, c. v. r. murty and sudhir kamle
TRANSCRIPT
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EXPERIMENTAL STUDY ON NATURAL FREQUENCY OF PRESTRESSED
CONCRETE BEAMS
Sudhir K. Jain1, C. V. R. Murty2 and Sudhir Kamle3
ABSTRACT
An experimental study to determine the effect of cracking and prestress loss of the concrete
beam on their fundamental frequency has been carried out. It has been argued that the
change in the natural frequency of the prestressed concrete beam is due to change in the
stiffness of the beam caused by closing or opening of cracks as the prestressing force is
applied or removed, not due to compression softening effect discussed by some researchers.
The study aims to contribute towards a non-destructive test method to assess the soundness of
the prestressed concrete (PSC) bridge girders.
INTRODUCTION
Prestressed concrete (PSC) bridge girders may undergo distress with age through loss
of prestressing force and through development of structural cracks in the concrete. It is
expected that such a distress will be reflected through a change of stiffness of the girder. As
the stiffness of the girder changes, the natural frequency will also change. Hence, it may be
possible to monitor the health of a bridge girder in a non-destructive in-situ manner by
measurements of the natural frequency at regular intervals.
Frequency equation of a uniform simply supported beam is rather well known (10). The nth
natural frequency nω (radians/sec) is given by:
1Professor, Dept. of Civil Engg., Indian Institute of Technology Kanpur, Kanpur 208 016, India; fax: 091-512-250260; phone: 091-512-597867; email: [email protected] 2 Associate Professor, Dept. of Civil Engg., Indian Institute of Technology Kanpur, Kanpur, 208 016, India; phone: 091-512-597267; email: [email protected] 3 Associate Professor, Dept. of Aerospace Engg., Indian Institute of Technology Kanpur, Kanpur 208016, India;
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m
EI4
L
n2n
=
πω (1)
Or, the first natural frequency (fundamental natural frequency) in units of cycles/sec (Hertz) is
given by:
fEI
mL=
π2 4 Hertz (2)
However, if the beam is carrying an axial load (termed as beam-column), the axial
compressive load has a softening effect (compression softening effect). That is, due to the
presence of axial compression the lateral stiffness of beam (and hence its natural frequency)
reduces. The expression in that case is given by [e.g., Tse et al. (17)]:
m
N2
L
n
m
EI4
L
n2n
−
=
ππω (3)
The problem of assessing the variation in natural frequency of a prestressed concrete
beam with loss of prestressing force and with development of cracks has been of considerable
interest to the profession, as seen in the available literature.
Singh (14) has treated the prestressed beam as a beam-column, and taken Eq.(3) as the
theoretical basis for variation in natural frequency with prestressing force. He has carried out
an experimental study on a number of prestressed girders to study the variation of natural
frequency with loss of prestress and presence of cracks. The natural frequency, obtained by
ambient vibration measurements in the laboratory, increases with increase in prestress force up
to a point; beyond it, the increasing rate is either very low or there is a decrease in frequency.
The development of cracks in the beam results in decrease of natural frequency. Saiidi et al.
(12) have carried out an experimental study of a prototype post-tensioned bridge with 155 ft
(47.2 m) span and 45 ft width and a laboratory specimen. They found that the natural
frequency of the bridge decreased with loss of prestress. The testing of the laboratory
specimen also supported this result.
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A research report by Grace et al. (3) provides some experimental results on
fundamental natural frequency of a few beams before and after prestressing. These clearly
showed that the prestressing force increases the natural frequency of the beam. Jain and Goel
(8) have pointed out that prestressing force is an internal force of the prestressed girder system
and therefore prestressing force does not cause compression softening effect. Kato and
Shimada (9) have found a decrease in natural frequency with damage in a bridge girder. They
have attributed this to loss of flexural rigidity due to opening up the cracks as load is
increased. Similar observations about decrease in flexural stiffness due to damage, resulting in
reduction in natural frequency, have been reported by Mirza et al. (11) and Ambrosini et al.
