|
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 |
|
|
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 |
|
|
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) |
|
|
factor that considers the orientation of the fibers |
|
|
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 |
|
|
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 |
|
|
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 |
|
|
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 |
|
|
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 |