Punching Shear Behavior of Synthetic Fiber–Reinforced Self-Consolidating Concrete Flat Slabs with GFRP Bars

Acknowledgments

Notation

A_f

area of FRP reinforcement in concrete section;

A_p

projected horizontal area under critical shear crack over which σ_tf ­acts;

B

length of slab;

b

square column dimension;

b₀

perimeter of critical section at d/2 away from column face;

c

distance to neutral axis from extreme compression fiber;

d

effective depth of the slab;

d_f

diameter of fiber strand;

d_g

maximum aggregate size in concrete mix; taken as 0 for lightweight concrete;

d_g0

reference maximum aggregate size of 16 mm;

E_C

Young's modulus of concrete;

E_f

Young's modulus of FRP reinforcement;

EI

flexural stiffness – product of Young's modulus and second moment of area;

EI₀

uncracked flexural stiffness of concrete section;

EI₁

cracked flexural stiffness of concrete section;

E_s

Young's modulus of steel;

F_f,cr

force in FRP reinforcement at a strain equivalent to concrete ultimate crushing strain ɛ_cu;

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

28-day compressive strength of concrete cylinder;

f_ct

tensile strength of concrete;

f_f

force achieved in FRP bars at achievement of nominal moment;

h

slab total depth;

h_c

control depth from slab soffit;

k

ratio of depth of neutral axis to effective depth;

k_b

bond factor – 0.8 for hook ended fibers, 0.6 for crimped fibers, and 0.4 for straight fibers;

k_f

fiber-orientation factor;

l_f

length of fiber strand;

m_cr

cracking moment;

m_p,eq

equivalent plastic moment of an FRP-reinforced concrete section;

m_R

plastic moment of concrete section;

m_r

radial moment;

m_t

tangential moment;

m_u

ultimate moment of an FRP-reinforced section; nominal section moment;

n_f

Young's modulus ratio of FRP to concrete;

r₀

radius from center of slab to location of critical shear crack;

r_c

radius from center of slab to column face;

r_c,eq

radius from center of slab to equivalent column face;

r_p,eq

distance from center of slab to where χ_p,eq is achieved;

r_q

radius from center of slab to location of support;

r_s

radius from center of slab to free edge;

r_s,eq

radius from center of slab to equivalent location of free edge;

r_t

reinforcement-type dependent variable;

r_y

distance from center of slab to where χ_y is achieved;

V_R

punching shear resistance of slab;

V_R,c

concrete contribution to resistance punching shear force of slab;

V_R,f

fiber contribution to resistance punching shear force;

W

width of concrete section – taken as 1,000 mm or 1 m for slab unit width (SI);

w

crack width;

α_cc

factor corresponding to long-term effects on stress and to account for unfavorable load;

α_e

fiber engagement parameter – taken as 3.5;

α_f

fiber aspect ratio – ratio of fiber length to fiber diameter;

β

reduction factor equal to 1 for isometric reinforcement and to 0.6 for orthogonal reinforcement;

ɛ_cu

ultimate compressive concrete strain;

ξ

distance to slab soffit;

ρ

flexural reinforcement ratio;

ρ_f

fiber volume as a percentage of concrete volume;

σ_tf

tensile stress contribution of fiber;

τ_b

bond stress between fiber strand and concrete;

υ_R,c

concrete contribution to resistance punching shear stress of slab;

χ₁

curvature at crack stabilization;

χ_cr

curvature corresponding to cracking moment;

χ_p,eq

curvature corresponding to achievement of equivalent plastic moment m_p,eq;

χ_r

radial curvature;

χ_t

tangential curvature;

χ_TS

tension stiffening-compensating curvature;

χ_u

curvature corresponding to achievement of FRP-reinforced section nominal moment;

χ_y

curvature corresponding to achievement of plastic moment m_R; and

ψ

slab rotation.

References