Unformatted text preview: HOME PAGE CHAPTER 15 Volume Changes of Concrete
Concrete changes slightly in volume for various reasons, and understanding the nature of these changes is useful in planning or analyzing concrete work. If concrete were free of any restraints to deform, normal volume changes would be of little consequence; but since concrete in service is usually restrained by foundations, subgrades, reinforcement, or connecting members, significant stresses can develop. This is particularly true of tensile stresses. Cracks develop because concrete is relatively weak in tension but quite strong in compression. Controlling the variables that affect volume changes can minimize high stresses and cracking. Tolerable crack widths should be considered in the structural design. Volume change is defined merely as an increase or decrease in volume. Most commonly, the subject of concrete volume changes deals with linear expansion and contraction due to temperature and moisture cycles. But chemical effects such as carbonation shrinkage, sulfate attack, and the disruptive expansion of alkali-aggregate reactions also cause volume changes. Also, creep is a volume change or deformation caused by sustained stress or load. Equally important is the elastic or inelastic change in dimensions or shape that occurs instantaneously under applied load. For convenience, the magnitude of volume changes is generally stated in linear rather than volumetric units. Changes in length are often expressed as a coefficient of length in parts per million, or simply as millionths. It is applicable to any length unit (for example, m/m or ft/ft); one millionth is 0.000001 m/m (0.000001 in./in.) and 600 millionths is 0.000600 m/m (0.000600 in./in.). Change of length can also be expressed as a percentage; thus 0.06% is the same as 0.000600, which incidentally is approximately the same as 6 mm per 10 m (3/4 in. per 100 ft). The volume changes that ordinarily occur in concrete are small, ranging in length change from perhaps 10 millionths up to about 1000 millionths.
257 EARLY AGE VOLUME CHANGES
The volume of concrete begins to change shortly after it is cast. Early volume changes, within 24 hours, can influence the volume changes (such as drying shrinkage) and crack formation in hardened concrete, especially for low water to cement ratio concrete. Following are discussions on various forms of early volume change: Chemical Shrinkage
Chemical shrinkage refers to the reduction in absolute volume of solids and liquids in paste resulting from cement hydration. The absolute volume of hydrated cement products is less than the absolute volume of cement and water before hydration. This change in volume of cement paste during the plastic state is illustrated by the first two bars in Fig. 15-1. This does not include air bubbles from mixing. Chemical shrinkage continues to occur at a microscopic scale as long as cement hydrates. After initial set, the paste cannot deform as much as when it was in a plastic state. Chemical shrinkage Autogenous shrinkage (pre set) Autogenous shrinkage (after set) Autogenous shrinkage (apparent volume reduction) Cumulated voids Paste as cast Paste at initial set Voids generated by hydration Unhydrated cement and water Chemical shrinkage (absolute volume reduction) Paste after final set Paste after final set Fig. 15-1. Chemical shrinkage and autogenous shrinkage volume changes of fresh and hardened paste. Not to scale. Design and Control of Concrete Mixtures N EB001 during hydration (Powers 1935). Le Chatelier (1900) was the first to study chemical shrinkage of cement pastes. Therefore, further hydration and chemical shrinkage is compensated by the formation of voids in the microstructure (Fig. 15-1). Most of this volume change is internal and does not significantly change the visible external dimensions of a concrete element. The amount of volume change due to chemical shrinkage can be estimated from the hydrated cement phases and their crystal densities or it can be determined by physical test as illustrated in Fig. 15-2. The Japan Concrete Institute has a test method for chemical shrinkage of cement paste (Tazawa 1999). An example of long-term chemical shrinkage for portland cement paste is illustrated in Fig. 15-3. Early researchers sometimes referred to chemical shrinkage as the absorption of water Autogenous Shrinkage
Autogenous shrinkage is the macroscopic volume reduction (visible dimensional change) of cement paste, mortar, or concrete caused by cement hydration. The macroscopic volume reduction of autogenous shrinkage is much less than the absolute volume reduction of chemical shrinkage because of the rigidity of the hardened paste structure. Chemical shrinkage is the driving force behind autogenous shrinkage. The relationship between autogenous shrinkage and chemical shrinkage is illustrated in Figs. 15-1, 15-4, and 15-5. Some researchers and organizations consider that Water level at time zero 1.2 Shrinkage, cm3/100 g cement
Chemical shrinkage volume at time n 1 0.8 0.6 0.4 0.2 0 Autogenous shrinkage Chemical shrinkage Lime saturated water Water level at time n Start of setting 0 2 4 6 Time after mixing, hours 8 10 Cement paste Fig. 15-2. Test for chemical shrinkage of cement paste showing flask for cement paste and pipet for absorbed water measurement. Fig. 15-4. Relationship between autogenous shrinkage and chemical shrinkage of cement paste at early ages (Hammer 1999). Chemical shrinkage Subsidence Bleed water Chemical shrinkage Autogenous shrinkage Cumulative hydration voids Water 8 w/c = 0.50 6 Chemical shrinkage, %
Water Water Cement 4
Cement Ordinary portland cement 2 Cement Hydrated cement Hydrated cement 0 At casting At initial setting After hardening 0 1 10 Age, hours 100 1000 Fig. 15-3. Chemical shrinkage of cement paste (Tazawa 1999). 258 Fig. 15-5. Volumetric relationship between subsidence, bleed water, chemical shrinkage, and autogenous shrinkage. Only autogenous shrinkage after initial set is shown. Not to scale. Chapter 15 N Volume Changes of Concrete autogenous shrinkage starts at initial set while others evaluate autogenous shrinkage from time of placement. When external water is available, autogenous shrinkage cannot occur. When external water is not available, cement hydration consumes pore water resulting in self desiccation of the paste and a uniform reduction of volume (Copeland and Bragg 1955). Autogenous shrinkage increases with a decrease in water to cement ratio and with an increase in the amount of cement paste. Normal concrete has negligible autogenous shrinkage; however, autogenous shrinkage is most prominent in concrete with a water to cement ratio under 0.42 (Holt 2001). Highstrength, low water to cement ratio (0.30) concrete can experience 200 to 400 millionths of autogenous shrinkage. Autogenous shrinkage can be half that of drying shrinkage for concretes with a water to cement ratio of 0.30. Recent use of high performance, low water to cement ratio concrete in bridges and other structures has renewed interest in autogenous shrinkage to control crack development. Concretes susceptible to large amounts of autogenous shrinkage should be cured with external water for at least 7 days to help control crack development. Fogging should be provided as soon as the concrete is cast. The hydration of supplementary cementing materials also contributes to autogenous shrinkage, although at different levels than portland cement. In addition to adjusting paste content and water to cement ratios, autogenous shrinkage can be reduced by using shrinkage reducing admixtures or internal curing techniques. Some cementitious systems may experience autogenous expansion. Tazawa (1999) and Holt (2001) review techniques to control autogenous shrinkage. Test methods for autogenous shrinkage and expansion of cement paste, mortar, and concrete and tests for autogenous shrinkage stress of concrete are presented by Tazawa (1999). Plastic Shrinkage
