Starting in this issue of Composites Technology, I will discuss the use of composites in construction applications. This and upcoming columns, one in each 2007 issue of CT, are excerpted from chapters in my recent book Composites for Construction — Structural Design with FRP Materials. My purpose in writing the book — and this column — is to provide structural engineering students, educators and professionals with detailed, code-based design procedures for fiber-reinforced polymer (FRP) composites used in civil engineering structures. Code-based means that the design procedures are written in accordance with published structural engineering design codes, guides and specifications, and those codes will be referenced in this column where appropriate. The focus of this month's excerpt is the design basis for concrete structural members reinforced with FRP, taken from chapters 4 and 5 of the book.
FRP reinforcements for new concrete structural members can be divided into three primary areas: 1) FRP bars or grids for reinforced concrete (RC) members, 2) FRP tendons for prestressed concrete (PC) members, and 3) stay-in-place composite formwork for reinforced concrete. Here we examine reinforcing bars, or rebar as known in the construction trades. Table 1 shows the typical material properties of FRP rebar commercially available in North America. Glass fiber-reinforced vinyl ester bars are the most common and are primarily longitudinally reinforced with fiber volume fractions in the range of 50 to 65 percent. FRP rebar is usually produced in a process similar to pultrusion and has a surface deformation or texture to develop a bond to concrete. It is typically produced in sizes ranging from 3/8 inch to 1 inch (9 mm to 25 mm) in diameter (i.e., No. 3 to No. 8). FRP rebar cannot be bent; bends must be incorporated during manufacturing . The longitudinal strength of FRP rebar is bar size dependent, due to the materials used in different-sized bars and due to the effects of shear lag.
FRP rebar is typically elastic and brittle, such that the stress-strain relation in axial tension is linear elastic to failure. Fig. 1 shows the stress-strain curve for a glass FRP rebar coupon (i.e., a section cut from a length of rebar) tested in tension. The ultimate tensile strength of a glass FRP bar decreases as the diameter increases but, as noted in Table 1, the longitudinal modulus does not change appreciably.
FRP rebar should only be used at service temperatures below the glass transition temperature (Tg) of the polymer resin system used in the bar, around 200°F/95°C for vinyl ester. FRP rebar, especially those containing glass fibers, can fail catastrophically under sustained load at stresses significantly lower than their short-term static tensile strengths, a phenomenon known as creep rupture or static fatigue. The sustained load on FRP rebar is therefore limited by design guides.
Design basis for FRP-reinforced concrete
The design basis of the American Concrete Institute (ACI), presented in ACI 318-05 and ACI 440.1R-06 (referenced in chart at end of article), is followed with respect to design philosophy and load and resistance factors for design. Similar design bases are recommended by many standards and professional organizations. ACI 440.1R-06 recommends the use of traditional methods of strain compatibility and equilibrium to determine internal forces in an FRP-reinforced concrete section. This includes the assumption that there is no slip (i.e., local relative longitudinal displacement) between the rebar and the concrete in an FRP-reinforced section.
The resistance factors for flexural strength design of glass FRP reinforced members have been developed using the load and resistance factor design (LRFD) probability-based approach. A reliability factor, β, of at least 3.5 is obtained using the design methods presented in what follows. The calibration for the reliability factor was based on ASCE (American Society of Civil Engineers) 7 load combination 2 (1.2D + 1.6L) and a ratio of dead load to live load of 1:3.
The resistance factors for determination of the ultimate flexural capacity and ultimate shear capacity of transversely loaded members (i.e., beams, slabs, and beam-columns) reinforced with FRP rebar are listed in ACI 440.1R-06. Note that the well-known flexural resistance factor of φ = 0.90 that is used when ductile failure of a steel-reinforced concrete section is assured — when εs > 0.005 — can never be used for FRP-reinforced concrete.
