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1、20Electronic Journal of Structural Engineering, 1 ( 2001) Shrinkage, Cracking and Deflection-the Serviceability of Concrete StructuresR.I. GilbertProfessor and Head, School of Civil and Environmental EngineeringThe University of New South Wales, Sydney, NSW, 2052Email: i.gilbertunsw.edu.aueJSEIntern
2、ationalABSTRACTThis paper addresses the effects of shrinkage on the serviceability of concrete structures. It outlines why shrinkage is important, its major influence on the final extent of cracking and the magnitude of deflection in structures, and what to do about it in design. A model is presente
3、d for predicting the shrinkage strain in normal and high strength concrete and the time-dependent behaviour of plain concrete and reinforced concrete, with and without external restraints, is explained. Analytical procedures are described for estimating the final width and spacing of both flexural c
4、racks and direct tension cracks and a simplified procedure is presented for including the effects of shrinkage when calculating long-term deflection. The paper also contains an overview of the considerations currently being made by the working group established by Standards Australia to revise the s
5、erviceability provisions of AS3600-1994, particularly those clauses related to shrinkage.KEYWORDS Creep; Cracking; Deflection; Reinforced concrete; Serviceability; Shrinkage.1. IntroductionFor a concrete structure to be serviceable, cracking must be controlled and deflections must not be excessive.
6、It must also not vibrate excessively. Concrete shrinkage plays a major role in each of these aspects of the service load behaviour of concrete structures.The design for serviceability is possibility the most difficult and least well understood aspect of the design of concrete structures. Service loa
7、d behaviour depends primarily on the properties of the concrete and these are often not known reliably at the design stage. Moreover, concrete behaves in a non-linear and inelastic manner at service loads. The non-linear behaviour that complicates serviceability calculations is due to cracking, tens
8、ion stiffening, creep, and shrinkage. Of these, shrinkage is the most problematic. Restraint to shrinkage causes time-dependent cracking and gradually reduces the beneficial effects of tension stiffening. It results in a gradual widening of existing cracks and, in flexural members, a significant inc
9、rease in deflections with time.The control of cracking in a reinforced or prestressed concrete structure is usually achieved by limiting the stress increment in the bonded reinforcement to some appropriately low value and ensuring that the bonded reinforcement is suitably distributed. Many codes of
10、practice specify maximum steel stress increments after cracking and maximum spacing requirements for the bonded reinforcement. However, few existing code procedures, if any, account adequately for the gradual increase in existing crack widths with time, due primarily to shrinkage, or the time-depend
11、ent development of new cracks resulting from tensile stresses caused by restraint to shrinkage.For deflection control, the structural designer should select maximum deflection limits that are appropriate to the structure and its intended use. The calculated deflection (or camber) must not exceed the
12、se limits. Codes of practice give general guidance for both the selection of the maximum deflection limits and the calculation of deflection. However, the simplified procedures for calculating deflection in most codes were developed from tests on simply-supported reinforced concrete beams and often
13、produce grossly inaccurate predictions when applied to more complex structures. Again, the existing code procedures do not provide real guidance on how to adequately model the time-dependent effects of creep and shrinkage in deflection calculations.Serviceability failures of concrete structures invo
14、lving excessive cracking and/or excessive deflection are relatively common. Numerous cases have been reported, in Australia and elsewhere, of structures that complied with code requirements but still deflected or cracked excessively. In a large majority of these failures, shrinkage of concrete is pr
15、imarily responsible. Clearly, the serviceability provisions embodied in our codes do not adequately model the in-service behaviour of structures and, in particular, fail to account adequately for shrinkage.The quest for serviceable concrete structures must involve the development of more reliable de
16、sign procedures. It must also involve designers giving more attention to the specification of an appropriate concrete mix, particularly with regard to the creep and shrinkage characteristics of the mix, and sound engineering input is required in the construction procedures. High performance concrete