Plastic shrinkage refers to volume change occurring while the concrete is still fresh, before hardening. It is usually observed in the form of plastic shrinkage cracks occurring before or during finishing (Fig. 15-6). The cracks often resemble tears in the surface. Plastic shrinkage results from a combination of chemical and autogenous shrinkage and rapid evaporation of moisture from the surface that exceeds the bleeding rate. Plastic shrinkage cracking can be controlled by minimizing surface evaporation through use of fogging, wind breaks, shading, plastic sheet covers, wet burlap, spray-on finishing aids (evaporation retarders), and plastic fibers. Fig. 15-6. Plastic shrinkage cracks resemble tears in fresh concrete. (1312) Swelling
Concrete, mortar, and cement paste swell in the presence of external water. When water drained from capillaries by chemical shrinkage is replaced by external water, the volume of the concrete mass increases. As there is no self desiccation, there is no autogenous shrinkage. External water can come from wet curing or submersion. Swelling occurs due to a combination of crystal growth, absorption of water, and osmotic pressure. The swelling is not large, only about 50 millionths at early ages (Fig. 15-7). When the Subsidence
Subsidence refers to the vertical shrinkage of fresh cementitious materials before initial set. It is caused by bleeding (settlement of solids relative to liquids), air voids rising to the surface, and chemical shrinkage. Subsidence is also called settlement shrinkage. Subsidence of well-consolidated concrete with minimal bleed water is insignificant. The relationship between subsidence and other shrinkage mechanisms is illustrated in Fig. 15-5. Excessive subsidence is often caused by a lack of consolidation of fresh concrete. Excessive subsidence over embedded items, such as supported steel reinforcement, can result in cracking over embedded items. Concretes made with air entrainment, sufficient fine materials, and low water contents will minimize subsidence cracking. Also, plastic fibers have been reported to reduce subsidence cracking (Suprenant and Malisch 1999).
259 100 Swelling, 1 x 106 75 50 25 0 0.30 0.45 Demolding 0 24 Age, hours 48 w/c = 0.35 Fig. 15-7. Early age swelling of 100 x 100 x 375-mm (4 x 4 x 15-in.) concrete specimens cured under water (Atcin 1999). Design and Control of Concrete Mixtures N EB001
Swelling (x 10-6) external water source is removed, autogenous shrinkage and drying shrinkage reverse the volume change. Water curing 100
w/c = 0.45 0.35 Sealed Early Thermal Expansion
As cement hydrates, the exothermic reaction provides a significant amount of heat. In large elements the heat is retained, rather than dissipated as happens with thin elements. This temperature rise, occurring over the first few hours and days, can induce a small amount of expansion that counteracts autogenous and chemical shrinkage (Holt 2001). 0 7 14 -100 -200 -300 -400
Age, days 21 0.30 28 Shrinkage (x 10-6) 0.35 0.30 Drying 0.45 No water curing Video MOISTURE CHANGES (DRYING SHRINKAGE) OF HARDENED CONCRETE
Hardened concrete expands slightly with a gain in moisture and contracts with a loss in moisture. The effects of these moisture cycles are illustrated schematically in Fig. 15-8. Specimen A represents concrete stored continuously in water from time of casting. Specimen B represents the same concrete exposed first to drying in air and then to alternate cycles of wetting and drying. For comparative purposes, it should be noted that the swelling that occurs during continuous wet storage over a period of several years is usually less than 150 millionths; this is about onefourth of the shrinkage of air-dried concrete for the same period. Fig. 15-9 illustrates swelling of concretes wet cured for 7 days following by shrinkage when sealed or exposed Fig. 15-9. Length change of concrete samples exposed to different curing regimes (Atcin 1999). Stored in water Stored in air Swelling Specimen A Specimen B Drying Alternate wetting and drying Time Fig. 15-8. Schematic illustration of moisture movements in concrete. If concrete is kept continuously wet, a slight expansion occurs. However, drying usually takes place, causing shrinkage. Further wetting and drying causes alternate cycles of swelling and shrinkage (Roper 1960). 260 to air drying. Autogenous shrinkage reduces the volume of the sealed concretes to a level about equal to the amount of swelling at 7 days. Note that the concretes wet cured for 7 days had less shrinkage due to drying and autogenous effects than the concrete that had no water curing. This illustrates the importance of early, wet curing to minimize shrinkage (Atcin 1999). Tests indicate that the drying shrinkage of small, plain concrete specimens (without reinforcement) ranges from about 400 to 800 millionths when exposed to air at 50% humidity. Concrete with a unit drying shrinkage of 550 millionths shortens about the same amount as the thermal contraction caused by a decrease in temperature of 55C (100F). Preplaced aggregate concrete has a drying shrinkage of 200 to 400 millionths; this is considerably less than normal concrete due to point-to-point contact of aggregate particles in preplaced aggregate concrete. The drying shrinkage of structural lightweight concrete ranges from slightly less than to 30 percent more than that of normal-density concrete, depending on the type of aggregate used. The drying shrinkage of reinforced concrete is less than that for plain concrete, the difference depending on the amount of reinforcement. Steel reinforcement restricts but does not prevent drying shrinkage. In reinforced concrete structures with normal amounts of reinforcement, drying shrinkage is assumed to be 200 to 300 millionths. Similar values are found for slabs on ground restrained by subgrade. For many outdoor applications, concrete reaches its maximum moisture content in winter; so in winter the volume changes due to increase in moisture content and the decrease in average temperature tend to offset each other. The amount of moisture in concrete is affected by the relative humidity of the ambient air. The free moisture content of concrete elements after drying in air at relative Shrinkage Chapter 15 N Volume Changes of Concrete humidities of 50% to 90% for several months is about 1% to 2% by weight of the concrete; the actual amount depends on the concrete's constituents, original water content, drying conditions, and the size and shape of the concrete element. After concrete has dried to a constant moisture content at one relative humidity condition, a decrease in humidity causes it to lose moisture while an increase causes it to gain moisture. The concrete shrinks or swells with each such change in moisture content due primarily to responses of the cement paste to moisture changes. Most aggregates show little response to changes in moisture content, although there are a few aggregates that swell or shrink in response to such changes. As drying takes place, concrete shrinks. Where there is no restraint, movement occurs freely and no stresses or cracks develop (Fig. 15-10a top). If the tensile stress that results from restrained drying shrinkage exceeds the tensile strength of the concrete, cracks can develop (Fig. 15-10a bottom). Random cracks may develop if joints are not properly provided and the concrete