Australian Journal of Structural Engineering
ISSN: (Print) (Online) Journal homepage: https://www.tandfonline.com/loi/tsen20
Shear capacity of inverted-U reinforced concrete
bridge beams
Mahes P. Rajakaruna, Vanissorn Vimonsatit & Koon W. Wong
To cite this article: Mahes P. Rajakaruna, Vanissorn Vimonsatit & Koon W. Wong (2022):
Shear capacity of inverted-U reinforced concrete bridge beams, Australian Journal of Structural
Engineering, DOI: 10.1080/13287982.2022.2060546
To link to this article: https://doi.org/10.1080/13287982.2022.2060546
Published online: 13 Apr 2022.
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AUSTRALIAN JOURNAL OF STRUCTURAL ENGINEERING
https://doi.org/10.1080/13287982.2022.2060546
ORIGINAL ARTICLE
Shear capacity of inverted-U reinforced concrete bridge beams
Mahes P. Rajakarunaa, Vanissorn Vimonsatitb and Koon W. Wongc
a
Structures Design and Standards Engineer, Structures Engineering, Planning and Technical Services Directorate, Main Roads Western
Australia, Australia; bAssociate Professor in Civil Engineering, School of Engineering, Faculty of Science and Engineering, Macquarie
University, Sydney, NSW, Australia; cStructural engineering, Main Roads Western Australia, Australia
ABSTRACT
ARTICLE HISTORY
Existing reinforced concrete inverted-U beam bridges in Western Australia built using standard
beams designed by Public Works Department between 1957 and 1969 were found to have
reinforcement anchorage detail at supports not adequate when assessed using recent design
standards. Tests were carried out on six full-size bridge beams recovered from a bridge
scheduled for replacement to determine whether the deficient detailing adversely affects the
shear capacities of these beams. These beams were the longest of the series designed in 1957.
In addition, the mean shear strengths of the five bridge beams to AS 5100.5–2004 and to the
most recent design standard AS 5100.5–2017 were determined and these were compared with
their corresponding test values. It was found from testing that the detail does not affect the
shear strength much. The predicted mean shear capacities using AS 5100.5–2017 were found
to be more conservative than the corresponding values using AS 5100.5–2004. This suggests
the likelihood of low load ratings for shear using the latest design standard (based on the
Modified Compression Field Theory) for existing reinforced concrete bridges designed to
previous standards.
Received 3 February 2020
Accepted 29 March 2022
1. Introduction
Western Australia has a number of existing bridges
built using standard precast reinforced concrete (RC)
inverted-U beams designed by the then Public Works
Department (PWD) between 1957 and 1969. Most of
these bridges are located in the South West Region of
Western Australia. This type of bridge was popular
during that period owing to its ease of construction.
Water Corporation of Western Australia owns a large
number of these bridges, and Main Roads Western
Australia (MRWA) inspects and provides advice on
their maintenance and where necessary, their
replacement.
In US, similar beams, referred to as channel beams
(Durham, Heymsfield, and Schemmel 2003; Wipf et al.
2006), were used in bridges. Wipf et al. stated there
were 600 precast channel RC bridges in the state of
Iowa and they were constructed primarily in the 1950s
and 1960s. They were different from the Western
Australian bridges in the way they were connected
together transversely and they have different shear
reinforcement detail. Durham et al. stated there were
in the order of 400 precast channel RC bridges in the
state of Arkansas and they were constructed from
mid-1950s through the mid-1970s. These standard
5.79 m (19 ft) beams were fabricated without any
shear reinforcement, and they were not connected
together transversely.
CONTACT Vanissorn Vimonsatit
vimonsatit@mq.edu.au
Engineering Macquarie University Sydney, NSW Australia
© 2022 Engineers Australia
KEYWORDS
Reinforced concrete; shear;
end anchorage
Several issues of concern were identified with the
detailing of these precast RC inverted-U beams. Three
main beam series were identified from drawings, and
they were referred to in this paper as PWD1957,
PWD1969 and PWD1972. The number in each desig­
nation shows the year the design was approved by
PWD. These beams have adverse detailing issues
which made the determination of their design
strengths for shear to the more recent Australian
design standards difficult, if not impossible.
