Design recommendations for reinforced concrete cylindrical storage ...

Design recommendations for reinforced concrete cylindrical storage structures for aqueous materials' J. C. JOFRIET School of Engineering, University of C~telph,Cuelph, Ont., Canada N I C 2 W l

R. GREEN Civil Engineering Departrrzerlt, University of Wr~terloo,Waterloo, Ont., Canada N2L 3G1 AND

T. I. CAMPBELL

Can. J. Civ. Eng. Downloaded from www.nrcresearchpress.com by 99.225.101.131 on 07/08/16 For personal use only.

Civil Engineering Deprrrtmerzt, Q~teerl'sU~~iversiry, Kirzg.ston, Ont., Canada K7L 3N6 Rcceived May 12, 1986 Revised manuscript accepted March 24, 1987 The design of cylindrical non-prestressed concrete storage structures in Ontario does not appear governed by any standard or building code. Many aboveground water storage reservoirs In Ontario have deteriorated badly in a relatively short period of use. Many farm silos suffer from problems similar to those of the watcr storage reservoirs. This paper is concerned with the selection of the wall thickness and the hoop reinforcement for cylindrical storage tanks and silos for llquids or wet materials where tensile cracking of the concrete is to be limited. Three design criterla are presented. The first limits the circumferential tenslle stress in the concrete from lateral wall pressure, shrinkage, and temperature gradients in the wall. The second is concerned with the tension in the hoop reinforcement and guards against collapse. The thlrd limits the crack widths of the cracked concrete section. The most important design loads are discussed. Maximum values for hoop tension are provided for liquid pressures. A design temperature gradient of 15°C is recommended for design in southern Ontario. As well, appropriate values of shrinkage tensile stress are suggested. The collapse limit state criterion must be evaluated for the hoop steel stresses due to the lateral wall loads. The limit state criterion related to the hoop tensile stress in the concrete must be investigated for all possible load combinations of lateral wall load, shrinkage, and temperature gradients. Reasonable load combination factors have been recommended. Recommendations on the tensile strength of concrete and on appropriate strength factors have been made. Key words: cylindrical tank, design criteria, hoop stresses, reinforced concrete, silo, standpipe, storage of liquids, storage of saturated bulk materials. La conception des structures de stockage cylindriques en bCton non-prkcontraint ne semble soumise 51 aucune norme ou aucune exigence en Ontario. De nombreux rkservoirs d'eau en surface ont subi des dCsordres strieux durant une periode d'utilisation relativement courte. De nombreux silos ont connu des problkmes semblables a ceux des rCservoirs d'eau. Cette communication examine le choix de I'Cpaisseur de la paroi et du frettage dans le cas des rCservoirs de stockage cylindriques et des silos pour liquides ou matCriaux dCtrempCs lorsque la fissuration du bCton doit &trelimitCe. Trois critkres de conception sont prCsentCs. Le premier limite la contrainte de traction circonfCrentielle dans le bCton, causte par la pression de la paroi laterale, le retrait et les gradients de temperature dans le mur. Le second tient compte de la traction au niveau du frettage et prkvient l'effondrement. Le troisikme limite la largeur des fissures de la section de bCton ICzardt. Les plds importantes charges de calcul sont discuttes. Les valeurs maximales de traction du frettage sont fournies pour les pressions de liquide. Un gradient de tempirature de calcul de 15°C est recommand6 dans le sud de I'Ontario. De plus, des valeurs approprites de contrainte de traction due au retrait sont proposCes. Le critkre d'effondrement B 1'Ctat limite doit &tre CvaluC pour les contraintes circonfCrentielles causCes par les charges de la paroi laterale. Le critkre aux Ctats limites reliC i la contrainte de traction circonfCrentielle dans le bCton doit &treCtudit pour toutes les combinaisons possibles de charges (charge de la paroi lattrale, retrait et gradients de tempkrature). Des coefficients de simultanCitC de charges raisonnables sont recommandCs. Des recommandations relatives a la rCsistance 51 la traction du bCton et a des coefficients de resistance appropriCs sont Cgalement incluses. Mots clds : rCservoirs cylindriques, critkre de conception, contraintes circonftrentielles, bCton armC, silo, tuyau d'adduction, stockage de liquides, stockage de matCriaux en vrac saturCs. [Traduit par la revue] Can. J. Civ. Eng. 14, 542-549 (1987)

Introduction cylindrical non-prestressed reinforced concrete structures have for years provided economical and containers for the storage of liquids and solids in mild climates. cases where the height of the silo or tank is small to the diameter ( ~ i 1)~ bending . in the wall dominates. H ~in tall containers circumferential tension controls the design. NOTE: Written discussion of this paper is welcomed and will be received by the Editor until November 30, 1987 (address inside front cover). %is paper was presented at the Annual Conference of the Canadian Society for Civil Engineering, Toronto, Ontario, May 1986.