element is restrained from shortening (Fig. 15-10b). Contraction joints for slabs on ground should be spaced at distances of 24 to 36 times the slab thickness to control random cracks (Fig. 15-10c). Joints in walls are equally important for crack control (Fig. 15-10d). Fig. 15-11 illustrates the relationship between drying rate at different depths, drying shrinkage, and mass loss for normal-density concrete (Hanson 1968). Shrinkage may continue for a number of years, depending on the size and shape of the concrete mass. The rate and ultimate amount of shrinkage are usually smaller for large masses of concrete than for small masses; on the other hand, shrinkage continues longer for large masses. Higher volume-to-surface ratios (larger elements) experience lower shrinkage as shown in Fig. 15-12. The rate and amount of drying shrinkage for small concrete specimens made with various cements are shown in Fig. 15-13. Specimens were initially moist-cured for 14 days at 21C (70F), then stored for 38 months in air at the same temperature and 50% relative humidity. Shrinkage recorded at the age of 38 months ranged from 600 to 790 millionths. An average of 34% of this shrinkage occurred within the first month. At the end of 11 months an average of 90% of the 38-month shrinkage had taken place. Shrinkage and cracking Slab Rollers Video Shrinkage + freedom to move = no cracks Slab Granular fill a Shrinkage + subbase restraint = cracks c b d Fig. 15-10. (a) Illustration showing no crack development in concrete that is free to shrink (slab on rollers); however, in reality a slab on ground is restrained by the subbase (or other elements) creating tensile stresses and cracks. (b) Typical shrinkage cracks in a slab on ground. (c) A properly functioning contraction joint controls the location of shrinkage cracking. (d) Contraction joints in the slabs and walls shown will minimize the formation of cracks. (A-5271, 4434, 1144) 261 Design and Control of Concrete Mixtures
100 90 80 70 60 50 N EB001
1200 Relative humidity, percent Normal-density concrete Cement content: 270 kg/m3 (454 lb/yd 3 ) w/c ratio: 0.66
1000 Environment: Air-dry specimens at 21C (70F), 50% RH Specimens sealed in rubber tubes and stored in a fog room (bottom curve only) 100 mm (4 in.) diameter specimens in air 75 mm (3 in.) depth 45 (13/4)
Shrinkage strain, millionths 20 (3/4) 6 (1/4) 800 150 mm (6 in.) 200 mm (8 in.
300 m ) m (12 in.) 400 mm (16 in.) 400
600 mm 0 in.) 500 mm (2
(24 in.) 800
200 Shrinkage, millionths 600
150 mm (6 in.) diameter sealed specimens 400 0 0 200
Time, days 400 600 200 Normal-density concrete
0 Fig. 15-12. Drying shrinkage of various sizes of cylindrical specimens made of Elgin, Illinois gravel concrete (Hansen and Mattock 1966). 0.6 0.5 0.4
Mass loss, kg
1000 1200 0.3 0.2 0.1 0 0 75 150 225 Time of drying, days 300 375 Normal-density concrete
Drying shrinkage, millionths 800 Specimens: 100 x 100 x 1000 mm (4 x 4 x 40 in.) concrete beams Cement content: 335 kg/m3 (564 lb/yd3) Curing: 14 days moist at 21C (70C), then in air at 50% RH and 21C (70C) 38 mo. 28 mo. 11 mo. 1 mo. 600 400 Fig. 15-11. Relative humidity distribution at various depths, drying shrinkage, and mass loss of 150 300-mm (6 12in.) cylinders moist-cured for 7 days followed by drying in laboratory air at 23C (73F) and 50% RH (Hanson 1968). 200 0 I II III Type of cement IV V Fig. 15-13. Results of long-term drying shrinkage tests by the U.S. Bureau of Reclamation. Shrinkage ranged from 600 to 790 millionths after 38 months of drying. The shrinkage of concretes made with air-entraining cements was similar to that for non-air-entrained concretes in this study (Bureau of Reclamation 1947 and Jackson 1955). 262 Chapter 15 N Volume Changes of Concrete Effect of Concrete Ingredients on Drying Shrinkage
The most important controllable factor affecting drying shrinkage is the amount of water per unit volume of concrete. The results of tests illustrating the water content to shrinkage relationship are shown in Fig. 15-14. Shrinkage can be minimized by keeping the water content of concrete as low as possible. This is achieved by keeping the total coarse aggregate content of the concrete as high as possible (minimizing paste content). Use of low slumps and placing methods that minimize water requirements are thus major factors in controlling concrete shrinkage. Any practice that increases the water requirement of the cement paste, such as the use of high slumps (without superplasticizers), excessively high freshly mixed concrete temperatures, high fine-aggregate contents, or use of smallsize coarse aggregate, will increase shrinkage. A small amount of water can be added to ready mixed concrete at the jobsite without affecting drying shrinkage properties as long as the additions are within mix specifications (Suprenant and Malisch 2000). The general uniformity of shrinkage of concretes with different types of cement at different ages is illustrated in Fig. 15-13. However, this does not mean that all cements or cementing materials have similar shrinkage. 0.1 Control 0.08 Drying shrinkage, % Class C 0.06 Class F 0.04 0.02 ASTM C 157 0 0 7 14 21 28 35 Age, weeks 42 49 56 63 Fig. 15-15. Drying shrinkage of fly ash concretes compared to a control mixture. The graphs represent the average of four Class C ashes and six Class F ashes, with the range in drying shrinkage rarely exceeding 0.01 percentage points. Fly ash dosage was 25% of the cementing material (Gebler and Klieger 1986). Water, lb/yd3 210 1400 250 290 340 380 420 460 1200 1000 Drying, shrinkage, millionths 800 600 400 200 0 125 150 175 200 225 Water, kg/m3 250 275 Fig. 15-14. Relationship between total water content and drying shrinkage. A large number of mixtures with various proportions is represented within the shaded area of the curves. Drying shrinkage increases with increasing water contents. 263 Supplementary cementing materials usually have little effect on shrinkage at normal dosages. Fig. 15-15 shows that concretes with normal dosages of selected fly ashes performed similar to the control concrete made with only portland cement as the cementing material. Aggregates in concrete, especially coarse aggregate, physically restrain the shrinkage of hydrating cement paste. Paste content affects the drying shrinkage of mortar more than that of concrete. Drying shrinkage is also dependent on the type of aggregate. Hard, rigid aggregates are difficult to compress and provide more restraint to shrinkage than softer, less rigid aggregates. As an extreme example, if steel balls were substituted for ordinary coarse aggregate, shrinkage would be reduced 30% or more. Drying shrinkage can also be reduced by avoiding aggregates that have high drying shrinkage properties and aggregates containing excessive amounts of clay. Quartz, granite, feldspar, limestone, and dolomite aggregates generally produce concretes with low drying shrinkages (ACI Committee 224). Steam curing will also reduce drying shrinkage. Most chemical admixtures have little effect on shrinkage. The use of accelerators such as calcium chloride will increase drying shrinkage of concrete. Despite reductions in water content, some water-reducing admixtures can increase drying shrinkage, particularly those that contain an accelerator to counteract the retarding effect of the admixture. Air entrainment has little or no effect on drying shrinkage. High-range water reducers usually have little effect on drying shrinkage (Fig. 15-16). Drying shrinkage can be evaluated in accordance with ASTM C 157 (AASHTO T 160). Design and Control of Concrete Mixtures
