Civil Engineering Reference
In-Depth Information
Changes in de
fl
ections due to shrinkage (Equations (9.15) and (9.16) )
are
8
2
8 × 0.6
(
∆
D
1
)
cs
=
250 × 10
−6
× 0.27
=
0.90 mm
8
2
8 × 0.6
(
∆
D
2
)
cs
=
250 × 10
−6
× 0.97
=
3.23 mm.
Lower and upper bounds on de
fl
ection at time
t
(Equations (9.21) and
(9.22) ) are
D
1
=
4.05
+
8.00
+
0.90
=
12.95 mm
D
2
=
16.72
+
5.85
+
3.23
=
25.8 mm.
Value of bending moment which produces cracking in state 1 at mid-
span (Equation (9.25) ) is:
bh
2
6
0.3 × (0.65)
2
6
M
r
f
ct
=
2.5 × 10
6
=
52.8 kN-m.
(The reinforcement could be included in calculations of section modu-
lus, but this is ignored here.) Actual bending moment at mid-span is
17 ×
8
2
M
=
8
=
136.0 kN-m.
Interpolation coe
cient, using
β
1
=
1 assuming high-bond reinforce-
ment and
β
2
=
0.5 for sustained loading (Equation (9.24) ) is
1 × 0.5
52.8
ζ
=
1
−
136.0
=
0.81.
Probable de
fl
ection at time
t
(Equation 9.23) is
(1
−
0.81)12.95
+
0.81 × 25.8
=
23.4 mm (0.920 in).
The de
ection for the same beam is calculated by a more accurate
procedure involving numerical integration in Example 8.4. The answers
are almost identical.
fl
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