Time-dependent Deflection of Continuous Composite Concrete Slabs

Transcription

1 Time-dependent Deflection of Continuous Composite Concrete Slabs Alireza Gholamhoseini 1, Ian Gilbert 2 and Mark Bradford 3 1 PhD student, 2 Emeritus Professor, 3 Scientia Professor Centre for Infrastructure Engineering and Safety, The University of New South Wales Abstract: Relatively little research has been reported on the time-dependent in-service behaviour 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, and this has only recently been quantified. This paper presents the results of long-term laboratory tests on continuous composite slabs subjected to both drying shrinkage and sustained loads. The 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. Keywords: composite slabs; creep; deflection; profiled steel decking; shrinkage. 1. Introduction Composite one-way concrete floor slabs with profiled steel decking as permanent formwork are commonly used in the construction of floors in buildings (Figure 1). The steel decking supports the wet concrete of a cast in-situ reinforced 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 (Figure 1b). Despite their common usage, relatively little research has been reported on the in-service behaviour of composite slabs. In particular, the drying shrinkage profile through the slab thickness (which is greatly affected by the impermeable steel deck) and the restraint to shrinkage provided by the deck have only recently been quantified (1), (2), (3), (4) and (5). In their research, Gilbert, Gholamhoseini et al. (1) measured the nonlinear variation of shrinkage strain through the thickness of several slab specimens, with and without steel decking at the soffit, and sealed on all exposed concrete surfaces except for the top surface. Carrier, Pu et al. (6) 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 significant only in the top 5 mm of the slab with profiled steel decking and in the top and bottom 5 mm of the conventionally reinforced slab. Gholamhoseini, Gilbert et al. (2) proposed a non-linear shrinkage profile through the thickness of a composite concrete slab, together with an analytical model based on provisions of Australian Standard AS36-29 (7) for calculating the instantaneous and time-dependent curvature of the cross-section due to the effects of both load and non-linear shrinkage. Notwithstanding the research mentioned above, little design guidance is available to practising engineers for predicting the in-service deformation of composite slabs. The techniques used to predict deflection and the on-set of cracking in conventionally reinforced concrete slabs are often applied inappropriately. Although techniques are available for the time-dependent analysis of composite slabs (Gilbert and Ranzi, 8), due to lack of guidance in codes of practice, structural designers often specify the decking as sacrificial formwork, in lieu of timber formwork, and ignore the structural benefits afforded by the composite action. This provides a conservative estimate of strength and is quite unsustainable. It may well result in a significant under-estimation of deflection because of the shrinkage gradient and the restraint provided by the deck. In this paper, the results of an experimental study of the long-term deflection of continuous composite concrete slabs under sustained loads are presented. The deflections caused by creep and shrinkage of the concrete were measured, together with the time-dependent strain profiles at the critical moment regions and the redistribution of internal actions with time. The effects of the steel decking on the drying shrinkage profile and the significant redistribution of internal actions that occurs as a result of shrinkage are presented and discussed.

2 R F Fielders (KF4) decking K4 F 7mm mm Fielders (KF7) trapazoidal decking K F mm (a) Soffit of a one-way composite slab and beam floor system. (b) Dimensions (in mm) of steel decking profile KF7. 2. Experimental Program 2.1 Overview Figure 1. Profiled steel decks (Fielders Aust, 9). The experimental program involved the testing of three large scale two-span composite one-way slabs under different sustained, uniformly distributed service load histories for periods of up to 348 days. The decking profile was KF7 and supplied by Fielders Australia (9) as shown in Figures 1b. The section properties of the steel decking profile are provided in Table 1. Table 1. Section properties of steel profile used in the experiments. Deck Profile Sheet Thickness t s (mm) Section Area A sh(mm 2 /m) Height to Centroid y sh(mm) Mass (kg/m 2 ) I xx (mm 4 /m) KF The creep coefficient and drying shrinkage strain for the concrete were measured on companion specimens cast with the slabs and cured similarly. Additionally, the compressive 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 1 mm diameter cylinders; while the concrete flexural tensile strength (modulus of rupture) was measured on 1 mm by 1 mm by 5 mm concrete prisms. The elastic modulus E s and the yield stress f y of the steel decking were also measured on coupons cut from the decking. Crack locations and crack widths were recorded throughout the long-term test, together with the timedependent change in concrete and steel strains, mid-span deflection and the slip between the steel decking and the concrete at each end of the specimens. The objectives of the experimental program were to obtain benchmark, laboratory-controlled data on the long-term structural response of continuous composite slabs under different sustained service loads, in particular the time-varying deflection, and to analyse the effect of creep and shrinkage on the long-term behaviour of composite slabs. 2.2 Test Specimens and Instrumentation Each slab was 69 mm long, with a cross-section 15 mm deep and 12 mm wide, and contained no bottom reinforcement (other than the external steel decking). Each slab was tested as a uniformly loaded continuous slab with two equal spans of 335 mm centre to centre of supports. Each specimen was continuous over the interior support and simply-supported on a roller at each of the two exterior supports. Longitudinal and transverse reinforcement was provided in the top of the slab in the negative moment region over the interior support, as shown in Figures 2 and 3a. Two load cells were placed underneath the interior