PWD1957 series is the weakest since its design vehi­
cular loading is the lowest. Laboratory testing of these
full-size beams of type PWD1957 was found to be
feasible using available testing facilities in Western
Australia. The replacement of Bridge 3985 located on
Coronation Road in South West Region of Western
Australia provided a good opportunity to recover
bridge beams belonging to the longest of the precast
beams of series PWD1957 for testing. Figure 1 shows
the bridge before replacement.
The overall length of the standard beam-type
PWD1957 ranges from 12 ft (3.66 m) to 22 ft
(6.71 m) in 2 ft (609.6 mm) increments. The
main reinforcement, four plain bars of 1 18 in
(28.58 mm) diameter, is not curtailed within the
span. Shear reinforcement for these beams is 3/8 in
(9.53 mm) diameter at 6 in (152.4 mm) centres and
is uniform along the beams, and this uniformity
Associate Professor in Civil Engineering, School of Engineering, Faculty of Science and
2
M. P. RAJAKARUNA ET AL.
Figure 1. Bridge 3985.
allows the effect of the degree of end anchorage of
reinforcing steel on shear strength to be studied
through testing.
The reinforcing bars of the test beams had their end
cogged, as shown in Figure 2. The vertical extent from
the top of the horizontal portion of the cogs is 3 in
(76.2 mm). The detail provided was found to be inade­
quate for the cogs to be classified a standard cog to the
current design standard, and therefore it was not certain
whether the detail provided was sufficient to provide
adequate anchorage to enable the full design shear
capacity of these beams to be reached. It is expected
that the cog, though non-standard, contributes to
anchoring, although the extent of this is not known.
The testing of the full-size beams aims to investigate
whether the use of non-standard cogs in these test beams
adversely affects the loads they can carry in shear.
Figure 2. Detail of cogs at the end of a beam.
2. Beam Testing
Six beams recovered from Bridge 3985 were tested in
three test series: T1V, T2V and T3M. Figure 3 is the
cross-sectional detail shown on the engineering draw­
ing of PWD. The beams tested were inner beams of the
bridge without the upstands shown in this figure. The
reinforcement detail (see Figure 4), after the removal
of concrete from a tested beam, was found to be
slightly different from that shown on drawings. The
top longitudinal reinforcing bars were all placed above
the stirrups resulting in no longitudinal bearing bars
inside the top corners of the stirrups. In this figure,
part of the horizontal bar was missing owing to an
earlier coring of the concrete for strength testing.
The beams, each of overall length of approxi­
mately 6.71 m (22 ft), were tested to failure. Each
end had a solid diaphragm with thickness ranging
AUSTRALIAN JOURNAL OF STRUCTURAL ENGINEERING
Figure 3. Cross-section from engineering drawing.
from 9 in (229 mm) at beam soffit level increasing
to 9.5 in (241 mm) at slab soffit level. Series T1V
consists of five beams with supported at their
ends, and they were loaded predominantly under
shear. Owing to the beams having a uniform sec­
tion with uniform shear reinforcement along its
length, to determine the shear capacity of the
section (or rather segment) with adequate reinfor­
cement end anchorage, test series T2V was carried
out. Series T2V used the same T1V beams after
being tested, with them supported farther from
their ends to provide full anchorage of the main
reinforcement to the current standard at the two
supports. The distance from the point load to its
nearest support was kept the same as in the first
series. The end closer to the shear span was cho­
sen to be the one not damaged during testing T1V
to ensure adequate end anchorage. The third series
consists of the single remaining beam; it was
tested under bending with two point loads, spaced
1.2 m apart, placed symmetrically about the centre
of the span.
Figure 4. Half-width showing the location of top rebars.
3
To transfer the load directly from the loading jacks
to the webs of the beams bypassing the flanges, strong
cross beams were used. The load transmission steel
struts and cross beams were designed, fabricated and
proof loaded by Curtin University to provide a safe
working load of 55 tonnes. Figure 5 shows the load
transmission assemblages. They were designed to
allow swivelling about both the longitudinal and trans­
verse directions to accommodate lateral movements of
the beams during loading.
2.1. Series T1V
The test setup is shown diagrammatically in Figure 6
and the photograph of the setup in Figure 7. The
results from the testing of series T1V are presented
in Table 1.
