an investigation of the block shear strength of coped ... · of the potential modes for the failure...
TRANSCRIPT
An investigation of the block shear strength of coped beams with a welded
clip angles connection – Part I: Experimental study
Michael C. H. Yama*, Y. C. Zhongb, Angus C. C. Lamb, V. P. Iub
aDepartment of Building and Real Estate, The Hong Kong Polytechnic University, Hung Hom, Kowloon,
Hong Kong, China
bDepartment of Civil and Environmental Engineering, University of Macau, Macau, China
Abstract
The ends of a coped beam are commonly connected to the web of a girder by double
clip angles. The clip angles may either be bolted or welded to the web of the beam. One
of the potential modes for the failure of the clip angles connection is the block shear of
the beam web material. To investigate the strength and the behavior of the block shear
of coped beams with welded end connections, ten full-scale coped beam tests were
conducted. The test parameters included the aspect ratio of the clip angles, the web
shear and tension area around the clip angles, the web thickness, beam section depth,
cope length, and connection position. The test results indicated that the specimens
failed, developing either tension fractures of the web near the bottom of the clip angles
or local web buckling near the end of the cope. Although the final failure mode of the
six specimens was local web buckling, it was observed during the tests that these
specimens exhibited a significant deformation of the block shear type prior to reaching
their final failure mode. No shear fracture was observed in all of the tests. A
comparison between the ultimate loads in the test and the predictions using the current
design equations indicates that the current design standards such as the AISC-LRFD,
CSA-S16-01, Eurocode 3, BS5950-1:2000, AIJ and GB50017, are inconsistent in
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predicting the block shear strength of coped beams with welded end connections. The
analytical study of the strength of the test specimens using the finite element method, a
parametric study, and a proposed design model for designing block shears for coped
beams with welded clip angles are included in a companion paper.
Keywords: Block shear tests, Coped beams, Welded clip angles, Tension fracture, Local web
buckling
*Corresponding author: Tel. (852) 27664380; fax: (852) 27645131 Email address: [email protected] (Michael C. H. Yam)
1. Introduction
In steel construction, beams are often coped (cut away) at the flanges to provide
clearance for the framing beams or to maintain the same elevation for intersecting
beams. The cope can be at the top (Fig. 1), the bottom, or both flanges near the
connection in order to facilitate construction. The ends of the coped beam are
commonly connected to the web of the girder by double clip angles. The clip angles
may be either bolted or welded to the web of the coped beam. One of the potential
modes of the failure of the coped beam with a clip angles connection is the block shear
of the beam web material.
Block shear is a phenomenon of rupturing or tearing, where a block of material is
torn out by a combination of tensile and shear failure (Birkemoe and Gilmor [1]).
Figure 2 shows the potential block shear failure mode in a coped beam at the shear
connection. The web block can be partially or entirely torn out from the remaining part
of the beam. Block shear is usually associated with bolted details, because a reduced
area is present in such cases. However, block shear may also be a potential failure
mode in welded connections depending on the details of the connection. The block
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shear failure mode appears in different types of bolted structural members such as
gusset plates, coped beams, angles, or tee-sections (Hardash and Bjorhovde [2]; Epstein
[3]; Epstein and Stamberg [4], Epstein and McGinnis [5], Franchuk et al. [6], Orbison
et al. [7], etc.).
The block shear failure mode of coped beams was first identified by Birkemoe and
Gilmor [1]. In their tests, the coped beam failed by the tearing of the web as a block of
material at the shear connection. The authors suggested that the failure model of block
shear was provided by a combination of tensile and shear stresses acting over their
respective areas (across plane AA and plane BB, respectively) as shown in Fig. 3. Yura
et al. [8] conducted a series of twelve coped and uncoped beam tests with bolted double
clip angle connections. Among eight coped beam tests, three exhibited failure of the
block shear type. The specimens with two lines of bolts had a lower capacity than
desired. A further investigation by Ricles and Yura [9] was carried out to examine the
block shear failure mode of coped beams for bolted connections. The test parameters
included the end and edge distance, bolt arrangement, and the type of holes. All seven
coped beam specimens failed in the block shear mode and the web buckled at the cope
in four of them. Based on the test and the finite element analysis results, the authors
suggested assuming shear yielding for the vertical side of the web and tensile fracture
for the horizontal side (perpendicular to the applied reaction force at the coped end) in
evaluating the block shear strength of the connection. It was further noted that the shear
yielding that occurred along the gross vertical area of the web was based on the
experimental observation. This implied that the connection capacity was the sum of a
triangular normal stress on the net area of the tension face and shear yielding on the
gross shear area as shown in Fig. 4. The proposed capacity equation is as follows:
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0.5 0.6= +u nt y gvP F A F A (1)
where:
P is the ultimate connection capacity;
Fu is the tensile strength;
Fy is the yield strength;
Ant is the net tension area, and
Agv is the gross shear area.
Aalberg and Larsen [10] examined the behavior of coped I-beams with bolted end
connections fabricated from high-strength steel and normal structural steel. Identical
failure modes were observed for both normal and high-strength steels except that the
connection ductility was reduced for the high-strength steel specimens. A
comprehensive review of block shear issues was conducted by Kulak and Grondin [11],
[12]. They revisited the block shear failure mode in different cases of coped beams,
gusset plates, and angles. The review showed that the failure modes were significantly
different in two important categories, namely: gusset plates and the web of coped
beams. Taylor [13] discussed the issue of the lack of experimental data for the block
shear strength of coped beams with welded connections. Most recently, Franchuk et al.
[6], [14] conducted an extensive experimental program consisting of seventeen tests to
investigate the block shear behavior of coped beams with bolted connections. The test
results indicated that magnitudes of tension and shear areas significantly affect
connection capacity. The test results also substantiated the previous experimental
observation that shear yielding on the gross (vertical) area should be used in the block
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shear design of coped beams. The latest research was performed by Topkaya [15]. A
finite element parametric study on the block shear failure of steel tension members was
carried out to develop a block shear capacity prediction equation. The parametric study
was conducted to identify the important parameters, such as ultimate-to-yield ratio,
connection length, and boundary conditions.
Based on the above discussion, it can be seen that all of the available experimental
and analytical studies on the block shear of coped beams concentrated on bolted end
connections. Therefore, the main objective of this study is to provide experimental data
for the block shear strength and behavior of coped beams with welded clip angle
connections. The evaluation of the ultimate strength of the test specimens using current
design codes (AISC-LRFD [16], CSA-S16-01 [17], Eurcode 3 ENV 1993-1-1 [18],
BS5950-1:2000[19], AIJ [20] and GB50017 [21]) will also be presented.
