CHAPTER 3: WIDE BEAMS

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Nov 15, 2013 (3 years and 8 months ago)

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Shear Behaviour of Large, Lightly-Reinforced Wide Beams
Concrete Beams and One-Way Slabs

51

CHAPTER 3: WIDE BEAMS

“The most exciting phrase to hear in science, the one that heralds new discoveries, is not 'Eureka!'
(I found it!) but 'That's funny ...'” -Isaac Asimov

This Chapter presents the results of an experiment consisting of load-testing a
shear critical reinforced concrete beam measuring 2 meters wide by 1 meter tall
by 6 meters long. The beam design is inspired by the design of the alternate beam
for the Bahen Centre transfer girder discussed in Chapter 1. It is tested to shear
failure to investigate the effect that web width has on shear capacity. It is found
that the web width has no effect on the failure shear stress, and that the ACI-318-
05 design code is dangerously unconservative when designing large, lightly-
reinforced concrete beams such as the Bahen alternate beam.
3.1 General
The experiment described in this Chapter addresses the design situation identified in
Chapter 1 relating to a large transfer girder in the Bahen Centre, a new engineering
building at the University of Toronto. Refer to Figures 1-2 to 1-5. The experiment was a
collaboration between the author and Adam Lubell (Lubell (2006)).
The design of the as-built transfer girder is shown in Figure 1-4. Since this design
consists of a large, heavy and complicated rebar cage, the design engineer may have
wished to modify the beam width so as to both reduce flexural steel requirements and
reduce, or possibly eliminate, the use of stirrups. While the engineer could have also
modified the beam depth, architectural and sightline restrictions prevented this. Had the
design of the Bahen Centre been carried out using the 2005 ACI concrete design code,
the engineer may have chosen to use an exception to the requirements for minimum shear
reinforcement in clause 11.5.6.11(c) (Table 3-1 and Figure 3-1). In this clause, the ACI
code exempts beams with widths, b
w
, greater than twice their thickness, h, from the
requirement that a minimum quantity of stirrups specified by Equation 3-1 (11-13 in the
ACI code) be provided where V
u
exceeds ½φV
c
. The same exemption applies to slabs.
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Table 3-1: 1971 and 2005 ACI Code Minimum Stirrup Requirements (emphasis added)
ACI 318 Code Clause Relevant Commentary
ACI 318-71
Clause 11.1.1 –Minimum shear reinforcement
A minimum area of shear reinforcement shall be
provided in all reinforced, prestressed, and non-
prestressed concrete flexural members except:

(a) Slabs and footings;
(b) Concrete joist floor construction defined by 8.8;
(c) Beams where the total depth does not exceed

10in., two and one-half times the thickness of
the flange, or one-half the width of the web
,
whichever is greater.
(d) Where v
u
is less than one-half of v
c
.
1971 Commentary

Stirrup reinforcement restrains the growth of inclined
cracking and hence increases ductility and provides a
warning in situations where in an unreinforced web the
sudden formation of inclined cracking might lead
directly to distress. Such reinforcement is of great
value if a member is subjected to an unexpected tensile
force or catastrophic loading. Accordingly, a minimum
area of shear reinforcement not less than that given by
Eq. (11-1) or (11-2) is required wherever the nominal
ultimate shear stress v
u
is greater than ½ of v
c
. Three
types of members are excluded from this
requirement: slabs
, floor joists, and wide, shallow
beams
.
ACI 318-05
Clause 11.5.6.11 –Minimum shear reinforcement
A minimum area of shear reinforcement shall be
provided in all reinforced concrete flexural members
(prestressed and nonprestressed) where factored
shear force V
u
exceeds one-half the shear strength
provided by concrete, φV
c
, except:

(a) Slabs and footings;
(b) Concrete joist construction defined by 8.11;
(c) Beams with total thickness not greater than

10in., 2.5 times thickness of flange, or 0.5 the
width of web
, whichever is greatest.


2005 Commentary
Shear reinforcement restrains the growth of inclined
cracking. Ductility is increased and a warning of
failure is provided. In an unreinforced web, the sudden
formation of inclined cracking might lead directly to
failure without warning. Such reinforcement is of great
value if a member is subjected to an unexpected tensile
force or an overload. Accordingly, a minimum area of
shear reinforcement not less than that given by Eq. (11-
13) or (11-14) is required wherever the total factored
shear force V
u
is greater than one-half the shear
strength provided by concrete φV
c
. Slabs, footings
and
joists are excluded from the minimum shear
reinforcement requirement because there is a
possibility of load sharing between weak and strong
areas
. However, research results
11.23
have shown that
deep, lightly-reinforced one-way slabs, particularly if
constructed with high-strength concrete, may fail at
shear loads less than V
c
calculated from Eq. (11-3).



Figure 3-1: Shear Stress, v
u
, at which Stirrups are Required -ACI 318-05
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53
'
c
w
yminv,
f0.062
sb
fA
=
(MPa units) (3-1)
'
c
w
yminv,
f0.75
sb
fA
=
(psi units)
The advantage of using this exemption is that, in wide beams, the full value of φV
c
may
be employed in resisting the factored shear force, V
u
, before stirrups are required. This is
in contrast to narrow beams, in which the ACI code requires minimum stirrups where
V
u
>0.5φV
c
. Thus, a possible alternate beam design is shown in Figure 1-3, in which V
u

is 98% of φV
c
. In this alternate design, b
w
/h = 2.32, thus minimum stirrups are not
required, and the shear resistance is provided by the concrete alone. To take advantage of
the larger cross-section, the concrete strength has been doubled. According to the ACI
code, this alternate design will safely resist the column load from the upper eight stories.
The reasoning behind the wide beam exemption is described in the commentary to this
clause, reproduced in Table 3-1. It is believed that redistribution of load may occur
between weak and strong areas. However, there is no requirement that the beam be cast
integrally with a slab or any other part of the structure. Thus, the full beam cross-section
of a wide beam meeting the requirements of this exemption may be called upon to resist
the full shear force. Also note that there is no limit on the depth of the beam beyond
which the exemption does not apply. Further note that the small quantity of side face
steel on either side of the beam required for surface crack control will not be effective at
controlling cracking within the centre of the beam. In fact, this side face steel may
narrow surface crack widths, thereby reducing or eliminating possible visible evidence of
overloading.
Unlike failures occurring due to flexural yielding of the longitudinal steel, shear failures
are brittle, occurring after relatively little deflection and axial lengthening. Thus, while
arching, restraint and membrane actions may allow for significant increases in flexural
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54
capacity for beams cast integrally with the surrounding structure, it is unlikely that a
comparable increase in the shear capacity would occur for a very large, wide beam.
It is interesting to compare the 2005 clauses and commentary with the equivalent clauses
in the 1971 version of the code, in which the current wide beam exemption was first
implemented (Lubell et. al. (2004)). While the code clause has remained essentially
unchanged, the commentary made clear that this wide beam exemption applied to wide,
shallow beams. No guidance is provided, however, on what exactly differentiates a
shallow beam from a thick beam. A similar wide beam exemption in the 1994 CSA
A23.3 design code is limited to beams shallower than 600mm. In the 2004 CSA code,
the wide beam exemption has been rewritten to apply to beams cast integrally with slabs
with depths below the slab not exceeding 350mm nor one-half the width of the web. The
2004 CSA wide beam exemption is thus identical to the 1994 CSA exemption for a slab
thickness of 250mm.
Because the alternate beam relies solely upon concrete to provide shear resistance, it is
important that the design code expression used to calculate the concrete shear strength
accurately account for the size effect. The ACI code predicts that the alternate beam
would fail at a shear stress of v
c
=V
c
/b
w
d=0.167
'
c
f
=0.167(8.3)=1.39MPa
. The
simplified method in the 1994 CSA code (Equation 2-16), on the other hand, predicts that
the failure shear would be the greater of either:
v
c
=V
c
/b
w
d=(0.167/0.2)(260/(1000+d)
'
c
f

