Structural behaviour of beams under simultaneous load and steel corrosion

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Concrete Repair, Rehabilitation and Retrofitting II – Alexander et al (eds)
© 2009 Taylor & Francis Group, London, ISBN 978-0-415-46850-3
645
Structural behaviour of beams under simultaneous load
and steel corrosion
G. Malumbela, P. Moyo & M. Alexander
University of Cape Town, South Africa
ABSTRACT: This paper presents the results of an experimental study conducted to characterize the structural
behaviour of beams corroded whilst subjected to a constant sustained load. Corrosion on tensile steel bars was
induced by an accelerated corrosion process using a 5% solution of NaCl and a constant impressed current. Four
RC beams were tested, each with a width of 153 mm, a depth of 254 mm and a length of 3000 mm. Beams were
tested whilst under self-weight, under 10% of the ultimate load and under 33% of the ultimate load. Longitudi-
nal tensile strains and longitudinal compressive strains were monitored during the corrosion process. Measured
strains were used to determine the depth of the neutral axis, the curvature and the moment of inertia of beams.
The results indicate that the longitudinal strains, depth of the neutral axis and curvature depend on both the level
of corrosion and the applied load whilst the moment of inertia only depends on the level of corrosion.
1 INTRODUCTION
Corrosion of steel bars embedded in concrete is a
worldwide problem that affects numerous reinforced
concrete structures Roberge (1999). It is accepted
that as corrosion of steel bars occurs there is a cor-
responding reduction in the area of the bars and cor-
rosion products deposited around the steel bar occupy
a larger volume than the volume of steel lost. The
expansive corrosion products create tensile stresses
in the concrete surrounding the corroding steel bar,
which can cause cracking and spalling of concrete.
The structural integrity of a reinforced concrete
structure undergoing corrosion damage is reduced by
the loss of bond between the steel and the concrete
as well as the loss of area of reinforcing steel Soudki
et al (2000).
A great deal of research has been done on the effects
of corrosion of tensile steel bars on the structural per-
formance of RC members. Majority of the work done
has focussed on corrosion damage under no sustained
load, Ballim et al (2003). In real structures however
corrosion normally takes place whilst the structure
is under a sustained load. The limited work that was
done on structural behaviour of corroded beams
under a constant sustained load mainly investigated
the interaction between central deflections of beams,
degree of corrosion and the sustained load, Ballim
et al (2003), El Maaddawy et al (2005) and Yoon et al
(2000). In spite of the limited work, the results by the
researchers clearly indicate that deflections of beams
increase with an increase in degree of corrosion and
the magnitude of the applied load. Whilst deflections
of beams can be used as an indicator of structural per-
formance, models of structural behaviour of beams
(including deflections) require variations of strains,
depth of neutral axis, curvatures and stiffness as input
parameters. Hence research is needed to clarify the
variation between these input parameters with degree
corrosion in the presence of a sustained load. This
paper presents an experimental programme and a dis-
cussion of results on the interactions between longi-
tudinal strains, depth of neutral axis, curvatures and
stiffness of beams with magnitude of sustained load
and corrosion of tensile steel bars.
2 BEHAVIOUR OF RC BEAMS UNDER
SERVICE LOADS
There are two distinct stages in the structural behav-
iour of flexural RC beams under service loads namely
uncracked stage and cracked stage, CEB-FIP (1990).
It is evident that if uncorroded beams under the
uncracked and cracked stages have distinct structural
behaviours, they should equally have distinct struc-
tural behaviours when corroded.
2.1 Uncracked stage
Under the uncracked stage, majority of applied
stresses on a RC beam are balanced by the concrete
646
and not by the steel bars. Loss in area of tensile
steel bars due to corrosion on a beam in this stage
is therefore unlikely to disturb the equilibrium of the
internal forces and moments resisted by the beam.
There is little published data to describe the behav-
iour of uncracked RC beams under simultaneous load
and corrosion of steel bars.