(1). Tang and Leu (16) have studied a three span countryside prestressed concrete bridge and
concluded that the change of dynamic characteristics can be used as an indicator for damage
detection of the bride.
It is therefore clear that prestressing force does not have the compression softening
effect. Hence, natural frequency of a uniform simply-supported prestressed concrete beam is
given by Eq.(2). Prestressing force influences the natural frequency of the prestressed beams in
a different way. Prestressing force closes the cracks in concrete (micro cracks as well as the
structural cracks, if any). Cracks reduce the beam stiffness (natural frequency) and closing of
cracks should increase the stiffness (and hence the natural frequency).
However, there are serious difficulties in evaluating values of modulus of elasticity of
concrete and moment of inertia of concrete sections. Even under the ideal conditions of a
uniform simply supported prestressed concrete beam, it is not possible to accurately calculate
the natural frequencies of vibration. The calculations can, at best, give an approximate
estimate of the natural frequency.
In the present study, an attempt has been made to prove the qualitative assumption that
prestress loss can be determined from natural frequency measurements. Damage determination
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of prestressed bridges by frequency measurements is advantageous in the sense that it gives a
global view of the damage that may either be due to prestress loss or other factors leading to
cracking.
SPECIMEN TESTED IN THE LABORATORY
The experimental study is conducted in two phases. In the first phase, simple
rectangular prestressed beams are studied. In the second phase, a scale model of a typical
girder-slab bridge usually adopted by the Indian Railways is studied. In both phases, focus was
on studying the effect of cracking and prestress force on the natural frequency.
The post-tensioning method of prestressing is employed using a mono-wire
prestressing jack. The wedges and barrels are made of high strength steel. The maximum force
through the prestressing jack is controlled by the hydraulic hand pump and the associated
pressure gauge indicating the fluid pressure. No bond is allowed to develop between
prestressing wires and surrounding concrete. This is ensured by oiling the wires and then
twisting them periodically until concrete is hardened.
Four rectangular beams of 4 meter span each are used in this study. The geometry of
these beams is shown in Fig. 1(a) and reinforcement details are shown in Fig. 1(b). The four
beams differ only in the amount of prestressing force. The locations of the 7mm diameter HTS
prestressing wires within the cross-section of the beams are shown in Fig. 1(c).
Steel moulds are used to cast the 4-meter span beams. The reinforcement cage of
HYSD bars is prepared and placed in position. The prestressing wires of the required length
(specimen length of 4 meters plus grip length of 1.5 meters for prestressing jacks) are cut and
placed in the desired position. A post-tensioning system of prestressing is employed. However,
to ensure that the wires remain straight during concreting, a very small prestress is given to the
wires. The wires are oiled and the concreting is completed. Before the final setting time of
concrete is elapsed, the load in each of the wires is released, and the wires are twisted in
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position to ensure that bond is not developed between the wires and the neighbouring
concrete. This process is repeated periodically to keep the wires free from the concrete around
them.
One 4 meter span 1:5 scale model of a typical 20 meter span girder-slab bridge is
prepared. The geometry of this scale model is shown in Fig. 2(a), and the details of the HYSD
reinforcement bars are shown in Fig. 2(b). As in the case of the prestressed beams, post-
tensioning scheme is employed and the 7 mm diameter prestressing wires are kept straight.
The position of the prestressing wires in the cross-section is shown in Fig. 2(c).
A wooden mould is used to cast this specimen. As in the case of beams, the
prestressing wires are stressed slightly to ensure a straight profile during concreting. The
concreting is completed with the steel reinforcement cage. The small load in each of the
prestressing wires, intended to keep the wires straight during concreting, is released. And, the
wires are regularly twisted to release the nominal bond between the wires and the concrete.