In this table, Pjack is the force applied by the jack, Ptest
is the test load after including the weight of the load
transmission assemblages below the jack, estimated to
be 3 kN. Vtest1 is the applied shear within the shear span,
and Mtest1 is the applied bending moment of the section
under the point load. Vtest is the shear at the section
vertically aligned with the inner edge of the support
plate closest to the applied load and Mtest is the bending
moment of the section under the point load. The esti­
mated shear from self-weight of the beam Vsw is 11 kN,
and the estimated bending moment from self-weight
Msw is 8 kNm. These were determined using crosssectional areas from dimensions shown on the engineer­
ing drawing. The area of the cross-section of the dia­
phragm is 0.294 m2 and that of the inverted-U is
0.141 m2. Unit weight of reinforced concrete was
assumed to be 25 kN/m3.
4
M. P. RAJAKARUNA ET AL.
weight of the beam Vsw at the inner face of the support
plate is 7 kN, and the estimated bending moment from
self-weight Msw of the section under the point load is
1 kNm.
The anchoring horizontal distance of the
bottom layer of reinforcing steel from the inner edge
of the support plate to the end of the cog is approxi­
mately 1375 mm (assuming 1 inch end cover), greater
than the development length of 1243 mm calculated
for mean development length for plain bar to AS
5100.5–2017 (Standards Australia 2017). The lowest
mean concrete strength of the test beams was used in
the calculation. Beams in this test series were assumed
to have adequate end anchorage for reinforcing steel
to develop their yield strength before anchorage
failure.
2.3. Comparison of the shear capacities between
the two test series
Figure 5. Load transmission assemblages.
The jack load versus vertical deflection plots are
shown in Figure 8. The vertical deflection is at the
location of the point load. These plots show that
these beams have substantial ductility before reaching
their peak loads.
Side bursting of concrete accompanied by the pull-in
of the cogs was observed upon continued jacking after
reaching peak load. A typical side bursting is shown in
Figure 9.
The crack formation of Beam 2 is shown in
Figure 10.
2.2. Series T2V
The test setup is shown diagrammatically in Figure 11,
and the result from the testing of series T2V is pre­
sented in Table 2. The estimated shear from self-
Figure 6. Test setup for series T1V (five beam tests).
The test shear capacities from series T1V were com­
pared with those from series T2V to study the effect of
end anchorage on shear capacity.
The results of the comparison are presented in
Table 3. The increases in shear strengths range
5–15%.
2.4. Series T3M
The test setup is shown in Figure 12 and the load from
the jack versus vertical deflection plots are shown in
Figure 13. Up to a jack load of 20 kN, the vertical
deflection reading was zero but the fault was corrected
as the loading progressed. The straight portion of the
curve when extrapolated passes through the origin
which suggests the fault at the early stage of loading
was a loose contact in the system affecting the reading
of the deflection.
The results from the testing of series T3M are pre­
sented in Table 4. The estimated bending moment Msw
of the section under the point load from the selfweight of beams is 18 kNm.
AUSTRALIAN JOURNAL OF STRUCTURAL ENGINEERING
5
Figure 7. Photograph of test setup for series T1V (five beam tests).
Table 1. Results for T1V.
Beam
1
2
4
5
6
Pjack
Ptest
Vtest1
Mtest1
Vtest ¼
Mtest =
Mtest1 + Msw
(kNm)
214
225
217
224
220
(kN)
(kN)
(kN)
(kNm)
Vtest1 + Vsw
(kN)
288
303
291
301
296
291
306
294
304
299
255
268
257
266
262
206
217
209
216
212
266
279
268
277
273
3. Material testing
Concrete cores and reinforcing steels from the beams
were tested, and the results from the testings are
reported in sections 3.1 and 3.2, respectively.
Figure 8. Load versus deflection plots for T1V.
3.1. Testing of reinforcing steel
Four pieces of the main reinforcement and four
pieces of stirrups were tested by a NATA accre­
dited laboratory. They were all round plain steel
bars. Owing to limited capacity of the test equip­
ment, the diameter of these bars had to be
machined down before testing. The main reinforce­
ment pieces gave lower yield values of 258, 254, 250
and 271 MPa. The average value is 258 MPa and
the standard deviation of 9.1 MPa. The stirrup
pieces gave lower yield values of 326, 355, 351
and 342 MPa. The average value is 344 MPa and
the standard deviation is 12.9 MPa.
