MARCO TEÓRICO
CAPÍTULO 2: LA TEORÍA DE LA ACCESIBILIDAD
The in-service thermomechanical properties of FRP composite materials deteriorate due to aging and other factors (e.g., exposure to UV rays, chemical environment)
[Arockiasamy and Zhuang 1995; Barger 2000; Green and Bisby 1998; Homam and Sheikh 2000; Javed 1996; Soudki and Green 1997; Vijay and GangaRao 1998; Vijay et al. 2002]. Therefore, FRP properties obtained through tests or those provided by manufacturers should be adjusted using reduction (or adjustment) factors for satis-factory structural performance over a service life of a minimum of 50 years. These reduction factors depend on fiber type, application, and nature of environmental exposure (see Equation 5.1 and Table 5.1). The design ultimate strength (ffu) and rupture strain (εfu) are obtained by the product of the corresponding ultimate tensile strength (ffu*) and strain (εfu*) of the FRP material as reported by the manufacturer with appropriate environmental reduction factors (CE) suggested by ACI 440.2R-02.
(5.1)
(5.2)
(5.3)
Environmental reduction factors (CE) for different environmental exposure condi-tions are shown in Table 5.1.
FRP-ER obeys Hooke’s law (a linear stress-strain relationship, Equation 5.3).
The design ultimate strength and rupture strain (elongation) are lower than the manufacturer-reported values (ffu* and εfu, respectively) because of the use of envi-ronmental exposure based reduction factor (CE). However, for all practical purposes the modulus of elasticity (Equation 5.3) is unaffected by the environmental exposure conditions and remains the same as given by the manufacturer.
TABLE 5.1
Environmental-Reduction Factor (CE) for Different FRP Systems and Exposure Conditions
Exterior exposure (bridges, piers, and unenclosed parking garages)
Carbon/epoxy 0.85
Glass/epoxy 0.65
Aramid/epoxy 0.75
Aggressive environment (chemical plants and waste water treatment plants)
Carbon/epoxy 0.85
The environmental-reduction factors given in Table 5.1 are estimates based on the durability of fiber type, exposure conditions, and location. Three broad categories of exposure conditions are identified for concrete structures with FRP-ER in Table 5.1. The environmental reduction factors corresponding to the three categories are interior exposure, exterior exposure, and aggressive environment. These categories represent temperature variations associated with their location and exposure. Table 5.1 lists commonly used glass, carbon, and aramid fiber systems used specifically with epoxy resins because they are the most widely used for bonding FRP-ER to concrete structures. If other resin systems are selected, the CE values should be obtained from their manufacturers.
A perusal of Table 5.1 shows that penalties for FRP-ER are more severe with aggressive exposure conditions such as those located in chemical and wastewater treatment plants that may contain acid or alkali solutions, grease, purifiers, and other chemicals. FRP-ER properties are relatively less penalized for interior exposure conditions, where members are located within an enclosed environment such as a building. FRP-ER properties are penalized more for exterior exposure conditions than interior conditions. Examples of exterior or outdoor structures are bridges, piers, and unenclosed parking garages. These structures are subjected to deicing salts, high humidity and temperature variations, freeze-thaw cycles, and so on. Compared to interior and exterior exposure conditions, ACI 440.2R-02 cautions that future revi-sions of these reduction factors are possible as additional long-term performance data becomes available. Note that additional factors such as better resin systems, sizings, and protective coatings improve the durability of FRP systems.
Among the three types of fibers listed in Table 5.1, carbon fiber is the most durable under all types of exposure conditions, followed by aramid and glass fibers.
For example, environmental reduction factors for carbon/epoxy, aramid/epoxy, and glass/epoxy systems subjected to interior exposure are 0.95, 0.85, and 0.75, respec-tively. However, when the same carbon/epoxy, aramid/epoxy, and glass/epoxy sys-tems are subjected to aggressive environments, the reduction factors are more severe and change to 0.85, 0.70, and 0.50, respectively.
5.8.2 STRENGTH REDUCTION FACTORS
In designing steel-reinforced concrete beams, uncertainties of material strength, approximations in analysis, variations in dimensions of concrete sections, and vari-able field conditions are taken into account by applying a strength reduction factor to the nominal strength of a concrete member.
