Civil Engineering Reference
In-Depth Information
where
L
2
is the length of prestressed reinforcements from anchoring point to the first sup-
porting bar (Fig. 3.19); Δ
S
is the closure shrinkage deformation of original beam between
two prestressed reinforcements' anchoring points (as Eq. (3.31));
a
is the deformation of
anchor device, and
a
=0whenpoint
a
and
g
are welding points.
b. Frapping straight reinforcements at one point.
Fig. 3.20 shows a straight prestressed reinforcement that is frapped at one point. After
being frapped, prestressed reinforcement is moved from position abcde to position
a
b
c
d
e
.
Compared to Fig. 3.19, when
L
2
= 0, two-point frapping becomes one-point frapping, so
one-point shrinkage value can be calculated as Eq. (3.36), where
L
2
= 0 is ordered.
1
1
Δ
H
f f
g g
c
d
aa
bb
aa bb
c
c
d
d
e
e
m
n
Δ
S
L
2
Δ
S
L
2
2
Δ
H
L
2
L
1
L
3
L
3
L
1
L
2
L
2
L
1
L
3
L
3
L
1
L
2
L
0
L
0
Fig. 3.19 Frapping prestressed reinforcement by
two supporting rods at two points.
Fig. 3.20 Frapping prestressed reinforcement by
two supporting rods at one point.
c. Transversely frapping curved reinforcement.
When curved reinforcement is frapped transversely, the shrinkage value Δ
H
can still be
calculated as Eq. (3.35); however, Δ
S
of Δ
S
L
represents original beam's closure shrinkage
distortion at the range of curved reinforcement's horizontal length
L
which is under the
natural axis. That is to say,
L
should be given the horizontal length of curved reinforcement
under the natural axis when Δ
S
is calculated. As to one-point frapping,
L
3
=0inEq.
(3.36).
(4) Vertical stretching value calculation
Vertical stretching prestressed reinforcements cannot only produce opposite moment in
original beam as all kinds of prestress methods mentioned in the above, but can also produce
opposite load at original beam's top bracing point, resulting in larger opposite deflection
than the other prestress methods. This opposite deflection will counteract some vertically
stretching value, and decrease prestress effect. Consequently, this disadvantage factor of
opposite deflection should be considered in deducing formula of vertically stretching value.
When anchoring point of retrofitted reinforcement is near neutral axis, closure shrinkage
distortion will not cause an anchoring point to move; when the anchoring point is above
the natural axis, the anchoring point will move outwards. Ordinarily, anchoring point of
retrofitted reinforcement applying prestress by vertical stretching lays near or above the
neutral axis. So closure shrinkage distortion is not considered in the formula of vertically
stretching value calculation.
The initial position of prestressed reinforcement can be classified into straight line and
curved line. The following text takes curved prestressed reinforcement that is stretched at
two points for example, to illustrate calculation formula of stretching value.
a. Two-point vertically stretching curved reinforcement.
Fig. 3.21 shows vertically stretching curved prestressed reinforcement at two points to
retrofit beam. Before being stretched, prestressed reinforcement is positioned at
abcd
.After
point
b
and point
c
are vertically stretched, point
b
moves to
b
, while point
c
moves to