2.2 Cracked stage
Local curvatures in a cracked RC beam under a four-
point bending varies along the constant moment
region with high curvatures occurring at the crack
location and lowest curvatures occurring midway
between cracks, Ghali et al (1994). This is because
at the location of a crack, tensile stresses resulting
from beam loading are balanced only by the tensile
steel bars. The increased force resisted by the tensile
steel bars causes increased strains in the steel bars.
To ensure equilibrium of a section the depth of the
neutral axis reduces and consequently the curvature
increases and the stiffness reduces. Between adja-
cent cracks tensile forces are transmitted from the
steel to the surrounding concrete by bond stresses.
A reduction in the stresses in steel due to bond
stresses disturbs the newly established equilibrium
and hence causes a subsequent increase in the depth
of the neutral axis, a decrease in the curvature and
an increase in the stiffness. Despite the variation of
curvatures over a constant moment region of cracked
concrete, deformations of steel and concrete over the
region must be compatible, Cairns et al (1993). Con-
sequently mean curvatures and effective moment of
inertia along the cracked region are normally used to
calculate deflections of beams, ACI 318 (2005) and
CEB-FIP (1990).
Since majority of tensile stresses on the cracked
stage are balanced by the tensile steel bars, a loss in
area of the steel bars due to corrosion is likely to dis-
turb the equilibrium of the system. The depth of the
neutral axis is likely to decrease with a decrease in the
area of steel so as to maintain equilibrium of internal
forces and moments. Consequently the curvature is
likely to increase and the stiffness is likely to reduce
with an increase in degree of corrosion of cracked
beams. It should be noted that even under the cracked
stage majority of applied compressive stresses on a
RC beam continue to be balanced by the concrete.
3 EXPERIMENTAL PROGRAMME
3.1 Test programme
Four beams were used in the test programme. Beam 1
was tested under self-weight; Beam 2 was tested under
a constant sustained load that was equivalent to 10%
Table 1. Experimental programme.
Beam
load as
% of ultimate
capacity Corrosion
f
c
MPa
(s.d)
E
c
GPa
(s.d)
1 Self-weight Yes 35 (0.9) 22 (4)
2 10% Yes 34 (0.2) 23 (5)
3 33% Yes 44 (1.1) 33 (9)
4 33% No 44 (1.1) 33 (9)
*f
c
= compressive strength of concrete at the time of test-
ing and E
c
= modulus of elasticity of concrete at the time
of testing.
Figure 1. Reinforcement configuration for test beams and
accelerated corrosion set-up (tensile face up).
10x8 mm stirrups
at 100 mm spacing
Pond filled with 5%
NaCl solution
2x8 mm bars
3x12 mm bars
B
B
A
A
50
1000
254
1150
700
3000
Side view of beams
+ -
Stainless
steel bar
40
172
42
40
172
42
153
153
3x12 mm bars
3x12 mm bars
8 mm
stirrups
8 mm hooks
2x8 mm bars
Section AA
Section BB
2x8 mm
bars
DC Power supply
.
of the ultimate load capacity of the beam (uncracked
condition); and beams 3 and 4 were tested under a
constant sustained load that was equivalent to 33%
of the ultimate load capacity of the beam (cracked
condition). Beams 1 to 3 were corroded under their
respective loading systems whilst beam 4 was not
corroded. A summary of the test programme is shown
in Table 1.
3.2 Specimen configuration
Quasi-full scale RC beams were tested in this pro-
gramme each with a width of 153 mm, a depth of
254 mm and a length of 3000 mm. The reinforcement
details of the beams are shown in Figure 1.
Each beam was reinforced with three 12 mm
deformed bars in tension with a cover of 40 mm, and
two 8 mm smooth bars in compression also with a
cover of 40 mm. 8 mm diameter stirrups were used
647
as shear reinforcement spaced at 100 mm within
the shear span. No stirrups were placed in the mid-
dle span; instead compression reinforcement bars in
the middle span were tied together by 8 mm diameter
hooks at 200 mm spacing.