3 support to measure the support reaction and its variation with time. Three identical slabs with KF7 decking were poured at the same time from the same batch of concrete. The slump of the fresh concrete at the time of casting was 9mm. The cross-section of each of the slabs at the interior support is shown in Figure 3a. The cross-sectional area of steel decking in the 1.2 m wide specimens was A p = 132 mm 2, the depth from the bottom top surface reinforcement of the ratio slab for to the the centroid slab (with of decking the decking only) was dp p = A122.3 p /bd p = mm.9. and the bottom reinforcement ratio for the bottom slab (with reinforcement decking ratio only) for the was slab p (with = A p /bd decking p =.9. only) was p = A p /bd p =.9. 21LT-7- L T -3 S E C T IO N 2 L T -7-3 S E C T IO N 22LT-7-3 L T -3 S E C T IO N 3LT-7-63 L T -6 S E C T IO N Figure 2. Support and loading arrangements of test slabs. (a) Reinforcement details at interior support (b) Strain gauge locations at mid-span Figure 3. Cross-sectional details of test slabs. The composite slabs were cast with the profiled steel decking as permanent formwork and the steel decking was cleaned thoroughly before placing concrete. The steel decking was completely supported on the laboratory floor during casting of the concrete to minimize initial stress or deformation in the steel sheeting. Each slab was covered with wet hessian and plastic sheets within four hours of casting and kept moist for 28 days to delay the commencement of drying. At age 28 days the side forms were removed and the slabs were lifted onto the supports. Subsequently the slabs were subjected to different levels of

4 sustained loading by means of different sized concrete blocks. A photograph of the three KF7 slabs showing the different loading arrangements and the slab designations are shown in Figure 4. The first digit in the designation of each slab is the specimen number (1 to 3) 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 (where 7 means KF7 decking). The final digit indicates the approximate value of the maximum superimposed sustained loading in kpa. The mid-span deflections of each slab were 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 each slab at the roller supports. At mid-span and at the interior support of each slab, the longitudinal strains were measured on the top and bottom surfaces using 6 mm long strain gauges. The strain gauges were glued onto the concrete surface and steel sheeting after removing the wet hessian at age 28 days. Internal embedded wire strain gauges were used to measure the concrete strains at different depths through the thickness of slabs 1LT-7- and 3LT-7-6 at the locations shown in Figure 3b. The location, height and width of cracks were measured 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 4. The average relative humidity in the laboratory throughout the period of testing was 7%. 2LT-7-3 3LT-7-6 1LT-7- Figure 4. View of KF7 slabs under sustained load. 2.3 Loading Procedure Each slab specimen was weighed prior to testing using load cells at 24.8 kn (i.e. a uniformly distributed load of 3.6 kn/m). Each of the slabs was placed onto its supports at age 28 days and remained unloaded for 8 days (except for its self-weight). At age 36 days, slabs 2LT-7-3 and 3LT-7-6 were subjected to superimposed sustained loads in the form of concrete blocks. The block layouts are illustrated in Figure 2 (and are also shown in the photograph of Figure 4). Each concrete block was placed on 6 mm 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. Slab 1LT-7- remained unloaded except for self-weight for the duration of the test (348 days). Slabs 2LT-7-3 carried a constant superimposed sustained load of 3.1 kpa (3.72 kn/m) from age 36 days to 376 days (i.e. a total sustained load of 7.32 kn/m). Slab 3LT-7-6 carried a constant superimposed sustained load of 5.6 kpa (6.72 kn/m) from age 36 days to 376 days (i.e. a total sustained load of 1.32 kn/m). 3. Test Results 3.1 Material Properties The measured compressive strength, modulus of elasticity and flexural tensile strength for concrete are presented in Table 2, both at first loading (age 36 days) and after the test at age 376 days. The measured creep coefficient versus time curve for concrete cylinders first loaded at age 36 days is shown in Figure 5a. The creep coefficient at the end of test (age 376 days) was φ cc = 1.21.