Non-prestressed reinforced concrete design of structures neglects the contribution of concrete in tension. The concrete is assumed to be cracked under service loads and the reinforcing steel provided takes care of the tensile stresses present. However, tensile cracking of the concrete is not acceptable in many storage structures liquids or saturated ~ ~ ~if these are ~ to contain ~ , solids. For instance, there is evidence that freezing will cause deterioration of the walls of water reservoirs until, eventually, leakage results (Campbell 1984; Campbell and Kong 1985; tower the presence Of cracks S1ater 1986). In allows the acidic silage juices to gain access to and severely corrode the reinforcing steel. The Ontario Building Code (OBC 1984) includes elevated 19857

:T ET AL.

543

teria related to concentric and eccentric ring tension in cylindrical storage structures. Loads that are typical of structures, such as dead, occupancy, wind, and earthquake loads, are not considered. A

r

Ground Tanks (G) Standpipes (S)


4-

FIG. 1. Squat and tall cylindrical storage structures. water reservoirs as part of the jurisdiction but does not provide any special provisions for the design of such structures. Slater (1985) has described the poor condition of many concrete water standpipes in southern Ontario, and indicates that design recommendations covering the design of these water-retaining structures is overdue. Little or no guidance can be found by designers of concrete silo structures in North American building codes, especially where it concerns performance in cold regions (CSA 1984; ACI 1983). Such codes include sections dealing with axially loaded compression members but none with respect to members subjected to axial tension except for shear capacity. ACI Committee 350 (1983) does make recommendations for cylindrical tanks. These recommendations accept cracking and attempt to minimize the resulting crack widths by specifying an extremely low allowable steel tensile stress (96 MPa (14 ksi)). Klein et al. (1981) pointed out that such a low allowable stress for the circumferential reinforcing steel leads to the use of increased steel percentages; this in turn causes high shrinkage tensile stresses in the concrete and defeats in part the objective of the specification to minimize tensile stress in the wall. The use of limit states applied only to the cracked cross section of a wall in circumferential tension, proposed by ACI Committee 350, allows the selection of the amount of reinforcing steel. The limits placed on the maximum crack width affect the size and spacing of the reinforcing steel. The concrete wall thickness must be chosen in some other way; rules of thumb, related to depth of water, economy of section, and others, are in use. The authors are aware of at least one standpipe with 3.5% circumferential reinforcing steel in the bottom portion of the wall! Jofriet (1982) has suggested that it may be possible to include tensile cracking of the silo or tank wall as an additional limit state allowing the selection of a wall thickness. This proposition is explored here. The major loads causing circumferential stresses in cylindrical storage structures will be discussed, load combinations and load factors will be examined, and design criteria will be proposed. The proposed load factors are based on a comparison of the loads on storage structures with those on buildings for which load factors are well accepted and regulated. The paper is restricted to considering loads and design cri-

Loads The loads and restrained deformations that have an effect on the circumferential stress in a cylindrical storage structure are those due to the lateral wall pressure exerted by the contained materials, including ice, shrinkage of the concrete, temperature gradients, and creep of the concrete. A discussion of each of these loads follows. Lateral wall pressure The variation of the lateral pressure with depth in storage structures for liquids and saturated materials is usually known, and the lateral pressure at any depth can be used to calculate the resulting ring tension. Boundary conditions that restrict the circumferential expansion and rotation of the bottom or the top of the wall affect the ring tension and cause the maximum to occur some distance from the boundary. Away from the boundaries, a lateral wall pressure, w , in a cylindrical container with a thin wall (D/b > 10) causes a ring tension T : in which D is equal to the inside diameter of the container if the wall is considered uncracked, and a value between the inside and outside diameters if the wall is cracked. A Portland Cement Association publication (PCA 1947) provides tables for the calculation of the hoop tension and the boundary bending moments and shear forces in shallow tanks. Figure 2 provides the maximum value of ring tension for taller and more slender tanks and silos (H2/Db > 15) with fixed and hinged conditions at the wall-floor junction. Figure 2 also includes a curve to determine the position of the maximum hoop tension, a H . In both figures the wall pressure is assumed to increase linearly from zero at the top to a value of pgH at the bottom, where p is the mass density of the liquid, g the gravitational acceleration, and H the maximum liquid depth. Lateral wall pressure may also be exerted by an ice cap or ice cylinder within a cylindrical structure (Slater 1985; Tuomioja et al. 1973). At below-freezing temperatures an ice cap may form at the top surface of the contents, while an ice cylinder may form on the inside perimeter of the wall. Pressure due to expansion of an ice cap under increasing temperature is concentrated over the thickness of the ice cap and causes both circumferential tension and longitudinal bending in the wall. An approach to determining these stresses has been proposed by Kong and Campbell (1987). A similar approach may be used to determine the pressure, and related stresses in the wall, due to an expanding ice cylinder. Development of charts suitable for this process is underway at present.

