This is the fourth column in a series taken from my book Composites for Construction — Structural Design with FRP Materials (see end note). The focus in this issue is the design basis for shear strengthening under transverse loads and confining of reinforced concrete under axial loads using composite materials.
The design procedures presented here follow the American Concrete Institute’s (ACI) publication ACI 440.2R-02, Guide for the Design and Construction of Externally Bonded FRP Strengthening Systems for Strengthening Concrete Structures (ACI, 2002), which is compatible with ACI 318-99, Building Code Requirements for Structural Concrete and Commentary (ACI, 1999). The examples below and in my book are intended to spur critical analysis and consideration of alternative designs not presented in the ACI Guide.
Although shear strengthening and confining have been practiced for about as long as flexural strengthening (the subject of my last column), the behavior of shear-reinforced members is less well understood. In recent years, there have been significant applications of FRP shear strengthening and confining systems to deficient highway bridge columns in seismically active zones.
FRP materials used for shear strengthening and confinement are similar to those used for flexural reinforcement, but they differ in fiber orientation (for a list of material suppliers, see “Learn More,‿ p. 11). Materials are applied to the webs of beams or the vertical sides of columns and walls and function in a fashion similar to that of internal steel shear reinforcements, adding to the shear resistance of the member.However, from a structural mechanics and constructability point of view, FRP shear strengthening or confinement is significantly more complex than FRP flexural strengthening. First, because transverse shear force in a concrete member acts parallel to its structural depth, the composite reinforcement needs to be placed in this direction along the member’s sides, which are much shorter than the length — this limits the distance over which the reinforcement can act and leaves little room for anchorage. And unlike flexural strengthening, where the force varies along the member’s length, the force or stress in the shear strengthening case is constant through the depth of the section at any location along the member’s length.
To get the best possible bond length, the FRP is wrapped, where possible, completely around the member (a four-sided wrap) or, if the top isn’t accessible, around three sides (a three-sided wrap, see Fig. 1a and 1b, at right). When the system can’t be wrapped, placing the materials on both sides of the member (a two-sided system) may be the only option (Fig. 1c). Shear-strengthening designs that cannot be fully wrapped are susceptible to detachment failures at their ends, and strains are limited by a shear bond reduction coefficient. Further, beam corners need to be chamfered or rounded off to prevent otherwise sharp edges from causing stress concentrations and premature failure of the FRP wrap.
The use of FRP confinement systems to increase the seismic resistance of reinforced concrete columns, first employed in Japan in the 1980s, is more complex than either flexural or shear strengthening. This is because the design driver is not to increase member strength per se, but rather to increase the inelastic lateral displacement capacity (i.e., the ductility) of the column. That is accomplished by preventing failure in other modes, such as shear, and encouraging failure in flexure.
When it is wrapped around the circumference of a circular column, an FRP confining system acts like a thin-walled pressure vessel, with the cracked concrete in the interior as the pressurized “liquid.‿ The confining effect occurs only after the internal transverse reinforcing steel has yielded and the concrete has cracked under stress and begins to dilate. This is the significant difference between FRP flexural and shear strengthening and FRP confining: In flexural or shear strengthening, the FRP serves as an additional tensile component to that provided by the internal steel rebar. In confining, however, the exterior FRP jacket increases the effective compressive properties of the concrete. If the column is undamaged, the jacket serves no structural purpose and is considered to be a passive strengthening system. For noncircular columns, the confining pressure is not uniform around the perimeter and the FRP confining efficiency declines significantly, but partial confinement may be possible. Because confining pressure must be distributed around the entire column circumference, only full (four-sided) wraps can be used for confinement applications.
