Civil Engineering Reference
In-Depth Information
8.929
25.0
(2.25) {192.09,
{
A
r
(
t
2
,
t
1
)}
creep, member 1
=
−
−
192.09}
154.4, 154.4} kN
The restraining forces for shrinkage are the same for any of the
concrete members (1 to 6). Equation (6.7) gives:
=
{
−
{
A
r
(
t
2
,
t
1
)}
shrinkage members 1 to 6
=
8.929 GPa (
−
400 × 10
−6
) 0.4 {1,
−
1}
=
{
−
1428.6, 1428.6} kN
Table 6.6 gives abbreviated input and results of Computer run 2.
Because this structure is statically determinate externally, creep and
shrinkage do not a
ect the reactions (omitted in Table 6.6). The
changes in displacements due to creep and shrinkage in the period
t
1
to
t
2
are given in Table 6.6, including the change of mid-span de
ff
ection of
27.5 mm (node 10 or 11). The changes in member end forces are given in
Table 6.6 only for the members where the change is non zero.
fl
Example 6.5 Prestressed portal frame
Figure 6.11(b) represents a portal frame idealization. Member
BC
has a
post-tensioned T-section, shown in Fig. 6.11(a). Member
AC
is non-
prestressed. The prestressing steel tendon, having parabolic pro
le, is
idealized as straight steel members connected by rigid arms to nodes on
the x-axis through the centroid of the gross concrete section of member
BC
. At time
t
1
member
BC
is subjected to a uniform gravity load
q
fi
26 kN-m (representing self weight and superimposed dead load),
combined with a prestressing force,
P
=
2640 kN, assumed constant
over the length of the tendon. Find the changes in the force in the
tendon and the de
=
ection at mid-span due to creep and shrinkage of
concrete and relaxation of prestressed steel occurring between
t
1
and a
later time
t
2
. Ignore presence of non-prestressed reinforcement and
cracking. Given data: modulus of elasticity of concrete at time
t
1
,
E
c
(
t
1
)
fl
=
25 GPa; creep and aging coe
cients,
φ
(
t
2
,
t
1
)
=
2.0 and
χ
(
t
2
,
t
1
)
=
0.8; free shrinkage,
ε
cs
(
t
2
,
t
1
)
=
−
300 × 10
−6
; reduced relaxation (Sec-
tion 1.5),
=
200 GPa. The cross-sections of the members have the following area
properties:
∆
σ
pr
=
−
60 MPa; modulus of elasticity of prestressed steel
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