Civil Engineering Reference
In-Depth Information
The shear resistance, V
Rd,F
, is assumed to be not smaller than the minimum
value, V
Rd,Fmin
,de
ned as:
b
w
d
V
Rd
;
Fmin
¼
v
min
þ
0
:
15
r
cp
ð
3
:
29
Þ
f
1
=
2
ck
On the other hand, in the recent Final Draft [
2
] a recent model computes the term
V
RdF
as follows:
035
k
3
=
2
where: v
min
¼
0
:
zb
w
p
f
ck
1
c
F
V
Rd
;
F
¼
k
v
þ
k
f
f
Ftuk
cot
h
ð
3
:
30
Þ
where f
Ftuk
is the characteristic value of the ultimate tensile strength for FRC, as
determined by direct tensile tests, taken at the crack width at ultimate, w
u
; k
f
= 0.8:
q
f
ck
=
4
1
þ
1500
e
x
0
:
1300
1000
þ
k
dg
z
k
v
¼
for
q
w
\
:
0
08
f
yk
ð
3
:
31
Þ
q
f
ck
=
4
1
þ
1500
e
x
0
:
k
v
¼
for
q
w
0
:
08
f
yk
q
w
ε
x
is the longitudinal strain at the mid-depth of the effective shear
depth, as determined by the same expressions for concrete without
In Eq.
3.31
,
bers;
z
is the
internal lever arm (in mm) between the
fl
exural tensile and compressive forces and
k
dg
, is an aggregate size in
fl
uence parameter.
The aggregate size in
fl
uence parameter in Eq.
3.31
,
k
dg
, is given by:
32
16
þ
d
g
0
k
dg
¼
:
75
ð
3
:
32
Þ
where
d
g
is the maximum aggregate size in mm. If the size of the maximum
aggregate particles is not less than 16 mm, this parameter may be taken as
k
dg
= 1.0.
The limits of the angle of the compressive stress
eld,
ʸ
, relative to the longi-
tudinal axis of the member are:
h
min
h
45
ð
3
:
33
Þ
where the minimum inclination angle is:
h
min
¼
29
þ
7000
e
x
ð
3
:
34
Þ
For the determination of where
f
Ftuk
, the crack width at ultimate (
w
u
) is taken as:
w
u
¼
0
:
2
þ
1000
e
x
0
:
125 mm
:
ð
3
:
35
Þ
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