1 Introduction
2 Current Design Guidelines for Shear
2.1 Shear Strength
2.2 Minimum Shear Reinforcement
Design codes | Minimum shear reinforcement |
---|---|
ACI 318-14 (2014) |
\( \rho_{{v,{\rm min}}} = 0.062{{{\sqrt {f_{c}^{\prime}}}}/{{f_{yt}}}} \ge {{0.35}/{{f_{yt}}}} \)
|
EC2 (2004) |
\( \rho_{{v,{\rm min}}} = 0.08{{{\sqrt {f_{c}^{\prime}}}}/{{f_{yt}}}} \)
|
CSA A23.3-04 (2004) |
\( \rho_{{v,{\rm min}}} = 0.06{{{\sqrt {f_{c}^{\prime}}}}/{{f_{yt}}}} \)
|
AASHTO-LRFD (2004) |
\( \rho_{{v,{\rm min}}} = 0.083{{{\sqrt {f_{c}^{\prime}}}}/{{f_{yt}}}} \)
|
MC2010 (2012) |
\( \rho_{{v,{\rm min}}} = 0.08{{{\sqrt {f_{c}^{\prime}}}}/{{f_{yt}}}} \)
|
2.3 Spacing Limits for Shear Reinforcement
3 Experimental Program
3.1 Specimen Description
Specimens |
f
ct
(MPa) |
V
f
(%) |
a/d
|
ρ
l
(%) |
ρ
v
(%) |
f
y
(MPa) |
f
yv
(MPa) |
s (mm) |
M
n
(kN-m) |
V
@Mn
(kN) |
V
n
(kN) |
V
@Mn
/V
n
|
---|---|---|---|---|---|---|---|---|---|---|---|---|
SB1 | 11.5 | 1.5 | 3 | 0.78 | – | 617.7 | 537.5 | – | 338.3 | 512.6 | 347.6 | 1.47 |
SB2 | 11.5 | 1.5 | 3 | 0.78 | 0.6 | 617.7 | 537.5 | 165 | 338.3 | 512.6 | 449.8 | 1.14 |
SB3 | 11.5 | 1.5 | 3 | 0.78 | 0.9 | 617.7 | 537.5 | 110 | 338.3 | 512.6 | 501.0 | 1.02 |
SB4 | 11.5 | 1.5 | 3 | 0.78 | 1.4 | 617.7 | 537.5 | 66 | 338.3 | 512.6 | 603.2 | 0.85 |
3.2 Test Set-Up and Instrumentation
4 Material Properties
4.1 Materials and Mix Design of UHPFRC
Water-binder ratio | Cement | Zirconium | Filler | Fine aggregate | Water-reducing admixture |
---|---|---|---|---|---|
0.2 | 1.0 | 0.25 | 0.3 | 1.1 | 0.02 |
4.2 Compressive Behavior of UHPFRC
4.3 Tensile Behavior of UHPFRC
4.4 Tensile Behavior of Reinforcing Bars
5 Test Results
5.1 Damage and Crack Patterns
5.2 Load–Displacement Relationship
Specimens | Failure mode | At initial cracking | At yielding | At peak | At failure |
V
test
(MPa) |
\( \frac{{v_{test}}}{{\sqrt {f_{cf}}}} \) (MPa) |
μ (Δ
failure
/Δ
y
) | ||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Δ
cr
(mm) |
V
cr
(kN) |
Δ
y
(mm) |
V
y
(kN) |
Δ
@Vpeak
(mm) |
V
peak
(kN) |
Δ
failure
(mm) |
V
failure
(kN) | |||||
SB1 | S | 2.1 | 339.7 | 6.7 | 347.8 | 8.2 | 475.8 | 26.4 | 172.0 | 14.4 | 1.12 | 2.04 |
SB2 | SY | 1.1 | 150.2 | 7.1 | 479.1 | 11.1 | 537.3 | 15.3 | 408.9 | 16.3 | 1.26 | 2.15 |
SB3 | C | 3.6 | 555.6 | 7.3 | 359.8 | 11.8 | 551.7 | 16.3 | 441.0 | 16.7 | 1.29 | 2.23 |
SB4 | F | 1.2 | 190.5 | 7.3 | 296.1 | 10.9 | 567.0 | 16.0 | 436.1 | 17.2 | 1.33 | 2.19 |
5.3 Strain Response