2. Experimental program
2.1 Test Specimens
The purpose of the experimental program was to examine the block shear failure
strength and behavior of a coped beam web with a welded clip angles connection. A
total of ten full-scale tests were conducted in the experimental program. The test
parameters included connection geometry and cope details such as the aspect ratio of
the clip angles, the tension and shear area of the web block, web thickness, beam
section depth, cope length, and connection position. The test was conducted
individually at each end of the 3.3 m long test beam. The schematics and details of the
specimens are shown in Figs. 5, 6, and 7. These five test beams were fabricated from
three different section sizes, including universal beam UB406x140x46, UB457x191x74,
and UB356x171x67 (SCI [22]). Grade 43 steel conforming to BS 4360 [23] was used
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for the beams. All of the double clip angles were fabricated by 16 mm steel plates
conforming to BS 4360 [23] Grade 50 to provide the required connection dimensions.
The angles were designed to provide enough strength for the connections and, at the
same time, to minimize the in-plane rotational stiffness in order to simulate a simply
supported boundary condition. The double angles were welded to the web of the beams.
The nominal and measured dimensions of the beam sections and the connection
details are shown in Table 1 and Table 2, respectively. These tables should be read in
conjunction with Fig. 5. The test beams were each designated by a letter (A through E),
and each end connection was designated by a number, 1 or 2, respectively. Each
specimen was also designated according to the beam type, and the testing variable was
assigned to facilitate the identification. For example, A1-406r3 represents beam A,
connection 1, and UB406x140x46 section with an aspect ratio of around 3. Figure 6
illustrates the typical overall design dimensions of the coped beam specimens and the
clip angles, and Fig. 7 presents the connection details of all of the specimens.
As summarized in Table 3, the test parameters included the aspect ratio of the clip
angles, the tension and shear area of the web block, web thickness, beam section depth,
cope length, and connection position. Only one parameter was varied in each group of
tests. The specimens with various configurations were carefully designed to fail in the
block shear mode by the current design practice. Note that for the aspect ratio series,
the design capacities of the related tests were nearly identical for the purpose of
comparison. The top flange was coped for all specimens. In general, the cope
dimensions were fixed, with the cope depth extending 30 mm below the top flange and
the cope length extending 50 mm away from the end of the clip angles except for the
specimens that were employed to study the effect of cope length.
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In order to obtain the material properties, tension coupon tests were carried out.
Tension coupons were prepared from the web and the flange of the test beams and then
tested according to the ASTM A370 standard [24]. An extensometer with a 50 mm
gauge length was used to measure the strain in the coupon and the load was obtained as
a read-out of the testing machine. Pairs of strain gauges were mounted on both faces of
the coupons in order to determine the modulus of elasticity (E) of the steel in the elastic
range. The static readings were taken on the yield plateau, along the strain hardening
curve, and near the ultimate tensile strength.
2.2 Test setup, instrumentation, and test procedures
The test setup is shown schematically in Fig. 8. The beam specimen with welded
clip angle connections was installed to the column by 24 mm diameter bolts. Washers
were also placed between the outstanding leg of the angles and the supporting column
in all tests to minimize the end rotational stiffness. The bolts were then tightened to a
snug-tight condition. Load was applied to the beam vertically by a 890 kN hydraulic
cylinder. The load position was chosen to produce block shear failure in the connection
and to avoid either shear or bending failure of the test beam. The chosen load position
also has little effect on the stress distribution in the coped region. The distance, L, from
the load position to the reaction end was 510 mm (1.3D), 600 mm (1.3D), and 550mm
(1.5D) for the test beams Beam406, Beam457, and Beam356, respectively, as
illustrated in Fig. 8.
Roller assemblies were used at the load position and the support so that both
rotation and longitudinal movements were allowed. Lateral bracings were provided at
the load position and the support to prevent lateral movements of the test beam.
Additional lateral bracings were provided at the top flange of the beam near the cope
end to improve the lateral stability of the connection. Stiffeners were welded on both
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sides of the web at the load position in order to avoid local web crippling. Load cells
were used to record the applied load and the support reaction.
Linear variable differential transformers (LVDT) were employed to measure the
displacements. The locations of the LVDTs are typically shown in Fig. 9. To measure
the main features, LVDTs were placed separately at the bottom of the beam underneath
the load point, and at the top and the bottom of the beam at the connection. The
displacement of the clip angle at the column was also recorded. The overall deflection
was determined by taking the difference between the displacement under the applied
load and the displacement of the clip angles, which excluded the displacements due to
bolt bearing and slippage. In addition, the deformation between the vertical
displacements measured from below and above the connection provided a good
indication of the significant tensile yielding or sudden fracture of the beam web.
Another LVDT was set at the top flange near the loading position to detect lateral
movements. The rotation of the angles and the tested beam end were also recorded by
LVDTs. In addition, an inclinometer was mounted on the web at the centroid of coped
section to monitor end rotation. Longitudinal strain gauges and rosettes were
extensively mounted around the connection to measure the strain distribution at the
critical area, as shown in Fig. 10. More details regarding the instrumentation can be
found in Zhong et al. (2004). All readings were collected by a data acquisition system.
Before the test, the specimen was whitewashed to make it possible to detect the
yielding process, and 50 mm square grid lines were drawn to show the web
deformations.
In general, the test procedures were similar for all of the specimens. The loading
process was divided into two stages: load control in the beginning and stroke control
when nonlinear behavior commenced. Load was applied incrementally and a smaller
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load increment was used to capture the nonlinear behavior in the inelastic stage of the
tests. During the test, it was necessary to hold the loading at regular intervals for static
equilibrium so that the specimens could redistribute the stress and deform completely,
therefore making it possible to obtain the reading on static load. Readings of load cells,
strain gauges, and LVDTs were taken continually during the loading process. The
yielding pattern and process were recorded in detail. The test was terminated when the
maximum load was reached and the load decreased significantly. After the test on one
end was completed, the other end of the beam was installed to the column, and a new
test was then conducted.
3. Test results
3.1 Material test results
The tension coupon test results for all specimens are summarized in Table 4, and
the results for clip angles are included as well. Since the block shear failure was mostly
associated with the beam web, the mean values of the coupons from the web of test
beams were used as the basic material properties for the specimens. The average static
yield strength for the specimens ranged from 304.1 MPa to 371.6 MPa, whereas the
average static ultimate strength ranged from 442.2 MPa to 487.7 MPa. Although Grade
50 steel was assumed in the design of the clip angles, it was believed that Grade 43
steel was used instead for the clip angles based on the tension coupon test results as
illustrated in Table 4. The material properties for S275 and S335 (EN10025 -2:2004)
are also included in the table for comparison purpose.
3.2 General
The test results are summarized in Table 5, where the static values of the ultimate
load are reported, and the connection reactions and moments were calculated from
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static equilibrium. For simplicity, only the letter and the first number in the specimen
designation were used to identify the specimens (for example, specimen A1 instead of
specimen A1-406r3). The moment developed in the connection was found to be small
compared with the yield moment of the beam. In general, there were two kinds of
failure modes in the tests: the block shear of the beam web with tension fractures
underneath the clip angles and local web buckling near the end of the cope. Two
specimens failed in the block shear mode while six specimens ultimately failed in local
web buckling near the cope due to combined shear and bending. Although the final
failure mode of the six specimens was web local buckling, it was observed during the
tests that these specimens exhibited a significant block shear type deformation prior to
reaching their final failure mode. In the block shear cases, necking of the tension area
in the web underneath the clip angles was observed before the web fractured abruptly.
