 Sample calculations for the determination of the short-term and time-dependent curvature at midspan of Slab 6LT-40-0 are provided in the Appendix,* together with the determination of the shrinkage profile through the thick-ness of the slab.

For each slab, the same load history was considered in the analytical modeling as was applied to the real slab. Where two identical slabs with identical loading histories were tested, the analytical deflection-time curves are compared with the average of the two experimental curves. In those parts of the slabs where the numerical study showed that cracking had occurred, the effect of tension stiffening was considered using an approach similar to that outlined in Eurocode 2.13 The average curvature (κave) used in deflec-tion calculation is determined according to Eq. (8)

κave = ζκcr+ (1 – ζ)κuncr (8)

*The Appendix is available at www.concrete.org/publications in PDF format, appended to the online version of the published paper. It is also available in hard copy from ACI headquarters for a fee equal to the cost of reproduction plus handling at the time of the request.Fig. 10—Proposed shrinkage strain profile.

Fig. 11—Midspan deflection versus time (KF70 slabs).


where κcr is the time-dependent curvature on the cracked cross section (ignoring tension in the concrete); κuncr is the time-dependent curvature on the uncracked cross section; and ζ is the distribution coefficient given by

ζ = −

1

2M

Mcr t

s

. (9)

where Mcr.t is the cracking moment at the time under consid-eration, and Ms is the in-service moment imposed on the cross section.

The shrinkage-induced deflection calculated using the proposed shrinkage profile for each decking type (Eq. (6)), together with the instantaneous and time-dependent deflec-tion caused by the applied load (elastic and creep deflec-tion), are in good agreement with the measured response of the slabs.

A summary of the measured and calculated midspan deflections is presented in Table 7, where comparisons between the measured and predicted deflections are made at 42 days after the commencement of drying and at the end of the test.

Fig. 12—Midspan deflection versus time (KF40 slabs).

Table 7—Measured and calculated midspan deflections

Slab



Measured (test) Calculated Measured/calculated Measured (test) Calculated Measured/calculated

1LT-70-0 2.67 (0.105) 2.80 (0.110) 0.95 4.04 (0.159) 4.34 (0.171) 0.93

2LT-70-3 3.27 (0.129) 2.80 (0.110) 1.17 6.72 (0.265) 5.92 (0.233) 1.14

3LT-70-3 2.74 (0.108) 2.80 (0.110) 0.98 5.84 (0.230) 5.92 (0.233) 0.99

4LT-70-6 2.16 (0.085) 2.80 (0.110) 0.77 6.40 (0.252) 7.27 (0.286) 0.88

5LT-70-8 2.69 (0.106) 2.80 (0.110) 0.96 7.23 (0.285) 7.98 (0.314) 0.91

Slab



Measured (test) Calculated Measured/calculated Measured (test) Calculated Measured/calculated

6LT-40-0 3.77 (0.148) 3.28 (0.129) 1.15 4.99 (0.197) 5.08 (0.200) 0.98

7LT-40-3 5.50 (0.217) 4.40 (0.173) 1.25 7.30 (0.287) 6.64 (0.261) 1.10

8LT-40-3 5.26 (0.207) 4.40 (0.173) 1.20 6.57 (0.259) 6.64 (0.261) 0.99

9LT-40-6 5.67 (0.223) 6.09 (0.240) 0.93 6.94 (0.273) 8.33 (0.328) 0.83

10LT-40-6 6.36 (0.250) 6.09 (0.240) 1.04 8.26 (0.325) 8.33 (0.328) 0.99


SUMMARY AND CONCLUSIONSThe results of an experimental study of the long-term

deflection of composite concrete slabs under sustained loads have been presented. The deformation caused by applied load, creep of the concrete, and the effects of drying shrinkage have been reported and discussed for 10 simply supported slabs, with either KF70 or KF40 steel decking,10 subjected to different loading histories. The measured slab deflections confirmed the dominant effect of drying shrinkage over load for normal levels of sustained loads.

Also proposed is a nonlinear shrinkage profile through the thickness of a composite concrete slab, together with an analytical model for calculating the instantaneous and time-dependent curvature of the cross section due to the effects of both load and nonlinear shrinkage. The agreement between the calculated deflection and the measured deflec-tion for each of the 10 slabs is good.

AUTHOR BIOSAlireza Gholamhoseini is a PhD Research Student in the Centre for Infrastructure Engineering in the School of Civil and Environmental Engi-neering at the University of New South Wales, Sydney, Australia.