5 Height(mm)) Height(mm)) Height(mm)) Height(mm)) Shrinkage strain ( µε ) Table 2. Concrete strength and elastic modulus. Property At Age 36 days At Age 376 days Mean compressive strength, f cm (MPa) Mean flexural tensile strength, f ct.fm (MPa) Mean elastic modulus, E cm (MPa) The development of drying shrinkage strain for the concrete in the slabs is shown in Figure 5b. The curve represents the average of the measured shrinkage on two standard shrinkage prisms ( mm) 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 ε sh = 616 με. The average of the measured values of yield stress and elastic modulus taken from three test samples of the KF7 decking were f y = 532 (MPa) and E s = 23 (GPa), respectively. Similarly, from three test samples of the reinforcing bars, average values were f y = 544 (MPa) and E s = 212 (GPa), respectively. Creep coefficient coefficient, φ cc cc Time Time after loading (days) (a) Creep coefficient vs time 3.2 Time-dependent Strains Time after Time commencement after of of drying (days) 12 (b) Shrinkage strain vs time Figure 5. Creep coefficient and shrinkage Day-98 strain versus versus time. time. The measured strain variations with time through the thickness of slabs 1LT-7- and 3LT-7-6 at midspan and are shown in Figures 6a and 6b, respectively Day-1 Day-8 Day-29 Day-98 Day-271 Day Day-1 Day-29 Day-98 (a) 1LT-7- Strains Strain(με) ( ) Shrinkage strain ( ) Day-1 Day-8 Day-29 Day-271 Day-348 Day-1 Day-29 Day-98 (a) 1LT-7- Strains Strain(με) ( ) Day-8- Day-271 (b) 3LT Day-348- Day Day-8- Day-271 (b) 3LT Day-348- Day Strains Strain(με) ( ) 15 Figure 6. Strain profiles at mid-span. Figure 6. Strain profiles at mid-span. The measured curvatures ( ) at mid-span at selected times for each of these slabs are given in Table

6 Table 3. Measured curvature at mid-span. Slab 1 day drying Curvature 1-6 (mm -1 ) 8 days drying 98 days 182 days 348 days drying Before After drying drying Before After 1LT LT Cracking Because of the steel decking at the slab soffit, it was difficult to inspect for flexural cracking in the mid-span regions of these continuous slabs. None of the slabs exhibited any signs of cracking at midspan or at the interior support at the time of placing the specimens onto the supports. However, at the time of first loading, slabs 2LT-7-3 and 3LT-7-6 both cracked over the interior support. Time-dependent flexural cracking was observed in all of the slabs in the tensile zone in the negative moment region over the interior support but, with the exception of 3LT-7-6, these cracks remained fine and well-controlled for the duration of the test. The maximum measured crack width at the end of the test was.2 mm,.3 mm and.6 mm for slabs 1LT-7-, 2LT-7-3 and 3LT-7-6, respectively. The average crack spacing on the top surface of the slabs in the negative moment region of the slabs 1LT-7-, 2LT- 7-3 and 3LT-7-6 was 152 mm, 174mm and 172mm, respectively. No cracking was observed on the side surfaces of any specimen in the positive moment region at mid-span. The final cracking patterns on the top and side surfaces of the slabs in the vicinity of the interior support (the only observed cracks) are presented in Figure 7. interior support interior support interior support (a) 1LT-7- (b) 2LT-7-3 (c) 3LT-7-6 Figure 7. Observed cracks in test specimens. 3.4 Mid-span Deflection and End Slip The variation of average mid-span deflection and the deflection of both the west and east spans with time for all three slabs are shown in Figure 8. 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 superimposed loads (concrete 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 age 28 days due to self-weight (which has been calculated to be about.2 mm for all slabs). For slab 1LT-7-, the average deflections after 8 days, 98 days and 348 days of drying were.47 mm, 1.62 mm and 2.11 mm, respectively. For slab 2LT-7-3, the average deflections after 8 days, before and after the concrete blocks were applied, were.28 mm and.76 mm, respectively, while the average deflections after 348 days, before and after the concrete blocks were removed were 3.2 mm