The ACI Building Code specifies the following strength reduction factors (φ-factors) for steel-reinforced concrete beams under various load conditions [ACI 318-02] (see Figure 5.17):
1. Flexure (without axial loads): 0.9 2. Shear and torsion: 0.75
3. Bearing on concrete: 0.65
For FRP-reinforced beams, a set of different strength reduction factors have been suggested to account for following parameters:
1. Basis of derivation of material properties (φmat) 2. Processing methods (φproc)
3. Manufacturing location (φloc)
4. Long-term degradation of FRP properties (φdegr) 5. Cure conditions (φcure)
The aforestated factors highlight several conditions that affect strength reduction factors. When applied in combination, these factors should be such that the reduction in material properties is not excessive. According to ACI 440.2R-02, the above five factors are not directly used in the current design practice suggested because suffi-cient data on their validity is not available; use of only the CE factor is recommended for the design of FRP-ER.
5.8.3 FRP REINFORCEMENT FOR FLEXURAL STRENGTHENING
To increase flexural strength, FRP fabrics are bonded as an external reinforcement on the tension side of steel-reinforced concrete beams with fiber orientation along the member length [Hota et al. 1995; Ichimasu et al. 1993; Lee et al. 1998; Saadat-manesh and Ehsani 1991]. Depending on the ratio of FRP reinforcement area to the beam’s cross-sectional area and the area of internal steel reinforcement, the increase in flexural strength can be more than 100%. However, a flexural strength increase up to 50% would be more realistic, which depends on practical considerations such as the concrete member dimensions, serviceability limits, ductility, and effective thickness of FRP fabric reinforcement [Arduini and Nanni 1997; Hota et al. 1995].
Although this chapter presents the design philosophy of strengthening rectangular RC beams, note that it is equally applicable to other shapes such as T- and I-sections having non-prestressed reinforcement.
FIGURE 5.17 Strength-reduction factor as a function of ductility. (Adapted from ACI 318-02).
0.7 0.9
0.005 0.005 − εsy
0.2(εs − εsy) φ
0.7 +
εy(εsy)
Steel strain at ultimate
5.8.4 EFFECT OF BENDING STRENGTH INCREASEON
SHEAR STRENGTH
When the flexural strength of a concrete beam is increased by using FRP-ER, verifying that the member has adequate shear strength to support the increased loads is important. If necessary, the shear strength of a reinforced concrete member can be increased by using externally bonded FRP reinforcement. Shear strengthening using FRP-ER can be carried out by orienting fibers at an angle (typically 45°) or in a transverse direction (90° orientation) with respect to the longitudinal axis of the beam (additional details are provided in Section 5.16).
5.8.5 INITIAL MEMBER STRAIN PRIORTO BONDING
FRP-ER design should account for the initial strain existing in a concrete member prior to attaching the FRP-ER. FRP wraps or fabrics (FRP-ER) can be installed after partially or fully relieving the existing loads and corresponding strains on the con-sidered member. If the strains corresponding to the existing loads including self-weight are not relieved prior to FRP-ER application, then those strains (also called initial member strains at the typical bonding location in tension, εbi) should be accounted for in the subsequent analysis and design. Initial member strain in tension at a bonding location can be determined based on elastic analysis of the cracked member (see Section 5.11, Examples 5.1 and 5.6).
5.8.6 NOMINAL AND DESIGN STRENGTH
The nominal flexural strength (Mn) of a FRP-bonded concrete member is determined based on the governing failure mode, strain compatibility, and internal force equi-librium. In the strength-design approach, the design flexural strength (φMn) should be equal to or greater than the required flexural strength (Mu) as given by Equation 5.4.
(5.4) In addition to the strength reduction factor (φ) required by ACI 318 (discussed in Section 5.8.2), an additional strength reduction factor (Ψf = 0.85) is applied to the flexural strength provided by the FRP-ER to account for the higher (uncertain) reliability of FRP-ER strength properties [ACI 440.2R-02]. Use of this additional strength reduction factor is explained in the design examples on flexure.
