Civil Engineering Reference
In-Depth Information
D
=
(1
−
0.28)12.05
+
0.28 × 22.57
=
15.0 mm
(0.59 in).
If the de
fl
ection due to shrinkage is excluded in Example 9.1, the
probable de
ection will be 20.6 mm (0.810 in). Thus, the compressive
force
N
reduces the de
fl
fl
ection in this example by 27 per cent.
9.8 Estimation of probable deflection: method of
'global coefficients'
In the majority of cases in practical design, particularly in preliminary stud-
ies, the engineer is only interested in an estimate of the probable de
fl
ection.
To this e
ect, Favre
et al.
5
have prepared graphs based on the bilinear
method, permitting a simple and rapid estimation (within ±30 per cent) of
long-term de
ff
fl
ections due to sustained loads and shrinkage.
9.8.1 Instantaneous plus creep deflection
Equations (9.5-8), (9.21-23) can be combined in one equation for the de
fl
ec-
tion due to a sustained load including the e
ff
ect of creep (but not shrinkage):
D
=
D
c
[(1
−
ζ
)
κ
s1
(1
+
φ
κ
φ1
)
+
ζ
κ
s2
(1
+
φ
κ
φ2
)]
(9.37)
where
cient (Equation (9.24) ).
Based on parametric study, this equation may be replaced by the following
approximation:
ζ
is the interpolation coe
h
d
3
κ
t
D
D
c
(1
−
20
ρ
′
)
(9.38)
This equation was derived for rectangular sections;
h
is total height;
d
is the
distance between tension reinforcement and extreme compressive
fi
bre;
ρ
′
=
A
′
s
/
bd
;
b
is the breadth of section and
A
′
s
is the cross-section area of compres-
sion reinforcement.
κ
t
is a global correction coe
cient which depends on the level of loading
expressed by the ratio (
M
r
/
M
) at the determinant section, creep coe
cient
φ
and the product
αρ
, with
α
=
E
s
/
E
c
(
t
0
) and
ρ
=
A
s
/
bd
;
A
s
is the cross-section
area of tension reinforcement.
The graphs in Fig. 9.8 give the global correction coe
cient
κ
t
. These were
prepared by calculating a value
κ
t
such that the terms between the square
brackets in Equations (9.37) and (9.38) are equal. The following parameters
are assumed constants;
d
/
h
=
0.9;
d
′
/
h
=
0.1;
α
=
E
s
/
E
c
(
t
0
)
=
7;
χ
=
0.8;
β
1
=
1 and
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