Temperature During operation of the cylindrical container substantial temperature differences can occur between the inside and outside faces of the wall, during both summer and winter seasons. If the temperature difference, AT, is uniform around the circumference, the cylinder will retain a circular shape; tensile stresses will develop on the cold face and compressive ones on the warm side. A constant temperature gradient through the wall thickness is a reasonable assumption for design. A linear stress

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C A N , J . CIV. ENG. VOL. 14, I987 1.05

Fixed Bow


r PCA limit

1

FIG. 3. Radial tensile stresses, f,, in a cylindrical wall due to a temperature gradient, AT.

FIG.2. Maximum hoop tension, T.,,,, and position of maximum hoop tension, Z, in tall cylindrical tanks. Upper graphs for fixed-base, lower graphs for pinned-base assumption.

variation will result. The overall diameter will increase or decrease as determined by the temperature change at the centre of the wall, AT/2, and maximum stresses, f,,, at the extreme fibres will be AT [2] f,, = -E,a, 2 in which a, and E , are the coefficient of linear expansion and Young's modulus of the concrete, respectively. The stresses in [2] act on a curved circular shell and cause a secondary radial stress, which varies quadratically from zero at the outside fibres to a maximum on the neutral axis. For small ratios of the wall thickness, b , to the diameter, D , the maximum radial stress is b/2D times the value found from [2j (see Fig. 3). The radial stress is tensile when f,, is compressive on the outside face, i.e., when the outside wall temperature is higher than that of the inside face. The radial stress would be quite small under normal circumstances. However, if heavy concentrations of reinforcing steel are placed in the centre of the wall this secondary effect of the through-the-wall temperature gradient should be calculated on the net available concrete area. The resulting stress should be multiplied by an appropriate stress concentration factor (Peterson 1953). A single layer of reinforcement placed at the centre of the wall is frequently used in practice. Such an arrangement must be considered ineffective for walls subjected to stresses due to a temperature gradient ([2]) and detrimental when subjected to a radial tensile stress. The use of a single layer of reinforcement placed in the centre of the wall should be discouraged.

*

The selection of the temperature difference AT for design is difficult. The outside of the wall is subjected to ambient conditions that, in most cases, vary diurnally and from site to site. The inside temperature will be a function of the outside temperature, the wall thickness, and the thermal properties of the wall concrete and of the material stored. In addition, for fluids, convective currents at the wall-fluid interface, and possible heat input to the contents, have an effect. As an added complication, nonuniform solar radiation and cooling by wind cause the exposed face of the wall to heat and cool nonuniformly, leading to changes in shape of the circular reservoir and resulting in circumferential bending moments. Priestley (1975) carried out a study of thermal stresses in cylindrical water reservoirs in New Zealand. Thermal analyses included the influence of solar radiation, wind effects, and the water temperature. For a "worst summer day" analysis with a diurnal ambient temperature variation from 10 to 32"C, Priestley calculated a maximum outside wall temperature of 48°C at a fairly constant inside temperature of 11°C for a 200 mm thick prestressed concrete wall of a water reservoir. Wood and Adams (1977) measured inside and outside wall temperatures of a 39.6 m diameter, 7.9 m wall height precast concrete water reservoir with a 178 mm thick wall near Upper Hutt City, New Zealand. The measured peak radiation of about 800 W/m2 resulted in peak temperature differences of 1820°C. Typical maximum ambient temperatures were 24-27°C and water and inside wall temperatures were 12-14°C. Jofriet and Jiang (1986) measured outside wall temperatures of a 6.1 m diameter by 22 m high concrete tower silo with a 140 mm thick wall near Baden, Ont. The silo was filled with 50% moisture content alfalfa silage. The highest outside wall temperature recorded was 41°C on August 4, 1985, on the east face. This resulted in a gradient, AT, through the wall of about 15°C. Similar differences were also observed in February on the south face. Reinforced concrete tanks will typically have thicker walls than those tested by Wood and Adams (178 mm) and by Jofriet and Jiang (140 mm). This additional wall thickness provides greater thermal inertia and therefore moderates the diurnal variation. For southern Ontario, a design gradient of 15°C for the

TABLEI. Tensile stresses in concrete wall due to shrinkage Tensile stress (MPa) Method of calculation Step-by-step analysis 30 days from casting Step-by-step analysis 60 days from casting Eq. [31 (A€,,, = 300 1 . ~ ~ 1

