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. 2019 Mar 19;12(6):917. doi: 10.3390/ma12060917
a shear span, distance between left of loading plate and left of support
av clear shear span, distance between face of loading plate and face of support
bw web width
c height of compression zone
d effective depth
da maximum aggregate size
df fiber diameter
dv shear depth
e factor to take effect of shear span to depth ratio into account
fc specified concrete compressive strength
fc,cube average measured concrete cube compressive strength
fc,cyl average measured concrete cylinder compressive strength
fcfIk,L2f characteristic value of post-cracking flexural strength for a deflection of 3.5 mm
fck characteristic concrete cylinder compressive strength
fctk characteristic tensile strength of concrete
fctR,uf uniaxial tensile strength of SFRC
fcuf cube compressive strength of fiber reinforced concrete
fFtuk characteristic value of post-cracking strength for ultimate crack opening
fRk,4 characteristic residual flexural strength for the ultimate limit state at a CMOD of 3.5 mm
fspfc splitting tensile strength of fiber reinforced concrete
ft specified tensile strength of concrete mix
ftenf tensile strength of the fibers
fy yield strength of the reinforcement steel
h height of cross-section
hf height of flange
k size effect factor
kf factor that considers the contribution of flanges in T-sections (= 1 for rectangular sections)
kFf factor that considers the orientation of the fibers
kGf size factor, which accounts for the fact that fibers are better distributed in larger elements
lf fiber length
lspan span length
ltot total specimen length
n parameter for effect of geometry of flanged sections
rf fiber radius
sx crack spacing
sxe equivalent crack spacing factor
vmax shear stress at maximum sectional shear Vmax
wlim limiting crack width
wmax maximum crack width permitted by the code
wu ultimate crack width, i.e., the value attained at the ULS for resistance to combined stresses on the outer fiber under the moment exerted in this section
vb shear strength attributed to fibers
z internal lever arm
Actf effective area bw × d, with d limited to 1.5 m
Af cross-sectional area of the fiber
As area of longitudinal tension reinforcement
Avf shear area over which fibers contribute
B failure of bond between concrete and longitudinal reinforcement
CRd,c calibration factor for the design shear capacity
DT diagonal tension failure
Ef modulus of elasticity of the fibers
Es modulus of elasticity of reinforcement steel
F fiber factor
Gm matrix shear modulus
K orientation coefficient
M sectional moment
NA the failure mode of the individual experiment is not given, but the text mentions that all experiments resulted in a shear failure
Pmax maximum load in experiment
Rg geometry factor from Yakoub [64]: 0.83 for crimped fibers, 1.00 for hooked fibers, and 0.91 for round fibers
S fiber spacing
S shear failure
SC shear-compression failure
S-FL shear-flexure failure
ST shear-tension failure
V sectional shear force
Vc concrete contribution to shear capacity
Vcd design value of concrete contribution to shear capacity
Vf fiber volume fraction
Vfd design value of fiber contribution to shear capacity
Vmax maximum sectional shear in experiment caused by applied load only (without self-weight)
Vmin lower bound to the shear capacity
Vpred predicted shear capacity
VRd design shear capacity
VRd,c design shear capacity of the concrete contribution
VRd,cf design shear capacity of fiber reinforced concrete
VRd,cf design shear capacity of the fiber contribution, notation used in German guideline
VRd,c,min lower bound to the design shear capacity of the concrete contribution
VRd,f design shear capacity of the steel fiber contribution
Vu ultimate shear capacity
Vutot experimental shear capacity, including contribution from self-weight
Y failure mode includes yielding of longitudinal reinforcement
αcf factor that accounts for the long term effects
β fiber and matrix property factor developed by Cox [56]
γc concrete material factor
γcf concrete material factor, notation used in French guideline
γctf partial factor for tensile strength of fiber reinforced concrete
γE additional safety factor
εel elastic strain
εlim limiting strain
εmax maximum strain
εu ultimate strain at the ULS for bending combined with axial forces on the outer fiber under the moment exerted in the section
εx strain at mid-depth of the cross-section
ηo fiber orientation factor = 0.41 for fibers with a 3D random orientation, as derived by Romualdi and Mandel [151], but can be larger for members with thin webs
ηl a length factor used to account for the variability in the fiber embedment length across the cracking plane
θ angle of compression strut
ξ size effect factor from Bažant and Kim [62]
ρ reinforcement ratio
ρf fiber bond factor: 0.5 for straight fibers, 0.75 for crimped fibers, 1 for hooked fibers
σRd,f residual tensile strength of fiber reinforced cross-section
σf(ε) experimentally determined relation between stress in fiber concrete and strain
σf(w) experimentally determined relation between post-cracking stress and crack width w
σtu average stress at the ultimate limit state in the equivalent tensile stress block used for bending moment analysis of SFRC
τ bond strength between fibers and matrix
τfd design value of bond strength between fibers and matrix
ψ size effect factor from Imam et al. [63]
ω reinforcement ratio that includes the effect of fibers