Civil Engineering Reference
In-Depth Information
To limit the value of
A
,
min
, the transverse steel area per unit length
A
t
/
s
in the second term
on the right-hand side of Equation (2.105) must not be taken less than 0
f
yt
.
Two equations are required for the design of longitudinal torsional steel. Equation (2.104)
is needed to determine the torsional strength, while Equation (2.105) is needed to ensure
ductility. Both equations are applicable to solid and hollow sections, as well as nonprestressed
and prestressed concrete. The longitudinal torsional bars required by these two equations
should be distributed uniformly along the perimeter of the cross-section. They should meet
the maximum spacing requirement of
s
≤
.
17(MPa)
b
w
/
305 mm (12 in.) and the minimum bar diameter of
d
b
≥
s
/
16 or 9.5 mm (3
/
8in.).
2.3.2 Shear Steel Design
The design of shear steel could be based on the three equilibrium equations derived in Section
2.1.3, specifically, Equations (2.38)-(2.40). These three equilibrium equations for beam shear
have also been summarized in Table 2.1. Equations (2.38) and (2.39) could be used to size
the longitudinal torsional steel and the transverse torsional steel, respectively. Equation (2.40)
could be used to check the stresses in the concrete struts in order to avoid the concrete crushing
before the steel yielding.
The ACI methodology for the design of shear steel, however, is less conservative. In the
ACI Code, the nominal shear resistance
V
n
is assumed to be made up of two terms:
V
n
=
V
c
+
V
s
(2.106)
where
V
c
is the contributed of concrete, and
V
s
is the contributed of steel. Only the steel
contribution
V
s
will satisfy the beam shear equilibrium equation (2.39).
2.3.2.1 Concrete Contribution
V
c
The empirical expressions of concrete contribution
V
c
in ACI318-08 are given as follows:
For normal-weight reinforced concrete [ACI Equation (11-3)]
166
f
c
(MPa)
b
w
d
V
c
=
0
.
(2.107)
For normal-weight prestressed concrete [ACI Equation (11-9)]
0
b
w
d
05
f
c
(MPa)
82(MPa)
V
u
d
M
u
V
c
=
.
+
4
.
(2.108)
166
f
c
(MPa)
b
w
d
42
f
c
(MPa)
b
w
d
and
V
u
d
where 0
.
≤
V
c
≤
0
.
/
M
u
≤
1.
2.3.2.2 Transverse Shear Steel
The transverse shear steel in the beam web is designed according to Equation (2.39) using a
shear force of
V
s
=
(
V
u
/φ
)
−
V
c
. Taking
A
t
=
A
v
and
d
v
=
d
, and assuming the yielding of
45
◦
:
steel
f
t
=
f
yt
and
θ
=
A
s
V
s
df
yt
=
V
u
−
φ
V
c
=
(2.109)
φ
df
yt