p = 0.005

p = 0.01

p = 0.015

p = 0.02

0.28

0.52

0.74

0.93

0.39 0.29

0.73 0.56

1.04 0.81

1.30 1.05


NOTE:f: = 25 MPa, E, = 25 000 MPa, curing time

through-the-wall temperature gradient would seem adequate for a water tank. Other containers must be analyzed, bearing in mind the temperature conditions that might occur inside. The temperature gradient through the wall will not be uniform around the perimeter of the storage structure, since it is caused mainly by incident radiation from the sun, which is moving relative to the structure. Jofriet and Jiang (1986) measured a maximum difference in outside-face temperature of 12°C on August 16, 1985, between the north- and south-facing sides. This nonuniformity in temperature gradient causes the circular cross section of the cylinder to deform into an elliptical shape. A single finite element analysis of a 5.0 m inside diameter ring with 0.6 m wall thickness subjected to a linear temperature gradient through the wall but a nonuniform one around the circumference indicates that the tensile stresses given by [2] are increased by about 0.8 MPa around the circumference. Shrinkage Moisture loss from the concrete wall of a silo or tank occurs with time, causing drying and shrinkage; 30-60% of this movement is not recovered even if the concrete becomes saturated at a later time. Typical values of shrinkage of concrete specimens with an aggregate to cement ratio of 7 are 200 and 500 microstrain for waterlcement ratios of 0.4 and 0.7 respectively, stored at 50% relative humidity and 21°C for 6 months (Neville 1973). The internal restraint offered by the reinforcing steel as drying and shrinkage take place results in tensile stresses in the concrete. Additional stresses are introduced when the wall dries gradually from the surface inward. Fortunately, drying and shrinkage are fairly slow processes, so that the resulting stress is relieved partially by creep of the concrete. If a net increment of shrinkage strain, Ae,,, is assumed uniform across the wall thickness, the tensile stress increase, Af,,, that results in the concrete can be expressed as

in which Ec is Young's modulus of the concrete, n the modular ratio, both at the time the increment Ae,, occurs, and p is the reinforcing steel ratio A ,/Ac. The Portland Cement Association (PCA 1947) recommends a single-step application of shrinkage strain of 300 pe at 28 days. A step-by-step analysis for shrinkage and creep (ACI Committee 209 1971) was carried out for steel to concrete area ratios of 0.005, 0.010, 0.015, and 0.020. The time steps were 1 day starting at day 3 after casting. In the analysis it was assumed that at time t (in days):

=

3 days

in which f;(t) is the compressive strength at time t (days) and to is the loading age in days. For each time step the shrinkage strain increment Aesh(t)was reduced by a creep strain Ae,(t) calculated on the bases of a long-term creep function of 2.5ti0.Il8 assuming moisture curing. Table 1 provides the tensile stresses 30 and 60 days after placing of the concrete assuming a 3 day curing period. The stresses are shown for steel quantities, p , of 0.005, 0.01, 0.015, and 0.02. The values found with [3] using a single-step shrinkage strain of 300 pe are also given. It is evident from the values in Table 1 that the tensile stresses introduced by shrinkage can become very high if a high percentage of steel approaching 0.02 is used in design. With 2% reinforcing steel, the tensile stress would reach about 40% of the tensile strength of 30 MPa concrete. The simple shrinkage stress calculation based on [3] using a single increment of shrinkage strain of 300 pe predicts stresses that are 4-12% larger than those calculated using the incremental analysis over a period of 30 days. The simple stress calculation appears to be quite acceptable for design unless special circumstances exist. The 300 pe shrinkage strain applies at 30 days and should be increased to about 400 pe for shrinkage calculations over a period of 60 days. Creep Creep of the concrete will generally have a beneficial effect in reducing deformation-induced tensile stress considered in the design of cylindrical containers. The tensile stresses induced in an uncracked wall will be partially transferred to the reinforcing steel, thus reducing the maximum value in the concrete. The creep reduction in the tensile stresses induced by the lateral wall pressure is probably going to be minimum (thus causing a maximum stress) at initial filling. The value will depend, therefore, on the initial filling rate. For example, an initial filling 60 days after casting would lead to a long-term creep function of 2.5 x 60-0."8 = 1.54 and using a filling rate of 7 days would give a creep coefficient c$ of (ACI Committee 209):

This would reduce the effective concrete Young's modulus to 72% of the modulus at 60 days. An instantaneous modular ratio of 8 would be increased to 11; the equivalent concrete section would be increased by 2.8% for a wall with 1% steel. This would reduce the concrete stresses obtained from an uncracked-section analysis by 2.8%, which is a fairly insignificant amount.


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The effect of creep on the temperature stresses is minimal in the case of diurnal variations but should be considered when seasonal changes are considered for the analysis of an uncracked concrete wall. For a cracked-section analysis, creep reduction is not appropriate. The effect of creep on shrinkage stresses constitutes a reduction in concrete tensile hoop stresses. These were taken into account in the earlier discussion on shrinkage-induced stresses and the values in Table 1 from the step-by-step shrinkage analysis include the creep effect.

occur owing to lack of concentricity of the tank, variations in wall thickness, and moments in the tank wall due to unsymmetrical heating and shrinkage. Reasonable limits on crack widths are those suggested by ACI Committee 350 (1983):