6
M. P. RAJAKARUNA ET AL.
Figure 9. Side bursting at an end of a beam.
Figure 10. Crack formation of Beam 2.
Figure 11. Test setup for series T2V (five beam tests).
AUSTRALIAN JOURNAL OF STRUCTURAL ENGINEERING
Table 2. Results for T2V.
Beam
1
2
4
5
6
7
3.2. Testing of concrete
Pjack
Ptest
Vtest1
Mtest1
Vtest ¼
Mtest ¼
(kN)
(kN)
(kN)
(kNm)
Vtest1 þ Vsw
(kN)
Mtest1 þ Msw
(kNm)
For each beams, three concrete cores were tested at the
material testing laboratory of MRWA. The cores were
371
352
337
360
361
374
355
340
363
364
300
285
273
291
292
243
231
221
236
237
307
292
280
298
299
244
232
222
237
238
approximately 200 mm long with a diameter of
100 mm. The mean strengths of the cores are pre­
sented in Table 5.
4. Analysis
Table 3. Comparison of test capacities.
Beam
Vtest T2V /
Mtest T2V /
1
2
4
5
6
Vtest T1V
1.15
1.05
1.05
1.08
1.10
Mtest T1V
1.14
1.03
1.02
1.06
1.08
Figure 12. Test setup for series T3M (1 beam test).
Figure 13. Load versus deflection plot for T3M.
In this section, the capacities of the beams in shear
were predicted based on formula in Australian stan­
dards. The main reinforcing bars were assumed to be
adequately anchored at supports.
The following values were used in the analysis.
Overall width of cross-section in the plane of bending,
B=800.1 mm. Overall depth of cross-section in the
plane of bending, D=355.6 mm. Effective width of
8
M. P. RAJAKARUNA ET AL.
�
Table 4. Result for T3M.
Beam No.
3
Pjack
Ptest1
Mtest1
Mtest ¼
(kN)
(kN)
(kNm)
Mtest1 þ Msw
(kNm)
77
80
212
230
θvm ¼
�
Vum:min
� 15o þ 30o
Vum:max Vum:min
(2)
Asv fsym:f s
cot θvm
d0
(3)
V
Vums ¼
Vum ¼ Vumc þ Vums
Table 5. Strength of concrete cores in MPa.
Beam No.
1
2
3
4
5
6
Core 1
65.0
51.0
64.0
53.5
35.5
29.5
Core 2
52.0
56.0
64.5
44.5
34.5
35.5
Core 3
56.5
45.0
67.5
60.0
49.5
45.5
Mean, fcm
57.8
50.7
65.3
52.7
39.8
36.8
Std Dev.
6.6
5.5
1.9
7.8
8.4
8.1
web for shear, bv =266.7 mm. Cross-sectional area of
longitudinal tensile reinforcement in the plane of
bending, Ast =2565.5 mm2. Cross-sectional area of
shear reinforcement, Asv =142.5 mm2. Centre-tocentre distance of fitments for shear, s=152.4 mm.
Effective depth of cross-section in the plane of bend­
ing, d=269.1 mm. The distance of the extreme fibre of
the concrete to the centroid of the outermost layer of
tensile reinforcement, d0 =304.8 mm.
4.1. Analysis to AS 5100.5-2004
At the time of testing of the beams, the standard for the
design of bridge beam was AS 5100.5–2004 (Standards
Australia 2004). The design approach, similar to those
used in earlier Australian standards, uses empirical
formula (Walsh 1988). In this section, the shear capa­
city of these test beams was determined based on the
formulae for shear provided in AS 5100.5–2004.
To compare capacities between test and prediction,
the predicted capacities were determined using mean
values for material properties. The mean strength for
concrete fcm for each beam is assumed to be the value
given in Table 5. The mean yield strength for main
steel fsym and shear reinforcement fsym:f were assumed
to be 258 MPa and 344 MPa, respectively. These values
were from the material testing described earlier in this
paper. Where present in the equations of the
Australian standard, section strength reduction factors
of unity were used. Owing to this, these factors were
not included in the equations of this paper. The pre­
dicted mean shear capacity Vum was determined using
equations 1 through 4. Variables with a symbol not
defined in this paper have definitions provided in AS
5100.5–2004, several with an extra letter ‘m’ in their
subscripts to show they represent mean values.