= (0.835)(260/(1000+1700)(8.4) = 0.675MPa, or
v
c
=V
c
/b
w
d=(0.167/0.2)0.1
'
c
f
= (0.835)(0.1)(8.4) = 0.701MPa

The 1994 CSA code predicts a shear capacity of only 0.701/1.39 = 50% of that predicted
by the ACI code. The Bahen alternate beam would be completely inadequate according
to the 1994 CSA code. There is a clear discrepancy between the two codes which must
be addressed. Which code method, the ACI method, or the 1994 CSA simplified method,
provides an accurate prediction of the shear strength of the Bahen alternate beam?
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3.2 Experimental Program –Beam AT-1
Because of the large difference in shear strengths predicted by the ACI and CSA codes as
described above, it was decided that a large, wide beam similar to the Bahen alternate
beam should be constructed and load tested to failure at the University of Toronto. The
experimental program is described in this section.
3.2.1 Specimen Design and Construction
The design of this beam, designated Beam AT-1, is shown in Figure 3-2. The dimensions
of the beam were chosen such that it could fit within the largest testing frame in the
structures laboratory at the University of Toronto. The as-built beam measured 5960mm
long x 1005mm high x 2016mm wide. Flexural reinforcement consisted of twenty 30M
rebars spaced evenly over the beam width at an effective depth of 916mm, with a clear
cover of 75mm. Holes measuring 180mm x 230mm were cast into the beam at each end
to allow the installation of steel lifting beams to jack the beam into its testing position.
These holes were reinforced with 15M stirrups. No transverse shear reinforcement was
provided within the 5400mm loaded span.
The beam was designed with a width to thickness ratio of greater than 2, so that the ACI
wide beam exemption applies. The effective depth of about 36 in. was chosen as this is
the upper limit at which no side face steel is required by the ACI code (Note that the
upper limit in the metric version of the ACI code, ACI-318-05M, is 1000mm (39.37in.)).
Four D4 deformed wires were placed in the horizontal plane transverse to the
longitudinal reinforcement to hold it in place during casting. This horizontal transverse
reinforcement represents only 1% of the ρ
s+t
=0.18% shrinkage and temperature
reinforcement ratio required by the ACI code for slabs. Wide beams, however, do not
require shrinkage and temperature reinforcement. The effects of shrinkage and
temperature steel on the shear behaviour of wide members are discussed in Chapter 4.
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Beam AT-1 weighed about 30 short tons (29 tonnes), and this is 3 times the capacity of
the laboratory overhead crane. Thus, the formwork was built directly beneath the
Baldwin test frame (see Figure 3-3 and Figure 3-4) and the beam was cast in this position.
The formwork was carefully aligned relative to the test frame such that the beam could be
lifted vertically directly into its testing position using hydraulic jacks at each end. The
formwork was constructed on a base of two layers of 19.1mm (3/8 in.) plywood, and
consisted of 3/8in. formply supported using steel walers and braces. Following casting,
the concrete was cured under wet burlap and plastic sheeting for seven days. A series of
thermocouples embedded in the concrete indicated a maximum internal temperature of
about 73
o
C 24 hours after casting.
3.2.2 Material Properties
Material properties are summarized in Figure 3-2. The concrete was ordered from a local
ready-mix company with a specified 28-day strength of 50MPa and a maximum
aggregate size of 10mm (3/8 in.). The aggregate is commonly used in the Toronto
market. It is a crushed limestone supplied from a quarry in Milton, Ontario, and has been
observed in previous tests (Angelakos et. al. (2001)) to cleave at high concrete strengths.
The concrete was supplied in two ready-mix trucks and standard 6in. x 12in. (152mm x
305mm) concrete cylinders were cast from each load to test for compressive and split-
cylinder strength. Standard 6in.x6in.x21in. (152x152x457mm) modulus of rupture
prisms were also cast for each load. Concrete compressive strengths on the day of test,
47 days after casting, were 64MPa and 76MPa for the first and second trucks,
respectively. Split cylinder strengths on the day of test were 6.6MPa and 7.2MPa
respectively.
The concrete supplied in the first truck filled approximately the bottom two-thirds of the
formwork. Hence, it is appropriate to use the material results from this load for analysis
of this beam, as the properties of the concrete in the lower two-thirds of the beam will
govern shear behaviour, based on the aggregate interlock capacity at cracks.
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Figure 3-2: Design of Test Specimen AT-1
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Concrete Beams and One-Way Slabs

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Figure 3-3: Formwork for Beam AT-1

Figure 3-4: Construction of Beam AT-1
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3.2.3 Experimental Setup
The beam was loaded to failure in three-point bending in the Baldwin Test Frame. The
experimental setup is shown in Figure 3-2 and Figure 3-5. The beam was supported at
each end on 152mmx1200mm steel plates on steel rollers. The rollers in turn were
supported on steel beams bearing directly on the floor of the test frame. These rollers
were located at 2700mm from the centre of the beam and the line of action of the applied
load, giving a shear span to depth ratio (a/d) of 2.95. The beam was loaded through a
spherical head, and the load from the spherical head was applied to the specimen through
a stiff steel spreader beam supported on a 152mmx1200mm steel plate. Prior to loading,
this plate was embedded in a thin layer (about 5mm thick) of plaster-of-paris so as to
eliminate stress concentrations between the plate and the top of the beam.
Load was applied monotonically to the beam. Loading was halted at several stages
during the test at which point the load was reduced slightly. During these load stages
cracks were marked using a felt-tip pen and photographed, and dial gauge readings were
taken. Also, detailed data consisting of vertical, horizontal and transverse deformation
readings in a grid of externally-applied Zurich targets was collected at each stage.
Based on the concrete strength on the day of test, the ACI-318-05 code predicts that
Beam AT-1 has a nominal flexural capacity of 5770kN-m, which corresponds to an
applied load of about 4150kN, after accounting for the self-weight of the member. The
ACI code further predicts that the beam has a nominal shear capacity of 2470kN, which
corresponds to an applied load of 4770kN after accounting for self weight. In this case
the shear capacity is calculated using ACI-318 Equation (11-3) at a distance d from the
face of the support plate. The ACI code therefore predicts that the beam will be tension-
controlled, and will exhibit a ductile flexural failure at a load that is 87% of the load
required to cause shear failure. Assuming a dead load to live load ratio of 3:1, similar to
that of the Bahen Centre transfer beam, this results in a safe service applied load of about
P
app
=2700kN.
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Figure 3-5: Test Setup of Beam AT-1


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61
3.2.4 Instrumentation
The instrumentation used on Beam AT-1 is shown in Figure 3-6. Five linear variable
displacement transducers (LVDTs) were placed below the beam at mid-span to monitor
the mid-span displacement. LVDTs were also placed beside the supports to monitor
support settlements. Displacements recorded at midspan were then corrected for support
settlement. A series of twenty-five 5mm electrical resistance strain gauges were applied
to the longitudinal reinforcement at midspan, quarterspans and at 100mm from the
centerline of the supports. The rebars instrumented with strain gauges were aligned in
the beam such that the strain gauge was oriented on the side of the rebar. This alignment
reduces the chances of anomalous strain readings should the rebar bend at a crack due to
dowel action.
A grid of aluminum zurich targets was installed on the south face of the specimen, and
each grid square measured 300mm x 300mm. The targets were fastened to the face of the
specimen with superglue and two-part structural epoxy. Horizontal, vertical and
transverse distances between adjacent targets were measured using an existing custom-
built data acquisition system during each load stage. Comparison of these measurements
to those taken prior to the commencement of loading allowed for the calculation of
horizontal, vertical and shear strains at each load stage.
Four LVDTs were fastened 75mm below the top of the specimen on the north face, and
aligned at 45
o
as shown in the figure. A long, narrow aluminum tube was fastened to the
LVDT plungers and to aluminum reaction plates fastened 75mm above the soffit of the
specimen. These LVDTs formed an X-pattern measuring 850mm x 850mm, and each
“X” was centered on the quarterspan of the beam. This type of instrumentation allowed
for continuous monitoring of shear strains over the 850mm horizontal distance. A
discussion on how to calculate the shear strain in such a setup is provided in Appendix B
(Page 390).