The reduction in web thickness in the tension region is also included in Table 5. A
tensile crack developed in the web along the bottom of the welded clip angles rather
than a complete web block tear-out. No signs of shear fracture along the vertical plane
were observed. As to the remaining two specimens, the test loads exceeded the capacity
of the testing frame; hence, these two tests were terminated at the safe load of the test
setup.
The photographs of typical failed specimens at the ultimate stage are shown in Fig.
11. Figure 12 contains an illustration of typical local web buckling failure near the cope
end. In general, a similar yielding pattern was observed for the specimens. Yield lines
were usually initiated in the web either underneath the welded clip angles at the
extreme beam end or near the cope end. Eventually, the yield lines extended through
the web block and could be obviously observed below the welded clip angle and across
the cope end. These yield lines indicated that significant deformation had occurred in
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these regions. Yield lines could also be found in the shear area near the welded clip
angles in most cases.
The results showed that the web plate buckled to various extents at the cope end
even though the flange near the cope was braced against lateral movement. Severe
compression and shear yielding was observed near the cope end before the specimens
reached the ultimate loads. This indicated that local web buckling was also a potential
failure mode for coped beams with welded clip angle connections. This failure mode
was also observed by Ricles and Yura [9] in their coped beam tests. They pointed out
that the high horizontal compressive stresses in the web could cause the web to buckle
at the cope.
3.3 Load deflection behavior
A typical applied load versus deflection curves are shown in Fig. 13. Plotted on the
horizontal axis is the net deflection at the load point, which was determined by taking
the difference between the displacement under the applied load and the displacement of
the clip angles; hence, this net deflection excluded the displacements due to bolt
bearing and slippage. Thus, the overall behavior of the test beams can be presented.
Generally, similar behavior was observed of the specimens with regard to the two kinds
of failure modes. As the load was applied, yielding first appeared in the web
underneath the welded clip angles or near the cope end. Nonlinear behavior then
commenced. When the load continued to increase, shear yielding developed gradually
along the vertical area near the welded angles. High flexural stresses in the upper
region of the web increased and excessive deformation developed. The web block
deformed significantly before the web plate near the cope end became distorted or
buckled inelastically. Subsequently, for specimens C2 and E1, tension fractures
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developed abruptly underneath the clip angles, and the load therefore decreased
significantly. Continued loading caused further opening of the cracks. As to specimens
A1, A2, B1, B2, D1, and E2, at the ultimate load level severe compression as well as
shearing caused local web buckling at the cope end, and the load subsequently
descended.
3.4 Strain distribution
Strain distributions are presented in the critical area along the web block as
indicated by the locations of strain gauges and rosettes shown in the insets of Figs. 14
and 15. The strain distributions are plotted within the elastic stage, against the same
load levels of 70 kN and 183 kN. Only the strain distributions for specimen E1 are
presented since there is no significant difference in the strain distributions of other
specimens. The vertical longitudinal strain distribution along the horizontal plane
underneath the welded clip angles (the tension area) for specimen E1 is plotted in Fig.
14. As expected, the strain was largest at the beam end and decreased along the length
of the tension area. An almost linear strain distribution was found within the elastic
range. This kind of distribution reflected the load eccentricity on the connection that
caused the rotation of the web block. The line of action of the vertical reaction force at
the beam end was outside the centroid of the web block and consequently induced this
eccentricity. However, at same load level, the positions of the neutral axis for the
longitudinal strains were close to each other for specimens with the same beam sizes.
For the cases with a large area of tension, the longitudinal strains beneath the corner of
the clip angle indicated slight compression at the beginning of loading. It was believed
that the compressive strain would shift to tension as the load increased.
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Vertical shear strain distributions along the vertical plane near the welded clip
angles (the shear area) are also examined. Typically, the result for specimen E1 is
shown in Fig. 15, in which the dash line indicates the shape of the clip angle. It can be
seen from the figure that the shear stress distribution determined by three rosettes was
uneven. It differed from the shear distribution calculated by the shear formula for the
reduced beam section. The stress concentration around the top and the bottom corners
of the clip angle was believed to have some influence on the reading on strains
measured at these positions. In general, the shear strain distributions of the other
specimens were similar. Since the number of rosettes in the shear area was limited, the
shear strain profile obtained might not represent the entire shear strain distribution in
this area for the test specimen. Nevertheless, the shear strain values measured at the
critical locations provide the data for the calibration of the finite element model. It will
be seen that the measured shear strains are consistent with the numerical ones. The
calibration and discussion of the stress/strain distribution of the finite element model of
the test specimens can be found Yam et al. [25] and Zhong [26].
The local bending effect around the web block was caused by the connection
rotation. The distribution of flexural strains in the shear area can be illustrated by the
longitudinal strains in the horizontal direction (marked with No. 7, 10, and 13 in the
inset of Fig. 16). The distribution features are similar among all specimens. Take for
example specimen E1 as shown in Fig. 16. High flexural compressive strains
developed in the beam web near the cope, while tensile strains developed near the
bottom of the clip angle. It was believed that the high compression as well as the
shearing that developed in the compression region would cause early yielding of the
web plate; and that, consequently, at a high load significant yielding would induce
inelastic web buckling at the cope end.
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4. Discussion of the test results
4.1 Failure mode
Previous studies focused on the block shear failure of coped beam web with bolted
connections. For bolted end connections, a reduction in the cross-sectional area due to
the presence of holes has adverse effects on the strength of the connections. The
concentration of stress at the bolt holes initiated fracturing, and contributed to the block
shear failure mode. For welded end connections, since there is no reduction in gross
section area due to bolt holes, the behavior and failure mode of the connection would
be different.
As described before, two kinds of failure modes were observed in the tests, namely;
block shear failure and local web buckling at the cope end. Block shear failure was
exhibited in a partial tear-out of the web block with a tension fracture underneath the
clip angles. The tension fracture was triggered at the extreme end of the beam web, and
necking of the web plate was observed before a sudden rupture. Shear yielding rather
than shear fracture was observed along the vertical plane of the shear area. Shear
ultimate strength was difficult to achieve since the shear deformation was relatively
small compared with the tension deformation. Hence, tension fracture was reached
prior to shear fracture due to the significant deformation in the area of tension. Another
potential failure mode was local web buckling near the end of the cope. High
compressive stresses and shear stresses were localized in the web near the cope because
of the combination of bending and shear in the reduced section; hence resulting in
extensive yielding and consequently inducing local web buckling in that region.
As mentioned before, lateral bracing at the top flange near the cope was provided to
improve the lateral stability of the test beams. However, various degrees of web
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buckling were still observed in most cases, and six specimens among them ultimately
failed in the local web buckling mode. In fact, in previous studies, such as those by
Birkemoe and Gilmor [1] and Ricles and Yura [9], local web buckling was also
observed in cope beam tests for block shear with bolted connections. For those
specimens that failed due to local web buckling, excessive deformation developed
around the web block at a high load due to significant yielding in the tension and shear
areas. However, the deformation was insufficient to induce fracturing even though the
ultimate tensile stress was attained in the area of tension. On the other hand, severe
compression and shear yielding accumulated near the cope end, thus eventually
resulting in local web buckling. Nevertheless, observations showed that these
specimens exhibited a deformation of the block shear type prior to reaching their
ultimate loads with local web buckling failure.