�
�1
Ast fcm 3
Vumc ¼ β1 β2 β3 bv d0
(1)
bv d0
(4)
For a section of a beam, Vumc was first determined.
Then Vums was determined interactively using the
Goal Seek function in Excel modifying the trial value
of V in Equation 2 until the calculated value of Vum
from Equation 4 equal to the trial value. Upon con­
vergence, the value of Vum was taken as the mean shear
capacity of the section.
4.1.1. Predicted capacities for Series T1V
The predicted shear capacities Vum of the section ver­
tically aligned with the inner face of the support plate
closest to the applied load are shown in Table 6. In the
same table, the predicted bending capacities Mum
under the applied point load are also provided. Their
corresponding values Vtest and Mtest from testing are
also provided. They are from Table 1.
The ratios of test to prediction for shear range 0.89–
1.01, and for bending range 1.24–1.32.
4.1.2. Predicted capacities for Series T3M
The predicted bending capacities Mum of the key sec­
tions of the beams are shown in Table 7. Their corre­
sponding test values are also provided. The ratio of test
to prediction for moment is 1.33.
4.2. Analysis to AS 5100.5-2017
Since the testing of the beams, the bridge design stan­
dard AS 5100.5 has been revised, and the latest version
is AS 5100.5–2017 (Standards Australia 2017). In this
section, the mean shear capacities of these beams to
the current standard were determined. A major
change introduced for the design to shear is the mov­
ing away from the use of empirical formula to a more
accurate set of formula based on the Modified
Table 6. Result from Analysis of T1V using AS5100.5–2004.
Beam
fcm
Vum
Mum
Vtest
Mtest
Vtest =
Mtest =
1
2
4
5
6
(MPa)
58
51
53
40
37
(kN)
298
290
292
275
270
(kNm)
172
172
172
170
169
(kN)
266
279
268
277
273
(kNm)
214
225
217
224
220
Vum
0.89
0.96
0.92
1.01
1.01
Mum
1.24
1.31
1.26
1.32
1.30
Table 7. Result from Analysis of T3M using AS5100.5–2004.
Beam
fcm
Mum
Mtest
Mtest =
3
(MPa)
65
(kNm)
173
(kNm)
230
Mum
1.33
AUSTRALIAN JOURNAL OF STRUCTURAL ENGINEERING
Compression Field Theory (MCFT) (Vecchio and
Collins 1986).
For this analysis, similar to that for AS 5100.5–
2004, the mean yield strength for main steel fsym and
shear reinforcement fsym:f are 258 MPa and 344 MPa,
respectively. Similarly, all section strength reduction
factors were set to unity. The modulus of elasticity of
reinforcement, Es was assumed to be 200 × 103 MPa.
The value of dv for each beam was determined in
accordance with AS 5100.5–2017.
The predicted mean shear capacity Vum for
a section below the point load was determined using
equations 5 through 10, suitable for beams with trans­
verse reinforcement greater than minimum shear
reinforcement. The Goal Seek feature of Excel was
used whereby the theoretical jack load was varied
until the calculated applied shear V in Equation 5
equal to the calculated shear capacity Vum in
Equation 10. M is the corresponding bending
moment, and it is not directly proportional to V
owing to contribution from self-weight and load
transmission assemblage being invariance. Variables
with a symbol not defined in this paper have the same
definitions provided in AS 5100.5–2017, several with
an additional letter ‘m’ in their subscripts to show that
they represent mean values. This interactive approach
gave the lowest shear capacity for the corresponding
applied shear and bending moment, and at the same
time included the action effects from the following
dead loads: load transmission assemblages (struts
and cross beams) and self-weight of the beam.
When determining the mean shear capacity, it was
assumed the corresponding bending is not the govern­
ing mode of failure. It is of interest to note that the
moments, represented by the variable M in
Equation 5, were found to have a range between 0
and 6% higher than their corresponding calculated
mean flexural capacities.
