Civil Engineering Reference
In-Depth Information
When the member is uncracked,
ζ
=
0 and
κ
tcs
=
κ
cs1
(Equation (9.17) or
Fig. F.9).
Example 9.3 Non-prestressed beam: use of global coefficients
Estimate the de
ection at mid-span for the beam of Example 9.1 (Fig.
9.4) by the method of global coe
fl
cients.
The following values calculated in Example 9.1 are required here:
Basic de
fl
ection,
D
c
=
4.40 mm
M
r
=
52.8 kN-m
M
=
136.0 kN-m
ζ
=
0.81
200
30
×
0.6
αρ
=
100
=
0.04
M
r
M
52.8
=
136.0
=
0.39
Entering the last two values in the graph for
φ
=
2.5 in Fig. 9.8 gives
κ
t
=
3.8. The probable instantaneous plus creep de
fl
ection (Equation
(9.38) ) is
0.65
0.6
3
20 ×
0.15
100
4.4 × 3.8
1
−
=
20.6 mm.
Entering the graph of Fig. 9.9 with
ζ
=
0.81;
α
ρ
=
0.04 and
ρ
′
/
ρ
=
0.25
gives
κ
tcs
=
0.85. Thus, the de
fl
ection due to shrinkage (Equation (9.42) )
is
250 × 10
−6
)
8
2
(0.85)
8(0.6)
(
∆
D
)
cs
=
−
(
−
=
2.8 mm.
Estimated value of de
fl
ection including e
ff
ects of creep and shrinkage is
D
=
20.6
+
2.8
=
23.4 mm (0.94 in).
Example 9.4 Prestressed beam: use of global coefficients
Estimate the de
fl
ection at mid-span of the prestressed beam in Fig. 9.10
due to the e
ff
ects of a sustained load
q
=
20 kN/m (1.4 kip/ft) combined
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