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Figure 3-6: Instrumentation Layout -Beam AT-1

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3.3 Experimental Results –Beam AT-1
Beam AT-1 exhibited a brittle shear failure prior to reaching its designed flexural
capacity. This section will describe the observed experimental behaviour. A summary of
important experimental results is provided in Table 3-2. These results include the
following: experimentally determined failure load, P
exp
, the midspan deflection at the
failure load, Δ
ult
, the ratio of this deflection to one-half of the span-length, Δ
ult
/0.5L, the
shear strain at the failure load measured using the LVDTs on the north face of the
specimen, γ
ult
and the average mid-span steel strain at the failure load, ε
s
. Failure shear
stresses calculated at d from the face of the support and d from the line of application of
the load (a typical failure location chosen when using shear design methods that account
for the effect of moment) are shown.
The peak shear strains measured at the quarterspans (γ
ult
) using the externally-installed
LVDTs are shown, as are the ratios of the peak shear strain γ
ult
to Δ
ult
/0.5L (δ
shear
). If all
of the midspan deflection was caused by shear, the ratio Δ
ult
/0.5L would equal the
average shear strain. The shear strain listed, however, is located within an
850mmx850mm square centered on the quarterspans, and is hence not necessarily a
measure of the average shear strain. Thus δ
shear
can exceed 100% if there is a
considerable shear strain located within this square. The parameter δ
shear
is useful,
however, as a relative measure of the shear strains between specimens, or, in the case of
AT-1, between the east and west sides of the beam.
Table 3-2: Experimental Results -AT-1
h d
b
w
L
ρ
w
f'
c
a
g,eff
s
xe
P
exp
Δ
ult
Δ
ult
/0.5L γ
ult
ε
s,ult
V
exp
(1)
v
exp
(1)
V
exp
(2)
v
exp
(2)
(mm) (mm) (mm) (mm) (%) (MPa) (mm) (mm) (kN) (mm)
(x10
-3
) (x10
-3
)
East West
(x10
-3
)
(kN) (MPa) (kN) (MPa)
AT-1 -East 2266 5.7 2.11 0.64 30% 15% 1220 1218 0.66 1177 0.637
AT-1 -West 2441 9.4 3.48 0.70 118% 20% 1290 1305 0.707 1264 0.685
Notes:
(1) Calculated at d from support
(2) Calculated at d from load
0.76 64
Specimen Properties (as-built) Experimental Observations
Specimen
1005 916 2016 5400
δ
shear
3.8 1457

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3.3.1 Load-Deflection Response
A diagram showing the load vs. midspan displacement is shown in Figure 3-7. The
deflection plotted in Figure 3-7 is the average of the readings from the five LVDTs
placed below the midspan of the beam. Very small differences in the individual readings
of the LVDTs were noted. LVDTs VN and VNC generally measured deflections that
were smaller than VC by a maximum of 4% and 3% respectively. LVDTs VS and VSC
measured deflections that were slightly larger than VC by a maximum of 4.5% and 6.7%
respectively. The readings from the midspan LVDTs indicated that the beam rocked very
slightly on its supports about its longitudinal axis during loading and unloading, but this
rocking was minor, and is not significant. No differences in outer and inner LVDT
readings were noted due to the use of loading and support widths that were smaller than
the beam width.
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
0 2 4 6 8 10 12
Mid-Span Displacment,
Δ
(mm)
Applied Load (kN)
ACI Safe Service Load = 2700kN
(DL:LL = 3:1)
A
CI Predicted Shear Failure Load = 4770kN
Breakdown of Beam
Action on West End
P
app
=2441kN
Δ
/L=1/580
Breakdown of Beam
Action on East End
P
app
=2266kN
Δ
/
L= 1/950
A
CI Predicted Flexural Failure Load = 4150kN

Figure 3-7: Applied Load vs. Mid-Span Deflection -Beam AT-1
4
5
6
7
8
9
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65
Crack diagrams at load stages up until failure are shown in Figure 3-8 and Figure 3-9.
Photographs of the final failure on the west end of the beam are shown in Figure 3-10.
The first crack at midspan was visible at approximately 1000kN, and as the load
increased, a series of flexural cracks formed along the length of the span. By about load
stage 8, three cracks on the west side had rotated, clearly forming flexure-shear cracks.
At an applied load of 2266kN, crack (a) (labelled in Load Stage 7, Figure 3-8) rapidly
moved upwards, extending past the centre of the loading plate by almost 450mm. This
was accompanied by a rapid extension of the crack at its base along the plane of the
reinforcement. It can be seen in the load deflection response that the applied load
dropped by 3.3% and the midspan deflection increased rapidly. Eventually the load was
recovered, and a load stage was taken at an applied load of 2286kN. At this load stage
crack (a) was 1.8mm wide at the mid-height of the beam. Following the load stage, more
load was applied, and a sudden shear failure occurred on the east side of the specimen at
an applied load of 2441kN. The initial drop in load associated with the extension of the
crack on the east side occurred at a Δ/L ratio of 1/950, while final failure occurred at a
Δ/L ratio of 1/580.
It can be seen from the crack diagrams that crack widths tended to stay quite narrow
during the test. Even up to load stage 8, where the applied load was fully 90% of the
peak load, the maximum crack width was 0.25mm. The deflections also stayed quite
small. The deflection at load stage 8 was 5.3mm, representing about 1/1000
th
of the span
length. Thus, prior to the formation of the large shear crack on the east end at an applied
load of 2266kN, there was little or no warning that the beam was dangerously overloaded,
and at risk of imminent collapse. Had this beam been in service in a building, it is
unlikely that the cracks up to load stage 8 would have been readily visible. Had the beam
in service been concealed behind a drop ceiling, drywall or other such architectural finish,
cracks would not have been visible at all, nor is it likely that sufficient deflection would
occur so as to cause damage to non-structural elements to indicate that the structure was
in distress.
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Figure 3-8: Crack Patterns –Beam AT-1, South face
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67


Figure 3-9: Crack Patterns –Beam AT-1, North Face
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68


