Fatigue Behavior of Stirrup Free Reactive Powder Concrete Beams Prestressed with CFRP Tendons

Acknowledgments

Notation

a

shear span of the beams;

B_f

stiffness of the beams under a fatigue load;

B_n

stiffness of the normal concrete beams;

B_r

stiffness of the RPC beams;

B_s

stiffness of the beams under the initial static load;

b_f

growth rate of the fatigue deflection;

D_N

fatigue damage index of the RPC beams;

d_f

diameter of the steel fibers in the RPC;

E₀

elastic modulus of the RPC;

E_f

elastic modulus of the FRP bars;

E_fc

fatigue modulus of the RPC at 2 million cycles;

E_s

secant modulus of the RPC at the compressive strength;

F

external load of the beams;

F_max

upper limit of the fatigue load;

f₀

predicted deflection of the beams under a static load;

f_c

axial compressive strength of the RPC;

f_cu

cubic compressive strength of the RPC;

f_fc

uniaxial compressive fatigue strength of the RPC at 2 million cycles;

f_ftf

fatigue strength of the CFRP tendons at the permissible stress amplitude;

f_m

measured midspan deflection in the RPC beams under the maximum static load;

f_mf

measured midspan deflection in the RPC beams under the maximum fatigue load;

f_N

predicted deflection of the beams after N cycles;

f_p

predicted midspan deflection in the RPC beams under the maximum static load;

f_pf

predicted midspan deflection in the RPC beams under the maximum fatigue load;

f_t0

initial cracking strength of the RPC under axial tension;

f_tf

tensile strength of the CFRP tendons;

f_ts0

initial cracking strength of standard 100 mm RPC cubes under splitting;

f_tsu

splitting strength of standard 100 mm RPC cubes;

f_tu

tensile strength of the RPC;

G

shear modulus of the RPC;

I₀

inertial moment of the transformed section of the beams;

I_cr

transformed moment of inertia of the cracked RC section;

I_e

effective moment of inertia of the FRP-reinforced normal concrete section;

I_g

moment of inertia of the gross concrete section about the centroidal axis;

k

nonuniformity coefficient of the shear stress distribution;

l

span length of the beams;

l_f

length of the steel fibers in the RPC;

M_a

applied bending moment;

M_cr

cracking bending moment of the beams;

M_u

ultimate bending moment of the beams;

$\overline{M}$

bending moment of the beams under a unit load;

N

number of loading cycles;

N_f

fatigue life of the beams;

n

elastic modulus-to-secant modulus ratio of the RPC at the compressive strength;

R_f

permissible stress amplitude of the CFRP tendons;

$\overline{V}$

shear force of the beams under a unit load;

α

influence coefficient of the bonding properties on the deflection of the beams;

α_E

ratio of the modulus of the CFRP tendons to that of the RPC;

β

an FRP-dependent coefficient for calculating the effective inertial moment;

β_B

influence coefficient of the steel fibers on the stiffness of the beams;

γ_f

ratio of tensile flange area to the web area of the beams;

ΔF

load amplitude;

Δ_f

midspan deflection of the beams under the maximum fatigue load;

Δ_s

static midspan deflection of the beams under the corresponding static load;

ɛ_c

compressive strain of the RPC;

ɛ_c0

compressive strain of the RPC at the compressive strength;

ɛ_t

tensile strain of the RPC;

ɛ_t0

tensile strain of the RPC at the tensile strength;

ɛ_tu

ultimate tensile strain of the RPC;

θ

stiffness reduction coefficient of the beams;

λ_f

characteristic parameters of the steel fiber content;

ξ

ratio of the current RPC compressive strain that at the compressive strength;

ρ

reinforcement ratio of the beams;

ρ_f

volume fraction of the steel fibers in RPC;

σ_c

compressive stress of the RPC;

σ_frp

tensile stress of the CFRP tendons at the midspan of the beams;

σ_tp

nominal principal tensile stress of the RPC in the web within the shear span; and

φ

coefficient used to calculate the rate of fatigue deflection.

References