3.3 Material properties
The concrete had a 28 day compressive strength of 34
MPa (s.d = 1.1). It was not possible to test the beams
at the 28 day strength, the compression strengths and
the elastic modulus of the beams at the time of testing
are shown in Table 1. The elastic modulus was tested
in compression using 100 mm cylinders of 200 mm
length.
Maximum aggregate size of the concrete was
13.2 mm and w/c ratio was 0.7. Cement, fine sand
and coarse aggregate contents were 300 kg, 909 kg
and 950 kg/m
3
respectively. 12 mm deformed bars
used for tensile reinforcement had yield strength of
549 MPa and ultimate strength of 698 MPa. 8 mm
smooth bars used for stirrups, compression reinforce-
ment and hooks had yield strength of 385 MPa and
ultimate strength of 451 MPa.
3.4 Sustained loading
Figure 2 shows a schematic of the loading frame
used in the research programme to test beams 2, 3
and 4. Support columns of the frame were bolted
to a strong floor to provide adequate reaction force.
Weights were hung on a loading beam and trans-
ferred to the load distribution beam using a friction-
less bearing support and pinned struts. From the load
distribution beam, the load was transferred to the test
specimen to produce four point bending with a con-
stant moment in the middle third of the beam, using
rollers. The loading beam had a lever arm of 1 to 14
to magnify the hung weights. Ball joints were used
at the supports of the test specimens to allow for free
rotations.
3.5 Accelerated corrosion
Before the corrosion process, beams were inverted
such that tensile steel bars were at the top. Corro-
sion of tensile bars was concentrated over a region
of 700 mm in the middle of the beams. A pond with
a depth of 50 mm and a length of 700 mm was built
on the tensile face of the mid span of beams to be cor-
roded by bonding 5 mm thick polyvinyl (pvc) sheets
to the concrete such that the pond did not offer any
restraint to expansion of the concrete. The pond in
each corroded beam was filled with a 5% solution
of NaCl, and a 12 mm stainless steel bar of length
250 mm was placed in the NaCl solution. The tensile
steel bars and the stainless steel bar were connected
to a power supply to induce a constant current density
of 189 μA/cm
2
in the tensile steel bars. According to
El Maaddaway et al (2003) a current density lower
than 200 μA/cm
2
is small enough to prevent accel-
erated damage found at high current densities. The
direction of the current was such that the tensile steel
bars served as an anode while the stainless steel bar
served as a cathode. The corrosion process consisted
of a ponding cycle of four days wetting and two days
drying under natural air to promote corrosion. Cur-
rent was only applied during the wetting period.
3.6 Strain measurements
A 100 mm demountable mechanical (demec) strain
gauge was used to measure strains on the concrete.
For longitudinal strains on the tensile face of beams,
seven stainless steel targets for the demec gauge were
glued to the concrete surface at a spacing of 100 mm
in the induced corrosion region as shown in Figure 2.
The targets were covered with petroleum jelly dur-
ing the wetting period to protect them from corrosion
attack. To measure longitudinal compressive strains,
the targets were placed on the side of the beam and
30 mm from the extreme compressive fibre and
directly below the targets used to measure longitudi-
nal tensile strains. Strains were measured before and
after each wetting period.
4 RESULTS AND DISCUSSION
4.1 Longitudinal strains
Longitudinal strains were found to vary between
the 100 mm elements within the corroded region,
which indicates that the depth of the neutral axis and
curvatures varied along the corrosion region. Since
deflections on cracked beams are normally calculated
from mean curvatures, CEB-FIP (1990) and effec-
tive moment of inertia, ACI 318 (2005) measured
strains along the corroded region were averaged to
Figure 2. Loading rig.