MATERIALS PROPERTIES
High tension steel (HTS) wires of 7mm diameter are used. The material passes the
requirements for HTS wires noted in IS: 1785-1983. The ultimate tensile strength of the 7mm
wires are obtained as 1338 N/mm2. The maximum load in each wire is taken as 40 kN
corresponds to a stress of about a little less than 80% of the ultimate tensile strength.
Standard 150mm concrete cubes cast with the beam and scale model specimen are
tested as per IS:516-1959 at 28 days as well as on the day of testing the specimen. The target
grade of concrete is M35. The modulus of elasticity of concrete is calculated using the
following expression [IS: 456-1978]
Ec
fck
= 5700 (4)
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THEORETICAL ESTIMATES OF STIFFNESS AND NATURAL FREQUENCY
The properties of both the beam specimen and the scale model girder specimen as on
the day of the test are used to estimate their theoretical fundamental natural frequency.
The fundamental natural frequency f of the beams and the scale model bridge are obtained
using Eq.(2). The results so obtained are shown in Table 1.
EXPERIMENTAL STUDY
The fundamental natural frequency of the beam is obtained by a vibration survey
facility. A flow chart of the test strategy showing the test set-up for obtaining the natural
frequency of the prestressed beam is shown in Fig. 3.
One force balance accelerometer (FBA) is placed at the mid-span of the beam and
another accelerometer at the quarter span (with a view to see if there is a significant change of
mode shape). The specimen is tapped vertically with a hammer and the subsequent free
vibration response of the beam is ascertained. The FFT (Fast Fourier Transform) of this
acceleration response is used to obtain natural frequency of the specimen. This exercise is
done for different values of prestressing force (by introducing or releasing the prestressing
force in some of the wires), and with different levels of cracking introduced in the specimen.
Cracking in the specimen is introduced by carefully loading the specimen by an actuator in a
displacement-control mode and then releasing the load.
Tests on Prestressed Beam 1
The following step-wise procedure is employed to study the prestressed beam 1:
1. The fundamental natural frequency is measured on the virgin beam with no prestressing
force.
2. The specimen is now subjected to prestress force. Of the three wires in the beam, one wire
is stressed at a time (each wire being prestressed upto 40 kN) and natural frequency
measured with each new wire being prestressed.
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3. With all the wires carrying the prestress force, a transverse load of 4kN is applied on the
specimen at the mid-span using a displacement-controlled hydraulic actuator. After applying
the maximum load of 4kN, the load is released. When the load is completely removed and
the contact between the actuator and the specimen is released, the natural frequency is
measured again.
4. Now 8kN transverse load is applied in increments of 4kN each. After loading, unloading,
and releasing the contact between the actuator and the specimen, the natural frequency is
measured again.
5. Step 4 is repeated for transverse load of 12 kN and 16 kN.
6. The prestress force in the three wires is gradually removed in the reverse sequence in which
they were loaded.
7. The prestress wires are again loaded one by one, and natural frequency measured at each
level.
Table 2 gives the results. Arrow in the table represents sequence of testing.
Tests on Prestressed Beam 2
A different procedure was used in beam 2.
1. The fundamental natural frequency is measured on the virgin beam with no prestressing
force.
2. A transverse load of 4kN is applied and removed, with none of the four wires stressed. That
is, the beam is cracked even before any wire is carrying a prestress force. Natural frequency
of the cracked beam is measured.
3. A higher load of 6kN is now applied and removed and the natural frequency of this cracked
beam is measured.
4. Now, the prestress is applied in one wire at a time. At each level of prestress, the natural
frequency of the beam is measured.
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5. After all the wires are prestressed, the prestress force in the four wires is released one by
one in the reverse sequence in which they were loaded. At each level of prestress, the
natural frequency is ascertained.
This procedure is specially aimed to analyze the effect of closing of cracks by
prestressing force on the natural frequency. Table 3 gives the results. Arrow in the table
represents sequence of testing.