4.2 Effect of aspect ratio
Aspect ratio has been defined as the ratio of vertical shear area (b’) to the horizontal
tension area (a) of the web block, as indicated in Fig. 5. Note that the design capacities
of the related specimens are nearly identical for the purpose of comparison. The aspect
ratio was examined in two series of tests. In the first series, specimens A1, A2, and B2
had an aspect ratio of 3.6, 2.3, and 1.4, respectively. Their final failure mode was local
web buckling, as shown in Table 5. For specimens A2 and B2, the aspect ratio varied
from 2.3 to 1.4 while the capacity of A2 was 12% higher than that of B2. Although
specimen A1 had the largest aspect ratio, it was worth noting that the double clip angles
used in this specimen was different from those of the other specimens due to a
fabrication error. This had an adverse effect on the capacity of the specimen. Since the
bolted leg of the clip angle was fabricated shorter for the arrangement of the bolts, the
boundary condition of the pin support that was simulated by the clip angle was
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influenced to some extent. This meant that the position of the pin support for the beam
specimen was therefore lowered, while the rotational stiffness of the joint was reduced.
Since the negative moment that developed in the connection at the beam end was due
to a slight fixity in connection, the negative moment of A1 in the connection was
smaller than that of A2 and B2, as shown in Table 5. Hence, it was believed that the
reduction in the capacity of specimen A1, which failed because of the local web
buckling, was attributable to the influence of the clip angle. The results of the finite
element analyses that will be discussed in the companion paper (Yam et al. [25]) also
indicates that specimen A1 would have a larger capacity than specimen A2 by using
double clip angles similar to those of the others. For specimens C1 and D1 in the
second series, the aspect ratio was 3.8 and 1.6, respectively. Although the ultimate
failure of C1 did not occur before the test was terminated at the safe load of the test
setup, it was believed that C1 would have a much larger capacity than D1 from the
trend of the load deflection curve, which can be observed in Fig. 17.
In addition, further observations of the yield lines also led to an interpretation of the
effect of the aspect ratio on the deformation of the web. For specimen D1, many yield
lines were observed in the beam web near the bottom of the clip angle as shown in Fig.
11d. This might indicate that the web material in this region had been subjected to
excessive deformation caused by local bending due to the connection rotation. On the
other hand, for specimen C1, there were significantly fewer yield lines, as shown in Fig.
11b. Nevertheless, it can be seen that as the aspect ratio decreased, local bending of the
web near the clip angle due to the connection rotation was more significant. In fact, the
local bending would cause high compressive stress to the web material near the end of
the cope corner and hence might lead to a failure in the local buckling of the web. In
addition, the local bending also induced high tensile stress in the web near the bottom
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edge of the clip angle, which might initiate fractures of the web block similar to those
seen in specimens C2 and E1.
Based on the above discussion, it is believed that the block shear capacity of the
connection decreased as the aspect ratio decreased. As the aspect ratio decreased
(increase in a), the loading eccentricity between the welded clip angle and the support
(bolted end) at the column face increased, hence generating more local bending of the
web in the vicinity of the clip angle. Since the aspect ratio is associated with the ratio of
the shear area and the tension area, it is necessary to examine these two aspects
individually to reveal their relationship and the effect on the strength of the connection.
4.3 Effect of shear area and tension area
Specimens C1 and C2 were identical in all aspects except for the shear area. The
length of the shear area (b) of specimen C1 and C2 was 170 mm and 120 mm,
respectively. As shown in Fig. 18, the connection stiffness of C1 was higher than that
of C2. Specimen C2 failed due to block shear with tension fractures. However, the
strength of C1 exceeded the test setup capacity, so it was certainly larger than that of
C2. According to the test data, C1 was estimated to be at least 10% larger in capacity
than C2. As expected, the connection capacity was improved by increasing shear area.
For specimens C2 and D1, the length of the tension area (a) varied from 50 mm to
90 mm, while the shear area of the specimens was held at a constant value of 120 mm
in length. As shown in Table 5, the capacities of these two specimens were very close,
even though there was a significant difference in the tension area. Observed during
these two tests, the webs buckled similarly before their final failure. However,
specimen C2 eventually failed due to block shear with tension fractures, while
specimen D1 failed due to local web buckling. The yielding pattern of specimen D1
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showed that there was excessive deformation in the web around the clip angle caused
by significant connection rotation. The rotation was believed to have been produced by
the eccentricity of the reaction force on the web block, while the eccentricity was
associated with the area of tension. Hence, this indicated that increasing the area of
tension led to an increase in loading eccentricity and therefore generated more bending
stress to the edge of the beam web region near the clip angles and the cope end. This
increase in bending stress counteracted the increase in the connection strength due to
the additional area of tension and initiated either the earlier local web buckling in the
end of the cope or web tension fractures near the bottom of the clip angles. Therefore,
the capacity of specimen D1 did not increase considerably even though the area of
tension increased by 80%.
4.4 Effect of web thickness
Specimens B1, C2, and E1 were fabricated from three different beam sections with
identical connection dimensions. The nominal beam web thickness (tw) was 6.8 mm for
specimen B1, and 9.1 mm for specimens C2 and E1. As shown in Table 5, when the
web thickness of the specimens decreased the ultimate loads decreased; however, the
decrease was not directly proportional to the change in the thickness of the web. This is
illustrated in Fig. 19, where the original reaction versus web deformation curve of
specimen B1 was modified proportionally by multiplying a scale factor (9.1/6.8) to
account for the difference in thickness from the original one. It can be seen from this
figure that the modified ultimate load of specimen B1 (527 kN) was 14% less than that
of specimen E1 (601 kN), even though the two specimens had a similar ultimate tensile
strength (Fu). The figure also shows that the behavior of specimens C2 and E1, which
had the same web thickness, was nearly identical. For thin web specimen B1, its weak
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axis flexural stiffness was lower than that of the other two specimens and therefore
increased the susceptibility of the beam web to local buckling. Subsequently, like
specimens C2 and E1, B1 ultimately buckled rather than failed by block shear with
tension fractures.
4.5 Effect of Beam Section Depth
The effect of beam section depth can also be observed in Fig. 19. For specimens C2
and E1, the web thicknesses and the dimensions of the connections were identical while
the depth of the beam section varied from 457 mm to 363 mm. The results showed that
these two specimens had almost the same amount of connection ductility. Specimen C2,
with a section depth that was 26% deeper, only produced a 5% increase in capacity
regardless of the slight difference in the material tensile strength. In addition, the
failure modes (tension fractures) of these two specimens were similar, implying that
block shear capacity was not affected by section depth.