W
Loading
beam
Roller
support
1900
250
675
200
1375
3250
Pin struts
Support
column
Load distribution
beam
Support
column
500
Bearing
support
Fixed to
strong floor
Test beam
Nacl Pond
Targets
NB: All dimensions in mm
648
calculate the effective depth of the neutral axis, mean
curvatures and effective moment of inertia of beams.
Average strains along the corroded region are shown
in Figure 3. Whilst strains were measured prior to
and during the corrosion process, for corroded beams
only the tensile strains during the corrosion testing
are shown in Figure 3.
Not surprisingly Figure 3 shows that longitudinal
tensile strains on a beam that had transverse cracks
from applied load (beam 3) are higher than strains on
corroded beams without flexural cracks (beams 1 and
2). After 55 days of corrosion, tensile strains on beam
3 were about 1.5 times higher than strains on beams
1 and 2. Unexpectedly, tensile strains on beams 1 and
2 were almost the same but significantly higher than
strains on beam 4. Measured strains indicate that;
i) for beams without transverse cracks, longitudinal
tensile strains are influenced by the degree of cor-
rosion and barely affected by the magnitude of the
applied load; ii) longitudinal tensile strains induced
by corrosion of steel bars are significantly higher than
tensile strains due to transverse cracks from applied
load; iii) and longitudinal tensile strains on corroded
beams under a constant sustained load monotonically
increase with time of electrolysis but at a decreasing
rate whilst for an uncorroded beam (beam 4) longitu-
dinal tensile strains fluctuate around the same value.
The influence of corrosion on the longitudinal ten-
sile strains can be attributed to; the loss in area of ten-
sile steel bars; the loss in bond between the steel and
concrete; but mostly to secondary strains from lateral
tensile strains due to expansive corrosion products.
It is not the intension of this paper to deal with the
relation between lateral tensile strains and longitudi-
nal tensile strains from corrosion, which will be dealt
with in future publications.
Whilst longitudinal compressive strains on beams
1 and 2 like longitudinal tensile strains increased
monotonically with time, compressive strains in
beam 3 increased for the first 20 days after which
slightly decreased and became constant. After
25 days of testing, compressive strains in beams 1
and 2 were higher than compressive strains in beam
3. The increase in compressive strains in beams 2 and
4 is consistent with the general behaviour of beams
under simultaneous load and corrosion of steel. The
unexpected decrease in compressive strains on beam
3 with an increase in degree of corrosion is probably
a result of the position of the neutral axis being below
the point of strain measurements.
4.2 Depth of the neutral axis
The depth of the neutral axis along the corroded
region (Figure 4) was calculated by assuming that
the average tensile strains along the corrosion region
were linearly related to compressive strains. This
assumption is consistent with the assumption made
elsewhere to model displacements of cracked RC
members Ghali et al (1994).
Figure 4 shows that for beams 2 and 4, there is a
marginal change in the depth of the neutral axis whilst
for beam 3 there is about 50% reduction in the depth
of the neutral axis. This is consistent with the general
behaviour of cracked and uncracked beams corroded
under a constant sustained load. After 40 days of
testing, the depth of neutral axis of beam 3 is almost
equal to the cover depth of compression bars and
becomes constant till the end of the test. This indi-
cates that after 40 days, steel bars in beam 3 that were
initially subjected to compressive strains become
subjected to tensile strains. A change in the direction
of strains that are applied on compression steel bars
is not expected to disturb the equilibrium of forces
and moments since majority of compressive stresses
due to the applied load are resisted by the concrete.
However, with bars that were initially in compression
now in tension, it is evident that any additional tensile
strains due to corrosion of steel bars is balanced by
both the then compression steel bars and the tensile
steel bars. The depth of the neutral axis is therefore
Figure 3. Variation in longitudinal strains on the corroded
region with time.