SHEAR & AXIAL STRENGTHENING The nominal shear capacity of an FRP-strengthened beam with existing internal steel shear reinforcement is expressed by the following: Vn = Vc + Vs + ?f Vf
where Vc is the existing shear capacity of the concrete, Vs is the shear capacity of the existing steel shear reinforcement and Vf is the shear capacity of the FRP. It is assumed that the contribution of the three is linearly additive. The capacity reduction factor ?f used on the FRP contribution factor is taken as 0.95 for completely wrapped sections (called contact critical) and as 0.85 for two- and three-sided wrapped sections (called bond critical). (For term definitions, see “Learn More.‿)
There are two forms of the equation for the shear contribution provided by FRP shear strengthening, one for intermittent strips having width wf measured perpendicular to the major fiber orientation of the composite system spaced at spacing sf; and a second for continuous shear strengthening, that is, full side coverage with no overlapping. Intermittent wrapping is generally preferred, although harder to install in the field, because it allows moisture to migrate from the concrete to the air. Continuous wraps can trap moisture between the wrap and the concrete surface and lead to degradation of the interface, the concrete or the composite itself. For intermittent strengthening:
2ntf wf ffe df (sin a + cos a) df Vf = sf
where ffe is the effective tensile stress in the FRP material, a is the inclination of the fiber in the composite relative to the longitudinal axis of the member, n is the number of layers of shear reinforcement and df is the effective depth of the strengthening system (as shown in Fig. 2). Note that the spacing of the wraps sf has to be larger than the FRP wrap width (wf) divided by the sine of the fiber inclination.
FRP strengthening of circular columns can be achieved using either continuous or intermittent coverage as well. Because the axial load is constant along the full height of the column, the FRP wrap must cover the full height of the column, but it can be spaced intermittently. However, the equation presented below, for the theoretical concentric axial load capacity of an FRP-strengthened, nonslender, nonprestressed, normal-weight concrete column (with internal reinforced steel) applies only to continuous FRP wraps:
P0 = 0.85 ?f ƒ’cc (Ag – Ast) + ƒyAst
where Ag is the gross area of the concrete, Ast is the area of the internal longitudinal steel and ƒy is the yield stress of the internal longitudinal steel. Except for the strength reduction factor and use of confined concrete compressive strength factor ƒ’cc (instead of the conventional concrete compressive strength), this equation is the same as that used for conventional concrete columns.
The design procedure for shear streng-thening consists of the following steps:
Determine the current and future strength requirements and check the strengthening limits.
Choose an FRP composite system and configuration, determining whether precured strips or wet layup is best.
Determine the number of layers and geometry of the wrap. This step includes calculation of the shear bond reduction coefficient kv.
Calculate the actual shear capacity of the FRP wrap.
Calculate the factored shear capacity of the future strengthened beam and compare with the demand.
Check the maximum FRP reinforcement and spacing limits.
Finally, detail the strengthening system.
For confinement for axial strengthening:
Determine the nominal and factored capacities of the existing column, including original design dead and live loads and strengthening limit.
Determine the amount of strengthen-ing needed and whether it is to be an increase in dead load, live load or both.
Choose the FRP system and determine the effective design strength and strain for the hoop wraps.
Determine the number of layers for the chosen system.
Recalculate the capacity for the number of layers chosen.
Check the service-level stresses in the concrete and the steel.
ACI 440.2R-02 does not explicitly provide details on design of an FRP system to increase column ductility. Japanese guidelines exist, but the code equations are not presented in my book because many of the symbols are derivations and cannot be fully explained. However, engineers are encouraged to consult these code-based sources. A method developed by Professor Emeritus Nigel Priestley and colleagues at the University of California at San Diego for increasing the ductility of colums with confinement is presented in my book and explained briefly below.
The method is based on determination of a column's lateral displacement ductility. The ultimate lateral displacement, also known as drift, consists of an elastic portion and an inelastic (or plastic) portion. To increase seismic performance, the plastic ductility is increased by confining the concrete to increase its "plastic flexural hinge capacity" while preventing both premature shear failure in the column and debonding of the internal reinforcing bars that have been insufficiently overlapped and spliced. Seismic upgrades have to address all three factors: shear capacity and bar lap splice capacity, which are interrelated. For example, designs need to include FRP wraps in the location of the lap splice in the internal reinforcing bars.