M
d þV
2sm ¼ v
2Es Ast
(6)
θvm ¼ 29 þ 7000 2sm
(7)
pffiffiffiffiffi
fcm bv dv
(8)
Vumc ¼ kvm
4.2.1. Predicted capacities for Series T1V
The predicted shear capacities Vum and the predicted
bending capacities Mum of the section below the point
load are shown in Table 8. Values Vtest and Mtest are
also provided in the same table. They are calculated
using Mtest1 and Vtest1 given in Table 1. The estimated
shear Vsw and bending moment Msw at this section are
9 kN and 8 kNm, respectively.
The ratios of test to prediction for shear range 1.25–
1.40, and for bending range 1.24–1.32. The ratios for
bending are the same as those obtained using AS
5100.5–2004.
4.2.2. Shear capacities limited by yielding of
longitudinal reinforcement
An action effect limiting predicted shear capacity
of beams is yielding longitudinal reinforcements
on the flexural tension side and in the flexural
compression side from applied bending moment
and shear. The additional forces ΔFtd in the flex­
ural tension side and ΔFcd in the flexural compres­
sion side caused by shear action effect can be
calculated from the equations below. These equa­
tions are based on clauses 8.2.7 and 8.2.8 of AS
5100.5, and the variables are defined in the stan­
dard. As for earlier equations in this paper, an
extra letter ‘m’ has been included in their sub­
scripts to show they represent mean values.
ΔFtdm ¼ cotðθvm ÞðV
ΔFcdm ¼ cotðθvm ÞðV
0:5Vums Þ
0:5Vums Þ
Fcm
(11)
(12)
The additional-force capacities ΔFtdm:capacity and
ΔFcdm:capacity in equations 13 and 14, respectively,
are from rearranging Equation 8.2.7(3) and the
equation without a number in Section 8.2.8, and
adding the text ‘.capacity’ to their subscripts. The
variables on the right of these equations are defined
in the standard.
(5)
0:4
1 þ 1500 2sm
kvm ¼
9
ΔFtdm:capacity ¼ ΔAs fsym
(13)
ΔFcdm:capacity ¼ ΔAs fsym
(14)
To determine Vltm , shear capacity limited by the
additional force in the longitudinal reinforcement
on the flexural tension side, a trial value of V was
used. Equation 5 was used to calculate 2sm ,
Equation 7 to calculate θvm , and Equation 9 to
Table 8. Result from Analysis of T1V using AS5100.5–2017.
Vums ¼
Asv fsym:f dv
cot θvm
s
Vum ¼ Vumc þ Vums
Beam
fcm
Vum
Mum
Vtest
Mtest
Vtest =
Mtest =
1
2
4
5
6
(MPa)
58
51
53
40
37
(kN)
212
207
208
197
194
(kNm)
172
172
172
170
169
(kN)
264
277
266
275
271
(kNm)
214
225
217
224
220
Vum
1.25
1.34
1.28
1.40
1.40
Mum
1.24
1.31
1.26
1.32
1.30
(9)
(10)
10
M. P. RAJAKARUNA ET AL.
Table 9. Result from Analysis of T1V using AS5100.5–2017 for
additional forces in the longitudinal reinforcement.
Table 11. Comparison of predicted capacities (including addi­
tional-force induced in longitudinal reinforcement from shear).
Beam
fcm
Vtest
Vltm
Vtest /
Beam
1
2
4
5
6
(MPa)
58
51
53
40
37
(kN)
264
277
266
275
271
(kN)
152
152
152
151
151
Vltm
1.74
1.82
1.75
1.82
1.80
1
2
4
5
6
Vum 2017
Vum 2004
Vum 2017 /
(kN)
212
207
208
197
194
(kN)
298
290
292
275
270
Vum 2004
0.71
0.71
0.71
0.72
0.72
determine Vusm . Then ΔAs was calculated by sub­
tracting the area of steel required for flexural bend­
ing Astf from the total steel provided in the flexural
tension side (Equation 15). Astf was calculated by
using an elastic analysis using transformed area
method to determine the force in the bottom long­
itudinal steel and then divided the force by fsym .
The strength reduction factor in the denominator
was not included as described earlier in this paper.