4.6 Effect of Cope Length
The cope length (c) varied from 150 mm to 80 mm for specimens D1 and D2,
respectively, and the other details for these two specimens were identical. Specimen D2
had the smallest cope length of all of the specimens, in which the uncoped top flange
extended close to the end of the beam and beyond the region of the shear path near the
welded clip angle. As shown in Fig. 20, it can be seen from the comparison of
specimens D1 and D2 that cope length had a significant effect on connection capacity.
Connection D2 was much stiffer than D1. The web plate did not buckle and only a
small deformation was observed in specimen D2 at the maximum load of the test frame.
Therefore, the capacity of D2 was certainly larger than that of D1. Hence, for the
specimen with a shorter cope length the connection was strengthened by the uncoped
20
top flange; the susceptibility to local web buckling near the cope end was therefore
reduced. In other words, increasing the cope length increased the possibility of
instability and therefore led to a decrease in the connection capacity.
4.7 Effect of Connection Position
For specimens E1 and E2, the connected position (p) of the welded clip angles
varied from 20 mm to 45 mm (the vertical distance from the clip angle to the top edge
of the beam web as shown in Fig. 5) while other details were identical. Similar load
deflection behavior and a slight difference in capacity were observed between these
two cases. The capacity of E2 was 3% less than that of E1, even if the vertical shear
path (b’) of E2 was longer. In addition, E2 ultimately failed in local web buckling
mode rather than in the block shear with tension fractures as E1 did. This may indicate
that the final failure mode of the specimen was affected by the connected position of
the welded clip angles. Since high compressive and shear stresses developed in the
beam web between the top of the clip angle and the cope end, it was believed that a
local web buckling failure would likely occur in the case where the clip angles was
placed at a lower position.
5. Comparison of Test Results with Current Design Methods
5.1 General
The block shear design equations prescribed by the current standards of CSA-S16-
01 [17], AISC LRFD [16], Eurocode 3 ENV 1993-1-1 [18], BS 5950-1:2000 [19], AIJ
[20] and GB50017 [21] were used to evaluate the block shear strength of the test
specimens. However, it should be noted that the block shear design equations for coped
beams were mainly associated with bolted end connections. The failure mechanism in
welded end connections may be different from that of bolted end connections since, in
21
the former, there is no reduction in gross section area due to bolt holes. Nevertheless,
these equations are also used for welded end connections. Consequently, for the test
specimens in this study, the block shear failure was checked around the periphery of
the welded connections. As mentioned above, although the final failure mode of six
specimens was local web buckling, it was observed during the tests that these
specimens exhibited a significant deformation of the block shear type prior to reaching
their final failure mode. Therefore, it is believed that the use of the block shear design
equations for the specimens that failed in local web buckling would provide an
indication of the strength of the connection.
5.2 Current Design Standards
5.2.1 CSA-S16-01 (2001)
The CSA-S16-01 [17] standard provides two equations (Eq. (2) and Eq. (3)) to
evaluate the block shear strength of connections.
(0.5 0.6 )= +r u nt y gvP F A F Aφ (2)
(0.5 0.6 )= +r u nt u nvP F A F Aφ (3)
where:
Pr is the factored ultimate connection capacity;
φ is the resistance factor;
Fu is the tensile strength;
Fy is the yield strength;
Ant is the net tension area;
Agv is the gross shear area; and
22
Anv is the net shear area.
As suggested by Kulak and Grondin [12], the contribution of the area of tension is
reduced by one-half, which implies that a triangular stress block with a maximum stress
of Fu is assumed. Equation (2) assumes that the block shear capacity is determined by a
non-uniform stress distribution with an average stress of 0.5Fu at a net area of tension,
along with the shear yielding stress at the gross shear area; while Eq. (3) assumes that
the shear contribution is the shear rupture at the net shear area. The lesser of above two
equations should be used as the block shear capacity. A comparison of the previous
test data on coped beams with bolted end connections shows that this procedure
provides conservative results with an average test-to-predicted ratio of 1.20. In the
current study, since no shear fracture was observed for the failed specimens in this
study, only Eq. (2) (the lesser one) was used to evaluate the block shear strength of the
test specimens. Without the reduction in bolt holes when calculating area, the gross
area and the net area in Eq. (2) were identical.
5.2.2 AISC LRFD (1999)
For the AISC LRFD [16] standard, again, two equations (Eq. (4) and Eq. (5)) are
provided:
If 0.6≥u nt u nvF A F A :
( 0.6 ) ( 0.6 )= + ≤ +r u nt y gv u nt u nvP F A F A F A F Aφ φ (4)
If 0.6<u nt u nvF A F A :
( 0.6 ) ( 0.6 )= + ≤ +r y gt u nv u nt u nvP F A F A F A F Aφ φ (5)
23
where:
Agt is the gross tension area and the other symbols have been defined above.
When the ultimate rupture strength at the net section is used on one segment,
yielding at the gross section shall be used on the perpendicular segment. The design
equations incorporate two possible modes of failures: the rupturing of the net tension
area combined with yielding of the gross shear area, or yielding of the gross tension
area combined with rupture of the net shear area. The upper limit is the sum of tension
rupture on the net tension area and shear rupture on the net shear area. It should be
noted that the first failure model is reasonable and supported by test observations.
Experimental results in which block shear is evident tend to exhibit a failure mode
similar to that described by Eq. (4); however, the qualifying condition listed in the
specification makes it rarely control the design. Thus, Eq. (5) will commonly govern in
practice.
Kulak and Grondin [12] points out that the possibility of attaining the shear
ultimate strength in combination with the tension yield strength seems unlikely due to
the small ductility in tension as compared with shear, and there is insufficient tensile
ductility to permit the occurrence of shear fractures. Nevertheless, the use of Eq. (4)
and Eq. (5) does not provide good predictions of the available test results and produces
a high degree of variation. In particular, for the two-line bolted connections, the
equations are for the most part not conservative. In general, they do not accurately
represent the failure modes observed in tests. The AISC LRFD specification [16] also
indicates that the block shear failure mode should also be checked around the periphery
of welded connections. For the current study, the larger one of Eq. (4) and Eq. (5) was
used to evaluate the block shear strength of the test specimens.
24
5.2.3 Eurocode 3 ENV 1993-1-1
For Eurocode 3 [18], a single equation can be derived from a series of equations
according to the specifications for block shear on coped beams as follows:
0
1 1 1( )3 3
⎡ ⎤= − +⎢ ⎥⎣ ⎦r u gt ot w y gv
M
P F L kd t F Aγ
, (6)
where:
0Mγ is the partial safety factor for resistance (a vale of 1.0 is used in this study);
Lgt is the length of the gross tension area;
dot is the hole size for tension area; and
k is the coefficient for tension area as follows:
for a single line of bolts: 0.5=k ;
for two lines of bolts: 2.5=k .
The equation combines the reduced normal stress acting over the tension area with
shear yielding acting over the gross shear area. Franchuk et al. [6] indicated that the
reduction coefficient of 13
for the normal stress is considered similar to the 0.5 used
in CSA-S16-01, although this value appears to be derived from the von Mises yield
criterion. It is found that the equation provides a very conservative prediction even for
two-line bolted connections.