Figure 3-10: Failure Crack Pattern in the West End of Beam AT-1
As shown in Figure 3-7, the peak applied load of 2441kN represents only 59% of the load
predicted by the ACI code to cause flexural failure and 51% of the load predicted to
cause shear failure. Furthermore, this load represents only 90% of the ACI predicted safe
service load. Based on the observed crack patterns, deflections, and failure loads, it can
be concluded that, had this beam been in service in a building, there is a distinct
possibility that a brittle shear failure could have occurred under service loads, with little
to no warning prior to collapse.
Based on the formation of wide cracks and the load-deflection behaviour at the applied
load of 2266kN, it appears that beam action broke down on east side at this load. It
appears that a direct strut formed from the loading plate to the east support plate, thereby
allowing for the application of further load. This behaviour is similar to the so-called
“secondary strut” action identified by Kani (1964), though in normal strength concrete,
Kani noted that this secondary strut action is not a dependable shear transfer mechanism,
and should not be relied upon. It can therefore be argued that the applied load of 2266kN,
representing breakdown in beam action, should represent the first of two failure loads in
the specimen. The intention of the following sections is to examine this argument in
more detail by investigating the measured shear strains and longitudinal strains.
a) South Face b) North Face
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69
3.3.2 Shear Strain Response
The crack patterns in beam AT-1 at load stage 9 on the south face of the specimen are
shown in Figure 3-11a), superimposed upon the zurich target grid. The measured shear
strains for load stages 4 through 9 in the shaded individual 300mm x 300mm grid squares
are plotted in Figure 3-11b) and Figure 3-11c). The measured shear strains are plotted vs.
the average shear stress. The average shear stress includes the self-weight, calculated at
the middle of the vertical line of squares.
It can be seen that the shear strains in squares 1, 2, 3 and 4 are generally higher on the
east side than on the west side until load stage 8. This indicates that there was greater
shear strain on this side throughout the duration of the test, and it is therefore not
surprising that beam action broke down on this side first.
At load stage 9, following the formation of the large, wide crack on the east side, it can
be seen than the corresponding shear strains in squares 1, 2, 3 and 5 on the east end had
increased dramatically. Because the crack is almost horizontal in square 4, the increase
in shear strain is not as dramatic, though it is considerably larger in square 4 on the east
end than it is on the west end. Overall, the shear strains in squares 1, 2, 3 and 4 increased
by 7.4, 5.4, 3.4 and 1.1 times, respectively, from load stage 8 to load stage 9. In square 5,
the shear strain increased from almost 0 to 3.5mm/m. This sudden increase in shear
strain is not consistent with beam action. Rather, it is apparent that there was significant
shear strain and displacement occurring along the length of the crack, and this is
consistent with the section to the east and to the west of the crack acting as two largely
independent elements.
Comparison with Previous Tests
The load-deflection behaviour exhibited by beam AT-1, characterized by initial and final
peak loads, has been observed in previous tests of reinforced concrete beams at the
University of Toronto.
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a) Zurich Target Grid Layout

0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
-2 0 2 4 6 8 10 12 14 16
Shear Strain (mm/m)
Average Shear Stress (MPa)
West

db
V
w
East
Square 1
Square 2
Square 3

b) Squares 1, 2 and 3
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
-2 0 2 4 6 8 10 12 14 16
Shear Strain (mm/m)
Average Shear Stress (MPa)
Square 4
Square 5
West

db
V
w
East

c) Squares 4 and 5
Figure 3-11: Measured Shear Strains in Zurich Target Grid –Beam AT-1
Shear Behaviour of Large, Lightly-Reinforced Wide Beams
Concrete Beams and One-Way Slabs

71
Figure 3-12 shows the load-deflection curves obtained from tests of 1000mm deep,
300mm wide reinforced concrete beams reported by Angelakos et. al. (2001). As
summarized in Table 3-3, these beams, designated DB165 and DB180, had a
reinforcement ratio ρ
w
of 1.01%, an a/d ratio of 2.92, an effective depth of 925mm and
concrete strengths of 65MPa and 80MPa respectively. Thus, other than the reinforcement
ratio and beam width, these beams are very similar to beam AT-1. The load-deflection
curves shown in Figure 3-12 are compared to the load-deflection curve for beam AT-1. It
can be seen that these beams exhibited an initial peak load (indicated by the square
symbol), after which the load rapidly decreased. The load was then regained, and a
second, higher peak load reached (indicated by the round symbol) after a considerable
increase in deflection. Angelakos (1999) reported that the initial decreases in load
occurred after formation of a significant diagonal crack on one end of the beams, and that
final failure occurred on the opposite end at the second peak load. This behaviour was
exhibited by the high strength concrete beams in the test series, but not the regular
strength concrete beams. This is the same behaviour exhibited by AT-1. This behaviour
was also exhibited by a beam specimen described in more detail later in this thesis,
specimen L-10H, with an a/d ratio of 2.89, an effective depth of 1400mm, and a concrete
strength of 74MPa.
Further information about the shear strain response of beams AT-1, DB165 and DB180
can be found by analyzing the shear strain data obtained from continuous readings from
the LVDTs attached to the north faces of the specimens. As shown in Figure 3-13,
LVDTs were affixed to the north face of specimens DB165 and DB180 in similar
patterns and locations as AT-1, with the exception that the X’s on the DB series measured
950mm x 950mm. The shear strains measured by these X’s are plotted in Figure 3-13,
such that the shear strains measured on the sides where initial breakdown in beam action
occurred are plotted as positive, and the shear strains on the sides where final failure
occurred are plotted as negative. Shear strain data for these specimens are also
summarized in Table 3-4, in which data corresponding to the side on which initial and
final failure occurred are subscripted “IB” and “F” respectively.
Shear Behaviour of Large, Lightly-Reinforced Wide Beams
Concrete Beams and One-Way Slabs

72
Table 3-3: Beam Width and Depth Series –Experimental Data
h
b
w
d a/d
ρ
w
f'
c
a
g,eff
s
ze
V
exp
(1)
v
exp
(1)
V
exp
(2)
v
exp
(2)
(mm) (mm) (mm) (%) (MPa) (mm) (mm) (kN/m width) (MPa) (kN/m width)
AT-1
1005 2016 916 2.95 0.76 64 4 1443 604 0.660 584 0.637
Member Width Series
Angelakos DB165 1000 300 925 2.92 1.01 65 5 1388 630 0.681 610 0.660
DB180 1000 300 925 2.92 1.01 80 0 1821 575 0.622 555 0.600
Stanik BN100 1000 300 925 2.92 0.76 37 9.5 1143 658 0.712 638 0.690
BH100 1000 300 925 2.92 0.76 99 0 1821 662 0.715 642 0.694
Member Depth Series
Stanik BH25 250 300 225 3.0 0.89 99 0 443 284 1.264 283 1.258
BH50 500 300 450 3.0 0.81 99 0 886 444 0.986 439 0.975
Yoshida YB2000/0 2000 300 1890 2.9 0.76 34 9.5 2335 934 0.494 857 0.454
Notes:
(1) Calculated at d from face of support
(2) Calculated at d from centreline of load
Specimen Properties
Specimen
Experimental Observations

0
200
400
600
800
1000
1200
1400
0 2 4 6 8 10 12
Mid-Span Displacment, Δ (mm)
Applied Load per metre width (kN/m)
DB180
f'
c
= 80MPa
ρ
w
= 1.01%
DB165
f'
c
= 65MPa
ρ
w
= 1.01%
AT-1
f'
c
= 64MPa
ρ
w
= 0.76%
Initial Breakdown
in Beam Action

Figure 3-12: Load-Deflection Curves, Beams AT-1, DB165 and DB180
Shear Behaviour of Large, Lightly-Reinforced Wide Beams
Concrete Beams and One-Way Slabs

73
Table 3-4: Shear Strain Data –AT-1, DB165 and DB180
(kN) (MPa) (mm/m) (mm/m) (kN) (MPa) (mm/m) (mm/m)
(%) (%) (%)
AT-1 East 2266 0.648 0.636 0.324 West 2441 0.700 4.12 0.699 7.7% 548% 116%
DB165 East 353 0.661 0.373 0.212 West 357 0.667 1.31 0.247 1.0% 251% 17%
DB180 West 320 0.605 0.330 0.474 East 323 0.617 2.54 0.545 0.9% 670% 15%
Notes:
(1) Calculated at quarterspan (middle of "X")
(2) Shear strain on side where initial breakdown in beam action occurred
(3) Shear strain on side where final failure occurs
Increase
in Load
Increase
in
γ
IB
Increase
in
γ
F
Specimen
Shear
Stress
(1)
P
app
γ
IB
(2)
γ
F
(3)
P
app
Shear
Stress
(1)
Initial Breakdown in Beam Action (IB) Final Failure (F)
Side
γ
IB
(2)
γ
F
(3)
Side