0.06 N EB001 Steam curing will also reduce drying shrinkage. Computer software is available to predict the effect of curing and environmental conditions on shrinkage and cracking (FHWA and Transtec 2001). Hedenblad (1997) provides tools to predict the drying of concrete as effected by different curing methods and type of construction. 0.05 Drying shrinkage, % 0.04 C 0.03 N M 0.02 Cement content = 323 kg/m3 (545 lb/yd3) X TEMPERATURE CHANGES OF HARDENED CONCRETE
Concrete expands slightly as temperature rises and contracts as temperature falls, although it can expand slightly as free water in the concrete freezes. Temperature changes may be caused by environmental conditions or by cement hydration. An average value for the coefficient of thermal expansion of concrete is about 10 millionths per degree Celsius (5.5 millionths per degree Fahrenheit), although values ranging from 6 to 13 millionths per degree Celsius (3.2 to 7.0 millionths per degree Fahrenheit) have been observed. This amounts to a length change of 5 mm for 10 m of concrete (2/3 in. for 100 ft of concrete) subjected to a rise or fall of 50C (100F). The coefficient of thermal expansion for structural low-density (lightweight) concrete varies from 7 to 11 millionths per degree Celsius (3.6 to 6.1 millionths per degree Fahrenheit). The coefficient of thermal expansion of concrete can be determined by AASHTO TP 60. Thermal expansion and contraction of concrete varies with factors such as aggregate type, cement content, water-cement ratio, temperature range, concrete age, and relative humidity. Of these, aggregate type has the greatest influence. Table 15-1 shows some experimental values of the thermal coefficient of expansion of concretes made with aggregates of various types. These data were obtained from tests on small concrete specimens in which all factors were the same except aggregate type. In each case, the fine aggregate was of the same material as the coarse aggregate. The thermal coefficient of expansion for steel is about 12 millionths per degree Celsius (6.5 millionths per degree Fahrenheit), which is comparable to that for concrete. The coefficient for reinforced concrete can be assumed as 11 millionths per degree Celsius (6 millionths per degree Fahrenheit), the average for concrete and steel. Temperature changes that result in shortening can crack concrete members that are highly restrained by another part of the structure or by ground friction. Consider a long restrained concrete member cast without joints that, after moist curing, is allowed to drop in temperature. As the temperature drops, the concrete wants to shorten, but cannot because it is restrained longitudinally. The resulting tensile stresses cause the concrete to crack. Tensile strength and modulus of elasticity of concrete both may be assumed proportional to the square root of concrete compressive strength. And calculations show that a large enough tem264 0.01 ASTM C 157 0 0 8 16 Age, weeks 24 32 Fig. 15-16. Drying shrinkage of concretes made with selected high-range water reducers (N,M, and X) compared to a control mixture (C) (Whiting and Dziedzic 1992). Effect of Curing on Drying Shrinkage
The amount and type of curing can effect the rate and ultimate amount of drying shrinkage. Curing compounds, sealers, and coatings can trap free moisture in the concrete for long periods of time, resulting in delayed shrinkage. Wet curing methods, such as fogging or wet burlap, hold off shrinkage until curing is terminated, after which the concrete dries and shrinks at a normal rate. Cooler initial curing temperatures can reduce shrinkage (Fig. 15-17).
0.1 0.08 Drying shrinkage, % 0.06 23 C F) (73
F) (40 C 4 0.04
Cement content = 307 kg/m3 (517 lb/yd3) 0.02
ASTM C 157 0 0 8 16 24 32 40 Age, weeks 48 56 64 Fig. 15-17. Effect of initial curing on drying shrinkage of portland cement concrete prisms. Concrete with an initial 7day moist cure at 4C (40F) had less shrinkage than concrete with an initial 7-day moist cure at 23C (73F). Similar results were found with concretes containing 25% fly ash as part of the cementing material (Gebler and Klieger 1986). Chapter 15 N Volume Changes of Concrete Table 15-1. Effect of Aggregate Type on Thermal Coefficient of Expansion of Concrete
Aggregate type (from one source) Quartz Sandstone Gravel Granite Basalt Limestone Coefficient of expansion, millionths per C 11.9 11.7 10.8 9.5 8.6 6.8 Coefficient of expansion, millionths per F 6.6 6.5 6.0 5.3 4.8 3.8 Low Temperatures
Concrete continues to contract as the temperature is reduced below freezing. The amount of volume change at subfreezing temperatures is greatly influenced by the moisture content, behavior of the water (physical state-- ice or liquid), and type of aggregate in the concrete. In one study, the coefficient of thermal expansion for a temperature range of 24C to -157C (75F to 250F) varied from 6 x 10-6 per C (3.3 x 10-6 per F) for a low density (lightweight) aggregate concrete to 8.2 x 10-6 per C (4.5 x 10-6 per F) for a sand and gravel mixture. Subfreezing temperatures can significantly increase the compressive and tensile strength and modulus of elasticity of moist concrete. Dry concrete properties are not as affected by low temperatures. In the same study, moist concrete with an original compressive strength of 35 MPa at 24C (5000 psi at 75F) achieved over 117 MPa (17,000 psi) at 100C (150F). The same concrete tested ovendry or at a 50% internal relative humidity had strength increases of only about 20%. The modulus of elasticity for sand and gravel concrete with 50% relative humidity was only 8% higher at 157C than at 24C (250F than at 75F), whereas the moist concrete had a 50% increase in modulus of elasticity. Going from 24C to 157C (75F to 250F), the thermal conductivity of normal-weight concrete also increased, especially for moist concrete. The thermal conductivity of lightweight aggregate concrete is little affected (Monfore and Lentz 1962 and Lentz and Monfore 1966). Coefficients of concretes made with aggregates from different sources may vary widely from these values, especially those for gravels, granites, and limestones (Davis 1930). perature drop will crack concrete regardless of its age or strength, provided the coefficient of expansion does not vary with temperature and the concrete is fully restrained (FHWA and Transtec 2001 and PCA 1982). Precast wall panels and slabs and pavements on ground are susceptible to bending and curling caused by temperature gradients that develop when concrete is cool on one side and warm on the other. The calculated amount of curling in a wall panel is illustrated in Fig. 15-18. For the effect of temperature changes in mass concrete due to heat of hydration, see Chapter 18. High Temperatures
Temperatures greater than 95C (200F) that are sustained for several months or even several hours can have significant effects on concrete. The total amount of volume change of concrete is the sum of volume changes of the cement paste and aggregate. At high temperatures, the paste shrinks due to dehydration while the aggregate expands. For normal-aggregate concrete, the expansion of the aggregate exceeds the paste shrinkage resulting in an overall expansion of the concrete. Some aggregates such as expanded shale, andesite, or pumice with low coefficients of expansion can produce a very volume-stable concrete in high-temperature environments (Fig. 15-19). On the other hand, some aggregates undergo extensive and abrupt volume changes at a particular temperature, causing disruption in the concrete. For example, in one study a dolomitic limestone aggregate contained an iron sulfide impurity caused severe expansion, cracking, and disintegration in concrete exposed to a temperature of 150C (302F) for four months; at temperatures above and below 150C (302F) there was no detrimental expansion (Carette, Painter, and Malhotra 1982). The coefficient of thermal expansion tends to increase with temperature rise. Besides volume change, sustained high temperatures can also have other, usually irreversible, effects such as a