Tests on Prestressed Beams 3 and 4
The procedure of test adopted in beams 3 and 4 is identical to that employed for beam 1,
except that the number of wires is seven in beam 3 and nine in beam 4 (each wire being
prestressed upto 40 kN), as against three in beam 1. Consequently, beams 3 and 4 are loaded
transversely up to about 27kN. Tables 4 and 5 give the results.
Scale Model of a Girder-Slab Bridge
The procedure of testing the scale model specimen is as that adopted for beams 1, 3,
and 4. One major difference is that after every application of transverse load, the prestressing
cables were released and then loaded again (with natural frequency being measured at every
stage) before another cycle of transverse load was applied.
1. The bridge model is simply supported.
2. The fundamental natural frequency of the virgin bridge model is measured.
3. The specimen is subjected to prestress force. Out of the six wires in the model (three in
each web), the symmetric pair of wires (one wire in each girder) are prestressed at a time.
The sequence of prestressing employed with reference to the wire numbering is same as
given in Fig. 2(c).
4. At each level of prestress, the natural frequency of the scale model is obtained.
5. When the bridge model is subjected to the maximum prestress force, a transverse load of
20kN is applied on it at the mid-span using a displacement-controlled hydraulic actuator in
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increments of 5kN each. After applying the maximum load of 20kN, the load is released.
When the load is completely removed and the contact between the actuator and the
specimen is released, the natural frequency is measured again.
6. The prestress force in the six wires is gradually removed in pairs of two wires in the
reverse sequence in which they were loaded.
7. Steps 3 and 4 are repeated.
8. Again, when all the six wires are stressed, the hydraulic actuator is employed to apply a
transverse load, but this time with a larger amplitude of load of 40kN in increments of 5kN
each. After loading, unloading and releasing the contact between the actuator and the
specimen, the natural frequency is measured again.
9. This procedure is repeated until the amplitude of the transverse load is slowly increased to
near the ultimate load of the specimen. The loading history indicating the maximum
amplitude of the load in each cycle is shown in Table 6.
10. The experimental natural frequency of the scale model bridge specimen obtained by the
above procedure is given in Table 7.
DISCUSSION OF RESULTS
The following observations are made from the test results obtained during the tests:
1. Theoretical estimate of the natural frequency of the beams was 22.5 Hz. This matches
quite well with the observed natural frequency, and turns out to be an upper bound value
on the observed values. This is true as theoretical estimate of the flexural rigidity is always
higher than actual due to cracking of the concrete.
2. The scale model of girder-slab bridge shows a large variation in the fundamental natural
frequency as obtained by analysis (= 55.6 Hz) with the experimental values (in the range
30 to 37 Hz). Similar variation in analytical and measures frequency has also been reported
in other studies (Kato and Shimada, 1986; Saidi et al, 1994). This clearly illustrates that it
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is rather difficult to expect accurate estimation of natural frequency of concrete structures
due to difficulties in correctly modeling the modulus of elasticity and the moment of
inertia. In addition, dynamic characteristics are sensitive to changes in support conditions
that may have little structural consequence (Salawu, 1995).
3. Prestressing force in general has a tendency to increase the natural frequency of the
concrete beam. It does so by closing the micro cracks in the concrete, thereby making the
beam more stiff. Results in the first four columns of Table 2 show a difference of about
13% on this account.
4. Structural cracks in a concrete beam cause a reduction in the natural frequency. Table 3
shows a difference of about 16% due to cracking in the absence of prestressing force.
5. Prestressing force is able to close the structural cracks in the beam and restore the natural
frequency value. For instance, Table 2 shows the natural frequency in the presence of
prestressing force as about 20.4 Hz when the specimen was loaded and unloaded with the
transverse load. However, once the prestressed force is released the natural frequency
drops down to about 14.0 Hz.