The plots of shear stress vs. shear strain shown in Figure 3-13 are fairly similar to one
another, and follow the general pattern exhibited by the individual zurich grid squares in
AT-1 discussed previously. After the initial peak at which breakdown in beam action
occurred, the shear strain increased dramatically, and these increases were associated
with a drop in load. By the time final failure occurred, the load had increased by a range
of 0.9 to 7.7%, corresponding to an increase in shear strain from 251% to 670%. On the
side in which final failure occurred, corresponding increases in shear strain were
considerably smaller, ranging from 15% to 116%.
It can be seen from Table 3-2 that at a load of 2266kN, the value of δ
shear

ult
/(Δ
ult
/0.5L)
was 30% on the east end and 15% on the west end. At the second peak load, the value of
δ
shear
on the east end was 118% and on the west end it was 20%. The proportion of the
deflection caused by shear straining on the west end, therefore, remained largely
unchanged, while shear straining on the east end caused a considerable increase in the
deflection. Beams DB165 and DB180 show similar behaviour in δ
shear
values.
This analysis has shown that, on the sides in which failure initially occurred, beam action
apparently broke down (Fenwick and Paulay (1968)), resulting in an initial drop in load
and increase in deflection caused by shear straining. A secondary shear resisting
mechanism was then able to be engaged, which allowed the beams to recover the load to
such an extent that failure then occurred on the opposite end of the beam. Had the crack
pattern been different it would have been possible that no secondary strut could form.
Shear Behaviour of Large, Lightly-Reinforced Wide Beams
Concrete Beams and One-Way Slabs

74

0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
-1.0 0.0 1.0 2.0 3.0 4.0
Shear Strain (mm/m)
Shear Stress (MPa)
AT-1 -East
DB165 -East
DB180 -West
A
T-1
-West
DB165 -West
DB180
-East

Figure 3-13: Shear Strains Measured on North Face –Beam AT-1, DB165 and DB180
3.3.3 Longitudinal Rebar Strain Response
As shown in Figure 3-6 and in Figure 3-14, a total of twenty-five 5mm electrical
resistance strain gauges were applied to the longitudinal reinforcing bars at five locations
along the span prior to casting. Five each were located at 100mm from the east support
(Line 1), at the east quarterspan (Line 2), at midspan (Line 3) at the west quarterspan
(Line 4) and at 100mm from the centre of the west support (Line 5), and the gauges were
Final
Failure
Side
Initial
Failure
Side
Shear Behaviour of Large, Lightly-Reinforced Wide Beams
Concrete Beams and One-Way Slabs

75
evenly spaced across the width of the beam. Figures a) to e) in Figure 3-14 show the
profiles of the strain gauge readings across the beam width for various load stages (shown
in solid lines) and loads between stages (shown in dashed lines). Gauge D4, located in
the west quarterspan, malfunctioned and no data from this gauge is available. The
average strains at each line are plotted in Figure 3-15 as a function of the applied load.
For clarity the data points at load stages have been removed in Figure 3-15, with the
exception of load stage 6.
Rebar Strains Following Initial Breakdown in Beam Action
It is useful to analyze the strains measured in the longitudinal rebars after the initial peak
load of 2266kN was reached. In Figure 3-15 it can be seen that the strains in the east
quarterspan (line 2) were larger than the equivalent strains in the west quarterspan (line 4)
by about 20%. Also, the strains in the east quarterspan were about 69% of the strains at
midspan.
However, after the load began to drop from 2266kN, the longitudinal strains in the east
quarterspan increased dramatically, while the strains at other locations decreased due to
the drop in load. Four data points were recorded during this period of rapidly increasing
strains, representing a time interval of 18.5 seconds. Eventually the load was regained,
and at a load of 2245kN, the east quarterspan strains started to exceed the midspan strains,
and continued to increase faster than the midspan strains for the rest of the test. At the
second peak load of 2441kN, the east quarterspan gauges were 20% larger than the
midspan gauges and 77% larger than the west quarterspan gauges.
The considerable increase in steel strains at the east quarterspan after the initial peak load
is strongly suggestive of the development of direct strut action on this side after the
breakdown in beam action. Recall that in a strut and tie model the strains in the
longitudinal steel is predicted to be constant in the span.

Shear Behaviour of Large, Lightly-Reinforced Wide Beams
Concrete Beams and One-Way Slabs

76

Figure 3-14: Rebar Strain Profiles -Beam AT-1
Shear Behaviour of Large, Lightly-Reinforced Wide Beams
Concrete Beams and One-Way Slabs

77
0
500
1000
1500
2000
2500
3000
0 200 400 600 800 1000 1200 1400 1600 1800 2000
Rebar Strain (με)
Applied Load, P
app
(kN)
Line 1
(East Support)
Line 5
(West Support)
Line 4
(West Quarter-
span)
Line 3
(Mid-span)
Line 2
(East Quarter-
span)
P
app
= 2266kN
Breakdown of
Beam Action on
East Side
P
app
= 2396kN
1133με 1189με
2192kN

Figure 3-15: Average Rebar Strains at Midspan, Quarterspans and Supports –AT-1
It can be seen, therefore, that the increase in midspan displacement after the initial peak
load of 2266kN was not a result of increasing longitudinal strains at the midspan or west
quarterspan due to flexural action. Rather, it was a result of rapidly increasing shear
strains in the east span due to a breakdown in beam action, and the considerable increase
in longitudinal strains in the east quarterspan were associated with this increasing shear
strain. It is conservative to use an applied load of 2266kN as the failure load. Indeed, it
is appropriate to use this load when using design and analytical methods based on the
assumption of beam behaviour.
Effect of Narrow Supports and Loading Plates
Beam AT-1 was supported and loaded through steel plates whose widths were only 60%
that of the total beam width of 2m. Lubell (2006) has found that the use of supports and
loading plates that are narrower than the beam width can reduce one-way shear capacity.
Shear Behaviour of Large, Lightly-Reinforced Wide Beams
Concrete Beams and One-Way Slabs

78
A possible reason for this effect is that moment may be unevenly distributed across the
width of the cross section of a beam loaded and/or supported on narrow plates. That is,
moment may be higher along the support and loading lines, and smaller outside of these
lines. An analogy may be made with two-way slabs supported on isolated columns, in
which moment is higher in the column strips, and smaller in the middle strips. This
higher moment may result in wider cracks with a reduced aggregate interlock capacity.
Furthermore, an uneven moment distribution is associated with an uneven shear
distribution, and shear along support lines may be larger than outside the lines. Thus,
shear failure may be triggered inside a wide beam supported on narrow supports by a
combination of wider cracks and larger than average shear. Assuming a constant crack
pattern and crack spacing across the width of a beam supported on narrow supports,
wider cracks and larger moment in the middle of the beam would result in higher
longitudinal rebar strains. Hence, investigation of the strain gauge readings from beam
AT-1 offers some potential insight into the effect of using narrow loading and support
plates.
As shown in Figure 3-8 and Figure 3-9, the first crack occurred approximately 125mm to
the west of the midspan on both the north and south faces. Referring to Figure 3-14d),
which shows the strain readings at the midspan, it can be seen that prior to cracking (at
loads of 600kN and 900kN), the strain profiles are reasonably uniform. However, after
cracking, the strains at C3 (the middle gauge) were the first to start increasing. At load
stage 4, which was taken just shortly after cracking, gauge C3 indicated a strain that was
approximately 75% higher than the other rebar strains at line 3. Hence it is possible that
a crack was initiated in the middle of the beam, and this crack then spread out towards the
edges. Furthermore, it is possible that the first crack was wider in the middle of the beam
than at the edges. However, it can be seen that, after load stage 4, when a second crack
occurred directly at midspan along the line of gauges, the strain profiles became more
uniform. As the load increased, the outer gauges, A3 and E3, indicated rebar strains that
were larger than strains on inner bars. By the time the peak load was reached, gauges A3
and E3 indicated rebar strains that were about 7% greater than the inner gauges. Thus,
Shear Behaviour of Large, Lightly-Reinforced Wide Beams
Concrete Beams and One-Way Slabs