6 Discussion of Test Results
6.1 Effect of Shear Reinforcement on Shear Strength
Specimens |
s (mm) |
V
c
(kN) |
V
fb
(kN) |
V
s
(kN) |
V
test
(kN) |
\( \frac{{V_{test}}}{{V_{c}}} \)
|
\( \frac{{V_{test}}}{{V_{fb}}} \)
|
\( \frac{{V_{test}}}{{V_{s}}} \)
|
\( \frac{{V_{test}}}{{V_{c} + V_{fb}}} \)
|
\( \frac{{V_{test}}}{{V_{fb} + V_{s}}} \)
|
\( \frac{{V_{test}}}{{V_{c} + V_{fb} + V_{s}}} \)
|
---|---|---|---|---|---|---|---|---|---|---|---|
SB1 | – | 76.7 | 270.9 | – | 475.8 | 6.20 | 1.76 | – | 1.37 | 1.76 | 1.37 |
SB2 | 0.75d
| 76.7 | 270.9 | 102.2 | 537.3 | 7.01 | 1.98 | 5.26 | 1.55 | 1.44 | 1.19 |
SB3 | 0.5d
| 76.7 | 270.9 | 153.4 | 551.7 | 7.19 | 2.04 | 3.60 | 1.59 | 1.30 | 1.10 |
SB4 | 0.3d
| 76.7 | 270.9 | 255.6 | 567.0 | 7.39 | 2.09 | 2.22 | 1.63 | 1.08 | 0.94 |
6.2 Evaluation of Shear Strength
Authors | Shear strength models |
---|---|
Sharma (1986) |
\( v_{u} = kf_{t}^{\prime} \left({d/a} \right)^{0.25} \)
where k = 2/3; a/d is the shear span-to-depth ratio; f
t
′ = 0.17√f
cf
, if the tensile strength is unknown, and f
cf
is the concrete cylinder compressive strength |
Narayanan et al. (1987) |
\( v_{u} = e\left[{0.24f_{spfc} + 80\rho \frac{d}{a}} \right] + v_{b} \)
where f
spfc
is the computed split-cylinder strength of fiber concrete (= f
cuf
/(20 − √F) + 0.7 + 1.0√F); ρ is the longitudinal reinforcement ratio; F is the fiber factor (=(L
f
/D
f
)V
f
d
f
; e is the arch action factor, 1.0 for a/d > 2.8 and 2.8d/a for a/d ≤ 2.8; f
cuf
is the cube strength of fiber concrete; V
f
is the fiber volume fraction; d
f
is a bond factor, 0.5 for round fibers, 0.75 for crimped fibers, and 1.0 for indented fibers; v
b
is equal to the equations of 0.41τF, and τ is the average fiber matrix interfacial bond stress, taken as 4.15 MPa |
Ashour et al. (1992) | For a/d ≥ 2.5 \( v_{u} = \left({2.11\sqrt[3]{{f_{cf}}} + 7F} \right)\left({\rho \frac{d}{a}} \right)^{1/3} \)
|
Kwak et al. (2002) |
\( v_{u} = 3.7ef_{spfc}^{2/3} \left({\rho \frac{d}{a}} \right)^{1/3} + 0.8v_{b} \)
where e is the arch action factor, 1 for a/d > 3.4, and 3.4d/a for a/d ≤ 3.4 |
Specimens | Sharma (1986) | Narayanan and Darwish (1987) | Ashour et al. (1992) | Kwak et al. (2002) | AFGC (2013) |
---|---|---|---|---|---|
SB1 | 2.79 | 3.71 | 6.30 | 3.12 | 1.37 |
SB2 | 2.09 | 2.56 | 3.58 | 2.27 | 1.19 |
SB3 | 2.28 | 2.86 | 4.18 | 2.49 | 1.10 |
SB4 | 2.46 | 3.15 | 4.83 | 2.71 | 0.94 |
Mean | 2.41 | 3.07 | 4.72 | 2.65 | 1.15 |
SD | 0.30 | 0.49 | 1.17 | 0.36 | 0.08 |