5.8.7 FLEXURAL STRENGTHENING LIMITS
ACI 440.2R-02 suggests a conservative approach when using FRP-ER for structural strengthening to prevent the FRP debonding-related collapse of FRP-ER strength-ened structures. FRP-ER debonding from concrete can occur due to any of the following reasons:
1. Inadequate design
2. Improper or inadequate bonding during strengthening with FRP-ER φMn≥Mu
3. Loss of bond between adherend (concrete substrate) and adherent (FRP-ER) during the service life of the structure, wherein it is subjected to stresses and deformations, creep, fatigue, and environmental exposure 4. Fire
5. Vandalism and other causes
According to ACI 440.2R-02, the structural member without FRP reinforcement should not collapse and resist a certain level of future (new) loads along with the existing dead loads, prior to bonding FRP-ER and strengthening. This conservative approach of avoiding structural collapse even in the absence of FRP-ER under the action of a major portion of the new live load imposed on the member (85% of SLL corresponding to a FRP-ER strengthened condition) is expressed by Equation 5.5:
(5.5) where
φ = strength reduction factor
Rn = nominal member resistance prior to strengthening with FRP-ER SDL = dead load imposed on a member strengthened with FRP-ER
SL = live load on the member strengthened with FRP-ER 5.8.8 FAILURE MODES
A key factor influencing the flexural strength of a steel bar reinforced concrete beam strengthened with FRP-ER is the failure mode. Some of the failure modes observed in the tests of FRP-ER strengthened concrete beams subjected to flexure are [Ganga-Rao and Vijay 1998]:
1. Rupture of FRP-ER after yielding of tension steel reinforcement 2. Secondary concrete crushing after yielding of tension steel reinforcement 3. Primary concrete crushing in compression before yielding of the
reinforc-ing steel
4. Shear/tension delamination of the concrete cover (cover delamination) 5. Debonding of FRP-ER from the concrete substrate (FRP-ER debonding) Rupture of FRP-ER, secondary concrete crushing, and primary concrete crushing failure modes are generally used for designing FRP-ER strengthened concrete beams.
The design is typically based on the strain values induced in FRP-ER, steel, and concrete. Before 2002, ACI 318 emphasized a failure mode of reinforced concrete beams based on the yielding of steel reinforcement in tension. However, ACI 318-02 code emphasizes “adequate ductility” (a concept defined as a stage when strain in tension steel reinforcement, εS, is greater than or equal to 0.005) in concrete beams.
ACI 440.2R-02 defines the rupture of FRP-ER and concrete crushing (primary and secondary) failure modes in FRP-ER strengthened concrete beams as follows:
(φRn existing) ≥( .1 2SDL+0 85. SLL new)
1. Rupture of FRP-ER occurs when the tensile strain in the FRP-ER reaches its design rupture strain (εf = εfu), before the concrete reaches its maximum usable strain (εc = εcu = 0.003) or exceeds it.
2. Concrete crushing (primary and secondary) occurs when the compressive strain in concrete reaches a maximum usable strain (i.e., εc = εcu = 0.003).
Primary and secondary concrete crushing refer to the conditions where concrete crushing occurs prior to or after tension steel reinforcement yielding, respectively.
In some cases, the force in FRP-ER can be too large to be transferred to the bonded concrete substrate and can result in the delamination of the concrete cover or the debonding of FRP-ER [Arduini and Nanni 1997; Barger 2000; Maeda et al.
1997; Teng et al. 2001; Wan et al. 2004]. To prevent the debonding of FRP-ER, ACI 440.2R-02 recommends limiting the strain developed in the FRP-ER per unit bond width to a maximum value obtained by multiplying the rupture strain of the FRP fabric (εfu) with a bond-dependent factor, κm, as given by Equation 5.6:
(5.6)
Equation 5.6 shows that the value of κm decreases with increasing number of FRP-ER layers (n). An excessive number of FRP-FRP-ER plies or laminates can lead to a greater stiffness mismatch between concrete and FRP-ER than the cases with fewer (two or three) plies or laminates, resulting in the debonding of FRP-ER from the concrete substrate. For FRP-ER having a unit stiffness, nEftf > 1,000,000 lb/in., κm is designed to provide an upper limit on the force rather than strain in FRP-ER laminates.