79
with the exception of the strain profile at first cracking, a column strip/middle strip effect
was not clear at the midspan of beam AT-1.
The strain gauge profiles at the west quarterspan (line 4, shown in Figure 3-14b)),
however, showed considerably larger strains in the middle of the beam than at the edges.
As shown in Figure 3-8, a small, very narrow crack formed on the south face of the beam
about 100mm to the east of line 4 shortly before load stage 6. The formation of this crack
was not reflected in the strain gauge readings. However, beyond load stage 6, at a load of
about 1750kN, this crack widened and extended, and became visible on the north face as
well. At the same time, the strains measured at line 4 started to increase beyond what
would be expected based on an uncracked response. The strain measured by gauge C4,
however, located in the middle of the beam, increased more rapidly than the other strains
at line 4. By load stage 7, the strain at gauge C4 was 1.85 times larger than the other
strains along line 4. Throughout the rest of the loading, and up to the peak load, the
strain in gauge C4 was consistently larger than the strains measured by other gauges. At
the peak load, the strain at C4 was 1.2 times larger than the other strains.
The strain gauge profiles at the east quarterspan (line 2, shown in Figure 3-14a) ) also
consistently show that the longitudinal rebar strains were larger towards the middle of the
beam than they were towards the edges. Beyond load stage 6, and up to a load of
2266kN, it is very clear that the longitudinal rebar strains are larger at the inner gauges
than at the outer gauges.
The longitudinal strain profiles at the quarterspans thus exhibit a significant column
strip/middle strip effect, but the midspan gauges do not. It is therefore possible that
cracks were slightly wider in the interior of beam AT-1 at the quarterspans than they
were at the surface. Furthermore, it appears that shear was the cause of the
column/middle strip effect exhibited at the quarterspans since it was not observed at the
midspan, where the shear is equal to zero.
Shear Behaviour of Large, Lightly-Reinforced Wide Beams
Concrete Beams and One-Way Slabs

80
The behaviour of the rebar strains at the east support (line 1) following the initial
breakdown in beam action offer some interesting insight into the effect of the support on
the width of the longitudinal crack at the level of the steel. It can be seen in Figure
3-14c) that there were negligible strains measured at the east support at load stage 9, but
beyond this stage, the strains increased considerably. By the time the peak load was
reached, the average strain in the steel at the east support was 207με, while at the west
support (Figure 3-14e) ) it was only 27με. This behaviour can also be seen in Figure
3-15. The interesting aspect about the strains at the east support is that, as opposed to the
strains at the quarterspans, the strains at the outer gauges increased faster than the inner
gauges. At the peak load, the strains at gauges A1 and E1 were about 2.6 times greater
than the inner gauges.
What appears to have happened at the east support is that the longitudinal crack at the
level of the steel was slowly being driven back towards the support, and at a load of
2396kN, the crack had extended back to such an extent that the rebar at the support was
engaged. However, the vertical reaction at the support plate appears to have partially
clamped the crack at the middle of the beam. This may have both prevented it from
travelling as far back towards the support as it could on the outer edges of the beam, and
made it narrower in the middle of the beam. Because the crack could travel back further
and was wider on the outer edges, the strains in the outer rebars at the support are greater.
This effect was also manifested in the measured strains in the outer bars at the east
quarterspan (line 2, Figure 3-14a) ). It can be seen that following the breakdown in beam
action, the outer gauges (A2 and E2) increased faster than gauges B2 and D2.
Lubell (2006) has analyzed AT-1 and other specimens with supports that are narrower
than the beam width, including specimens described in Chapter 4. It was found that the
use of narrow suports can reduce shear strength, and a method was developed to account
for this reduction that is appropriate for inclusion into design codes.

Shear Behaviour of Large, Lightly-Reinforced Wide Beams
Concrete Beams and One-Way Slabs

81
3.4 Discussion –Beam AT-1
The experimental results described above offer considerable insight into the effects of
beam width and depth on the shear behaviour of large, lightly-reinforced concrete beams.
The above results also provide important information about the safety of the alternate
Bahen Centre transfer beam design presented in Figure 1-4, and the safety and accuracy
of various shear design methods.
3.4.1 Effect of Beam Width
As mentioned previously, Beam AT-1 is similar in several respects to a series of narrow
beams tested in previous experimental programs at the University of Toronto, and
summarized in Table 3-3. Comparing experimentally determined shear stresses from
these tests to that of beam AT-1 offers important information about the effect of beam
width on the failure shear stress.
These beams are specimens DB165 and DB180, tested by Angelakos (1999) and beams
BN100 and BH100, tested by Podgorniak-Stanik (1998). Beams DB165 and DB180
have an a/d ratio of 2.92, an effective depth of 925mm, a beam width of 300mm, a
reinforcement ratio of 1.01% and concrete strengths of 65MPa and 80MPa, respectively.
Thus, with the exception of the reinforcement ratio, beam DB165 can represent a beam
almost exactly identical to AT-1, with a width simply scaled down to 1/6.72 that of AT-1.
One could expect a slightly enhanced shear capacity due to additional longitudinal
reinforcement, and a slightly stiffer load-displacement response. Beam DB180 is also
similar to AT-1, with the added difference, however, of a concrete strength 25% greater
than that of AT-1. Beams BN100 and BH100 also represent scaled-width beams similar
to AT-1. These beams have similar reinforcement ratios as beam AT-1, but with
different concrete strengths.
While all these beams are similar to a scaled-width test of beam AT-1, they are not
identical. Various studies and approaches to reinforced concrete, including the simplified
Shear Behaviour of Large, Lightly-Reinforced Wide Beams
Concrete Beams and One-Way Slabs

82
MCFT, predict, however, that the shear strength varies approximately with the cubic root
of f’
c
and ρ
w
. Correcting the experimental shear stress of DB165 for the difference in ρ
w
,
for example, would reduce it by only approximately 100-(0.76/1.01)
1/3
= 9%. Correcting
the experimental shear stress of beam BH100 for the difference in concrete strength
would likewise reduce it by 100-(64/99)
1/3
= 13.5%. While perhaps DB165 represents
the beam closest to an exact scale-width test of beam AT-1, it is useful to employ a series
of tests as they can act as duplicate data points, enhancing the reliability of the analysis.
Furthermore, if beam width affects the failure shear stress to such an extent that the ACI
wide beam exemption is valid, it would be expected that the 572% difference in beam
width between AT-1 and the narrow beams would completely overshadow any effects
caused by differences in concrete strength and reinforcement ratio.
The failure shear stresses for beams DB165, DB180, BN100, BH100 and AT-1 are
plotted in Figure 3-16 as a function of the beam width. It can be clearly seen that the
beam width had almost no influence on the beam shear capacity per meter width. The
average failure shear stress for the beams at 300mm width is 0.67MPa, and the average
failure shear stress of the east and west sides of beam AT-1 is 0.68MPa. Beam AT-1,
therefore, with a width 6.72 times greater than the scaled-width beams failed at a shear
force, V
c
= v
exp
b
w
d that was 6.74 times greater than the average of the scale-width beams.
These values differ by only 3%. Comparing the initial shear failures of beams DB165
and AT-1 indicates that the failure shear stress decreased from 0.68MPa to 0.66MPa as
the beam width increased.
The failure crack surfaces are shown in Figure 3-17. It can be seen that the shape of the
crack is largely uniform across the beam width, suggesting that beam width does not have
an effect on the failure shear stress.
Because the beam width has no apparent effect on the failure shear stress, it seems
unwarranted to exempt wide beams from the minimum stirrup requirements that apply to
narrow beams, without regard for their effective depth or for their depth relative to an
integrally cast slab.
Shear Behaviour of Large, Lightly-Reinforced Wide Beams
Concrete Beams and One-Way Slabs