Design criteria This paper is restricted to actions that result in tensile stress in the circumferential direction in cylindrical storage containers, and the design criteria that follow relate to these effects. Not included in the discussion are those related to vertical wall stresses, the overall stability of the structure, and to the foundations. Some concrete water storage tanks subjected to the type of climate typical for most of Canada have deteriorated fairly rapidly with time as a result of ice action (Slater 1985). Freezing and thawing action increases the width of stress cracks to the extent that leakage occurs. Also, vertical delamination develops in the saturated concrete wall. The Slater (1985) survey of a large number of water standpipes confirms that rapid deterioration has occurred in Ontario, especially with reinforced concrete tanks. A design criterion is required to reduce to a minimum the development of vertical tensile cracking of the wall of those containers where leakage is to be avoided. Alternatively, the concrete silo or tank can be equipped with an effective waterproof liner. A cost analysis can provide the most economical solution. In cold regions, such as northern Ontario, a waterproof liner is a necessity if a water tank is not insulated. The Portland Cement Association publication for the design of nonprestressed tanks (PCA 1947) suggests that the wall thickness of reinforced concrete tanks should be determined by limiting the circumferential tensile stress in the concrete. Many design engineers appear to neglect this concept, and the recommendations of ACI Committee 350 (1983) do not make direct reference to this procedure. The maximum tensile stress in the concrete due to hoop tension effects, including lateral wall pressure, shrinkage, creep, and thermal gradients, can be limited by the following, which has the same format as used in the Ontario Building Code (OBC 1984):

Load factors and load combinations The most unfavourable effect has to be determined by considering stresses L , T, S , and C in [8] acting alone with $ = 1, or in combination. ACI Committee 350 recommendations (1983) for sanitary structures introduce strength design as an alternative to allowable stress design. The load factors presented are those used for buildings but increased by sanitary durability coefficients (Gogate 1981) in an attempt to create waterproof structures. The authors consider that the use of these large load factors, which can exceed 2 for hydrostatic pressure, does not clearly indicate the possible limit states being considered. A more direct approach is preferred. For [8] the authors propose, in the case of liquids, a load factor for the lateral pressure equivalent to that for dead load, i.e. 1.25. Positive, foolproof provisions should be in place to limit the maximum liquid level or tank pressure. In the absence of such provisions the designer should consider liquid pressures exceeding those associated with normal operation. For solid materials, including ice, the choice of lateral pressures for design is more difficult than for liquids. The variability is comparable to typical live loads and a factor of 1.5 is appropriate. The calculated stresses induced by nonuniform heating and cooling of the storage structure and by shrinkage or creep of the concrete should be multiplied by the load factor of 1.25 as recommended in the Ontario Building Code (OBC 1984). Equation [8] does not deal with a life-threatening limit state. It may be appropriate to use an importance factor, y, of 0.8, similar to that used for low human occupancy buildings and structures. This inclusion of the importance factor with the load factors will not be suitable for all storage structures. The use of non-prestressed unlined concrete construction for the storage of materials for which leakage is a critical limit state is inappropriate and not recommended. The load factors appropriate for [9] are identical to those for [8] except for the importance factor. A value of 1.0 would generally apply. Farm tower silos can in most instances be designed as low-occupancy structures, allowing an importance factor of 0.8. Potable water storage tanks could be classified as essential in a postdisaster situation and should be designed with an importance factor of 1.2. The limit state considered in [lo] is a serviceability-type limit state and thus the load factors would be 1.0. Equation [8] includes a large number of load combinations. The manner in which loads must be combined will depend on the probable mode of operation of the storage structure. However, some general comments can be made. Stresses due to the lateral wall load and the temperature gradient across the wall depend upon the content of the storage tank. If the tank or bin is filled to a design level most of the

+,

where = resistance factor for concrete in tension, r , = resistance of concrete in tension, y = importance factor, $ = load combination factor, L = stress due to lateral load, T = restraining stress due to temperature gradients, S = restraining stress due to shrinkage, C = stress due to creep, and a are the associated load factors. To guard against yield of the reinforcing steel, and thus collapse, the following applies: in which

4,

= resistance factor for the reinforcing steel and

f, = yield strength of the reinforcing steel. As a serviceability limit state, the reinforcing steel should be distributed in such a way as to limit crack widths. Cracking can

W,,,

< 0.25 mm for noncorrosive liquids

W,,

< 0.20 mm for corrosive liquids

[ 101

where W,,, = maximum crack width. Both lateral load and restrained deformations due to temperature gradients should be used when applying [lo].

547


lOFRlET ET AL.

time, it would appear reasonable to design for the full combined effect of both the lateral wall load and the temperature gradient. The effect of creep can be taken into account to get stress. If the a reasonable estimate of the tensile concrete h o o ~ content level fluctuates, it would be reasonable to assume a load factor appropriate for combining two loads that vary with time and the Ontario Building Code (OBC 1984) load combination factor of 0.7. In this case, creep should not be included. Since an ice cap forms only at the top surface level of the contents, lateral pressure due to ice and to contents should not be combined. he maximum of the hoop tensions due to ice pressure and to liquid pressure should be considered for all levels where an ice cap may form. Shrinkage tensile stresses will develop before the tank or silo is first filled. For the design criterion of [8] one load combination should consider shrinkage multiplied by the appropriate load factor. After filling starts, some shrinkage will be recovered and the amount of shrinkage remaining must be combined with maximum lateral load. The maximum combined effect depends on the rate of first filling, which is usually not under the control of the structural designer The authors consider that for a reasonably slow filling rate of approximately 1 week to operating level, 50% of the shrinkage stress present at the time of filling should be added to the stresses due to lateral load (L) $us temperature (T) with = 0.7. The shrinkage stresses should be reduced by creep (Table 1). Equation [lo] includes two loads, since both lateral pressure and temperature gradient need be considered. The same load combination factors, = 1.0 or 0.7, as were recommended for [8] are appropriate. It is difficult to generalize concerning all possible load combinations. Each designer should be familiar with the way in which the structure is built, tested, commissioned, and eventually used. Only then can reasonable decisions be made about load combinations and load combination factors using the guidance of the available codes for buildings.

