Shawn P. Gross

Effective Moment of Inertia for Glass Fiber-Reinforced Polymer-Reinforced Concrete Beams

This paper investigates deflection behavior of concrete flexural members reinforced with glass fiber-reinforced polymer (GFRP) reinforcing bars. It is recognized that serviceability plays a major role in the design of GFRP-reinforced concrete beams. Therefore, accurate modeling of flexural stiffness is critical and the effect of influencing parameters must be considered. This study accounts for variations in concrete strength, reinforcement density, and shear span-depth ratio. Experimental results from 48 simply supported concrete beams reinforced with GFRP are compared with ACI Committee 440s published deflection model. The ACI 440.1R model is found to overestimate the effective moment of inertia, and an appropriate modification is presented.

Flexural Behavior of Concrete Beams Strengthened with Near-Surface-Mounted CFRP Strips

Engineers have proposed relocating externally bonded strengthening fiber reinforced polymer (FRP) material from the unprotected exterior of the concrete to the protected interior. This technology is known as near-surface mounted (NSM) strengthening. In NSM reinforcement, the FRP is surrounded by concrete on three sides so the bond and damage problems associated with externally bonded FRP strengthening systems are reduced or eliminated. This paper presents experimental results from 12 full-scale concrete beams strengthened with NSM carbon FRP (CFRP) strips. Three companion unstrengthened specimens were also tested to serve as a control. Experimental variables include three different ratios of steel reinforcement and two different ratios of CFRP reinforcement. Yield and ultimate strengths, flexural failure modes, and ductility are discussed based on measured load, deflection, and strain data. Test results show measurable increases in yield and ultimate strengths in all beams strengthened with CFRP as well as predictable nominal strengths and failure modes. Force transfer between the CFRP, epoxy grout, and surrounding concrete was able to develop the full tensile strength of the CFRP strips. Energy and deflection ductilities were reduced for CFRP strengthened beams. Future research needs are addressed.

SHEAR STRENGTH OF NORMAL AND HIGH STRENGTH CONCRETE BEAMS REINFORCED WITH GFRP BARS

This paper evaluates the shear strength for normal and high strength concrete beams reinforced with longitudinal glass fiber reinforced polymer (GFRP) reinforcing bars and no web reinforcement. The effect of reinforcement ratio is examined, and experimental data is compared with values predicted by FRP shear strength expressions found in the literature, including the new design expression recommended by ACI Committee 440 (2001).

Equivalent Moment of Inertia Based on Integration of Curvature

This paper evaluates the benefits of computing deflection with an equivalent moment of inertia based on integration of curvature to account for changes in member stiffness along the span. Results are evaluated for steel and fiber-reinforced polymer reinforced (FRP-reinforced) concrete flexural members with different loading arrangements and support conditions. Closed-form solutions of integrated expressions for deflection are expressed in terms of an equivalent moment of inertia Ie′ and compared to deflection computed with an effective moment of inertia Ie based on the stiffness at the critical section. Results from this comparison are validated with measured deflections from an experimental database for FRP-reinforced concrete. Current code-related approaches are also compared to the experimental database. It is shown herein that the use of an integration-based expression for the moment of inertia can lead to improved prediction of deflection, though the use of an effective moment of inertia based on mem...

Design Approach for Calculating Deflection of FRP-Reinforced Concrete

Deflection of reinforced concrete is typically computed with an effective moment of inertia Ie that accounts for nonlinear behavior after the concrete cracks. Existing expressions for Ie tend to overpredict the member stiffness of concrete reinforced with fiber-reinforced polymer (FRP) bars, and an alternative expression is used as the basis for developing a practical design approach to compute deflection. The proposed expression has a rational basis that incorporates basic concepts of tension stiffening to provide a reasonable estimate of deflection for both steel and FRP-reinforced concrete without the need for empirically derived correction factors. Calculation of deflection with the proposed expression for Ie is recommended using the code value for the elastic modulus Ec of concrete because computed values of deflection are relatively insensitive to variations in Ec, and shrinkage restraint is taken into account by using a reduced cracking moment less than the code-based value of the cracking moment M...

