Civil Engineering Reference
In-Depth Information
1.25
Hsu
Lampert & Thürlimann
Leonhardt & Schelling
McMullen & Rangan
McMullen & Warwaruk
Bradburn & Zia
α
r
= 31° or 59°
α
r
1.0
= 45°
0.75
t
d
τ
n
1
t
d
=(0.082 + 3.405
)
t
do
f'
c
sin2
α
r
t
do
0.5
τ
n
t
d
4
0.25
t
do
f'
c
0
0.075
0.1
0.125
0.15
0.175
0.2
0.225
0.25
0.275
0.3
τ
n
f'
c
Thickness ratio
t
d
/
t
do
as straight line functions of shear stress ratio,
τ
n
/
f
c
Figure 7.12
The thicknesses
t
d
of these test beams are calculated and a linear regression analysis of the
thickness ratios
t
d
/
f
c
. This analysis provides the following
t
do
is made as a function of
τ
n
/
expression (Hsu and Mo, 1985b):
0
A
c
p
c
405
τ
n
f
c
1
sin 2
t
d
=
.
082
+
3
.
(7.79)
α
r
31
◦
or 59
◦
which were the limits adopted by the CEB-FIP Model Code (1978). The 61 test points are
also included and the correlation is shown to be excellent.
Although Equation (7.79) is found to be of excellent accuracy, it is considered to be
somewhat unwieldy for practical design. In the next section a simplified expression for
t
d
is
proposed. The simplicity is obtained with a small sacrifice in accuracy.
45
◦
and
Equation (7.79) is plotted in Figure 7.12 for the cases of
α
r
=
α
r
=
7.2.4 Simplified Design Formula for t
d
A simple expression for the thickness of shear flow zone
t
d
can be obtained directly from
Bredt's equation, (7.8) or [4], noting that
T
=
T
n
at the maximum load:
T
n
2
A
o
τ
t
t
d
=
(7.80)
m
2
f
c
, where
m
1
and
m
2
are nondimensional coeffi-
cients. Substituting them into Equation (7.80) gives
Assuming that
A
o
=
m
1
A
c
and
τ
t
=
T
n
A
c
f
c
t
d
=
C
m
(7.81)