83

0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
0 500 1000 1500 2000 2500
Beam Width (mm)
Shear Strength (MPa)
AT-1
BN100
BH100
DB180
FInal Failure Shears shown in Open Symbols

db
V
w
DB165

Figure 3-16: Effect of Beam Width on the Failure Shear Stress



Figure 3-17: Failure Crack Surfaces -Beam AT-1

East Failure Crack West Failure Crack
Shear Behaviour of Large, Lightly-Reinforced Wide Beams
Concrete Beams and One-Way Slabs

84
3.4.2 The Effect of Beam Depth
The ultimate reason that the wide beam exemption as implemented by the ACI code is
inappropriate is because the ACI expression for V
c
does not account for the size effect in
shear. The ACI code allows the use of thick beams whose entire shear resistance can be
provided by the concrete in the absence of stirrups, while the design expressions for V
c

overestimate the concrete contribution at large effective depths.
The inability of the ACI code to account for the size effect is illustrated in Figure 3-18
using data from other tests of shear critical beams. These tests consist of beams BH25,
BH50 (Podgorniak-Stanik (1998)) and YB2000/0 (Yoshida (1999)) summarized in Table
3-3, as well as two data points consisting of beams L-10H and S-10H described in
Chapter 5. All of these beams were tested with similar a/d ratios (2.89-3.0) and similar
reinforcement ratios (0.74-0.89%). Concrete strengths varied from 64MPa to 99MPa for
all beams except the deepest beam, which had a concrete strength of 34MPa. Like the
beam width analysis described above, these beams do not represent exact duplicate
beams scaled in depth. Nevertheless, they are reasonably similar to one another so as to
facilitate a comparison based on effective depth. All beams other than the largest have
the added advantage of (f’
c
)
1/2
values of about, or limited to, 8.3MPa, which is the same
as the Bahen alternate beam. In addition, the fact that the ACI limit on (f’
c
)
1/2
applies
means that the effect of concrete strength is filtered out of the ACI predicted shear
strengths. Also, the average ρ
w
value for all of the beams is 0.97%, which is only 4%
higher than the reinforcement ratio for the Bahen alternate beam of 0.93%.
The ACI Eq. 11-5 shear strength predictions are shown in Figure 3-18, along with
predictions generated by the 1994 CSA simplified equation (Eq. 11-7 in the 1994 CSA
code), Eq. 2-32 and the simplified MCFT. The predictions shown in Figure 3-18 were
generated based on (f’
c
)
1/2
= 8.3MPa, an a/d ratio of 2.95 and a ρ
w
=0.93%. Experimental
results are also summarized in Table 3-5, and predicted failure shears based on the actual
ρ
w
, a/d and concrete strengths for each beam are also presented in the table.
Shear Behaviour of Large, Lightly-Reinforced Wide Beams
Concrete Beams and One-Way Slabs

85
Table 3-5: Experimental vs. Predicted Shear Capacities –Size Effect Series
d a/d
ρ
w

c
a
本敦f
s

v
灲敤
v
數p

灲敤
v
灲敤
v
數p

灲敤
v
灲敤
v
數e

灲敤
v
灲敤
v
數e

灲敤
v
灲敤
v
數p

灲敤
(mm) ⡭m) ⠥) (䵐愩 (mm) (mm) (䵐愩 (Mμ愩 (䵐愩 (䵐愩 (䵐愩 (䵐愩 (Mμ愩
䉈㈵ ㈲2 2.㤲 〮㠹 㤹 0 㐴4 1.㈶ ㄮ㌹ 〮㤱 ㄮ㘶 〮㜶 ㄮ㈰ 1.〶 ㄮ㈶ ㄮ㌹ 〮01 ㄮ㄰ ㄮㄵ
匭㄰1
㈸2 2.㠹 〮㠳 㜷 0
㔵5 1.ㄱ ㄮ㌹ 〮㠰 ㄮ㐷 〮㜶 ㄮㄱ 1.〰 ㄮ㄰ ㄮ㌹ 〮09 ㄮ〳 ㄮ〷
䉈㔰
㐵4 2.㤲 〮㠱 㤹 0
㠸8 0.㤹 ㄮ㌹ 〮㜱 ㄮ㐹 〮㘶 〮㤲 1.〸 〮㤸 ㄮ㌸ 〮00 〮㤰 ㄮ〹
䅔-1
㤱9 2.㤵 〮㜶 㘴 ㌮3
ㄴ㔷 0.㘶 ㄮ㌴ 〮㐹 〮㤱 〮㜳 〮㘸 0.㤷 〮㘴 ㄮ㌲ 〮08 〮㜴 〮㠶
䰭㄰1
ㄴ〰 2.㠹 〮㠳 㜴 0
㈷㔶 0.㘰 ㄮ㌹ 〮㐳 〮㜸 〮㜷 〮㐶 1.㌱ 〮㔷 ㄮ㌹ 〮01 〮㔷 ㄮ〰
YB㈰〰⼰
ㄸ㤰 2.㠶 〮㜴 ㌴ 㤮9
㈳㌵ 0.㐹 〮㤷 〮㔱 〮㐴 ㄮㄳ 〮㌶ 1.㌶ 〮㐵 〮㤹 〮06 〮㐶 〮㤸
乯te猺
(1⤠)alc畬慴敤⁡u⁤⁦r潭⁳=灰潲p 䍯Cffici敮琠ef⁖慲楡瑩潮= ㈷2 ㄹ1 ㄳ1 ㌰3 㤥
(2⤠)alc畬慴敤⁡u⁤⁦r潭潡o
1.ㄳ 〮03 ㄮ〲Ov敲慬e⁁癥=慧攺 〮㘴 〮㠰
Properties
Specimen
v
exp
(1)
ACI (11-3) 1994 CSA Simp Eq. (2-23) ACI (11-5) SMCFT
v
exp
(2)

0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
0 500 1000 1500 2000 2500
Beam Depth (mm)
Shear Strength (MPa)
ACI
(Eq. 11-5)

db
V
w

'
c
ew
c
f
s1000
208
db
V
+
=
AT-1
Experiment
Bahen Alternate Beam
d=1700mm
AT-1 ACI
Prediction
ACI Bahen Alternate
Beam Prediction
(based on a/d=3.58)
SMCFT
Data points
ρ
w
= 0.76-1.01%
f'
c
= 64-99MPa

34MPa)(f
'
c
=
8.3MPaf
'
c
=
, a/d = 2.95, ρ
w
= 0.93%
Predictions
based on:
1994 CSA Simplified
f'
c
>64MPa

Figure 3-18: Effect of Beam Depth on Failure Shear Stress of High-Strength Beams
Shear Behaviour of Large, Lightly-Reinforced Wide Beams
Concrete Beams and One-Way Slabs