7 Mid-span deflection (mm)) LT LT LT Drying age (days) Figure 8. Average mid-span deflection versus time. and 2.74 mm, respectively. For slab 3LT-7-6, the average deflections after 8 days, before and after the concrete blocks were applied, were.5 mm and 1.11 mm, respectively, while the average deflections after 348 days, before and after the concrete blocks were removed were 4.84 mm and 3.79 mm, respectively. The measured end slips for these slabs at service loads were very small with the maximum values of about.1 mm in the east end support of 2LT-7-3 and.5 mm at the west end support of 3LT-7-6, respectively. The measured end slips were negligible in the other end supports of all slabs. 3.5 Redistribution of Internal Actions Shrinkage may cause significant changes in the distribution of internal actions with time in continuous slabs. If a slab is not free to shorten (e.g. due to restraint caused by the steel decking), shrinkage produces internal tension in the concrete and, as this tension is eccentric to the centroid of the concrete crosssection, shrinkage-induced curvature results. Shrinkage-induced curvature on each cross-section due to the restraint provided by steel decking can lead to significant reactions at the supports of statically indeterminate slabs, and hence, significant changes in the internal actions on each cross-section. Consider the uncracked, two-span composite slab with steel decking at the slab soffit shown in Figure 9a. If the weight of the slab and any applied loads are ignored and if the redundant reaction at the interior support is removed, thereby reducing the slab to a simply-supported statically determinate member, shrinkage would cause a positive curvature to develop with time on each cross-section. Hence, the slab would gradually develop a downward deflection of Δ m at its mid-length as shown in Figure 9b. Of course, no reactions are induced by shrinkage at the end-supports of the simply-supported slab (R e1 = R e2 = ). a A ssu m e d S h rin k a g e S tra in P ro file (a) b m R e1= (b) R e2 = m c R e1 (c) R i R e2 = d R e1 (d) R i R e2 Figure 9. Internal action redistribution due to creep and shrinkage.

8 M (KN.m) M (KN.m) M (KN.m) With the interior support in the actual two-span slab resisting downward movement, an upward reaction ΔR i gradually develops at the interior support with time, as well as downward reactions ΔR e1 and ΔR e2 at the two exterior supports, as shown in Figure 9c. This leads to an increase in the negative moment at the interior support with time and a decrease in the positive moment at mid-span. Shrinkage therefore causes the time-dependent change in reactions and deflections shown in Figure 9d. The response of a cracked region of slab to creep is different to that of the uncracked parts of the slabs. In addition, due to the variation of bending moment throughout the span, different portions of concrete are under tensile or compressive creep and therefore have different creep coefficients. In addition, although it is normally assumed that the concrete is homogeneous, this is rarely true, and the creep characteristics are not uniform throughout. Therefore, in statically indeterminate concrete structures, creep may also lead to redistribution of internal actions with time Day- Day-8 Day-42 Day Length(m) Figure 1. Variation of bending moment diagram with time for 1LT-7-. The measured variation in the bending moment distribution with time along the slab 1LT-7- (carrying only its own self-weight) is shown in Figure 1. The diagrams are calculated from the measured reactions and the known self-weight. Initially, the bending moment distribution was similar to that obtained from an elastic analysis (with the moment at the interior support equal to -7. knm). The magnitude of the negative moment at the interior support for such a lightly loaded and uncracked slab is significantly affected if the three supports are not exactly at the same elevation and this explains the difference between the measured moment and the calculated elastic moment based on ideal support conditions (-5.1 knm). For this slab, the interior reaction gradually increased and the exterior reaction gradually decreased. After just 8 days of drying, the moment at the interior support had increased in magnitiude to -1.6 knm. At age 348 days, the exterior reactions had reduced almost to zero and the bending moment at the interior support had increased in magnitude to knm. The dramatic effects of shrinkage on this lightly reinforced slab are evident. The measured variations in the bending moment distribution with time along the slab 2LT-7-3 from the time the slab was placed on the supports (Day ) to the time immediately after the concrete blocks were placed on the slab (Day 8+) are shown in Figure 11a. The negative moment at the interior support on Day was -2.7 knm and this increased to -7.7 knm after 8 days of shrinkage. When the blocks were applied, cracking occurred at interior support very significantly reducing the stiffness in this region. Due to the full superimposed load, the negative moment at interior support increase by just -1.9 knm to -9.6 knm, while the positive moment at mid-span increased from 1.2 knm to 5.4 knm. The measured variations in the bending moment distribution with time along 2LT-7-3 from (Day 8+) to the end of the test are shown in Figure 11b. As expected, shrinkage caused an increase in the negative moment at the interior support from -9.6 knm to knm (similar in magnitude to the unloaded slab). Upon unloading at Day 348+, the (a) Length(m) (b) Day-42 Day- Day-8- Day-348- Day Length(m) Figure 11. Variation of bending moment diagram with time for 2LT-7-3.