5.2.4 BS 5950-1:2000
In this updated BS 5950-1:2000 standard [19], block shear for bolted connections is
covered as follows:
25
0.6 ( ) 0.6y e t t w y v wP p K L kD t p L t= − + , (7)
where:
P is the ultimate connection capacity
yp is the design strength
Ke is the effective net area coefficient
t is the web thickness
Lt is the length of the tension area
Lv is the length of the shear area
k is defined above, and
Dt is the hole size for the tension area
For general purposes regardless of steel grade, 1.2
se
y
UKp
= , where Us is the minimum
tensile strength. Therefore, Eq. (7) becomes:
0.5 ( ) 0.6s t t w y gvP U L kD t p A= − + (8)
Disregarding the partial factor and the different definitions for design strength, this
equation is very similar to that of Eurocode 3, except that 0.5 instead of 13
is used
again for the reduction of the tension contribution. Compared with Eq. (2), there is a
slight difference in the calculation of the net tension area. Equation (8) is believed to
produce conservative results for two-line bolted connections in coped beams.
For welded end connection, if the design strength and the minimum tensile strength
in Eq. (8) is substituted by Fy and Fu respectively, an equation the same as Eq. (2) can
be deduced. This means that for a welded end connection, the prediction by BS 5950-
26
1:2000 [19] is exactly identical to that provided by the CSA-S16-01 standard [17].
Thus, the evaluation results for BS 5950-1:2000 [19] will not be repeated here.
5.2.5 Standard for limit state design of structures (AIJ 1990), Architectural Institute
of Japan,
The AIJ (1990) [20] provides the following conservative procedure:
1( )3
= +r u nt y nvP F A F Aφ (9)
1( )3
= +r y nt u nvP F A F Aφ (10)
where the symbols are similar to the ones defined before. The lesser of the equations is
used for the connection capacity. It combines tensile and shear stresses acting on both
net areas. The results show that these equations give more conservative predictions, but
with a high degree of variation. In addition, these equations cannot represent the actual
failure mechanism for block shear in coped beams.
In contrast with the equations of AISC LRFD [19] (Eq. (4) and Eq. (5)), there is
only a negligible difference in the coefficient. In fact, the AISC LRFD standard [19]
uses the larger of these two equations instead of the smaller.
5.2.6 Chinese Standard GB50017 (2003)
Based on the results of the gusset plates test, a block shear equation is derived and
added to the latest version of the Chinese standard for the design of steel structures
(GB50017-2003 [21]). From the commentary in the code, the following explicit
equation can be derived for coped beams:
27
13u nt u nvP F A F A= + , (11)
where the symbols are similar to the ones defined before. This equation assumes that
tensile rupture on the net tension area and shear rupture on the net shear area appear
simultaneously. The average test-to-predicted ratio for Eq. (11) on the results of the
gusset plates test provided in the code GB50017 [21] is 1.14. The code also shows that
the equation is applicable for both bolted and welded connections. It is interesting to
note, neglecting the partial factor, that this model is almost the same as that of the
former Canadian standard CAN/CSA-S16.1-94 [17], which is expressed as:
0.85 ( 0.6 )= +r u nt u nvP F A F Aφ (12)
5.3 Design Strength of Test Specimens Based on Current Design Standards
The ultimate strengths of the test specimens were compared to those predicted by
all of the above design equations from different design standards for block shear. The
results are summarized in Table 6. The predicted capacities were based on the
measured dimensions of the specimens, including the measured weld sizes and the
measured material properties. All resistance factors are taken as 1.0. The test-to-
predicted ratio (or termed professional ratio) of those failed specimens are listed in
Table 6.
As described before, for the six specimens that ultimately failed due to local
buckling of the web rather than block shear, the observation from test results showed
that the deformed block did appear prior to ultimate buckling of the web. Therefore,
qualitative comparisons of these specimens may still be made using the current design
28
standards. For the specimens that failed by block shear with tension fracture, the
average test-to-predicted ratios were 1.49 and 1.06 based on CSA-S16-01 [17] and
AISC LRFD [16], respectively. This may indicate that the CSA-S16-01 [17] design
model may be too conservative for block shear in coped beams with a welded clip
angles connection. At the same time, it is important to note that the average test-to-
predicted ratios for those specimens that failed due to local buckling of the web were
1.26 and 0.88, as estimated by the CSA-S16-01 [17] and the AISC LRFD [16] block
shear equations, respectively. Although the test results were not conclusive, it is
believed that current North American design standards are inconsistent to allow
predictions of the block shear of coped beams with welded end connections.
The approach of Eurocode 3 [18] produced very similar results in capacity
predictions as compared to CSA-S16-01 [17]. It was found that the capacity predicted
by Eurocode 3 [18] was about 3% larger than that of CSA-S16-01 [17], which could be
attributed to the slightly different coefficients used in the related equations. The
average test-to-predicted ratios were 1.45 and 1.22 for the block shear cases and the
local web buckling cases, respectively. Besides, as mentioned before, predictions by
BS 5950-1:2000 [19] were exactly identical to those by the CSA-S16-01 standard [17].
Consequently, it can be concluded that, in general, the current European and British
design standards are also conservative for block shear in coped beams with a welded
clip angles connection.
AIJ standard [20] did not provide a consistent prediction for both failure modes,
and generally overestimated the capacity of the specimens that failed due to local
buckling of the web. The average test-to-predicted ratios were 1.15 and 0.96 for the
block shear cases and the local web buckling cases, respectively. Nevertheless, the AIJ
standard [20] provides a safer estimation than AISC LRFD [16] because the former
29
adopts the smaller value of the two equations, while the latter uses the larger one.
However, the procedures of both the AIJ standard [20] and AISC LRFD [16] could not
accurately represent the actual failure modes observed in the tests, since no fractures
were found in the shear area.
It should be pointed out that GB50017 [21] overestimated the capacities of all
specimens. The average test-to-predicted ratios were 0.96 and 0.80 for the block shear
cases and the local web buckling cases, respectively. Hence, this standard produced
non-conservative estimates for the block shear strength of coped beams with a welded
clip angles connection. In addition, it was unlikely that the ultimate tensile strength of
the tension area and the ultimate shear strength of the shear area would be achieved
simultaneously; hence, the model did not reflect the actual failure mechanism.
Generally, the predictions using these design equations exhibited a vast degree of
variation with regard to the test data. For example, these methods often produced large
overestimations for specimens with large areas of tension, such as specimens B2 and
D1. Furthermore, in all cases, the predictions were less conservative for the specimens
that failed due to local buckling of the web, even though a significant deformation of
the block shear type occurred before the specimens reached their final failure mode.
Therefore, it is concluded that the existing design standards are inconsistent in
predicting the bock shear of cope beams with welded end connections.