17、 structures require the specification of high performance concrete (not necessarily high strength concrete, but concrete with relatively low shrinkage, not prone to plastic shrinkage cracking) and a high standard of construction, involving suitably long stripping times, adequate propping, effective
18、curing procedures and rigorous on-site supervision.This paper addresses some of these problems, particularly those related to designing for the effects of shrinkage. It outlines how shrinkage affects the in-service behaviour of structures and what to do about it in design. It also provides an overvi
19、ew of the considerations currently being made by the working group established by Standards Australia to revise the serviceability provisions of AS3600-1994 1, particularly those clauses related to shrinkage.2. Designing for ServiceabilityWhen designing for serviceability, the designer must ensure t
20、hat the structure can perform its intended function under the day to day service loads. Deflection must not be excessive, cracks must be adequately controlled and no portion of the structure should suffer excessive vibration. Shrinkage causes time-dependent cracking, thereby reducing the stiffness o
21、f a concrete structure, and is therefore a detrimental factor in all aspects of the design for serviceability.Deflection problems that may affect the serviceability of concrete structures can be classified into three main types:(a) Where excessive deflection causes either aesthetic or functional pro
22、blems.(b) Where excessive deflection results in damage to either structural or non-structural element attached to the member.(c) Where dynamics effects due to insufficient stiffness cause discomfort to occupants.3. Effects of ShrinkageIf concrete members were free to shrink, without restraint, shrin
23、kage of concrete would not be a major concern to structural engineers. However, this is not the case. The contraction of a concrete member is often restrained by its supports or by the adjacent structure. Bonded reinforcement also restrains shrinkage. Each of these forms of restraint involve the imp
24、osition of a gradually increasing tensile force on the concrete which may lead to time-dependent cracking (in previously uncracked regions), increases in deflection and a widening of existing cracks. Restraint to shrinkage is probably the most common cause of unsightly cracking in concrete structure
25、s. In many cases, these problems arise because shrinkage has not been adequately considered by the structural designer and the effects of shrinkage are not adequately modelled in the design procedures specified in codes of practice for crack control and deflection calculation.The advent of shrinkage
26、 cracking depends on the degree of restraint to shrinkage, the extensibility and strength of the concrete in tension, tensile creep and the load induced tension existing in the member. Cracking can only be avoided if the gradually increasing tensile stress induced by shrinkage, and reduced by creep,
27、 is at all times less than the tensile strength of the concrete. Although the tensile strength of concrete increases with time, so too does the elastic modulus and, therefore, so too does the tensile stress induced by shrinkage. Furthermore, the relief offered by creep decreases with age. The existe
28、nce of load induced tension in uncracked regions accelerates the formation of time-dependent cracking. In many cases, therefore, shrinkage cracking is inevitable. The control of such cracking requires two important steps. First, the shrinkage-induced tension and the regions where shrinkage cracks ar
29、e likely to develop must be recognised by the structural designer. Second, an adequate quantity and distribution of anchored reinforcement must be included in these regions to ensure that the cracks remain fine and the structure remains serviceable.3.1 What is Shrinkage? Shrinkage of concrete is the
30、 time-dependent strain measured in an unloaded and unrestrained specimen at constant temperature. It is important from the outset to distinguish between plastic shrinkage, chemical shrinkage and drying shrinkage. Some high strength concretes are prone to plastic shrinkage, which occurs in the wet co
31、ncrete, and may result in significant cracking during the setting process. This cracking occurs due to capillary tension in the pore water. Since the bond between the plastic concrete and the reinforcement has not yet developed, the steel is ineffective in controlling such cracks. This problem may b
32、e severe in the case of low water content, silica fume concrete and the use of such concrete in elements such as slabs with large exposed surfaces is not recommended.Drying shrinkage is the reduction in volume caused principally by the loss of water during the drying process. Chemical (or endogenous