Strength (called the guaranteed strength) and strain to failure (called the guaranteed rupture strain) of FRP rebar are defined by the mean minus three standard deviations of a minimum of 25 test samples and are expected to be supplied by the manufacturer. FRP rebar must be tested according to the procedures detailed in ACI 440.3R-04, which are included in Chapter 3 of my book. As with steel bars, the design of FRP-reinforced concrete uses only the longitudinal properties (ƒfu, εfu, Εf) of the bars. This assumes that the transverse and shear properties, which are known to be significantly lower than the longitudinal properties due to the anisotropic nature of FRP materials, do not significantly influence the flexural behavior of FRP-reinforced concrete. At this time, FRP reinforcing bars should not be used as compression reinforcement, because insufficient test data on compression properties have been obtained.
Even though FRP rebar is not susceptible to conventional electropotential corrosion that affects metallic materials, it can nevertheless deteriorate in a variety of chemical environments, both alkaline and acidic, and deterioration is accelerated at elevated temperatures. An environmental reduction factor of 0.7 should be applied for fiberglass rebar in concrete exposed to ground and weather.
Because FRP rebar doesn't yield (i.e., it is linear elastic to failure), the ultimate strength of the bar replaces the yield strength of the steel rebar, ƒy, in the traditional reinforced concrete analysis procedure and determination of nominal moment capacity, which assumes equilibrium of forces and that plane sections remain plane. The design of either under- or over-reinforced sections is permitted, but due to serviceability limits (deflections and crack widths), most glass FRP-reinforced flexural members will be over-reinforced. The strains, stresses, and resulting section forces in the balanced condition are shown in Fig. 2.
An Illustration in flexural design
The use of FRP rebar in highway bridge decks is viewed as a promising way to increase highway bridge durability, and a number of projects have been completed in North America in recent years. In this example, a simply supported two-lane highway bridge deck, 100 ft long by 42 ft wide (30.5m by 12.8m) with a minimum depth of 8 inches/203 mm, is designed with FRP rebar. The design follows AASHTO HS20-44 loading, according to the AASHTO Standard Specification for Highway Bridges (2002). The bridge superstructure consists of pre-stressed concrete I-girders with rigid flanges that act compositely with the deck slab and are spaced 7 ft/2.13m on center. The example assumes no overhang and that conventional steel-reinforced parapets will be used.
Calculation of the design loads and the required moment capacity yields a value of Mu equal to 8.98 kip-ft/ft. Using a No. 5 FRP glass/vinyl ester bar with a guaranteed design strength (ƒfu) equal to 95 ksi, the effective depth for the bottom bars for positive moment capacity can be calculated:
d = h – cover – 0.5 (bar diameter)= 8 – 0.75 – 0.5 (0.625) = 6.94 inches
Three No. 5 bars per foot of width are selected for the bottom bars. For the top bars (for negative moment over the girders), the cover will be larger and more bars may be needed, but cover depth can be slightly less than what is normal for steel — 2db is suggested for constructability. The balanced reinforcement ratio then is calculated, using the exterior exposure factor of 0.7, arriving at 0.0092. The nominal moment capacity of the section is then calculated, with the result = 28.8 kip-ft/ft. The flexural resistance factor calculation results in a value of φ equaling 0.60, resulting in a factored moment capacity of 17.3 kip-ft/ft, well above the previously derived design demand of 8.98 kip-ft/ft. However, the slab needs to be checked for shear before finalizing the design. The required distribution reinforcement is 67 percent of the main reinforcement; for this example, two No. 5 bars were chosen. Because the slab is overdesigned in flexure, it could be argued that too much distribution reinforcement is provided. However, it is common practice to have reasonably balanced bidirectional reinforcement in bridge deck slabs, where punching shear under wheel loads is the typical failure mode observed. Both deflections and crack widths also must be checked, as well as stresses under sustained service loads against creep rupture and fatigue stress limits. It's important to note that the deflection or crack width limits often control design.
Excerpt published with permission from John Wiley & Sons. Composites for Construction — Structural Design with FRP Materials (John Wiley & Sons Inc., New York, N.Y.) is available for $135 (USD) at www.wiley.com, or from www.bn.com, www.amazon.com or www.borders.com.