265 Warm side T1 = 20C Cold side T2 = -6C = (T1 T2) L 2 8t L = 3 m = 3000 mm = Coefficient of expansion per C t = Panel thickness = 2 mm When = 0.00001 per C (20 + 6) x 0.00001 x 30002 = 8 x 150 = 2 mm Concrete thickness t = 150 mm Fig. 15-18. Curling of a plain concrete wall panel due to temperature that varies uniformly from inside to outside. Design and Control of Concrete Mixtures
Temperature, F 800 N EB001 If stable aggregates are used and strength reduction and the effects on other properties are accounted for in the mix design, high quality concrete can be exposed to temperatures of 90C to 200C (200F to 400F) for long periods. Some concrete elements have been exposed to temperatures up to 250C (500F) for long periods of time; however, special steps should be taken or special materials (such as heat-resistant calcium aluminate cement) should be considered for exposure temperatures greater than 200C (400F). Before any structural concrete is exposed to high temperatures (greater than 90C or 200F), laboratory testing should be performed to determine the particular concrete's thermal properties. This will avoid any unexpected distress. 0 Expansion, mm/mm (in./in.) 400 1200 Siliceous 0.008 Carbonate 0.004 Sanded expanded shale 0 0 200 400 Temperature, C 600 Fig. 15-19. Thermal expansion of concretes containing various types of aggregate (Abrams 1977). CURLING (WARPING)
In addition to horizontal movement caused by changes in moisture and temperature, curling of slabs on ground can be a problem; this is caused by differences in moisture content and temperature between the top and bottom of slabs (Fig. 15-21). The edges of slabs at the joints tend to curl upward when the surface of a slab is drier or cooler than the bottom. A slab will assume a reverse curl when the surface is wetter or warmer than the bottom. However, enclosed slabs, such as floors on ground, curl only upward. When the edges of an industrial floor slab are curled upward they lose support from the subbase and become a cantilever. Lift-truck traffic passing over joints causes a repetitive vertical deflection that creates a great potential for fatigue cracking in the slab. The amount of vertical upward curl (curling) is small for a short, thick slab. reduction in strength, modulus of elasticity, and thermal conductivity. Creep increases with temperature. Above 100C (212F), the paste begins to dehydrate (lose chemically combined water of hydration) resulting in significant strength losses. Strength decreases with increases in temperature until the concrete loses essentially all its strength. The effect of high-temperature exposure on compressive strength of concretes made with various types of aggregate is illustrated in Fig. 15-20. Several factors including concrete moisture content, aggregate type and stability, cement content, exposure time, rate of temperature rise, age of concrete, restraint, and existing stress all influence the behavior of concrete at high temperatures. 100
Compressive strength, percent of original 70 400 Temperature, F 800 1200 Video Sanded expanded shale aggregate 75
Carbonate aggregate Siliceous aggregate 50 25 Heated unstressed, then stored 7 days at 21C (70F) Avg. original strength = 27 MPa (3900 psi) 0 20 200 400 Temperature, C 600 800 Fig. 15-20. Effect of high temperatures on the residual compressive strength of concretes containing various types of aggregate (Abrams 1973). Fig. 15-21. Illustration of curling of a concrete slab on ground. The edge of the slab at a joint or free end lifts off the subbase creating a cantilevered section of concrete that can break off under heavy wheel loading. 266 Chapter 15 N Volume Changes of Concrete Curling can be reduced or eliminated by using design and construction techniques that minimize shrinkage differentials and by using techniques described earlier to reduce temperature and moisture-related volume changes. Thickened edges, shorter joint spacings, permanent vaporimpermeable sealers, and large amounts of reinforcing steel placed 50 mm (2 in.) below the surface all help reduce curling (Ytterberg 1987).
Inelastic deformation Stress, f sti Lo c ran ad ge li n e cov e ry l ine Re ELASTIC AND INELASTIC DEFORMATION Compression Strain
The series of curves in Fig. 15-22 illustrate the amount of compressive stress and strain that results instantaneously due to loading of unreinforced concrete. With water-cement ratios of 0.50 or less and strains up to 1500 millionths, the upper three curves show that strain is closely proportional to stress; in other words, the concrete is almost elastic. The upper portions of the curves and beyond show that the concrete is inelastic. The curves for high-strength concrete have sharp peaks, whereas those for lower-strength concretes have long and relatively flat peaks. Fig. 15-22 also shows the sudden failure characteristics of higher strength, low water to cement ratio, concrete cylinders. When load is removed from concrete in the inelastic zone, the recovery line usually is not parallel to the original line for the first load application. Therefore, the amount of permanent set may differ from the amount of inelastic deformation (Fig. 15-23). Ela f Modulus of elasticity = E = f Strain, Permanent set Fig. 15-23. Generalized stress-strain curve for concrete. The term "elastic" is not favored for general discussion of concrete behavior because frequently the strain may be in the inelastic range. For this reason, the term "instantaneous strain" is often used. Modulus of Elasticity
The ratio of stress to strain in the elastic range of a stressstrain curve for concrete defines the modulus of elasticity (E) of that concrete (Fig. 15-23). Normal-density concrete has a modulus of elasticity of 14,000 to 41,000 MPa 60 Water-to-cement ratio: 0.33 50 0.40 P Concrete stress, 1000 psi 40 Concrete stress, MPa 0.50 30 4 6 8 150 mm (6 in.) 20 0.67 2 10 1.00 0 1000 2000 3000 Strain-concentric compression tests, millionths 4000 5000 Fig. 15-22. Stress-strain curves for compression tests on 150 (Hognestad, Hanson, and McHenry 1955). 267 300-mm (6 12-in.) concrete cylinders at an age of 28 days 300 mm (12 in.) Design and Control of Concrete Mixtures N EB001 (2,000,000 psi to 6,000,000 psi), depending on factors such as compressive strength and aggregate type. For normaldensity concrete with compressive strengths () between 20 MPa and 35 MPa (3000 psi and 5000 psi), the modulus of elasticity can be estimated as 5000 times the square root of (57,000 times the square root of in psi). The modulus of elasticity for structural lightweight concrete is between 7000 MPa and 17,000 MPa (1,000,000 psi and 2,500,000 psi). E for any particular concrete can be determined in accordance with ASTM C 469. Shear Strain
Concrete, like other materials, deforms under shear forces. The shear strain produced is important in determining the load paths or distribution of forces in indeterminate structures--for example where shear-walls and columns both participate in resisting horizontal forces in a concrete building frame. The amount of movement, while not large, is significant in short, stubby members; in larger members it is overshadowed by flexural strains. Calculation of the shear modulus (modulus of rigidity), G, is shown in Fig. 15-25; G varies with the strength and temperature of the concrete.
