Civil Engineering Reference
In-Depth Information
Consider an alternative strip pattern: de
fl
ection at centre of panel
1
=
2
(
δ
AD
+
δ
BC
)
+
δ
HI
. Similar calculations as above give
δ
AD
=
1.40 mm;
δ
BC
=
3.95 mm;
δ
HI
=
5.92 mm. The de
fl
ection at the centre of the panel due
to shrinkage is 8.60 mm.
The average of the two values obtained by the strip patterns con-
sidered is the probable de
ection at the centre of the panel due to
shrinkage and is equal to 7.7 mm (0.30 in). Addition of this value to the
de
fl
fl
ection value 44.6 mm (1.76 in) calculated in Table 9.3 gives the total
de
fl
ection including the e
ff
ects of creep, shrinkage and cracking.
For the indirect e
ff
ect of shrinkage, we determine the tensile stress at
bottom
ect of
shrinkage
i
s small and will be calculated for
st
rip AB only. At mid-sp
a
n,
we have:
E
c
fi
bre at mid-span of strips. In this problem the indirect e
ff
=
0.2207 m
2
; distance between centroid of
A
(the age-adjusted trans-
formed section) and the bottom
=
E
c
/(1
+
χφ
)
=
8.33 GPa;
α
=
E
s
/
E
c
=
24;
A
c
=
0.1991 m
2
;
A
0.093 m.
Curvature due to shrinkage if the strip were simply supported
(Equation (9.10) with
fi
bre,
y
b
=
κ
cs1
=
0.30) is
300 × 10
−6
0.30
(
∆
ψ
)
cs
=
0.17
=
536 × 10
−6
m
−1
.
Tensile stress at bottom
fi
bre caused by shrinkage (Equation (9.13) ) is
0.1991
0.2207
8.33 × 10
9
(536 × 10
−6
)0.093
300 × 10
−6
)
∆
σ
bot
=
−
(
−
1
−
=
0.660 MPa.
2.0 MPa may
now be reduced to 1.340 MPa. Cracking occurs at a reduced bending
moment (Equation (9.25) ),
M
r
The value of tensile strength of concrete in
fl
exure,
f
ct
=
=
8.93 kN-m/m. The corresponding
interpolation coe
cient (Equation (9.24) )
ζ
=
0.84, which is larger
than the value
ζ
=
0.76 calculated in Table 9.3. This means that the
indirect e
ff
ect of shrinkage is to bring the de
fl
ection closer to the fully
cracked state and gives
δ
AB
=
38.85 mm, instead of 37.05 mm calculated
in Table 9.3.
From the above, it can be seen that the indirect e
ect of shrinkage is
more conveniently accounted for by estimating a reduced value of
ƒ
ct
and then using it in the calculations for Table 9.3.
ff
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