The longitudinal steel in the flange of the beam was
not included in the analysis.
Using Goal Seek feature in Excel, V was varied until
the additional force (Equation 11) equal to additionalforce capacity (Equation 13). Upon convergence, value
of V was taken to be that of Vltm .
ΔAs ¼ Ast
Astf
Vum 2004
Vltm 2017 /
(kN)
152
152
152
151
151
(kN)
298
290
292
275
270
Vum 2004
0.51
0.52
0.52
0.55
0.56
5. Concluding Remarks
Table 10. Comparison of predicted capacities.
Beam
1
2
4
5
6
Vltm 2017
(15)
The additional force in the longitudinal reinforcement in
the flexural compression side was found not to be limit­
ing. The results from the analysis are summarised in
Table 9. The ratios of Vtest to Vltm range from 1.74 to 1.82.
4.3. Comparison of predicted shear capacities
between the two versions of standard
The mean capacities predicted for shear using AS
5100.5–2004 were compared with those from AS
5100.5–2017 for beam series T1V, and the results of
the comparison are summarised in Table 10.
When additional tensile force in the longitudinal
reinforcement was taken into consideration, the shear
capacities limited by this action effect were compared
with their corresponding shear capacities determined
from AS 5100.5–2004. The AS 5100.5–2004 shear
capacities were not limited by yielding of longitudinal
reinforcement. Results of the comparison are sum­
marised in Table 11.
The retrieved beams were found not built in accor­
dance with the engineering drawing. The shear rein­
forcing bars were not anchored by the longitudinal
bars near top corners. The top bars were placed
above the shear reinforcement, hence they were not
restrained by stirrups.
The test results show only small increase in shear
capacity (5–15%) when the beams were adequately
anchored at their supports. It is possible the slight
increase was caused by increased beam arching effect
from the use of a shorter span length in series T2V.
The non-standard cogs as provided were found not to
adversely affect much the shear capacity of these
beams.
Non-uniformity of loading to the webs was
observed during the testing where cracking was
found to occur first in the web with a larger flexural
stiffness. This observation shows that testing indivi­
dual beams might not provide information to the
actual behaviour of these beams on bridge decks. It is
expected that the webs are more equally loaded in an
inverted bridge deck with the webs bolted together.
The ratios of predicted mean shear capacities
between the current standard and the previous stan­
dard range 0.71–0.72, suggesting the previous stan­
dard is less conservative for the design of shear for
these beams.
The lower conservativeness of the previous stan­
dard is a result of the different shear provisions used in
the two standards. The previous standard predicts
shear capacity using empirical equations derived
from laboratory testing of small specimens subjected
to a limited number of influencing parameters. Coexisting bending moment, an important parameter,
was not included. The shear capacity of the current
standard is predicted using mainly theoretical equa­
tions based on the MCFT. The interactive effect of coexisting bending moment is included.
When the effect of the additional force in the long­
itudinal reinforcement from shear was considered, the
ratios reduce to a range between 0.51 and 0.56.
The conservativeness in the shear design in the
current standard is further compounded by the use
of a strength reduction factor of 0.7 as compared to 0.9
in the American standard AASHTO (2017) for normal
weight concrete. The strength reduction factor of 0.7 is
AUSTRALIAN JOURNAL OF STRUCTURAL ENGINEERING
the same as prescribed in the previous standard for
a method which uses empirical formula and is not
suitable for use with the design methodology of the
current standard.
The limited testing shows that prediction of strength
for shear for these beams using AS5100.5–2017 is con­
servative. Capacities for shear from testing of T1V range
125–140% of their corresponding predicted values, and
this range increases to 174–182% when the action effect
of additional force in the longitudinal reinforcement
from shear was considered. It is expected that the use
of AS5100.5–2017 to load rate existing reinforced con­
crete bridges designed to previous standards will result in
a low rating factor for shear and a low capacity/action
factor for additional force in the bottom longitudinal
reinforcement from shear.
The MCFT provisions of AS 5100.5–2017 for shear
gave ratios of test to prediction ranging from 1.25 to
1.40. These values were comparable to those obtained
for predictions using MCFT-based provisions. Collins
et al. (1996) compared failure shears from 528 tests
with predicted values by both ACI equations and
a method based on MCFT. A broad range of test
parameters was included. The MCFT approach was
found to be more accurate than the ACI equations.