Displacement 2 = 6wh 10GA Area = A Deflection
Deflection of concrete beams and slabs is one of the more common and obvious building movements. The deflections are the result of flexural strains that develop under dead and live loads and that may result in cracking in the tensile zone of concrete members. Reinforced concrete structural design anticipates these tension cracks. Concrete members are often cambered, that is, built with an upward bow, to compensate for the expected later deflection. Poisson's Ratio
When a block of concrete is loaded in uniaxial compression, as in Fig. 15-24, it will shorten and at the same time develop a lateral strain or bulging. The ratio of lateral to axial strain is called Poisson's ratio, . A common value used is 0.20 to 0.21, but the value may vary from 0.15 to 0.25 depending upon the aggregate, moisture content, concrete age, and compressive strength. Poisson's ratio (ASTM C 469) is generally of no concern to the structural designer; it is used in advanced structural analysis of flat-plate floors, shell roofs, arch dams, and mat foundations. w h E 2(1 + ) G= Fig. 15-25. Strain that results from shear forces on a body. G = shear modulus. = Poisson's ratio. Strain resulting from flexure is not shown. Torsional Strain
Plain rectangular concrete members can also fail in torsion, that is, a twisting action caused by bending about an axis parallel to the wider face and inclined at an angle of about 45 degrees to the longitudinal axis of a member. Microcracks develop at low torque; however, concrete behaves reasonably elastic up to the maximum limit of the elastic torque (Hsu 1968).
When concrete is loaded, the deformation caused by the load can be divided into two parts: a deformation that occurs immediately (elastic strain) and a time-dependent deformation that begins immediately but continues at a decreasing rate for as long as the concrete is loaded. This latter deformation is called creep. The amount of creep is dependent upon (1) the magnitude of stress, (2) the age and strength of the concrete
268 Video Fig. 15-24. Ratio of lateral to axial strain is Poisson's ratio, . Chapter 15 N Volume Changes of Concrete when stress is applied, and (3) the length of time the concrete is stressed. It is also affected by other factors related to the quality of the concrete and conditions of exposure, such as: (1) type, amount, and maximum size of aggregate; (2) type of cementing materials; (3) amount of cement paste; (4) size and shape of the concrete element; (5) volume to surface ratio of the concrete element; (6) amount of steel reinforcement; (7) prior curing conditions; and (8) the ambient temperature and humidity. Within normal stress ranges, creep is proportional to stress. In relatively young concrete, the change in volume or length due to creep is largely unrecoverable; in older or drier concrete it is largely recoverable. The creep curves shown in Fig. 15-26 are based on tests conducted under laboratory conditions in accordance with ASTM C 512. Cylinders were loaded to almost 40% of their compressive strength. Companion cylinders not subject to load were used to measure drying shrinkage; this was then deducted from the total deformation of the loaded specimens to determine creep. Cylinders were allowed to dry while under load except for those marked "sealed." The two 28-day curves for each concrete strength in Fig. 15-26 show that creep of concrete loaded under drying conditions is greater than creep of concrete sealed against drying. Concrete specimens loaded at a late age will creep less than those loaded at an early age. It can be seen that as concrete strength
Strain per MPa of stress, percent Load removed 0.0100 Instantaneous recovery 0.0075 Creep strain 0.0050 0.0025 Irrecoverable creep Creep recovery 0.08 0.06 0.04 0.02 Elastic strain 0 400 Permanent set 1600 800 1200 Time, days Fig. 15-27. Combined curve of elastic and creep strains showing amount of recovery. Specimens (cylinders) were loaded at 8 days immediately after removal from fog curing room and then stored at 21C (70F) and 50% RH. The applied stress was 25% of the compressive strength at 8 days (Hansen and Mattock 1966). decreases, creep increases. Fig. 15-27 illustrates recovery from the elastic and creep strains after load removal. A combination of strains occurring in a reinforced column is illustrated in Fig. 15-28. The curves represent deformations and volume changes in a 14th-story column of a 76-story reinforced concrete building while under construction. The 400 x 1200-mm (16 x 48-in.) column contained 2.08% vertical reinforcement and was designed for 60-MPa (9000-psi) concrete. 10 Concrete strength, 28 MPa (4000 psi) Age of loading 28 days 1.5 1500 Total 1.0 5 90 28 (sealed) 180 0.5 1200 Creep strain, millionths per kPa Creep strain, millionths per psi Compressive strain, millionths Creep 900 0 7.5 Concrete strength, 41 MPa (6000 psi) 5 Age of loading 28 days 0 1.0 Drying shrinkage 600 0.5 90 28 (sealed) 360 0 250 500 750 Age, days 1000 1250 0 300 Instantaneous deformation 0 0 500 Age, days 1000 1500 Fig. 15-26. Relationship of time and age of loading to creep of two different strength concretes. Specimens were allowed to dry during loading, except for those labeled as sealed (Russell and Corley 1977). 269 Fig. 15-28. Summation of strains in a reinforced concrete column during construction of a tall building (Russell and Corley 1977). Strain per 1000 psi of stress, percent Design and Control of Concrete Mixtures N EB001 in-place concrete is insignificant and does not have to be considered in engineering practice. Carbonation of paste proceeds slowly and produces little direct shrinkage at relative humidities of 100% and 25%. Maximum carbonation and carbonation shrinkage occurs at about 50% relative humidity. Irreversible shrinkage and weight gain occurs during carbonation. And the carbonated product may show improved volume stability to subsequent moisture change and reduced permeability (Verbeck 1958). During manufacture some concrete masonry units are deliberately exposed to carbon dioxide after reaching 80% of their rated strength; this introduction to carbonation shrinkage makes the units more dimensionally stable. Future drying shrinkage is reduced 30% or more (Toennies and Shideler 1963). One of the causes of surface crazing of concrete is the shrinkage that accompanies natural air carbonation of young concrete. More research is needed on the effect of early carbonation on deicer scaling resistance. Carbonation of another kind also can occur in freshly placed, unhardened concrete. This carbonation causes a soft, chalky surface called dusting; it usually takes place during cold-weather concreting when there is an unusual amount of carbon dioxide in the air due to unvented heaters or gasoline-powered equipment operating in an enclosure. moist-c 7 days ure d