6. Summary and Conclusions
To investigate the block shear strength and behavior of coped beams with welded
end connections, ten full-scale coped beam tests were conducted. The failure
mechanism in coped beams with welded end connections was different from that with
bolted end connections, since there was no reduction in the web section area due to bolt
30
holes. The test results showed that only two of the ten specimens failed by block shear
mode with tension fractures. Tension fractures occurred abruptly in the beam web
underneath the clip angles. No shear fractures were observed and no tear-out type of
block shear occurred. Local web buckling was also a potential failure mode for coped
beams with welded end connections. High compressive stresses and shear stresses were
localized in the web near the end of the cope due to the combination of bending and
shear in the reduced section, hence resulting in extensive yielding at the cope and
inducing local web buckling. However, these specimens exhibited significant
deformation of the block shear type prior to reaching their final failure mode.
The test parameters examined included the aspect ratio of the clip angles, the
tension and shear area of the web block, web thickness, beam section depth, cope
length, and connection position. The results showed that the connection capacity
increased as aspect ratio and shear area increased. A large area of tension would
increase the loading eccentricity and hence generate more bending moments to the edge
of the beam web region near the angle. A thin beam web and long cope length
increased the susceptibility to local web buckling. The depth of the beam section and
connected position did not greatly affect the connection capacity.
The design equations from current standards were used to evaluate the capacity of
the specimens. It was found that the existing design standards did not provide
consistent predictions of the block shear strength of coped beams with welded end
connections. In addition, the rules provided by the standards could not accurately
reflect the failure mode observed in the tests. For a better understanding of the
connection behavior and the failure mechanism, non-linear finite element analyses
(FEA) were carried out and presented in a companion paper (Yam et al. 2005), which
31
included a parametric study and a proposed design equation for the block shear strength
of coped beams with welded clip angles connections.
7. Acknowledgments
The authors would like to express their gratitude to the Research Committee of
the University of Macau for providing financial support for this project. The assistance
of the technical staff of the Structural Laboratory at the University of Macau, Macau,
China, is also acknowledged.
8. References
[1] Birkemoe, PC, and Gilmor, MI. “Behavior of bearing critical double-angle beam
connections,” Engineering Journal, AISC, 1978; Vol. 15, No. 4, pp. 109-115.
[2] Hardash, S, and Bjorhovde R. “New design criteria for gusset plates in tension,”
Engineering journal, AISC, 1985; Vol. 22, No. 2, second quarter.
[3] Epstein, HI. “An experimental study of block shear failure of angles in tension,”
Engineering journal, AISC 1992; Vol. 29, No. 2, second quarter.
[4] Epstein, HI, and Stamberg, H. “Block shear and net section capacities of structural
tees in tension: Test results and code implications,” Engineering Journal, 2002; Vol. 39,
No. 4, Fourth Quarter, pp. 228-239.
[5] Epstein, HI, and McGinnis, MJ. “Finite element modeling of block shear in
structural tees,” Computers and Structures 2000; Vol. 77, No. 5, pp. 571-582.
32
[6] Franchuk, CR, Driver, RG, and Grondin, GY. “Experimental investigation of block
shear failure in coped steel beams,” Canadian Journal of Civil Engineering, 2003; Vol.
30, No. 5, pp. 871-881.
[7] Orbison, JG, Wagner, ME, and Fritz, WP. “Tension plane behavior in single-row
bolted connections subject to block shear,” Journal of Constructional Steel Research,
1999; 49:225-239.
[8] Yura, JA, Birkemoe, PC, and Ricles, JM. “Beam web shear connections: an
experimental study,” Journal of the Structural Division, 1982; ASCE, Vol. 108, No.
ST2 , pp. 311-325.
[9] Ricles, JM, and Yura, JA. “Strength of double-row bolted-web connections,”
Journal of Structural Engineering, 1983; ASCE, Vol. 109, No. 12, pp.126-142.
[10] Aalberg, A. and Larsen, PK. “Strength and ductility of bolted connections in
normal and high strength steels,” In Proceedings of the Seventh International
Symposium on Structural Failure and Plasticity, Melbourne, Australia, 2000.
[11] Kulak, GL, and Grondin, GY. “Block shear failure in steel members – a review of
design practice,” In Proceedings of Fourth International workshop on Connections in
Steel Structures IV: Steel Connections in the New Millennium, Roanoke, Va., 22–25
October 2000. Edited by Leon, RT, and Easterling, WS., AISC, Chicago, Ill. pp. 329-
339, 2000.
[12] Kulak, GL, and Grondin, GY. “AISC LRFD rules for block shear in bolted
connections – a review,” Engineering Journal, AISC, 2001, 38(4): 199–203. See also
“Errata and Addendum,” Engineering Journal, AISC, 39(2).
33
[13] Taylor, JC. “More work is required,” In Proceedings of Fourth International
workshop on Connections in Steel Structures IV: Steel Connections in the New
Millennium, Roanoke, Va, Edited by Leon , R T, and Easterling, WS., AISC, Chicago,
Ill. pp 33-40, 2000.
[14] Franchuk, CR, Driver, RG, and Grondin, GY. “Block shear failure of coped steel
beams,” Proceedings of 4th Structural Specialty Conference of the Canadian Society
for Civil Engineering, Montreal, Quebec, Canada, 2002.
[15] Topkaya, C. “A finite element parametric study on block shear failure of steel
tension members,” Journal of Constructional Steel Research, 2004; Vol. 60, Issue 11,
pp. 1615-1635
[16] American Institute of Steel Construction (AISC). Load and resistance factor
design specification for structural steel buildings, Chicago, IL, USA, 1999.
[17] Canadian Standards Association. (CSA). CAN/CSA-S16-01 Limit states design of
steel structures. CSA, Toronto, ON, Canada, 2001.
[18] European Committee for Standardisation (ECS) (1992). Eurocode 3: design of
steel structures – Part 1.1: general rules and rules for buildings. ENV 1993-1-1,
Brussels, Belgium, 1992.
[19] British Standards Institution (BSI) BS 5950: Structural use of steelwork in
building – Part 1: Code of practice for design –rolled and welded sections, 2001.
[20] Architectural Institute of Japan (AIJ). Standard for limit state design of steel
structures, 1990.
[21] Ministry of Construction of PR China (2003). Code for design of steel structures
(GB50017–2003), Chinese Planning Press., Beijing, China, 2003 (in Chinese).
34
[22] Steel Construction Institute, Steelwork design guide to BS5950: Part 1:1990.
Volume 1: Section properties, member capacities, 4th edition, 1997.
[23] British Standards Institution (BSI) (1990). BS 4360: Specifications for weldable
structural steels, London. 1990.
[24] American Society for Testing and Materials (ASTM). Standard test methods and
definitions for mechanical testing of steel products, ASTM Standard A370-02,
Philadelphia, Pa, 2002.
[25] Yam, CHM, Zhong, YCJ, Lam, CCA, and Iu, VP. “ An investigation of the block
shear strength of coped beams with a welded clip angles connection, Part II: Analytical
Study,” Journal of Constructional Steel Research (companion paper).
[26] Zhong, YCJ. Investigation of block shear of coped beams with welded clip angles
connection. MSc thesis, University of Macau, Macau, 2004.
