MARCO EXPERIMENTAL
5. Diseño, desarrollo y evaluación de la prueba final.
(1)P Confinement of RC member with FRP is necessary for structural members subjected to con- centric or slightly eccentric axial loads larger than the corresponding axial capacity.
(2)P Good confinement can only be achieved by installing FRP fibers orthogonally to the mem- ber axis.
(3)P When FRP reinforcement is spirally arranged around the member perimeter, the confine- ment effectiveness shall be properly evaluated.
(4)P If the adopted FRP system is not initially prestressed, it exerts a passive confinement on the compressed member. The confinement action becomes significant only after cracking of the con- crete and yielding of the internal steel reinforcement due to the increased lateral expansion exhib- ited by the strengthened member. Prior to concrete cracking, FRP is practically unloaded.
(5)P Design at ULS of FRP confined members requires that both factored design axial load, NSd,
and factored axial capacity, NRcc,d, satisfy the following inequation:
Sd Rcc d,
N ≤N (4.39)
(6) For non-slender FRP confined members, the factored axial capacity can be calculated as fol- lows: Rcc d c ccd s yd Rd 1 , N A f A f γ = ⋅ ⋅ + ⋅ (4.40)
where the partial factor γRd shall be taken equal to 1.10 (Table 3-3, Section 3.4.2); Ac and fccd
represent member cross-sectional area and design strength of confined concrete as indicated in item (7), respectively; andAs and fyd represent area and yield design strength of existing steel rein- forcement, respectively.
(7) The design strength, fccd, of confined concrete shall be evaluated as follows: 2 3 l,eff ccd cd cd 1 2 6 / f f . f f ⎛ ⎞ = + ⋅⎜ ⎟ ⎝ ⎠ (4.41)
where fcd is the design strength of unconfined concrete as per the current building code, and f1,eff
is the effective confinement lateral pressure as defined in the following section. The same relation- ship shall be used also to attain the second objective mentioned in Section 4.5.1 (1)P.
(8) The confinement is effective if f1,eff fcd >0.05.
4.5.2.1 Confinement lateral pressure
(1)P The effectiveness of FRP-confined members only depends on a fraction of the confinement lateral pressure, f1, exerted by the system, namely effective confinement lateral pressure f1,eff.
(2) The effective confinement lateral pressure, f1,eff, is a function of member cross section and FRP configuration as indicated in the following equation:
l eff eff
l, k f
f = ⋅ (4.42)
where keff is a coefficient of efficiency (≤1), defined as the ratio between the volume, Vc,eff, of the effectively confined concrete and the volume, Vc, of the concrete member neglecting the area of ex- isting internal steel reinforcement.
(3) The confinement lateral pressure shall be evaluated as follows:
l f f fd,rid
1 2
f = ⋅ ⋅ ⋅ρ E ε (4.43)
where ρ is the geometric strengthening ratio as a function of section shape (circular or rectangu-f lar) and FRP configuration (continuous or discontinuous wrapping), Ef is Young modulus of elas- ticity of the FRP in the direction of fibers, and εfd,rid is a reduced FRP design strain, defined in the following item (9).
(4) The coefficient of efficiency, keff, shall be expressed as:
eff H V
k =k k k⋅ ⋅ (4.44) α
(5) The coefficient of horizontal efficiency, kH, depends on cross-section shape (see Sections 4.5.2.1.1 and 4.5.2.1.2).
(6) The coefficient of vertical efficiency, kV, depends on FRP configurations. For RC confined members with continuous FRP wrapping, it is assumed kV =1. For RC confined members with discontinuous FRP wrapping (Figure 4-11), such as FRP strips installed with a center-to-center spacing of pf and clear spacing of p′f, reduction in the confinement effectiveness due to the diffu- sion of stresses (approximately at 45°) between two subsequent wrappings shall be considered.
Figure 4-11 – Elevation view of circular member confined with FRP strips.
Regardless of the section shape, the coefficient of vertical efficiency, kV, shall be assumed as fol- lows: 2 f V min 1 2 p k d ⎛ ′ ⎞ = −⎜ ⎟ ⋅ ⎝ ⎠ (4.45) unconfined concrete
where dmin is the minimum cross-section of the member.
(7) In case of discontinuous wrapping the net distance between strips shall satisfy the limitation '
f min 2
p ≤d .
(8) Regardless of the section shape, the efficiency coefficient, kα, to be used when fibers are spirally installed with an angle α with respect to the member cross-section, shall be expressed as f follows: 2 f 1 1 (tan ) kα α = + (4.46)
(9) The reduced FRP design strain, εfd,rid, shall be computed as follows (see also Section 4.5.1, item (9)P):
fd,rid min{ a fk/ ; 0.004}f
ε = η ε γ⋅ (4.47)
where ηa and γ represent environmental conversion factor and partial factor as suggested in f Table 3-4 and Table 3-2, respectively.
4.5.2.1.1 Circular sections
(1)P FRP-confinement is particularly effective for a circular cross section subjected to both con- centric or slightly eccentric axial loads.
(2)P Fibers installed transversely to the longitudinal axis of the strengthened member induce a uniform pressure that opposes the radial expansion of the loaded member.
(3) The geometric strengthening ratio, ρ , to be used for the evaluation of the effective con-f finement pressure shall be expressed as follows:
f f f f 4 t b D p ρ = ⋅ ⋅ ⋅ (4.48)
where (Figure 4-11) tf, bf , and pf represent FRP thickness, width, and spacing, respectively, and
D is the diameter of the circular cross section. In case of continuous wrapping, ρ becomes f
D tf
4⋅ .
(4) For circular cross sections, the coefficient of horizontal efficiency, kH, is equal to 1.0. (5) For circular sections, the dimension dmin introduced in Equation (4.45) for the computation of the coefficient of vertical efficiency, is to be intended as the section diameter.
4.5.2.1.2 Square and rectangular sections
(1)P FRP-confinement of members with square or rectangular cross sections produce marginal increases of the member compressive strength. Therefore such applications shall be carefully vali-
dated and analyzed.
(2)P Prior to FRP application, the cross section edges shall be rounded to avoid stress concentra- tions that could lead to a premature failure of the system.
(3) The corner radius shall satisfy the following limitation:
c 20 mm
r ≥ (4.49)
(4) The strengthening geometric ratio, ρ , to be used for the evaluation of the effective con-f finement pressure shall be expressed as follows:
f f f f 2 t (b d b) b d p ρ = ⋅ ⋅ + ⋅ ⋅ ⋅ (4.50)
where tf , bf, and pf represent FRP thickness, width, and spacing, respectively, while b and d are cross section dimensions of the rectangular member. In case of continuous wrapping, ρ becomes f
(
b d) (
b d)
t ⋅ + −
⋅ f
2 .
(5)P For rectangular cross sections, the effectively confined concrete area may be considered to be only a fraction of the overall concrete cross section (Figure 4-12). The reason for such a behav- ior lies in the “arch effect” that forms within the concrete cross section. Such an effect depends on the values of the corner radius rc.
Figure 4-12 – Confinement of rectangular sections.
(6) For rectangular cross sections, the coefficient of horizontal efficiency, kH, that takes into account the arch effect shall be expressed as follows:
g 2 2 H 3 ' ' 1 A d b k ⋅ + − = (4.51)
where b′ and d′ are the dimensions indicated in Figure 4-12, and Ag is the cross section area. (7) The effect of FRP confinement shall not be considered for rectangular cross sections having
2 >
d
b , or max