-

+

+

Resistance The design criteria ([8]-[lo]) are expressed in terms of factored resistances. For [8], a concrete tensile strength is required. The tensile strength can be measured in a number of ways, each leading to a different strength value (ACI Committee 224 1986). Common types of measurement are (a) direct tensile strength, (b) splitting strength, and (c) modulus of rupture. The direct tensile strength is appropriate when considering a predominantly uniform tensile stress across the wall. This is the case with the hoop stress due to the lateral wall pressure, provided the wall thickness is small relative to the diameter (less than 0. ID). Uniform shrinkage and creep also give a uniform stress. The modulus of rupture is the applicable strength when considering the differential temperature stress f,,. When combining effects from the temperature load with a uniform stress distribution, the interaction equation is recommended. It is convenient to relate the tensile strengths to the 28-day compressive cylinder strength. Raphael (1984) recommends the following for the direct tensile strength, f,', under static loads: [ l l ] f,' = 0.32(f:)~/~ and for the modulus of rupture, f:: [12] f:

=

0.44(f:)'/~

in which f: is the 28-day compressive strength in MPa. The values obtained from [ l l ] are 20-25% higher than those in Table 3.2 of the report by ACI Committee 224 (1986). The moduli of rupture calculated with [12] agree well with those listed by ACI Committee 224. The direct tensile strength values are similar to those given by the CEB-FIP model code (CEB 1978). Standard CAN3-A23.3-M84 (CSA 1984) specifies a strength reduction factor of 0.6 for concrete at the ultimate limit state. No strength or stiffness reduction factor is used for serviceability limit states. The selection of the appropriate strength reduction factor, , for use in [8] requires an acceptable value for the probability of cracking during the life of the structure. Considering past experience (PCA 1947) and allowing a probability of approximately 3-5% that cracking will occur, the authors find that a strength reduction factor of 0.75 is appropriate for direct tension and flexural tension. This is based on a mean to specified strength ratio of 1.2, a separation factor of 0.7, a safety index of 2 corresponding to a probability of 0.002, and a coefficient of variation of 15%. Equation [9] applies to a cracked-section analysis and hence the yield strength of the circumferential reinforcing steel applies. The strength reduction factor of 0.85 (CAN3-A23.3-M84) should be used. For the determination of crack width due to direction tension for [lo], the work by Broms and Lutz (1965) is recommended over that by Gergely and Lutz (1968) incorporated in the ACI Committee 350 (1983) standard. Broms and Lutz recommend that

+,

[13] W,,, = ~ , c d 1 6+ ( s / c ) ~ where W ,, is the maximum crack width, c is the cover to the centre of the steel, E, is the strain in the reinforcing steel assuming a cracked section, and s is the spacing of the hoop steel. For a typical value of c = 60 mrn and a typical spacing of 150 mm, [13] limits the working stress in the steel to about 180 MPa at working loads. This limit agrees with CEB recommendations (Walther 1982). Finally, the authors recommend that an upper limit be placed on the amount of circumferential reinforcement. Such a limitation would indirectly guard against high shrinkage and radial tensile stresses if [8] is not properly applied or neglected. A limit of 1% of the gross cross-sectional area is recommended. Such a limit would lead to a minimum wall thickness of 575 mm in the lower portion of a 10 m diameter reservoir with 30 m water height reinforced with 400 MPa steel.

Summary and recommendations The design of cylindrical non-prestressed concrete storage structures for the hoop stresses has been examined in detail. This review was initiated through the apparent lack of design standards or codes that could be used in the design of concrete storage structures, and by the poor performance of some aboveground water tank designs in cold regions. This paper is not an in-depth research of hoop stresses in cylindrical non-prestressed concrete tanks and silos. However, it reflects the experience of the authors in reinforced concrete design and behaviour, and with cylindrical tanks and silos in particular. The paper was written with the intention of provoking discussion. It is the expectation that eventually a design standard or code may be developed. The recommendations presented include three design cri-