6. Loss of prestress together with the structural cracks in the beam can cause significant drop
in the natural frequency of the beam. For instance, as per Table 2, the natural frequency of
undamaged beam with prestressing force is 21.7 Hz which drops down to about 14.0 Hz
with total loss of prestressing force and with structural cracks: a drop of about 35%.
7. Results of Specimen 3 and 4 are very much similar to those obtained in the specimen 1.
This establishes that the results obtained are quite general and reflect the expected
behaviour of the PSC girders.
8. Natural frequency values of the scale model generally agree with the trends noted above
for the beam specimen. For instance, the prestressing increases the natural frequency of the
model by about 10%.
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SUMMARY AND CONCLUSIONS
The present study gives an idea about the variation in natural frequency of the girders
with loss of prestressing force and with structural cracks. Important conclusions of the study
are summarised here under:
1. The experimental and theoretical estimates of natural frequencies match reasonably well
for the rectangular beams but do not match well for the scaled bridge model. It clearly
underlines the fact that one cannot expect to analytically obtain natural frequency
accurately for PSC girders and then expect to make one-time experimental observations to
assess the health of the bridge.
2. There is no “compression softening” as reported in some literature. Thus, the prestressing
force does not reduce the natural frequency of the prestressed girders on this account.
3. Upto a certain value, prestressing force in general increases the natural frequency of the
beam. This is done by closing the micro-cracks present in the concrete, which increases the
flexural rigidity. This saturation effect is due to onset of compression cracks in concrete at
high levels of prestressing force.
4. Due to structural cracking in non-prestressed beams, there is significant reduction in the
natural frequency. However, prestressing force may effectively close these cracks and may
thereby restore the natural frequency of the beam.
5. It is expected that in case of actual bridges, if the structural cracks are accompanied by
loss of prestress force, periodic vibration measurements may be effective in identifying the
problem. However, if the prestress force does not reduce with time, some deterioration in
concrete in the form of cracks may not reflect much on the natural frequency.
6. It was not possible to observe a significant change in the fundamental mode shape of the
beams with cracking or with loss of prestress. This is in line with what was expected based
on theory of vibrations.
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ACKNOWLEDGEMENT
The financial assistance provided by the Research Designs and Standards Organisation
(RDSO), Ministry of Railways, Lucknow, to conduct this study is gratefully acknowledged.
We are particularly thankful to the Officers and Staff of RDSO for their support and
cooperation during this study.
The untiring efforts of the staff of the Structural Engineering Laboratory to complete
this experimental work are sincerely acknowledged. The help rendered by numerous students
in the experimental work is highly appreciated. A special mention must be mentioned of the
assistance from Dr. K. K. Bajpai of the Department of Civil Engineering in carrying out the
experiments.
APPENDIX I. – REFERENCES
1. Ambrosini, D., Luccioni, B. and Danesi, R. (1999) “Theoretical-Experimental damage
Determination in Prestressed Concrete Beams.” International Symposium on NDT
Contribution to the Infrastructure Safety Systems, Santa Maria, RS, Brazil.
2. Begg, R.D., Mackenzie, A.C., Dodds, C.J. and Loland, O. (1994) “Structural Integrity
Monitoring Using Digital Processing of Vibration Signals.” Proceedings, 8th Offshore
Technology Conference, Vol. 2, Houston, Texas.
3. Grace, N. F., Keiffer, J., Thomas, A., Higley, R., Rocha, J., Zazo, T., Bowdan, J.,
Eliassen, B., Ross, B. and Kytasty, J. (1994) “RUI: Prestressed Concrete Girders with
Openings under Static, Dynamic, Fatigue and Ultimate Loadings” Report, Department of
Civil Engineering, Lawrence Technological University, USA.
4. IS:456-1978, Indian Standard Code of Practice for Plain and Reinforced Concrete,
Bureau of Indian Standards, New Delhi, 1979.
