Effect of U-Wrap Anchors on Flexural Behavior of Reinforced Concrete Beams Flexurally Strengthened with Externally Bonded CFRP Sheets

Acknowledgments

Notation

A_f

area of longitudinal FRP reinforcement (mm²);

A_fanchor

area of transverse FRP U-wrap for anchorage of flexural FRP reinforcement calculated per ACI 440.2R (ACI 2017) to prevent end peeling failure mode (mm²);

A_prov

total area of FRP U-wrap(s) for anchorage of flexural FRP reinforcement along one shear span (mm²);

A_s

area of flexural internal steel reinforcement (mm²);

A_vf

cross-sectional area of one U-wrap laminate (mm²);

b

concrete cross section width (mm);

C_E

environmental reduction factor, per ACI 440.2R (ACI 2017);

d

distance from extreme compression fiber to centroid of tension internal steel reinforcement (mm);

E_f

tensile modulus of elasticity of FRP reinforcement in the fiber direction (MPa);

$f_c^{\mathrm{\prime }}$

specified compressive strength of concrete (MPa);

f_fe

effective stress in the longitudinal FRP attained at section failure, computed per ACI 440.2R (ACI 2017) (MPa);

f_y

yield stress of longitudinal internal steel reinforcement (MPa);

h

concrete cross section height (mm);

M_cr

cracking moment (kN · m);

M_exp

experimentally observed moment capacity (kN · m);

M_FRP,anchored

experimentally recoded moment contribution of FRP to total moment capacity in an anchored beam (kN · m);

M_FRP,control

experimentally recoded moment contribution of FRP to total moment capacity in an unanchored control beam (kN · m);

M_pred

predicted nominal moment strength (kN · m);

M_nfpred

contribution of longitudinal CFRP to M_pred (kN · m)

M_ns

contribution of internal steel reinforcement to M_pred (kN · m)

M_u

moment at ultimate flexural capacity (kN · m);

M_y

moment at internal tensile steel reinforcement yielding (kN · m);

N

number of longitudinal FRP plies;

n

the ratio of tensile modulus of CFRP to modulus of elasticity of steel;

n_U

number of U-wraps along one shear span;

s

U-wrap anchor spacing (mm);

t_f

nominal thickness of one ply of longitudinal FRP (mm);

t_U

nominal thickness of the CFRP laminate used in the U-wraps (mm);

w_U

width of a single U-wrap (mm);

Δ_y

midspan displacement at internal steel yielding (mm);

Δ_u

midspan displacement at ultimate flexural capacity (mm);

ɛ_c

compressive strain in extreme compression fiber of concrete at section capacity (mm/mm);

ɛ_fd

debonding strain of longitudinal FRP (mm/mm);

ɛ_fe

effective strain in U-wrap reinforcement attained at failure, computed per ACI 440.2R (ACI 2017) (mm/mm);

ɛ_fu

design rupture strain of FRP;

ɛ_t

tensile strain in flexural internal steel reinforcement at section capacity (mm/mm);

ɛ_ty

yield strain of flexural internal steel reinforcement (mm/mm);

ϕ

flexural strength reduction factor;

κ_a

U-wrap anchorage coefficient;

κ_v

bond-dependent coefficient for shear, calculated per ACI 440.2R (ACI 2017);

μ

deformability coefficient;

ρ_equiv

equivalent flexural reinforcement ratio considering both internal steel reinforcement and longitudinal FRP reinforcement; and

ρ_s

flexural reinforcement ratio of internal steel reinforcement.

References