Civil Engineering Reference
In-Depth Information
β
2
0.5 (assuming use of high-bond reinforcement and sustained load). The
compression steel reduces the long-term de
=
ection by approximately 5 to 10
per cent. In preparation of the graphs of Fig. 9.8,
fl
ρ
′
=
A
′
s
/
bd
is considered
zero, but the term (1
−
20
ρ
′
) approximately accounts for the e
ff
ect of the
compression reinforcement.
Equation (9.38) is applicable for cracked or uncracked members. When the
bending moment at the determinant section does not exceed cracking (
M
M
r
),
0 and the corresponding graph in Fig. 9.8 may be employed to
determine
ζ
=
κ
t
for uncracked and cracked
members shows that when
M
is close to
M
r
it is important to determine
whether cracking occurred or not, because the value
κ
t
. Comparison of the values of
κ
t
and hence the
de
ection can increase by a factor of 1 to 3 once cracking occurs.
The approximate Equation (9.38) may be employed for members having
cross-sections other than rectangular, but with less accuracy. For this pur-
pose, when calculating
fl
the section is transformed into a rectangle of
the same height and with a width calculated such that the moment of inertia
of the gross area is the same. Calculation of
M
r
should be based on section
modulus of the actual section.
The tensile reinforcement has a great in
ρ
and
ρ
′
fl
uence on de
fl
ection in the cracked
state (
M
uence is small in the uncracked state.
The amount of the tensile reinforcement is accounted for in
M
r
); on the other hand, its in
fl
κ
t
and its
position is included in Equation (9.38) by the ratio
h/d
.
The value
M
r
of the cracking moment at the determinant section and
consequently the tensile strength of concrete
f
ct
(see Equations (9.25) and
(9.36) ), play an important role, particularly when the bending moment in the
vicinity of the determinant section is close to
M
r
, because the de
fl
ection may
then vary greatly. On the other hand, the in
fl
uence of
f
ct
diminishes in the
cracked stage.
The method of global coe
cients was designed for members subjected to
fl
exure, without axial force. If bending is combined with axial compression,
produced for example by prestressing, the method may be used but again with
less accuracy. The e
ect of the axial force will be limited to increasing the
value
M
r
(Equation (9.36) ).
ff
9.8.2 Shrinkage deflection
Equations (9.15, 16), (9.21-23) may be combined in one equation for the
de
ection at mid-span of a cracked reinforced concrete simple beam due to
shrinkage:
fl
−
ε
cs
l
2
(
∆
D
)
cs
=
8
d
[(1
−
ζ
)
κ
cs1
+
ζ
κ
cs2
]
(9.39)
where
ε
cs
is the value of free shrinkage of concrete (generally a negative
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