ACI member R. Ian Gilbert is Emeritus Professor and Deputy Director of the Centre for Infrastructure Engineering in the School of Civil and Environmental Engineering at the University of New South Wales. He is a member of ACI Committee 209, Creep and Shrinkage in Concrete. His research interests include the time-dependent serviceability of concrete and composite structures.

ACI member Mark Bradford is Scientia Professor and Australian Laureate Fellow in the Centre for Infrastructure Engineering in the School of Civil and Environmental Engineering at the University of New South Wales, and a Fellow of the Australian Academy of Technological Sciences and Engi-neering. His research interests include the strength and serviceability of steel, concrete, and composite structures, and structural sustainability.

Zhen-Tian Chang is a Research Associate in the Centre for Infrastructure Engineering in the School of Civil and Environmental Engineering at the University of New South Wales. He received his PhD at the University of New South Wales in 2005. His research interests include the serviceability and durability of concrete structures.

ACKNOWLEDGMENTSThe work reported herein has been undertaken with the financial

support of the Australian Research Council, decking manufacturer Fielders Australia PL, and Prestressed Concrete Design Consultants (PCDC). This support is gratefully acknowledged.

REFERENCES1. Gilbert, R. I.; Bradford, M. A.; Gholamhoseini, A.; and Chang, Z.-T.,

“Effects of Shrinkage on the Long-Term Stresses and Deformations of Composite Concrete Slabs,” Engineering Structures, V. 40, July 2012, pp. 9-19.

2. Ranzi, G.; Ambrogi, L.; Al-Deen, S.; and Uy, B., “Long-Term Exper-iments of Post-Tensioned Composite Slabs,” Proceedings of the 10th Inter-national Conference on Advances in Steel Concrete Composite and Hybrid Structures, Singapore, July 2012, pp. 477-484.

3. Ranzi, G.; Leoni, G.; and Zandonini, R., “State of the Art on the Time-Dependent Behaviour of Composite Steel-Concrete Structures,” Journal of Constructional Steel Research, V. 80, Jan. 2013, pp. 252-263.

4. Bradford, M. A., “Generic Modelling of Composite Steel- Concrete Slabs Subjected to Shrinkage, Creep and Thermal Strains Including Partial Interaction,” Engineering Structures, V. 32, No. 5, May 2010, pp. 1459-1465.

5. Carrier, R. E.; Pu, D. C.; and Cady, P. D., “Moisture Distribution in Concrete Bridge Decks and Pavements,” Durability of Concrete, SP-47, American Concrete Institute, Farmington Hills, MI, 1975, pp. 169-192.

6. Gilbert, R. I., “Deflection Calculation for Reinforced Concrete Struc-tures—Why We Sometimes Get It Wrong,” ACI Structural Journal, V. 96, No. 6, Nov.-Dec. 1999, pp. 1027-1032.

7. Brock, G., RAPT Reinforced and Post-Tensioned Structural Concrete Design Software, 2008, www.raptsoftware.com.

8. Gilbert, R. I., and Ranzi, G., Time-Dependent Behavior of Concrete Structures, Spon Press, London, UK, 2011, 426 pp.

9. ACI Committee 209, “Guide for Modeling and Calculating Shrinkage and Creep in Hardened Concrete (ACI 209.2R-08),” American Concrete Institute, Farmington Hills, MI, 2008, 45 pp.

10. Fielders Australia Pty. Ltd., “Specifying Fielders—KingFlor; Composite Steel Formwork System Design Manual,” 2008, 220 pp.

11. Dilger, W., and Neville, A. M., “Method of Creep Analysis of Struc-tural Members,” Designing for Effects of Creep, Shrinkage and Tempera-ture in Concrete Structures, SP-27, American Concrete Institute, Farm-ington Hills, MI, 1971, pp. 349-379.

12. Bažant, Z. P., “Prediction of Creep Effects Using Age-Adjusted Effective Modulus Method,” ACI Journal, V. 69, No. 4, Apr. 1972, pp. 212-217.

13. BS EN 1992-1-1(2004), “Eurocode 2: Design of Concrete Struc-tures—Part 1-1: General Rules and Rules for Buildings,” British Standards Institution, European Committee for Standardization, Brussels, Belgium, 2004, 230 pp.


NOTES:

Paper ACI

Documents

slab thickness

reinforced slab

slab soffit

composite action

slab speci

posttensioned concrete

test slabs

concrete sets