Cyclic Loading of Glued-In FRP Rods in Timber: Experimental and Analytical Study

Acknowledgments

Notation

A_eff

effective tensile area in timber (tension stiffening effect) (mm²);

A_r

cross-sectional area of the rod based on the core diameter (mm²);

A_ro

cross-sectional area of the rod based on the outer apparent diameter (mm²);

A_w

net timber cross-sectional area (mm²);

B₁₅

coefficient in the bond strength equation of the Fu et al. (2000) model;

B₂₆

coefficient in the bond strength equation of the Fu et al. (2000) model;

C₂₁

coefficient in the bond strength equation of the Fu et al. (2000) model;

C₂₂

coefficient in the bond strength equation of the Fu et al. (2000) model;

D

core diameter of the rod (mm);

D_h

hole diameter (mm);

D_o

outer apparent diameter of the rod (mm);

E_e

elastic energy stored during cyclic loading (kN · mm);

E_r

longitudinal elastic modulus of the rod;

E_p = E_storage−E_e

energy dissipation (kN · mm);

E_storage

total energy stored during cyclic loading (kN · mm);

E_w

longitudinal elastic modulus of the timber (GPa);

e

edge distance of glued-in rods (mm);

F_r

axial load (kN);

F_ru

failure load (kN);

F_rult,mon

ultimate failure load under monotonic tensile loading (kN);

f_cw,0,m

timber mean compressive strength (MPa);

f_ru

mean tensile strength (MPa);

f_tw,0,m

timber mean tensile strength (MPa);

f_v

shear strength (MPa);

f_vw,//,m

timber mean shear strength parallel to the grain (MPa);

f_vw,┴,m

timber mean shear strength perpendicular to the grain (MPa);

G

bond fracture energy (MPa · mm);

G_a

adhesive shear modulus (GPa);

G_v

shear modulus (MPa);

G_w

timber shear modulus (MPa);

G_II

mode II fracture toughness (MPa · mm);

K_e1

bond stiffness in the linear ascending branch of the bond stress–slip model (MPa/mm);

K_e2

bond stiffness in the linear descending branch of the bond stress–slip model (MPa/mm);

K_II

stress intensity factor (MPa · mm^1/2);

k_b

bar type coefficient in the NZTDS (2007) design equation for the axial load capacity of glued-in rods;

k_e

epoxy coefficient in the NZTDS (2007) design equation for the axial load capacity of glued-in rods;

k_m

moisture coefficient in the NZTDS (2007) design equation for the axial load capacity of glued-in rods;

L_b

bonded length (mm);

L_e

length of a discretized element = 1 mm;

L_m

material factor in the GIROD design formula;

L_ph

πD_hL_b = hole surface area (mm²);

L_pr

πD = rod perimeter (mm);

L_un

free unbonded length;

l_geo

geometrical factor in the GIROD design formula;

MC

moisture content (%);

p_a

constant in the Lamè form of the through thickness shear stress in adhesive [Fu et al. (2000) model];

p_w

constant in the Lamè form of the through thickness shear stress in timber [Fu et al. (2000) model];

q_a

constant in the Lamè form of the through thickness shear stress in adhesive [Fu et al. (2000) model];

q_w

constant in the Lamè form of the through thickness shear stress in timber [Fu et al. (2000) model];

RH

relative humidity (%);

r

radial coordinate, radius (mm);

r_o

radial coordinate at the rod/adhesive interface (mm);

r₁

radial coordinate at the wood/adhesive interface (mm);

r₂

radial coordinate at the timber face (mm);

u_a

axial displacement in the adhesive (mm);

u_w

axial displacement in timber (mm);

sl

loaded end slip (mm);

sl_anal

analytical loaded end slip value (mm);

sl_exp

experimental loaded end slip value (mm);

s_m

maximum slip in the ascending branch of the bond stress–slip model (mm);

s_u

maximum slip in the descending branch of the bond stress–slip model (mm);

t_a

glue-line thickness (mm);

x

horizontal coordinate in the horizontal axis along the bonded length (mm);

α_L

thermal coefficient of wood in the longitudinal direction;

α_R

thermal coefficient of wood in the radial direction;

α_T

thermal coefficient of wood in the transverse direction;

β

coefficient in the bond strength equation of the Fu et al. (2000) model;

γ_a

adhesive shear strain;

ɛ_r

longitudinal rod strain;

ɛ_ru

elongation at break;

ɛ_w

longitudinal timber strain;

ν

Poisson’s ratio;

ξ

ξ = E_p/2π · E_storage= damping ratio (%);

ρ_k

characteristic timber density (kg/m³);

ρ,_mean

mean timber density (kg/m³);

σ_ro

rod axial stress (MPa);

τ

bond strength (MPa);

τ_a

through thickness shear stresses in the adhesive (MPa);

τ_fr

frictional bond strength (MPa);

τ_m

maximum bond strength in the ascending branch of the bond stress–slip model (MPa);

τ_ra

bond strength at the rod/adhesive interface (MPa);

τ_w

through thickness shear stresses in the wood (MPa);

τ_wa

bond strength at the wood/adhesive interface (MPa); and

ω

parameter in the GIROD design formula for the axial load capacity of glued-in rods.

References