-c ure d Creep deformation m heric stea Atmosp Note: Same concrete strength at time of loading in all cases High-pressure steam-cured 0 50 100 150 200 250 300 350 Time after loading, days Fig. 15-29. Effect of curing method on magnitude of creep for typical normal-density concrete (Hanson 1964). The method of curing prior to loading has a marked effect on the amount of creep in concrete. The effects on creep of three different methods of curing are shown in Fig. 15-29. Note that very little creep occurs in concrete that is cured by high-pressure steam (autoclaving). Note also that atmospheric steam-cured concrete has considerably less creep than 7-day moist-cured concrete. The two methods of steam curing shown in Fig. 15-29 reduce drying shrinkage of concrete about half as much as they reduce creep. Sulfate Attack
Sulfate attack of concrete can occur where soil and groundwater have a high sulfate content and measures to reduce sulfate attack, such as use of a low water to cementing materials ratio, have not been taken. The attack is greater in concrete that is exposed to wetting and drying, such as foundation walls and posts. Sulfate attack usually results in an expansion of the concrete because of the formation of solids from the chemical action or salt crystallization. The amount of expansion in severe circumstances has been significantly higher than 0.1%, and the disruptive effect within the concrete can result in extensive cracking and disintegration. The amount of expansion cannot be accurately predicted. CHEMICAL CHANGES AND EFFECTS
Some volume changes of concrete result from chemical reactions; these may take place shortly after placing and finishing or later due to reactions within the hardened concrete in the presence of water or moisture. Carbonation
Hardened concrete containing some moisture reacts with carbon dioxide present in air, a reaction that results in a slight shrinkage of the surface paste of the concrete. The effect, known as carbonation, is not destructive but actually increases the chemical stability and strength of the concrete. However, carbonation also reduces the pH of concrete. If steel is present in the carbonated area, steel corrosion can occur due to the absence of the protective oxide film provided by concrete's high pH. Rust is an expansive reaction and results in cracking and spalling of the concrete. The depth of carbonation is very shallow in dense, high-quality concrete, but can penetrate deeply in porous, poor-quality concrete. Because so little of a concrete element carbonates, carbonation shrinkage of cast270 Alkali-Aggregate Reactions
Certain aggregates can react with alkali hydroxides in concrete, causing expansion and cracking over a period of years. The reaction is greater in those parts of a structure exposed to moisture. A knowledge of the characteristics of local aggregates is essential. There are two types of alkalireactive aggregates, siliceous and carbonate. Alkali-aggregate reaction expansion may exceed 0.5% in concrete and can cause the concrete to fracture and break apart. Structural design techniques cannot counter the effects of alkali-aggregate expansion, nor can the expan- Chapter 15 N Volume Changes of Concrete sion be controlled by jointing. In areas where deleteriously reactive aggregates are known to exist, special measures must be taken to prevent the occurrence of alkali-aggregate reaction. Bureau of Reclamation, "Long-Time Study of Cement Performance in Concrete--Tests of 28 Cements Used in the Parapet Wall of Green Mountain Dam," Materials Laboratories Report No. C-345, U.S. Department of the Interior, Bureau of Reclamation, Denver, 1947. Carette, G. G.; Painter, K. E.; and Malhotra, V. M., "Sustained High Temperature Effect on Concretes Made with Normal Portland Cement, Normal Portland Cement and Slag, or Normal Portland Cement and Fly Ash," Concrete International, American Concrete Institute, Farmington Hills, Michigan, July 1982. Carlson, Roy W., "Drying Shrinkage of Concrete as Affected by Many Factors," Proceedings of the Forty-First Annual Meeting of the American Society for Testing and Materials, vol. 38, part II, Technical Papers, American Society for Testing and Materials, West Conshohocken, Pennsylvania, 1938, pages 419 to 440. Copeland, L. E., and Bragg, R. H., Self Desiccation in Portland Cement Pastes, Research Department Bulletin RX052, Portland Cement Association, http://www.port cement.org/pdf_files/RX052.pdf, 1955. Cruz, Carlos R., Elastic Properties of Concrete at High Temperatures, Research Department Bulletin RX191, Portland Cement Association, http://www.portcement.org/ pdf_files/RX191.pdf, 1966. Cruz, C. R., and Gillen, M., Thermal Expansion of Portland Cement Paste, Mortar, and Concrete at High Temperatures, Research and Development Bulletin RD074, Portland Cement Association, http://www.portcement.org/pdf_ files/RD074.pdf, 1980. Davis, R. E., "A Summary of the Results of Investigations Having to Do with Volumetric Changes in Cements, Mortars, and Concretes Due to Causes Other Than Stress," Proceedings of the American Concrete Institute, American Concrete Institute, Farmington Hills, Michigan, vol. 26, 1930, pages 407 to 443. FHWA and Transtec, HIPERPAV, http://www.hiperpav. com, 2001. Gebler, Steven H., and Klieger, Paul, Effect of Fly Ash on Some of the Physical Properties of Concrete, Research and Development Bulletin RD089, Portland Cement Association, http://www.portcement.org/pdf_files/RD089.pdf, 1986. Hammer, T. A., "Test Methods for Linear Measurement of Autogenous Shrinkage Before Setting," Autogenous Shrinkage of Concrete, edited by E. Tazawa, E&FN Spon and Routledge, New York, 1999, pages 143 to 154. Also available through PCA as LT245. Hanson, J. A., Prestress Loss As Affected by Type of Curing, Development Department Bulletin DX075, Portland Cement Association, http://www.portcement.org/pdf_ files/DX075.pdf, 1964.