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CAN. 1. CIV. ENG. VOL. 14. 1987

teria. The first attempts to guard against vertical cracking of the cylinder wall by limiting the tensile hoop stresses in the concrete. It provides a first estimate of wall thickness. The lateral load from the stored material, shrinkage, creep, and the various effects of temperature fluctuations are considered as force effects in this first criterion. The second criterion deals with a "cracked section" collapse limit state. Shrinkage, temperature gradients, and creep are not considered here. Finally, the third design criterion suggests limits for the crack widths and so provides a serviceability limit state in the event of cracking. The paper includes initial recommendations on the magnitude of temperature gradients, shrinkage, and creep stresses, and on applicable load combinations. It provide's tentative recommendations for load factors, importance factors, and load combination factors, and for strength reduction factors. T o illustrate the recommendations, they have been applied to the partial design of the wall of a potable water standpipe with 7 m inside diameter and a maximum water depth of 30 m. The design calculations (see Appendix) are for the wall thickness and the circumferential reinforcement near the bottom and at mid-height. The implication of the recommendations in this paper is that the design of trouble-free cylindrical storage structures for liquids or wet materials will require proportionally less circumferential steel and thicker walls than has been the case in some tanks and silos constructed in the past.

Acknowledgement The authors appreciate the helpful comments made by Mr. W. M. Slater of W. M. Slater and Associates Inc. during the preparation of this paper. ACI. 1983. Building Code requirements for reinforced concrete and commentary (ACI 318-83). American Concrete Institute, Detroit, MI. ACI COMMITTEE 209. 1971. Prediction of creep, shrinkage, and temperature effects in concrete structures. American Concrete Institute, Special Publication SP-27, pp. 51 -94. ACI COMMITTEE 224. 1986. Cracking of concete members in direct tension. Journal of the American Concrete Institute, 83(1): 3- 13. ACI COMMITTEE 350. 1983. Concrete sanitary structures. Journal of the American Concrete Institute, 80(6): 467-486. BROMS,B. B., and LUTZ,L. A. 1965. Effects of arrangement of reinforcement on crack width and spacing of reinforced concrete members. Journal of the American Concrete Institute, 62(11): 1395- 1410. CAMPBELL, T. I. 1984. Environmental loading in concrete water tanks. 1st interim report to Ministry of the Environment, Ontario. CAMPBELL, T. I., and KONG,W. L. 1985. Environmental loading of concrete water tanks. 2nd interim report to Ministry of the Environment, Ontario CEB. 1978. Comitk Euro-International du BCtonlFkdCration Inter.. nationale de la Prkcontrainte model code for concrete. ComitC Euro-International du Bkton, Paris, France, Bulletin d'information no. 1251125-E. CSA. 1984. Design of concrete structures for buildings. National Standard CAN3-A23.3-M84, Canadian Standards Association, Rexdale, Ont. GERGELY, P., and LUTZ,L. A. 1968. Maximum crack width in reinforced concrete flexural members. American Concrete Institute, Spacia Publication SP-20, pp. 87-117. GOGATE, A. B. 1981. Structural design of reinforced concrete sanitary structures - past, present and future. Concrete International: Design & construction, 3(4): 24-28. JOFRIET,J. C. 1982. Discussion of: Application of strength design

methods to sanitary structures by F. Klein et al. Concrete International: Design & Construction, 4(2): 58-59. JOFRIET, J. C., and JIANG, S. 1986. Measured temperatures of haylage in a 6.1 m diameter silo. Annual Meeting, North Atlantic Region, American Society of Agricultural Engineers, Quebec City, Que. KLEIN,F., HOFFMAN, E. S., and RICE,P. F. 1981. Application of strength design methods to sanitary structures. Concrete International: Design & Construction, 3(4): 35-40. KONG,W. L., and CAMPBELL, T. I. 1987. Ice pressure in elevated water tanks. Canadian Journal of Civil Engineering, 14(4): 519-526. NEVILLE,A. M. 1973. Properties of concrete. Pitman Publishing, London, England. OBC. 1984. Ontario Building Code. Ontario Ministry of Municipal Affairs and Housing, Toronto, Ont., 0. Reg. 549184. PCA. 1947. Circular tanks without prestressing. Portland Cement Association, Publication no. IS072D. PETERSON, R. E. 1953. Stress concentration design factors. John Wiley and Sons, New York, NY. PRIESTLEY, M. J. N. 1975. Thermal stresses in cylindrical prestressed concrete water reservoirs. Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand, Research report 75/13. RAPHAEL, J. M. 1984. Tensile strength of concrete. Journal of the American Concrete Institute, 82(2): 158- 165. SLATER, W. M. 1985. Concrete water tanks in Ontario. Canadian Journal of Civil Engineering, 12(2): 325 -333. 1986. Inspection, maintenance, repair and strengthening of above ground concrete water tanks damaged in cold region environments. loth International Congress of the Fkdkration Internationale de la Prkcontrainte, New Delhi, pp. 245-248. TuoMIOrA, M., JUMPPANEN, P., and RECHARDT, T. 1973. Jaan lujuudesta ja muodonmuutoksista (The strength and deformation of ice). Rakennustekniika, 1: 233-326. WALTHER, R. 1982. Fkdkration Internationale de la Prkcontrainte recommendations on practice design. Ecole Polytechnique FCdkrale de Lausanne, Lausanne, Switzerland. WOOD,J. H., and ADAMS,J. R. 1977. Temperature gradients in a cylindrical concrete reservoir. 6th Australasian Conference on the Mechanics of Structures and Materials. University of Canterbury, Christchurch, New Zealand.