5. IS:516-1959, Indian Standard Method of Test for Strength of Concrete, Bureau of Indian
Standards, New Delhi, 1960.
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6. IS:1343-1980, Indian Standard Code of Practice for Prestressed Concrete, Bureau of
Indian Standards, New Delhi, 1981.
7. IS:1785(Part 1 and 2)-1983, Indian Standard Specification for Plain and Hard Steel Wire
for Prestressed Concrete, Bureau of Indian Standards, New Delhi, 1984.
8. Jain, S. K. and Goel, S. C. (1996) “Discussion on Prestress Force Effect on Vibration
Frequency of Concrete Bridges.” Journal of Structural Engineering, ASCE, 122(4), pp
459-460.
9. Kato, M. and Shimada, S. (1986) “Vibration of PC Bridge during Failure Process.”
Journal of Structural Engineering, ASCE, 112(7), pp 1692 – 1703.
10. Meirovitch, L. (1975) Elements of Vibration Analysis, McGraw Hill.
11. Mirza, M. S., Ferdjani, O., Hadj-Arab, A., Joucdar, K. and Khaled, A. (1990) “An
Experimental Study of Static and Dynamic Responses of Prestressed Concrete Box Girder
Bridges.” Canadian Journal of Civil Engineering, 17, pp 481 – 493.
12. Saiidi, M., Douglas, B. and Feng, S. (1994) “Prestress Force Effect on Vibration
Frequency of Concrete Bridges.” Journal of Structural Engineering, ASCE, 120(7), pp
2233-2241.
13. Salawu, O. S. (1997) “Detection of Structural Damage through Changes in Frequency: A
Review.” Engineering Structures, 19(9), pp 718 – 723.
14. Singh, S. N. (1991) “Effect of Prestress on Natural Frequency of PSC Beams.” M.Tech
thesis, Department of Civil Engineering, Indian Institute of Technology, Kanpur.
15. Slastan, J. and Pietrzko, S. (1993) “Changes of RC- Beam Modal Parameters due to
Cracks.” Proceedings, 11th International Modal Analysis Conference, pp 70 – 76, Florida.
16. Tang, J. P. and Leu, K. M. (1989) “Vibration Tests and Damage Detection of P/C
Bridges” Proceedings of ICOSSAR ’89, 5th International Conference on Structural Safety
and Reliability, pp 2263 – 2266, San Francisco.
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17. Tse, F. S., Morse, I. E., and Hinkle, R. T. (1978) Mechanical Vibrations: Theory and
Applications, Allyn and Bacon, Inc., Boston, MA, USA.
APPENDIX II. – NOTATIONS
The following symbols are used in this paper:
E = Modulus of elasticity of the material of the beam;
ckf = The average compressive strength obtained from the tests on cube specimen;
I = Moment of inertia of the prismatic section;
m = Mass per unit length of the beam;
L = Span of the beam between the simple supports;
n = An integer value indicating the mode number;
N = Axial force on the beam (positive, if N is compressive; negative, if N is tensile).
Table 1: Properties of the various specimens and their fundamental natural frequency.
