Civil Engineering Reference
In-Depth Information
rectangle section,
ρ
et
=
A
s
0
.
5
bh
where
h, h
0
is sectional height, sectional effective height of original beam, respectively.
The particular calculation steps of shrinkage distortion, which occur when the beam is
stretched, are as follows:
a. Based on
M
1
, which is the moment acted on the beam before prestress is applied,
extension value Δ
S
i
of original reinforcements before retrofit can be calculated by Eq. (3.29).
b. Compute internal force caused by external prestressed reinforcements. The method is
to solve internal force, considering prestress as external force to apply on original beam.
c. Solve the action of moment
M
2
after original beam is applied prestress, which is the
difference between load moment
M
1
and prestressed moment
M
p
,thatis
M
2
=
M
1
−
M
p
.
d. According to
M
2
, judge the beam stress after being retrofitted, and calculate extension
value of original reinforcements.
If
M
2
>M
cr
, crack has not been closed, and the remnant extension Δ
S
2
of original
reinforcement can be calculated as Eq. (3.29).
If 0
M
cr
, crack is almost closed, or the remnant crack's width is very small. For
convenience, it can be adopted as Δ
S
2
.
If
M
2
<
0, crack is already closed, original reinforcements have changed from tensile status
to compression status, so Δ
S
2
=0. Where,
M
cr
is crack moment of original beam, and can
be calculated as formula in codes. As to rectangle section,
M
2
M
cr
=0
.
235
bh
2
f
tk
e. Calculate shrinkage distortion Δ
S
of beam
Δ
S
=Δ
S
1
−
Δ
S
2
(3
.
31)
(2) Stretching value calculation when using jack to stretch
a. Stretching value calculation of straight-line reinforcements. As to prestress straight
reinforcements, stretching value Δ
L
can be obtained by the following formula:
σ
con
E
s
Δ
L
=
L
+2
a
+Δ
S
(3
.
32)
where
L
is the distance between stretching point and anchoring point;
α
is anchor device
deformation at anchoring point and prestress reinforcements' shrinkage value
(Table 3.5)
;
Δ
S
is beam's longitude close shrinkage distortion caused by prestress (calculation by Eq.
(3.31));
σ
con
is stretching control stress of prestressed reinforcements.
Anchor device deformation should be considered if stretching is performed in the middle
regions of retrofitted reinforcements.
b. Stretching value calculation of curved reinforcements.
When curved reinforcements are stretched by jacks, the method of stretching at two ends
is usually used (shown in Fig. 3.18). There is more prestress loss caused by friction at
lower supporting points. When one end is stretched, a lot of stress is lost at the other end.
Applying two-end stretching, total stretching value Δ
L
can be calculated as the following
formula:
L
1
Δ
L
=
σ
con
−
σ
l
2
L
2
+2
σ
con
E
s
+
h
1
+Δ
S
(3
.
33)
E
s
where
σ
l
2
is prestress loss caused by friction at lower-supporting point;
L
1
is horizontal
length of oblique bar;
L
2
is the length of horizontal reinforcements between two supporting
points;
h
1
is the height of prestress oblique reinforcement.
