High-Performance/High-Strength Lightweight Concrete for Bridge Girders and Decks (2013)

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69 Attachment A Proposed Changes to AASHTO LRFD Bridge Design Specifications

70 5.4.3.2 – Creep The creep coefficient may be taken as: Ψ(t,ti) = 1.9kskhckfktdti-0.118 (5.4.2.3.2-1) In which: ks = 1.45 – 0.13(V/S) ≥ 1.0 (5.4.2.3.2-2) khc = 1.56 – 0.008H (5.4.2.3.2-3) c f f k − = 1 5 (5.4.2.3.2-4) tfs t k ci f +− = 11 (5.4.2.3.2-5) Where: H = relative humidity (%). In the absence of better information, H may be taken from Figure 5.4.2.3.3-1 ks = factor for the effect of the volume-to-surface ratio of the component kf = factor for the effect of concrete strength khc = humidity factor for creep ktd = time development factor C5.4.2.3.2 The methods of determining creep and shrinkage, as specified herein and in Article 5.4.2.3.3, are based on Huo et al. (2001), Al-Omaishi ( 2001), Tadros (2003), and Collins and Mitchell (1991). These methods are based on the recommendation of ACI Committee 209 as modified by additional recently published data. Other applicable references include Rusch et al. (1983), Bazant and Wittman (1982), and Ghali and Favre (1986). Based on the work of Cousins, Roberts-Wollmann and Brown (2013), the AASHTO method for determining creep and shrinkage of sand lightweight concrete yields reasonable results.

71 5.4.2.4 – Modulus of Elasticity In the absence of measured data, the modulus of elasticity, Ec, for concretes with unit weights between 0.090 and 0.155 kcf and specified compressive strengths up to 15.0 ksi may be taken as: (5.4.2.4-1) where: K1 = correction factor for source of aggregate to be taken as 1.0 unless determined by physical test, and as approved by the authority of jurisdiction wc = unit weight of concrete (kcf); refer to Table 3.5.1-1 or Article C5.4.2.4 f ′c = specified compressive strength of concrete (ksi) C5.4.2.4 See commentary for specified strength in Article 5.4.2.1. For normal weight concrete with wc = 0.145 kcf Ec may be taken as: Ec = 1,820 f ′ Ec = 33,000K1wc 1.5 f ′ (C5.4.2.4-1) Test data show that the modulus of elasticity of concrete is influenced by the stiffness of the aggregate. The factor K1 is included to allow the calculated modulus to be adjusted for different types of aggregate and local materials. Unless a value has been determined by physical tests, K1 should be taken as 1.0. Use of a measured k1 factor permits a more accurate prediction of modulus of elasticity and other values that utilize it. Based on the work of Cousins, Roberts- Wollmann, and Brown (2013), the AASHTO method for determining modulus of elasticity of sand lightweight concrete yields reasonable results. As with normal weight concrete, the factor K1 is included to allow the calculated modulus to be adjusted for different types of aggregate and local materials. c c

72 5.4.2.6—Modulus of Rupture Unless determined by physical tests, the modulus of rupture, fr ksi, for specified concrete strengths up to 15.0 ksi, may be taken as: • For normal weight and sand lightweight concrete: o When used to calculate the cracking moment of a member in Articles 5.7.3.4, 5.7.3.6.2, and 6.10.4.2.1 ................0.24√f′c o When used to calculate the cracking moment of a member in Article 5.7.3.3.2 ........................................................ 0.37√f′c o When used to calculate the cracking moment of a member in Article 5.8.3.4.3 ........................................................ 0.20√f′c • For lightweight concrete: o For sand lightweight concrete ....... 0.20√f′c o For all-lightweight concrete .......... 0.17√f′c When physical tests are used to determine modulus of rupture, the tests shall be performed in accordance with AASHTO T 97 and shall be performed on concrete using the same proportions and materials as specified for the structure. 5.4.2.7—Tensile Strength Direct tensile strength may be determined by either using ASTM C900, or the split tensile strength method in accordance with AASHTO T 198 (ASTM C496). C5.4.2.6 Data show that most modulus of rupture values for normal weight concrete are between 0.24√f′c and 0.37√f′c (ACI 1992; Walker and Bloem 1960; Khan, Cook, and Mitchell 1996) and for sand lightweight concrete are between 0.26√f′c and 0.31√f′c (Cousins, Roberts-Wollmann, and Brown 2013). It is appropriate to use the lower bound value when considering service load cracking. The purpose of the minimum reinforcement in Article 5.7.3.3.2 is to assure that the nominal moment capacity of the member is at least 20 percent greater than the cracking moment. Since the actual modulus of rupture could be as much as 50 percent greater than 0.24√f′c , the 20 percent margin of safety could be lost. Using an upper bound is more appropriate in this situation. The properties of higher strength concretes are particularly sensitive to the constitutive materials. If test results are to be used in design, it is imperative that tests be made using concrete with not only the same mix proportions, but also the same materials as the concrete used in the structure. The given values may be unconservative for tensile cracking caused by restrained shrinkage, anchor zone splitting, and other such tensile forces caused by effects other than flexure. The direct tensile strength stress should be used for these cases. C5.4.2.7 For normal-weight concrete with specified compressive strengths up to 10 ksi, the direct tensile strength may be estimated as fr = 0.23√f′c.