Appendix The design recommendations are applied to a potable water standpipe, 7 m inside diameter, 30 m absolute maximum water depth. The water level fluctuates with water demand. The design temperature gradient through the wall is 15°C. An additional tensile stress of 0.5 MPa (estimated) allows for nonuniform heating of the outside face of wall by solar radiation. Materials: Concrete: fi = 35 MPa; E, = 29 600 MPa; a, = 11 x 10-6/0C; eq. [ l l ] , f; = 3.42 MPa; eq. [12], f: = 4.71 MPa. Reinforcing steel: f, = 400 MPa; E , = 200 000 MPa. Two depths will be considered: the first is where the maximum circumferential tension occurs near the bonom of the standpipe, the second at 15 m water depth. The wall will be considered fixed at the bonom.

( a ) Near the bottom Assume b = 700 mm, H2/bD = 184, a = 0.89,

P = 0.925

(Fig. 2):

T,, = 0.925

X

9.81 X 30 X 7.012 = 953 kN/m (uncracked)

(cracked)

549

JOFRIET ET AL.

Reinforcing steel applying [9]: aL = 1.25, y = 1.O,

+, = 0.85 L

=

0.85

S L

+ C acting alone is insignificant.

+ T + 0.5(S + C ) acting together: y = 0.8, JI = 0.7:

T6,,/AS X

400 > 1.0

X

1.25

1055 OOO/A,

X

A, > 3880 m2/m (20 M at 150 E.F. provides 4000 mm2/m) Equation [lo] limits maximum crack width to 0.25 mm. Assuming a cover of 50 mm:


Eq. [13]: W,

=

1055000 x60\/16+2S2 4 000 x 200 000

In summary, at about 26 m depth (&), a 700 mm thick wall with 20 M at 120 circumferential steel each face appears adequate. (b) At 15 m below top water level Assume b = 375 mm: T

Reduce spacing to 120 mm, A, 120160 = 2: Eq. [13]: W,

=

=

T'

5000 mm2/m, and s/c =

X

60-

L

=

953 000/(700 000

X

15

X

=

1512

X

+ 5.75 X 5 000) = 1.308 MPa

3.42 > 0.8

29000

X

X

1

X

1.25

X

1.308

11 x

=

2.44 MPa

=

2.44

T acting alone: y

clL

=

1.25, y

=

1 .O,

=

Reduce spacing to 150 mm, A, = 2667 mm2/m: 543 000 Eq. [13]: W,, = x 502 667 x 200 000 =0.254mm OK Wall thickness applying [8]; try 375 mm L

0.8; JI = 1; a7 = 1.25; 4, = 0.75:

Eq. [8]: 0.75 x 4.71 > 0.8 x 1 x 1.25 x 2.94 L and T acting together: y = 0.8; JI = 0.75:

+,

543 kN/m (cracked)

543 Oo0 x 502 000 x 200 000 = 0.383 mm

Eq. [13]: W,

+ 0.5 = 2.94 MPa =

=

Use 15 M at 150 E.F.

Add 0.5 MPa tension to allow for nonuniform heating: T

7.37512

515 kN/m (uncracked)

Check maximum crack width. Assuming a cover of 40 mm:

Restraint stress due to uniform temperature gradient of 15°C: T

X

=

(15 M at 200 E.F. provides 2000 mm2/m)

L acting alone: y = 0.8, JI = 1, clL = 1.25, 4, = 0.75: Eq. [8]: 0.75

7.012

A, > 2000 mm2/m

A, = A, + (n - 1)A,

where

9.81

X

L = T/A,

Wall thickness applying [8]; try a thickness of 700 mm Stress due to lateral load, L: T,,,/&

=

15

X

+, = 0.85

Acceptable: use 20 M at 120 E.F.

=

9.81

Reinforcing steel applying [9]:

OS5 O0O 5 000 x 200 000

L

=

=

OK

=

515 000/(375 000

L acting alone: y

=

Eq. [8]: 0.75

0.7; aL= a~ = 1.25;

0.8, X

JI

+ 5.75 X 2 667) = 1.319 MPa

= 1, aL= 1.25,

3.42 > 0.8

X

1

X

+, = 0.75:

1.25

X

1.319 OK

Temperature stresses are not wall thickness dependent: T = 2.94 MPa

+

L T acting together about the same as before. Shrinkage and creep: Restraint stress due to shrinkage, S , and creep, C:

p L

Say drying period is 30 days; Table 1 provides an estimate for S C of 0.38 MPa.

+

=

2 6671375 000

=

0.0071 1

same as before

+ T + 0.5(S + C) about the same as before.

In summary, at 15 m depth the wall thickness can be reduced to 375 rnm with 15 M at 150 circumferential steel each face.