Specimen A (mm2)
ckf
(N/mm2)
Ec (N/mm2)
I (××106 mm4)
m (kg/m)
L (m)
f (Hertz)
Beam 1 29900 47.6 39300 99.7 74.7 4 22.5 Beam 2 29800 47.6 39300 99.6 74.6 4 22.5 Beam 3 29700 45.9 38600 99.4 74.3 4 22.3 Beam 4 29700 45.9 38600 99.2 74.1 4 22.3 Scale model (Bridge girder)
124770 48.4 39700 2520.5 311.9 4 55.6
Table 2: Variation of fundamental natural frequency f of the prestressed beam 1 with
prestressing force and with damage induced by transverse loading
Prestress Natural frequency f (Hertz) Force Virgin Transverse Load Cycle (kN) (kN) 4 8 12 16
0 kN 19.3 18.8 18.8 14.2 13.6 40 kN 20.1 20.3 19.2 18.8 18.9 80 kN 21.3 21.8 21.3 20.8 20.7 120 kN 21.7 21.7 20.8 20.4 20.4 20.4 20.3 21.5 21.5
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Table 3: Variation of fundamental natural frequency f of the prestressed beam 2 with prestressing force and with damage induced by transverse loading
Prestress Natural frequency f (Hertz)
Force Virgin Transverse Load Cycle (kN) (kN) 4 6
0 kN 19.3 16.2 16.0 17.0 40 kN 19.1 18.5 80 kN 20.0 20.4 120 kN 19.5 20.6 160 kN 20.1 20.1
Table4: Variation of fundamental natural frequency f of the prestressed beam 3 with
prestressing force and with damage induced by transverse loading
Prestress Natural frequency f (Hertz) Force Virgin Transverse Load Cycle (kN) (kN) 18 24 27.4
0 kN 19.2 16.3 40 kN 19.0 16.5 80 kN 20.8 19.7 120 kN 20.8 20.0 160 kN 19.6 20.4 200 kN 20.3 20.0 240 kN 21.0 20.3 280 kN 21.4 20.9 20.3 20.5
Table 5: Variation of fundamental natural frequency f of the prestressed beam 4 with
prestressing force and with damage induced by transverse loading
Prestress Natural frequency f (Hertz) Force Virgin Transverse Load Cycle (kN) (kN) 12 18 24 27.4
0 kN 19.3 16.8 40 kN 19.5 16.8 80 kN 20.5 17.4 120 kN 20.5 19.0 160 kN 20.3 19.8 200 kN 19.8 19.1 240 kN 19.5 19.0 280 kN 20.0 19.0 320 kN 20.0 19.4 360 kN 20.3 20.3 20.4 20.4 20.0
Table 6: Maximum transverse load applied in increments of 5kN in each cycle on the scale
model bridge.
Maximum Transverse Load (kN) Cycle 1 Cycle 2 Cycle 3 Cycle 4 Cycle 5 Cycle 6 Cycle 7
20 40 60 80 100 120 159.65
Table 7: Variation of fundamental natural frequency f of the Scale Model Bridge specimen with prestressing force and with damage
induced by transverse loading: consolidated data.
Prestress Natural Frequency (Hz) Force Virgin Cycle1 Cycle 2 Cycle 3 Cycle 4 Cycle 5 Cycle 6 Cycle 7 (kN) Add
Prestress Remove Prestress
Remove Prestress
Add Prestress
Remove Prestress
Add Prestress
Remove Prestress
Add Prestress
Remove Prestress
Add Prestress
Remove Prestress
Add Prestress
Remove Prestress
Add Prestress
Remove Prestress
0 32.0 31.2 31.6 31.6 31.6 31.6 32.0 32.0 32.0 32.0 32.4 32.4 32.4 32.4 34.4 80 34.8 30.8 31.2 34.0 31.6 32.8 32.0 32.8 32.0 33.2 32.4 33.2 32.4 35.6 36.0 160 35.6 32.8 32.4 34.0 32.0 33.2 32.0 33.2 32.4 33.6 32.0 34.0 32.8 34.4 37.6 240 35.2 35.2 36.8 33.6 33.2 33.2 33.2 33.6 33.6 33.6 34.0 34.0 34.8 34.8 37.2
Fig. 1(a): Specimen dimensions of Beams
Fig. 1(b): Cage reinforcement details of beams.
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Fig. 1(c): Details of prestressing wires in beams
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Fig. 2(a): Geometry and dimensions of the scale model
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Fig. 2(b): Reinforcement details of the scale model
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Fig. 2(c): Position of prestressing wires in the scale model
Fig. 3: Natural frequency measurement scheme
Signal Conditioner
Spectrum Analyser
Natural Frequency
Sensor
PSC Beam
Hammer