9 M (KN.m) M (KN.m) M (KN.m) negative moment at the interior support reduced by only 2.6 knm to knm and the positive moment at mid-span reduced from +.9 knm to -3. knm. The measured variations in the bending moment distribution with time along the slab 3T-7-6 followed the same trends as were observed in 2LT-7-3. The bending moment distributions for 3LT-7-6 at Day when the slab was placed on the supports, and at Day 8 both before and after the blocks were placed on the slab are shown in Figure 12a. The negative moment at mid-span on Day was -7.8 knm and this increased to knm after 8 days of shrinkage. When the blocks were applied, cracking occurred at interior support and due to the full superimposed load, the negative moment at interior support increase by just -3.4 knm to knm, while the positive moment at mid-span increased from -1.7 knm to 6. knm. The variations in the bending moment distribution for 3LT-7-6 from (Day 8+) to the end of the test are shown in Figure 12b. As expected, shrinkage caused an increase in the negative moment at the interior support from knm to knm. Upon unloading at Day 348+, the negative moment at the interior support reduced by only 4.2 knm to knm and the positive moment at mid-span reduced from +2.6 knm to -4.7 knm. (a) Length(m) (b) Day-42 Day- Day-8- Day-348- Day Length(m) Figure 12. Variation of bending moment diagram with time for 3LT-7-6. The variations with time of the negative moment at the interior support and the moment at mid-span for each slab are shown in Figure 13. As can be seen, the redistribution of moments (primarily due to shrinkage) is most pronounced in the first 56 days after the commencement of drying, with relatively little redistribution thereafter Drying Age(Day) (M-) 1LT-7- (M+) 1LT-7- (M-) 2LT-7-3 (M+) 2LT-7-3 (M-) 3LT-7-6 (M+) 3LT-7-6 Figure 13. Variation of moment at mid-span (M+) and at the interior support (M-) versus time. 4. Concluding Remarks The results of an experimental study of the long-term deflection of continuous composite concrete slabs under sustained loads have been presented. Deformation caused by applied load, creep of the concrete and the effects of drying shrinkage have been reported and discussed for three slabs, all with KF7 steel decking (Fielders Australia, 9), subjected to different loading histories. The slab deflections and

10 the redistribution of bending moments measured in this study have confirmed the dominant effect of drying shrinkage for composite slabs under normal levels of sustained service loads. The moments at the interior support (M-) and moments at mid-span (M+)are summarized in Table 4. The loads are carried largely by bending in the mid-span span regions of the slab, since upon unloading the change in the support moments is relatively small. The increase in support moments with time due to shrinkage is largely independent of the load level. Slab Load from days 8 to348- (kn/m) Table 4. Summary of support and mid-span moments. Day 8+ Day 348- Day 348+ M- (knm) M+ (knm) M- (knm) M+ (knm) M- (knm) M+ (knm) 1LT LT LT Acknowledgement The work reported herein has been undertaken with the financial support of the Australian Research Council through Linkage Project LP991495, decking manufacturer Fielders Australia PL and Prestressed Concrete Design Consultants (PCDC). This support is gratefully acknowledged. 6. References 1. Gilbert, RI, Bradford, MA, Gholamhoseini, A & Chang, Z-T, Effects of Shrinkage on the Long-term Stresses and Deformations of Composite Concrete Slabs, Engineering Structures, Vol. 4, July 212, pp Gholamhoseini, A, Gilbert, RI, Bradford, MA & Chang, Z-T, Long-term Deformation of Composite Concrete Slabs, Concrete in Australia, Vol. 38, December 212, pp Ranzi G, Ambrogi L, Al-Deen S, Uy B, Long-term Experiments of Post-tensioned Composite Slabs, Proceedings of the 1th International Conference on Advances in Steel Concrete Composite and Hybrid Structures, 2-4 July 212, Singapore. 4. Ranzi G, Leoni G, Zandonini R, State of the Art on the Time-dependent Behaviour of Composite Steel-Concrete Structures, Journal of Constructional Steel Research, in press, Shayan S, Al-Deen S, Ranzi G, Vrcelj Z, Long-term Behaviour of Composite Concrete Slabs: An Experimental Study, Proceedings of the 4 th International Conference on Steel & Composite Structures (ICSCS 1), July 21, Sydney, Australia. 6. Carrier, RE; Pu, DC and Cady, PD, Moisture Distribution in Concrete Bridge Decks and Pavements. Durability of Concrete, SP-47, American Concrete Institute, Farmington Hills, Michigan, 1975, pp AS36-29, Australian Standard for Concrete Structures, Standards Australia, Gilbert, RI and Ranzi, G, Time-dependent Behaviour of Concrete Structures, Spon Press, London, Fielders Australia PL, Specifying Fielders KingFlor; Composite Steel Formwork System Design Manual, 28.