Civil Engineering Reference
In-Depth Information
to the stress difference of sections as well as the eccentricity
e
0
between additional rein-
forcements and original reinforcements (see Fig. 3.11(a)), additional moment and induced
flexural deformation are obtained.
The flexural deformation not only aggravates stress lag of additional reinforcements but
causes asymmetrical stress of original reinforcements at both sections of welding points,
which should be given close attention in retrofit design.
Existing beam
Original reinforcement
Weld
σ
sl
1
A
sl
σ
sl
2
A
sl
Added reinforcement
Stub bars
Fig. 3.11
Local flexural deformation of original reinforcements at both sides of welding points.
3. Retrofit design of beams
(1) Calculation of bearing capacity
Based on previous analyses, it is clear that stress of additional reinforcement lags behind
that of original reinforcements; therefore design strength of additional reinforcement should
be multiplied by reduction factor 0.9.
⎫
⎬
f
cm
bx
=
f
y
A
s
+0
.
9
f
y
1
A
s
1
M
u
=
f
cm
bx
h
01
−
2
(3
.
11)
x
⎭
Eq. (3.11) may be rewritten as
M
f
cm
bh
01
α
s
=
(3
.
12)
where
α
s
is coecient of sectional resistance moment. Provided that the internal lever arm
γ
s
is obtained from
α
s
by design chart, the cross-section area needed could be given as
M
f
y
A
s
γ
s
b
0
0
.
9
f
y
1
γ
s
h
01
−
A
s
1
=
(3
.
13)
where
f
cm
is design value of flexural compressive strength of concrete and may be taken
as 1
.
1
f
c
;
x
is concrete compression height;
f
y
and
f
y
1
are design value of tensile strength
of original reinforcements and additional reinforcements respectively;
A
s
and
A
s
1
are sec-
tional area of original reinforcements and additional reinforcements;
h
01
is effective depth
of retrofitted section, which is the distance from extreme compression fiber to the point
of resultant forces of the original reinforcements and additional reinforcements, and could
roughly be substituted for effective depth of existing beams with regard to small numbers
of additional reinforcements. M represents design value of the moment and
M
u
denotes the
design values of flexural capacity of retrofitted beams.
Application range of Eqs. (3.11) to (3.13) is the same as that for under-reinforced beams
specified in the code.
(2) Calculation and control of steel stress in service
Stress lag of additional reinforcements is likely to induce the result that original rein-
forcements enter strain-hardening range prior to additional reinforcements; deflection and
crack width are much larger than those of primary loading members at ultimate load. It is
indicated that stress lag will give rise to higher service stress for original reinforcements and