The mean ratios of Vexp =Vcalc were 1.39 and 1.32,
respectively, and their corresponding coefficients of
variation were 19.7% and 33.7%, respectively.
Kuchma et al. (2008) reported a mean value of
Vtest =Vcode of 1.27 with a coefficient of variation of
0.224 for 160 reinforced concrete test specimens with
shear reinforcement for prediction using provisions of
AASHTO LRFD specifications. The corresponding
values for prediction using ACI 318–02 were 1.35
and 0.277, respectively. Most of the specimens had
rectangular sections and were simply supported on
bearings.
Shear enhancement was found to occur for beams
with a ratio of flange thickness tf to the shear effective
depth d0 equal or greater than 0.25 (Giaccio, AlMahaldi, and Taplin 2002). Giaccio (2012) reported
of a previous investigation carried out on two test RC
T-beam specimens where flange overhang was found
to resist approximately 25% of the applied shear. The
value of tf /d0 of the inverted-U beams is 0.25 making
them susceptible to an effect not allowed for in the
shear provisions of Australian design standards.
The test capacities for shear for the T1V series range
89–101% of their corresponding predicted values based
on the equations of AS 5100.5–2004. This apparent
accurate prediction (within approximately 10%) is likely
caused by this standard being less conservative (predict­
ing a larger capacity) than the current standard.
The T1V beams failed in combined flexure-shear
mode. The bending moments from testing were found
to range 24–32% higher than their corresponding
11
predicted values. The T3M beam under predominantly
flexure was found have a 33% higher capacity than its
predicted value, which suggests that the beams tested in
shear were likely close to their bending capacities at
failure.
Acknowledgments
We acknowledge the contribution of the technical staff
members of Curtin University, including Arne Bredin,
Mick Elliss and Luke English, for setting up and testing
the beams; and Samuel Barbas and Hyuk Lee, undergradu­
ate and postgraduate student, respectively (at the time of
testing), for their assistance with setting up and testing.
We acknowledge the contribution of the Main Roads
Western Australia Asset Manager of South West Region,
Peter Newhouse for his coordination in the acquisition of
these beams.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Funding
Main Roads Western Australia provided the major portion
of the total funding through the Innovation and Research
Program.Water Corporation Western Australia funded the
removal of the bridge beams on site and the transportation
of the beams to Curtin University for testing.Curtin
University provided in-kind funding for fabricating the
load transmission assemblages, assisting with the setting
up, coring of concrete and testing of the beams.
Notes on contributors
Mahes Rajakaruna is Structures Design & Standards
Engineer at Main Roads Western Australia. He has been
with MRWA since 2002. He is involved in the review and
development of standards and processes for bridge design,
construction and maintenance. Prior to moving to Perth, he
was a lecturer in Civil Engineering at the University of South
Australia for over 12 years.
Dr. Vimonsatit is an Associate Professor in Civil
Engineering at the School of Engineering, Faculty of
Science and Engineering, Macquarie University, Sydney,
NSW, Australia and an Adjunct Associate Professor at
Curtin University, Western Australia. Before joining
Macquarie University, she was an academic with Curtin
University for over 12 years. The inverted-U beam testing
research project was carried out when she was with Curtin
University. Prior to being an academic, she worked as a
practising structural engineer in tall building design and
construction for over 10 years. Her research interests
include lightweight composite concrete, properties of low
carbon cement, nanome- chanical properties of composite
materials, multiscale link models, tall buildings and
constructability.
Dr. Wong is currently retired from full-time employment
and he maintains an interest in structural engineering. He
was Engineer (Structures) with Main Roads Western
12
M. P. RAJAKARUNA ET AL.
Australia from 2007 to early 2019, during which the
inverted-U beam testing research project was carried out.
Prior to working with MRWA, he was a senior lecturer in
Civil Engineering at Central Queensland University, where
he taught for more than 7 years. He has also worked as a
post-doctoral research fellow at the University of Adelaide
for 4 years and a practising structural engineer in Asia for
more than 11 years. He is a past joint recipient of two
Chapman medals and a Warren medal.
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