86
It can be seen that the ACI code is unconservative for all six of the tests summarized in
the above figure, and becomes more unconservative as the effective depth increases. The
average value of v
exp
/v
pred
for the ACI Equation (11-5) is 0.63, with a coefficient of
variation of 30%. The average value of v
exp
/v
pred
for the more commonly used ACI Eq.
11-3 is 0.64, with a coefficient of variation of 27%.
It is also instructive to compare the experimental shears to the shear predicted by the
1994 CSA simplified method (Equation (2-29) in Chapter 2). It can be seen that the
shape of the size effect term in the 1994 CSA method, (217/(1000+d)), generally
accounts for the behaviour of the experimental results with respect to depth, but the
method consistently overestimates the shear strength of the high-strength concrete beams.
The average value of v
exp
/v
pred
for all the beams other than YB2000/0 was 0.74, with a
coefficient of variation of just 5%. It is instructive to note that the 1994 CSA code
conservatively predicts the shear strength of YB2000/0, which was constructed with
normal strength concrete. Thus, it appears that the 1994 CSA simplified method is
unconservative for high-strength concrete.
In this regard, the development of Equation (2-23) represents a clear improvement. The
average v
exp
/v
pred
for this equation is 1.13, with a coefficient of variation of 13%. The
equation is better able to predict the shear strength of the high-strength specimens
because it is formulated in terms of the effective crack spacing, s
xe
, in which the effective
aggregate size in high-strength concrete is set to 0, and in which the concrete strength is
limited to 69MPa.
Finally, comparison of the predictions of the simplified MCFT with the experimental
results reveal that this method has an average v
exp
/v
pred
ratio of very close to 1.0, and the
lowest coefficient of variation. At 0.86, however, the ratio of v
exp
/v
pred
for beam AT-1 is
low. Nevertheless, the simplified MCFT does the best of all the methods at predicting
the failure shear stresses of the beams summarized above. Lubell (2006) offers an
explanation for the lower v
exp
/v
pred
value for AT-1 based on the use of supports narrower
than the beam width.
Shear Behaviour of Large, Lightly-Reinforced Wide Beams
Concrete Beams and One-Way Slabs

87
3.4.3 Comparison with Bahen Centre Transfer Beams
In Section 3.1, a comparison was made between the 1994 CSA and the ACI predictions
for the failure shear stress of the Bahen alternate beam. It was shown that the ACI code
predicted that the failure shear stress was greater than that predicted by the 1994 CSA
code, the code used to design the Bahen Centre, by a factor of two. It was noted that this
represents a clear conflict between two prominent concrete design codes, and this lead to
the test of beam AT-1. With the benefit of the experimental results from beam AT-1 and
other beams, it becomes possible to address the conflict between the two codes, and to
answer the very simple question, “Which code method, the ACI method, or the 1994
CSA simplified method, provides an accurate prediction of the shear strength of the
Bahen alternate beam?” The answer to the question is that neither method is adequate at
predicting the shear strength of the alternate beam, although the 1994 CSA simplified
method is significantly more accurate than the ACI code. The most accurate method, of
those considered, is the SMCFT.
It would have been preferable to test an exact 1:1 replica of the Bahen alternate beam.
However, it would have been far too large to fit into the largest test frame at the
University of Toronto, not to mention the fact that it would greatly exceed its load
capacity. Thus, a similar but smaller beam, specimen AT-1, was constructed and tested.
As the SMCFT prediction appears to best match the experimental results over the entire
range of effective depths, let us assume that, had an exact replica of the alternate beam
been tested, the value of v
exp
/v
pred
for the SMCFT would be 1.0. This allows for the
calculation of predicted experimental shears as summarized in Table 3-6.
Table 3-6: Predicted Shear Capacities –Bahen Alternate Beam
d a/d
ρ
w

c
a
本敦f
s

v
灲敤
v
數p
v
灲敤
v
數p
v
灲敤
v
數p
v
灲敤
v
數p
v
灲敤
v
數p
⡭m) ⡭m) ⠥( (䵐愩 ⡭m) ⡭m) ⡍μa) (Mμ愩
v
灲敤
⡍μa)
v
灲敤
⡍(a)
v
灲敤
⡍μa) (Mμ愩
v
灲敤
⡍(a)
v
灲敤
䉡桥渠䅬琮=䉥慭 ㄷ〰 ㌮㔳 〮㤳 㜰 0 ㌳㐷 〮㔹 ㄮ㌹ 〮㐲 〮㜰 〮㠳 〮㐰 ㄮ㐷 〮㐹 ㄮ㌷ 〮㌶ 〮㐹 ㄮ〰
乯Nes:
⠱⤠䍡汣畬慴敤⁡琠搠fr潭⁳異灯牴
⠲⤠䍡汣畬慴敤⁡琠搠fr潭潡=
SMCFT1994 CSA Simp Eq. (2-23)
v
exp
(2)
ACI (11-5)
Specimen
Properties
v
exp
(1)
ACI (11-3)

Shear Behaviour of Large, Lightly-Reinforced Wide Beams
Concrete Beams and One-Way Slabs

88
Because the 1994 CSA simplified method does not accurately account for the effect of
high-strength concrete, the expected v
exp
/v
pred
for the alternate beam would be about 0.83.
This is somewhat low. However, because the 1994 CSA simplified method prediction is
only 50% of the ACI prediction, it still predicts that the specific case of the Bahen
alternate beam is dangerously unconservative. Because it is formulated in terms of the
effective crack spacing, Equation (2-23) provides a conservative prediction of the Bahen
alternate beam.
As shown in Figure 3-18, the ACI method is systematically unconservative when
calculating the shear strength of large beams without stirrups. The results summarized in
Table 3-6, in fact, suggest that the Bahen alternate beam would fail at a shear stress of
only about 42% of the failure shear stress predicted by the commonly used Eq. 11-3 of
the ACI code. This is unacceptably and dangerously low.
3.5 Concluding Remarks –Beam AT-1
The test described in this chapter, and the comparison of its shear strength to similar
beams scaled in width, have shown that beam width has no appreciable effect on the one-
way shear stress capacity. The test has also shown that had a structure such as the Bahen
Centre been designed using the ACI code, it is possible that a large transfer beam could
have been constructed that would have been at risk of collapse at a load of less than half
of that predicted by the shear provisions of the ACI code.
The test has also shown that longitudinal strains in the steel can vary across the width of a
wide beam, if that beam is supported and loaded through plates that are significantly
narrower than its width. The test has also shown that in thick beams constructed with
high-strength concrete, there is a possibility of a secondary strut forming after the initial
breakdown in load. This strut may be sufficiently strong enough to allow failure to occur
on the opposite side of the member. This behaviour was also observed in another beam
tested as part of the experimental program described later in this thesis (specimen L-10H),
and more discussion will be presented on this topic in Chapter 5.
Shear Behaviour of Large, Lightly-Reinforced Wide Beams
Concrete Beams and One-Way Slabs

89
Clearly the wide beam exemption as written in the ACI code is inappropriate. It is
recommended (Lubell et. al. (2004)) that clause 11.5.6.1 c) of the 2005 ACI code be
deleted and replaced with the following, which will return the ACI provisions to the
intention of the original writers of the exemption, who meant for it to apply only to
shallow beams:
“(c) Beams with total depth not greater than 10 in. (250mm); and
(d) Beams cast integrally with slabs, where the overall depth is not greater than ½ the
width of the web, nor 24 in. (600mm).”
A simple modification to the above is suggested. To enhance the likelihood of load
sharing between structural elements, it is recommended that exemption (d) be modified
as follows:
(d) Beams cast integrally with slabs, where the overall depth is not greater than ½ the
width of the web, nor 24 in. (600mm), and where the slab thickness is at least 40% the
overall depth of the beam.
This modification will ensure that a 600mm deep beam cast with a particularly shallow
slab will be constructed with stirrups.
Partly as a result of the test described in this Chapter, ACI 318 Committee has chosen to
eliminate the wide beam exemption from the 2008 edition of the code. While this change
addresses the immediate design situation of transfer beams such as those in the Bahen
Centre, it is interesting to note that other types of one-way reinforced concrete elements
will still be excluded from minimum reinforcement requirements until v
u
=φv
c
rather than
0.5φv
c
. These are slabs and footings, as specified in clause 11.5.6.1 (a). Yet, since slabs
are typically designed on a per meter width basis, it seems likely that they would be just
as susceptible as beams to the size effect. The intention of the next Chapter is to address
the further issue of one-way shear in slabs.