Abrams, M. S., Compressive Strength of Concrete at Temperatures to 1600F, Research and Development Bulletin RD016, Portland Cement Association, http://www. portcement.org/pdf_files/RD016.pdf, 1973. Abrams, M. S., Performance of Concrete Structures Exposed to Fire, Research and Development Bulletin RD060, Portland Cement Association, http://www.portcement.org/ pdf_files/RD060.pdf, 1977. Abrams, M. S., Behavior of Inorganic Materials in Fire, Research and Development Bulletin RD067, Portland Cement Association, http://www.portcement.org/pdf_ files/RD067.pdf, 1979. Abrams, M. S., and Orals, D. L., Concrete Drying Methods and Their Effects on Fire Resistance, Research Department Bulletin RX181, Portland Cement Association, http:// www.portcement.org/pdf_files/RX181.pdf, 1965. ACI Committee 209, Prediction of Creep, Shrinkage, and Temperature Effects in Concrete Structures, ACI 209R-92, reapproved 1997, American Concrete Institute, Farmington Hills, Michigan, 1997, 47 pages. 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Design and Control of Concrete Mixtures N EB001 Kosmatka, Steven H., "Floor-Covering Materials and Moisture in Concrete," Concrete Technology Today, PL853, Portland Cement Association, http://www.portcement. org/pdf_files/PL853.pdf, 1985. Le Chatelier, H., "Sur les Changements de Volume qui Accompagent le durcissement des Ciments," Bulletin Societe de l`Encouragement pour l`Industrie Nationale, 5eme serie, tome 5, Paris, 1900. Lentz, A. E., and Monfore, G. E., Thermal Conductivities of Portland Cement Paste, Aggregate, and Concrete Down to Very Low Temperatures, Research Department Bulletin RX207, Portland Cement Association, http://www.portcement. org/pdf_files/RX207.pdf, 1966. Lerch, William, Studies of Some Methods of Avoiding the Expansion and Pattern Cracking Associated with the AlkaliAggregate Reaction, Research Department Bulletin RX031, Portland Cement Association, http://www.portcement. org/pdf_files/RX031.pdf, 1950. Malhotra, M. L., "The Effect of Temperature on the Compressive Strength of Concrete," Magazine of Concrete Research, vol. 8., no. 23, Cement and Concrete Association, Wexham Springs, Slough, England, August 1956, pages 85 to 94. Monfore, G. E., A Small Probe-Type Gage for Measuring Relative Humidity, Research Department Bulletin RX160, Portland Cement Association, http://www.portcement. org/pdf_files/RX160.pdf, 1963. Monfore, G. E., and Lentz, A. E., Physical Properties of Concrete at Very Low Temperatures, Research Department Bulletin RX145, Portland Cement Association, http:// www.portcement.org/pdf_files/RX145.pdf, 1962. Nawy, Edward G.; Barth, Florian G.; and Frosch, Robert J., Design and Construction Practices to Mitigate Cracking, SP-204, American Concrete Institute, Farmington Hills, Michigan, 2001, 284 pages. PCA, Effect of Long Exposure of Concrete to High Temperature, ST32, Portland Cement Association, 1969. 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Hedenblad, Gran, "Concrete Drying Time," PL982, Concrete Technology Today, Portland Cement Association, http: //www.portcement.org/pdf_files/PL982.pdf, July 1998. Hedenblad, Gran, Drying of Construction Water in Concrete, Byggforskningsradet, The Swedish Council for Building Research, Stockholm, 1997 [PCA LT229]. Helmuth, Richard A., and Turk, Danica H., The Reversible and Irreversible Drying Shrinkage of Hardened Portland Cement and Tricalcium Silicate Pastes, Research Department Bulletin RX215, Portland Cement Association, http:// www.portcement.org/pdf_files/RX215.pdf, 1967. Holt, Erika E., Early Age Autogenous Shrinkage of Concrete, VTT Publication 446, Technical Research Center of Finland, Espoo, 2001, 194 pages. Also available through PCA as LT257. Holt, Erika E., and Janssen, Donald J., "Influence of Early Age Volume Changes on Long-Term Concrete Shrinkage," Transportation Research Record 1610, Transportation Research Board, National Research Council, Washington, D.C., 1998, pages 28 to 32. Hognestad, E.; Hanson, N. W.; and McHenry, D., Concrete Stress Distribution in Ultimate Strength Design, Development Department Bulletin DX006, Portland Cement Association, http://www.portcement.org/pdf_files/DX006.pdf, 1955. Hsu, Thomas T. C., Torsion of Structural Concrete--Plain Concrete Rectangular Sections, Development Department Bulletin DX134, Portland Cement Association, http:// www.portcement.org/pdf_files/DX134.pdf, 1968. Jackson, F. H., Long-Time Study of Cement Performance in Concrete--Chapter 9. Correlation of the Results of Laboratory Tests with Field Performance Under Natural Freezing and Thawing Conditions, Research Department Bulletin RX060, Portland Cement Association, http://www.portcement. org/pdf_files/RX060.pdf, 1955. 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Roper, Harold, Volume Changes of Concrete Affected by Aggregate Type, Research Department Bulletin RX123, Portland Cement Association, http://www.portcement. org/pdf_files/RX123.pdf, 1960. Russell, H. G., and Corley, W. G., Time-Dependent Behavior of Columns in Water Tower Place, Research and Development Bulletin RD052, Portland Cement Association, http:// www.portcement.org/pdf_files/RD052.pdf, 1977. Steinour, Harold H., "Some Effects of Carbon Dioxide on Mortars and Concrete--Discussion," Proceedings of the American Concrete Institute, vol. 55, American Concrete Institute, Farmington Hills, Michigan, 1959, pages 905 to 907. Suprenant, Bruce A., and Malisch, Ward R., "The Fiber Factor," Concrete Construction, Addison, Illinois, October 1999, pages 43 to 46. Suprenant, Bruce A., and Malisch, Ward R., "A New Look at Water, Slump, and Shrinkage," Concrete Construction, Addison, Illinois, April 2000, pages 48 to 53. Tazawa, Ei-ichi, Autogenous Shrinkage of Concrete, E & FN Spon and Routledge, New York, 1999, 428 pages [PCA LT245]. Toennies, H. T., and Shideler, J. J., Plant Drying and Carbonation of Concrete Block--NCMA-PCA Cooperative Program, Development Department Bulletin DX064, Portland Cement Association, http://www.portcement.org/pdf_ files/DX064.pdf, 1963. Tremper, Bailey, and Spellman, D. L., "Shrinkage of Concrete--Comparison of Laboratory and Field Performance," Highway Research Record Number 3, Properties of Concrete, Transportation Research Board, National Research Council, Washington, D.C., 1963. Verbeck, G. J., Carbonation of Hydrated Portland Cement, Research Department Bulletin RX087, Portland Cement Association, http://www.portcement.org/pdf_files/ RX087.pdf, 1958. Whiting, David A.; Detwiler, Rachel J.; and Lagergren, Eric S., "Cracking Tendency and Drying Shrinkage of Silica Fume Concrete for Bridge Deck Applications," ACI Materials Journal, American Concrete Institute, Farmington Hills, Michigan, JanuaryFebruary, 2000, pages 71 to 77. Whiting, D., and Dziedzic, W., Effects of Conventional and High-Range Water Reducers on Concrete Properties, Research and Development Bulletin RD107, Portland Cement Association, 1992. Ytterberg, Robert F., "Shrinkage and Curling of Slabs on Grade, Part I--Drying Shrinkage, Part II--Warping and Curling, and Part III-- Additional Suggestions," Concrete International, American Concrete Institute, Farmington Hills, Michigan, April 1987, pages 22 to 31; May 1987, pages 54 to 61; and June 1987, pages 72 to 81. 273 ...
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