FLEXURAL DESIGN METHODOLOGY FOR CONCRETE BEAMS REINFORCED WITH FIBER-REINFORCED POLYMERS

This paper evaluates safety in fiber-reinforced polymer (FRP) reinforced flexural members with respect to energy consumption and reserve. It is proposed that service stresses in FRP reinforced flexural members be limited such that a minimum energy reserve at service relative to the ultimate limit-state is ensured. The minimum energy reserve is determined as per existing code-mandated stress limits established for steel reinforcement. The result is a rational justification for allowable stress limits in FRP reinforced members and a guaranteed minimum level of energy reserve equivalent to that provided by existing steel-design methodology. The feasibility of the method is demonstrated through a worked bridge deck design example.

TIME-DEPENDENT BEHAVIOR OF NORMAL AND HIGH STRENGTH CONCRETE BEAMS REINFORCED WITH GFRP BARS UNDER SUSTAINED LOADS

This paper presents results of a study in which time-dependent strains and deflections were monitored for normal and high strength concrete beams reinforced with glass fiber reinforced polymers. Sustained load behavior was observed to be similar to that of steel reinforced beams. The effect of additional flexural cracking over time was found to be significant.

Effect of Sustained Load Level on Long-Term Deflections in GFRP and Steel-Reinforced Concrete Beams

ACI 440.1R [1] applies an adjustment factor of 0.6 to the long-term deflection multiplier for steel-reinforced beams to reflect the experimentally observed differences between FRP and steel-reinforced members. The objective of this study is to evaluate the effect of the level of sustained load on the long-term multiplier in GFRP-reinforced beams. Five beams, including four GFRP-reinforced beams and one steel-reinforced control beam, were tested in four-point bending on a simply supported span with different temporary service loads (Ma = 1.80 Mcr–2.36 Mcr) and sustained load (Msus = 0.58 Ma–0.85 Ma) levels. Mid-span deflections were recorded twice weekly over a period of 100 days, and the long-term deflection multiplier, λΔ, was plotted vs. time. The results indicate that the temporary service load level, rather than the sustained load level, affects the long-term deflection multiplier with larger temporary service loads causing a smaller long-term multiplier. The current 0.6 multiplier on the time factor for FRP-reinforced beams also appears to underestimate long-term deflections. In addition, the multiplier to capture the effects of GFRP vs. steel-reinforcement may not be a constant value.

Fatigue behavior of GFRP and steel reinforced bridge decks designed using traditional and empirical methodologies

In this research study, experimental behavior of two full-scale bridge decks, one each reinforced with steel and GFRP, and subjected to fatigue loading is investigated. Reinforcement is provided as required by traditional (TR) and empirical (EM) design methodologies on each transverse half of each deck. The decks are subjected to load cases corresponding to an HS25 truck axle positioned for critical positive and negative bending. Measured response before, during and after the two million cycles of fatigue loading per load case is used to evaluate compliance with serviceability limits on crack-width, deflection and material stress. For the GFRP reinforced deck, results show both TR and EM are compliant with allowable limits, and that the EM load-sensor slope response is measurably less than the TR for like load cases. Similar results were found for the steel reinforced deck. Importantly, the study validates the EM design methodology for use with GFRP reinforced concrete bridge decks.

Investigation of alternative technologies for cast-in-place concrete bridge decks

Concrete bridge decks are designed using traditional methodology (TM) or empirical methodology (EM). TM models the deck as a continuous beam in flexure, and EM recognizes the compressive membrane action that aids in distributing wheel loads. An extension of membrane behavior is complete removal of reinforcement from within the deck; this is referred to as steel free deck (SF). In this research study three full-scale bridge decks are investigated, one reinforced with steel, a second is reinforced with glass fiber reinforced polymer (GFRP), and a third is SF. For each the steel and GFRP reinforced decks, the south and north sides are reinforced as required by the TM and EM, respectively. The SF deck is based on research done in Canada. Each deck is subjected to four load cases, corresponding to an AASHTO truck axle positioned for critical positive and critical negative bending on each the north and south sides. Measured response for crack width, deflection, and concrete strain is used to evaluate behavior at the service limit state.