73 5.5.4.2—Resistance Factors 5.5.4.2.1—Conventional Construction Resistance factor φ shall be taken as: • For tension-controlled reinforced concrete sections as defined in Article 5.7.2.1 ..............................................................0.90 • For tension-controlled prestressed concrete sections as defined in Article 5.7.2.1 ..............................................................1.00 • For shear and torsion: Normal weight concrete ..........0.90 Sand lightweight concrete…....0.85 All lightweight concrete ..........0.70 • For compression-controlled sections with spirals or ties, as defined in Article 5.7.2.1, except as specified in Articles 5.10.11.3 and 5.10.11.4.1b for Seismic Zones 2, 3, and 4 at the extreme event limit state ..............................................................0.75 • For bearing on concrete .......................0.70 • For compression in strut-and-tie models ............................................................. 0.70 C5.5.4.2.1 In applying the resistance factors for tension- controlled and compression-controlled sections, the axial tensions and compressions to be considered are those caused by external forces. Effects of prestressing forces are not included. In editions of and interims to the LRFD Specifications prior to 2005, the provisions specified the magnitude of the resistance factor for cases of axial load or flexure, or both, in terms of the type of loading. For these cases, the φ-factor is now determined by the strain conditions at a cross-section, at nominal strength. The background and basis for these provisions are given in Mast ( 1992) and ACI 318-02. A lower φ-factor is used for compression- controlled sections than is used for tension-controlled sections because compression-controlled sections have less ductility, are more sensitive to variations in concrete strength, and generally occur in members that support larger loaded areas than members with tension-controlled sections. For sections subjected to axial load with flexure, factored resistances are determined by multiplying both Pn and Mn by the appropriate single value of φ. Compression-controlled and tension-controlled sections are defined in Article 5.7.2.1 as those that have net tensile strain in the extreme tension steel at nominal strength less than or equal to or greater than 0.005, respectively. For sections with net tensile strain εt in the extreme tension steel at nominal strength between the above limits, the value of φ may be determined by linear interpolation, as shown in Figure C5.5.4.2.1-1. The concept of net tensile strain εt is discussed in Article C5.7.2.1. Classifying sections as tension-controlled, transition or compression-controlled, and linearly varying the resistance factor in the transition zone between reasonable values for the two extremes, provides a rational approach for determining φ and limiting the capacity of over-reinforced sections.

74 Previous editions of AASHTO LRFD have given a φ of 0.7 for shear and torsion of lightweight concrete. Research by Cousins, Roberts-Wollmann and Brown (2013) shows that a φ of 0.85 for sand lightweight concrete yields a safety index similar to that achieved when using a φ of 0.9 for normal weight concrete.

75 5.8.2.2—Modifications for Lightweight Concrete Where lightweight aggregate concretes are used the following modifications shall apply in determining resistance to torsion and shear. • Where the average splitting tensile strength of lightweight concrete, fct, is specified, the term √f′c in the expressions given in Articles 5.8.2 and 5.8.3 shall be replaced by: 4.7fct ≤ cf ′ • Where fct is not specified, the term 0.75√f′c for all lightweight concrete, and 0.85√f′c for sand lightweight concrete shall be substituted for √f′c in the expressions given in Articles 5.8.2 and 5.8.3. No modification factor is required for sand lightweight concrete. C5.8.2.2 The tensile strength and shear capacity of all lightweight concrete is typically somewhat less than that of normal weight concrete having the same compressive strength. Tests have shown that the previous reduction factor for tensile strength of sand lightweight concrete (0.85) is not needed (Cousins, Roberts-Wollmann, and Brown (2013)).

76 5.8.4 – Interface Shear Transfer – Shear Friction 5.8.4.1 – General The interface shear strength Eqs. 5.8.4.1-3, 5.8.4.1-4, and 5.8.4.1-5 are based on experimental data for normal weight, nonmonolithic concrete strengths ranging from 2.5 ksi to 16.5 ksi; normal weight, monolithic concrete strengths from 3.5 ksi to 18.0 ksi; sand lightweight concrete strengths from 2.0 ksi to 6.0 8.0 ksi; and all-lightweight concrete strengths from 4.0 ksi to 5.2 ksi.

