Experimental Investigation of Concrete Beams Strengthened with Embedded Through-Section Steel and FRP Bars

Acknowledgments

Notation

A_v

cross-sectional area of the FRP shear reinforcement (mm²);

a/d

shear span ratio of the beam;

d

effective depth of the beam section, where d is the height (h) of the beam section in ETS reinforcement (mm);

d_b

diameter of the bent portion of the FRP bar (mm);

E_ad.

Young’s modulus of the adhesive (GPa);

E_fw

Young’s modulus of the FRP bar (GPa);

E_s

Young’s modulus of the tensile reinforcement (GPa);

E_sw

Young’s modulus of existing transverse steel (GPa);

$\overline{E_{\mathrm{web}}}$

Young’s modulus of the shear reinforcement for Sato et al. (1997) model (GPa);

f_ad.

tensile strength of the adhesive (MPa);

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

concrete compressive strength (MPa);

f_f

Effective strength of the FRP shear reinforcement or yield strength of the steel reinforcement (MPa);

f_f,bend

tensile strength of the bent FRP bar (MPa);

f_f,u

ultimate strength of the FRP bar (MPa);

h

height of the beam section (mm);

L_str

vertical projected length of the shear cracking zone (mm);

L_web

horizontal projected length of the shear cracking zone (mm);

r_b

bending radius of the FRP bar (mm);

s

reinforcement spacing (mm);

V_f

shear contribution of the ETS or NSM bars (kN);

V_str

shear force carried by concrete in the compression zone above a neutral axis (kN);

V_web

shear force carried by the shear reinforcement in the shear cracking zone (kN);

z

7d/8= moment lever arm length (distance between the compressive force and tensile force) (mm);

α

inclination of the shear reinforcement (°);

ɛ_fe

effective strain of the shear strengthening system (µɛ);

ɛ_y/u

yield strain of the steel reinforcement or ultimate strain of the FRP reinforcement (µɛ);

$\overline{{\epsilon }_{\mathrm{web}}}$

average tensile strain of the shear reinforcement in the shear cracking zone (µɛ);

ρ_fw

amount of ETS or additional shear reinforcement (%);

ρ_s

amount of tensile reinforcement (%);

ρ_sw

amount of existing steel stirrups (%);

$\overline{{\sigma }_{\mathrm{web}}}$

average tensile stress of shear reinforcement in the shear cracking zone (MPa);

$\overline{{\tau }_{\mathrm{str}}}$

average shear stress at the shear cracking zone (MPa); and

θ

crack angle (°).

References