Behavior of Reinforced Concrete Beams without Stirrups and Strengthened with Basalt Fiber–Reinforced Polymer Sheets

Acknowledgments

Notation

D

damage factor in the Mode I, Modes II/III, and mixed-mode conditions;

D₂

weakening factor of the reinforcement–concrete interface;

E

elastic modulus;

E₀

original elastic modulus of the BFRP sheet (25 GPa);

f

friction coefficient;

F_t

tensile strength of the interface;

$F_t^r$

relative tensile strength of the interface;

f_ck

concrete compression strength;

$G_{\mathrm{I}}$

fracture energy in the Mode-I condition;

G_II/III

fracture energy in the Modes II/III condition;

$G_{\mathrm{I}}^r$

energy release rate in the normal direction;

$G_{\mathrm{II}/\mathrm{III}}^r$

energy release rate in the tangential direction;

h_rib

height of the rib;

k_n

interface stiffness in the normal direction;

k_s

interface stiffness in the tangential direction;

$\overline{k_s}$

antislide stiffness of the interface (for calculating friction stress);

T_fx, T_fy

friction stresses in the tangential directions;

α

constant parameter of the ascending branch (for calculating bond–slip relation of reinforcement–concrete interface);

δ

total relative displacement;

δ_f

total relative displacement at the onset of interfacial failure in the mixed-mode condition;

δ_n

displacement in the normal direction;

${\delta }_{nf}^r$

relative normal displacement at the onset of interfacial failure in the mixed-mode condition;

δ_nf

normal displacement at the onset of interfacial failure in the Mode-I condition;

δ_n0

normal displacement at the onset of interfacial softening in the Mode-I condition;

${\delta }_{n0}^r$

relative normal displacement at the onset of interfacial softening in the mixed-mode condition;

δ_s

total displacement in the tangential plane;

δ_sf

tangential displacement at the onset of interfacial failure in the Modes II/III condition;

${\delta }_{sf}^r$

relative tangential displacement at the onset of interfacial failure in the mixed-mode condition;

δ_sx,δ_sy

tangential displacements;

δ_sx,^slideδ_sy^slide

tangential sliding displacements that have been generated during the loading process;

$\begin{array}{rl}& {\delta }_{sx}^{\mathrm{slide},\mathrm{old}},{\delta }_{sy}^{\mathrm{slide},\mathrm{old}}\end{array}$

sliding displacements before being updated;

δ_s0

tangential displacement at the onset of interfacial softening in the Modes II/III condition;

${\delta }_{s0}^r$

relative tangential displacement at the onset of interfacial softening in the mixed-mode condition;

δ_s1

tangential displacement corresponding to τ_max;

δ_s2

tangential displacement corresponding to τ_res;

δ₀

total relative displacement at the onset of interfacial softening in the mixed-mode condition;

σ

normal stress;

τ

total shear stresses;

τ_f

total friction stress;

τ_max

bond strength of the reinforcement–concrete interface;

τ_res

residual strength of the reinforcement–concrete interface;

τ_x, τ_y

shear stresses;

τ₀

shear strength; and

${\tau }_0^r$

relative shear strength.

References