33、) shrinkage results from various chemical reactions within the cement paste and includes hydration shrinkage, which is related to the degree of hydration of the binder in a sealed specimen. Concrete shrinkage strain, which is usually considered to be the sum of the drying and chemical shrinkage comp
34、onents, continues to increase with time at a decreasing rate. Shrinkage is assumed to approach a final value, , as time approaches infinity and is dependent on all the factors which affect the drying of concrete, including the relative humidity and temperature, the mix characteristics (in particular
35、, the type and quantity of the binder, the water content and water-to-cement ratio, the ratio of fine to coarse aggregate, and the type of aggregate), and the size and shape of the member.Drying shrinkage in high strength concrete is smaller than in normal strength concrete due to the smaller quanti
36、ties of free water after hydration. However, endogenous shrinkage is significantly higher.For normal strength concrete (MPa), AS3600 suggests that the design shrinkage (which includes both drying and endogenous shrinkage) at any time after the commencement of drying may be estimated from(1)where is
37、a basic shrinkage strain which, in the absence of measurements, may be taken to be 850 x 10-6 (note that this value was increased from 700 x 10-6 in the recent Amendment 2 of the Standard); k1 is obtained by interpolation from Figure 6.1.7.2 in the Standard and depends on the time since the commence
38、ment of drying, the environment and the concrete surface area to volume ratio. A hypothetical thickness, th = 2A/ ue, is used to take this into account, where A is the cross-sectional area of the member and ue is that portion of the section perimeter exposed to the atmosphere plus half the total per
39、imeter of any voids contained within the section.AS3600 states that the actual shrinkage strain may be within a range of plus or minus 40% of the value predicted (increased from 30% in Amendment 2 to AS3600-1994). In the writers opinion, this range is still optimistically narrow, particularly when o
40、ne considers the size of the country and the wide variation in shrinkage measured in concretes from the various geographical locations. Equation 1 does not include any of the effects related to the composition and quality of the concrete. The same value of ecs is predicted irrespective of the concre
41、te strength, the water-cement ratio, the aggregate type and quantity, the type of admixtures, etc. In addition, the factor k1 tends to overestimate the effect of member size and significantly underestimate the rate of shrinkage development at early ages.The method should be used only as a guide for
42、concrete with a low water-cement ratio (0.4) and with a well graded, good quality aggregate. Where a higher water-cement ratio is expected or when doubts exist concerning the type of aggregate to be used, the value of ecs predicted by AS3600 should be increased by at least 50%. The method in the Sta
43、ndard for the prediction of shrinkage strain is currently under revision and it is quite likely that significant changes will be proposed with the inclusion of high strength concretes.A proposal currently being considered by Standards Australia, and proposed by Gilbert (1998) 9, involves the total s
44、hrinkage strain, ecs, being divided into two components, endogenous shrinkage, ecse, (which is assumed to develop relatively rapidly and increases with concrete strength) and drying shrinkage, ecsd (which develops more slowly, but decreases with concrete strength). At any time t (in days) after pour
45、ing, the endogenous shrinkage is given byecse = e*cse (1.0 - e-0.1t)(2)where e*cse is the final endogenous shrinkage and may be taken as e*cse , where is in MPa. The basic drying shrinkage is given by(3)and at any time t (in days) after the commencement of drying, the drying shrinkage may be taken a
46、s(4)The variable is given by(5)where and is equal to 0.7 for an arid environment, 0.6 for a temperate environment and 0.5 for a tropical/coastal environment. For an interior environment, k5 may be taken as 0.65. The value of k1 given by Equation 5 has the same general shape as that given in Figure 6
47、.1.7.2 in AS3600, except that shrinkage develops more rapidly at early ages and the reduction in drying shrinkage with increasing values of th is not as great.The final shrinkage at any time is therefore the sum of the endogenous shrinkage (Equation 2) and the drying shrinkage (Equation 4). For exam
48、ple, for specimens in an interior environment with hypothetical thicknesses th = 100 mm and th = 400 mm, the shrinkage strains predicted by the above model are given in Table 1.Table 1 Design shrinkage strains predicted by proposed model for an interior environment.(x 10-6)(x 10-6)Strain at 28 days(x 10-6) Strain at 10000 days(x 10-6)100252590023449472258859105010070094349443100690790751755001642494131754936681002503002351503852502965464002525900231141372554356850100700948818210042252275175500164