77 5.8.4.3 – Cohesion and Friction Factors The following values shall be taken for cohesion, c, and friction factor, µ: • For a cast-in-place concrete slab on clean concrete girder surfaces, free of laitance with surface roughened to an amplitude of 0.25 in: c = 0.28 ksi µ = 1.0 K1 =0.3 K2 =1.8 ksi for normal weight concrete =1.3 ksi for lightweight concrete • For normal weight concrete placed monolithically: c = 0.40 ksi µ = 1.4 K1 =0.25 K2 =1.5 ksi • For lightweight concrete placed monolithically, or nonmonolithically, against a clean concrete surface, free of laitance with surface intentionally roughened to an amplitude of 0.25 in.: c = 0.24 ksi µ = 1.0 K1 = 0.25 K2 = 1.0 ksi C5.8.4.3 The values presented provide a lower bound of the substantial body of experimental data available in the literature (Loov and Patnaik, 1994; Patnaik, 1999; Mattock, 2001; Slapkus and Kahn, 2004: Cousins, Roberts-Wollmann, and Brown (2013)). Furthermore, the inherent redundancy of girder/slab bridges distinguishes this system from other structural interfaces. The values presented apply strictly to monolithic concrete. These values are not applicable for situations where a crack may be anticipated to occur at a Service Limit State. The factors presented provide a lower bound of the experimental data available in the literature (Hofbeck, Ibrahim, and Mattock, 1969; Mattock, Li, and Wang, 1976; Mitchell and Kahn, 2001). Available experimental data demonstrates that only one modification factor is necessary, when coupled with the resistance factors of Article 5.5.4.2, to accommodate both all-lightweight and sand lightweight concrete. Note that this deviates from earlier specifications that distinguished between all- lightweight and sand lightweight concrete. Due to the absence of existing data, the prescribed cohesion and friction factors for nonmonolithic lightweight concrete are accepted as conservative for application to monolithic lightweight concrete. Tighter constraints have been adopted for roughened interfaces, other than cast-in-place slabs on roughened girders, even though available test data does not indicate more severe restrictions are necessary. This is to account for variability in the geometry, loading, and lack of redundancy at other interfaces.

78 5.9.5.4 – Refined Estimates of Time-Dependent Losses 5.9.5.4.1 – General For nonsegmental Prestressed members, more accurate values of creep-, shrinkage-, and relaxation- related losses than those specified in Article 5.9.5.3 may be determined in accordance with the provisions of this Article. For precast pretensioned girders without a composite topping and for precast or cast- in-place nonsegmental post-tensioned girders, the provisions of Articles 5.9.5.4.4 and 5.9.5.4.5, respectively, shall be considered before applying the provisions of this Article. C5.9.5.4.1 See Castrodale and White (2004) for information on computing the interaction of creep effects for prestressing applied at different times. Estimates of losses due to each time- dependent source, such as creep, shrinkage, or relaxation, can lead to a better estimate of total losses compared with the values obtained using Article 5.9.5.3. The individual losses are based on research published in Tadros (2003), which aimed at extending applicability of the provisions of these Specifications to high-strength concrete. Research by Cousins, Roberts-Wollmann, and Brown (2013) indicated that these provisions yield reasonable results when used to calculate prestress loss in members made with sand lightweight concrete. Also, best results are achieved with sand lightweight concrete when using the AASHTO creep and shrinkages models with the Refined Method.

79 5.11.4 – Development of Prestressing Strand 5.11.4.1 – General In determining the resistance of pretensioned concrete components in their end zones, the gradual buildup of the strand force in the transfer and development lengths shall be taken into account. The stress in the prestressing steel may be assumed to vary linearly from 0.0 at the point where bonding commences to the effective stress after losses, fpe, at the end of the transfer length. Between the end of the transfer length and the development length, the strand stress may be assumed to increase linearly, reaching the stress at nominal residence, fps, at the development length. For the purpose of this Article, the transfer length may be taken as 60 strand diameters and the development length shall be taken as specified in Article 5.11.4.2. The effects of debonding shall be considered as specified in Article 5.11.4.3. C5.11.4.1 Between the end of the transfer length and development length, the strand stress grows from the effective stress in the prestressing steel after losses to the stress in the strand at nominal resistance of the member. Research by Cousins, Roberts-Wollmann, and Brown (2013) indicated that these provisions yield reasonable results when used to calculate transfer and development length in members made with sand lightweight concrete.