-200
0
200
400
600
0 10 20 30 40 50 60
70
beam 1
beam 2
beam 3 beam 4
Comp. strains
(
μ
strains)
Tensile strains
(μ strains)
Time (days)
0
50
100
150
200
0
beam 2
beam 3
beam 4
Depth of neutral axis (mm)
Time (days)
10 20 30 40 50 60 70
Figure 4. Variation in depth of the neutral axis on the cor-
roded region with time.
649
of inertia of beam 4 fluctuates around the same value,
the moment of inertia of beams 2 and 3 reduces with
an increase in degree of corrosion. The large reduction
of effective moment of inertia of beam 3 is consist-
ent with large deflections found by other researchers
on beams corroded under load, Ballim et al (2003),
El Maaddawy et al (2005) and Yoon et al (2000). At
the start of the test, the moment of inertia of beam 2 is
as expected much higher than the moment of inertia
of beams 3 and 4 because beams 2 is free from flexu-
ral cracks due to applied. Unexpectedly, after 20 days
of corrosion, the moment of inertia of beams 2 and 3
are almost equal. This indicates that the stiffness of
beams tested under simultaneous load and corrosion
is the same for beams with transverse cracks and for
beams without transverse cracks due to applied load.
5 CONCLUSIONS
1. Longitudinal tensile strains are influenced by the
applied load but mostly by the level of corrosion
of steel bars
2. Longitudinal tensile strains of corroded beams
increase monotonically with time at a decreasing
rate
3. Depth of the neutral axis is independent of the
level of corrosion for beams free from flexural
cracks and beams free from corrosion but signifi-
cantly reduces with an increase in degree of corro-
sion for corroded beams with flexural cracks
4. Curvatures of corroded beams increase monotoni-
cally with degree of corrosion but at a decreasing
rate
5. The effective moment of inertia of corroded beams
decreases monotonically with time of electrolysis
but at a decreasing rate
6. For corroded beams, the effective moment of
inertia of beams with flexural cracks is almost the
same as the effective moment of inertia of beams
free from flexural cracks
expected to remain constant with time of electrolysis
as indicated by the results.
4.3 Curvatures
Similar to the calculation of average depth of the neu-
tral axis, mean curvatures of beams 2 to 4 (Figure 5)
were calculated by assuming a linear relation between
average tensile strains and compressive strains shown
in Figure 3. As expected from the variation of strains,
curvatures in beam 3 increase for the first 25 days
after which become constant whilst curvatures in
beam 2 increase monotonically at a decreasing rate
till the end of the test. The curvature in beam 3 is sig-
nificantly higher than the curvature in beams 2 and
4. The figure shows that there is a sudden increase
in the curvature of beams 2 and 3 after 14 days and
5 days respectively. These times coincide with the
times of appearance of visible corrosion cracks on the
tensile face of the beams. The increase in curvature
can therefore be attributed to transverse cracks due
to applied load and longitudinal cracks due to corro-
sion of steel bars. To assess the reliability of the test
results, curvatures in Figure 5 were used to evalu-
ate central deflections of beams and compared with
measured deflections. The curvatures were found
to yield deflections that were consistent with meas-
ured deflections on the beams. The detailed relation
between curvatures and deflections is left out for
future publications. This paper will instead use the
curvatures to determine the moment of inertia of the
beams.
4.4 Moment of inertia
Figure 6 shows the moment of inertia of beams 2 to
4 derived from the curvatures in Figure 5, the applied
moment and measured elastic moduli of beams shown
in Table 1. The figure shows that whilst the moment
Curvature: 1/mm (×10
–6
)
Time (days)
0
0.5
1
1.5
2
2.5
3
0 10 20 30 40 50 60 70
beam 2
beam 3
beam 4
Figure 5. Variation in curvature on the corroded region
with time.
Moment of inertia: mm3 (×10
8)
Time (days)
0
1
2
3
4
5
6
7
8
0 10 20 30 40 50 60 70
beam 2
beam 4
beam 3
Figure 6. Variation in moment of inertia on the corroded
region with time.
650
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