35
Table 1 Cross-sectional dimensions of the test beams
Beam Designation
Beam Serial
tw (mm)
T (mm)
D (mm)
B (mm) Note
A, B (Beam406) UB406x140x46
6.8 11.2 403.2 142.4 Nominal 6.8 11.1 404.2 140.9 Measured
C, D (Beam457) UB457x191x74
9.1 14.5 457.0 190.4 Nominal 9.2 14.2 456.3 189.1 Measured
E (Beam356) UB356x171x67
9.1 15.7 363.4 173.2 Nominal 9.1 15.2 362.6 171.5 Measured
TB
twD
36
Table 2 Connection dimensions of the test specimens
Designation
Connected Length
ConnectionPosition
Cope Length
Cope Depth
Weld Size Note a
(mm) b
(mm) p
(mm) c
(mm) dc
(mm) s
(mm)
A1-406r3 50 160 20 100 30 8 Nominal 50 160 20 100 33 8.9 Measured
A2-406r2 70 140 20 120 30 8 Nominal 70 140 20 120 31 9.4 Measured
B1-406t 50 120 20 100 30 9 Nominal 50 120 20 100 30 10.0 Measured
B2-406r1 90 110 20 130 30 9 Nominal 90 110 20 130 30 9.9 Measured
C1-457R3 50 170 20 100 30 9 Nominal
50.5 170 20 99.5 30 11.2 Measured
C2-457T 50 120 20 100 30 11 Nominal 50 120 20.5 99 30 12.3 Measured
D1-457R1 90 120 20 150 30 11 Nominal 90 120 20 150 30 11.8 Measured
D2-457L 90 120 20 80 30 11 Nominal 90 120 20 80 30 12.6 Measured
E1-356T 50 120 20 100 30 11 Nominal 50 120 20 100 30 13.1 Measured
E2-356P 50 120 45 100 30 11 Nominal 50 120 45 100 30 13.5 Measured
c
dc
b b'
a
p
ss
37
Table 3 Summary of the test parameters
Test Parameter Specimen Designation Nominal Value
Aspect ratio (b'/a) A1-406r3, A2-406r2, B2-406r1 3.6, 2.3, 1.4 C1-457R3, D1-457R1 3.8, 1.6
Shear area, b (mm) C1-457R3, C2-457T 170, 120 Tension area, a (mm) C2-457T, D1-457R1 50, 90 Web thickness, tw (mm) B1-406t, C2-457T, E1-356T 6.8, 9.1, 9.1 Beam depth C2-457T, E1-356T UB457, UB356 Cope length, c (mm) D1-457R1, D2-457L 150, 80 Connection position, p (mm) E1-356T, E2-356P 20, 45
38
Coupon Specimen
Elastic Modulus
(MPa)
Static Yield, Fy
(MPa)
Static UltimateStrength, Fu
(MPa)
Final Elongation
(%) Beam406 (Beam A, B)
Flange 1 210476 308.3 439.9 21.8 Flange 2 211426 289.1 440.3 23.2 Average 210951 298.7 440.1 22.5 Web 1 182170 353.6 458.8 20.0 Web 2 199375 282.5 425.9 30.3 Average 190772 318.1 442.4 25.2
Beam457 (Beam C, D) Flange 1 215029 318.6 470.2 32.2 Flange 2 214906 329.8 469.5 31.0 Average 214967 324.2 469.9 31.6 Web 1 205786 372.7 487.9 32.4 Web 2 200683 370.5 487.4 26.6 Average 203234 371.6 487.7 29.5
Beam356 (Beam E) Flange 1 203706 297.1 433.3 28.9 Web 1 202210 305.0 444.4 19.7 Web 2 204720 303.1 443.8 18.3 Average 203465 304.1 444.1 19.0
Clip Angle Angle 1 201050 295.9 498.2 28.2 Angle 2 206292 314.9 499.6 29.6 Average 203671 305.4 498.9 28.9
Material properties according to EN 10025-2:2004
Steel Grade Elastic
Modulus(MPa)
Minimum Yield, Fy (MPa)
Tensile Strength, Fu
(MPa)
Minimum Percentage Elongation
(%) S275 210000 275 430 21 S355 210000 355 510 20
Table 4 Summary of the tension coupon test results
39
Table 5 Summary of the test results
Specimen Ultimate Load (kN)
Ultimate Reaction
(kN)
Connection Moment*
(kN.m)
Web Thickness Reduction+(%) Failure Mode
A1-406r3 483.8 395.2 -7.5 7.9 Buckling A2-406r2 531.5 437.4 -17.0 7.1 Buckling B1-406t 479.0 394.0 -14.8 5.9 Buckling B2-406r1 475.1 390.3 -13.3 4.9 Buckling C1-457R3 885.0 690.1 -4.8 5.6 Exceeded** C2-457T 804.9 630.0 -10.7 15.8 Fracture D1-457R1 795.1 623.0 -12.4 14.0 Buckling D2-457L 880.9 684.5 1.7 5.4 Exceeded** E1-356T 751.0 601.2 -8.6 15.3 Fracture E2-356P 725.4 581.0 -9.1 7.6 Buckling Note: * A negative moment indicates tension in the top flange. ** Failure did not take place at the maximum applied load. + Reduction in web thickness near the bottom of the clip angles.
40
Table 6 Summary of the predicted capacity and test capacity of the specimens
Specimen Failure Mode
Fy (MPa)
Fu (MPa)
Test Ultimate Reaction
CSA-S16-01 (2001)Eq. (2)
AISC LRFD (1999) Larger of Eq. (4) or
Eq. (5)
Eurocode 3 (1992) Eq. (6)
AIJ (1990) Lesser of Eq. (9) or
Eq. (10)
GB50017 (2003) Eq. (11)
PredictedCapacity
Test PredictedCapacity
Test PredictedCapacity
Test PredictedCapacity
Test PredictedCapacity
Test Predicted Predicted Predicted Predicted Predicted
A1-406r3 Buckling 318.1 442.4 395.2 336.8 1.17 472.7 0.84 341.5 1.16 417.8 0.95 510.5 0.77 A2-406r2 Buckling 318.1 442.4 437.4 341.0 1.28 479.9 0.91 351.3 1.25 453.0 0.97 535.9 0.82 B1-406t Buckling 318.1 442.4 394.0 284.9 1.38 400.5 0.98 291.5 1.35 367.8 1.07 441.0 0.89 B2-406r1 Buckling 318.1 442.4 390.3 332.1 1.18 482.5 0.81 348.5 1.12 459.5 0.85 544.0 0.72 D1-457R1 Buckling 371.6 487.7 623.0 540.6 1.15 769.4 0.81 564.2 1.10 742.5 0.84 851.4 0.73 E2-356P Buckling 304.1 444.1 581.0 422.8 1.37 606.0 0.96 431.4 1.35 539.0 1.08 669.9 0.87
Average 1.26 0.88 1.22 0.96 0.80 C2-457T Fracture 371.6 487.7 630.0 450.9 1.40 621.2 1.01 460.6 1.37 578.2 1.09 671.9 0.94 E1-356T Fracture 304.1 444.1 601.2 381.3 1.58 545.3 1.10 391.4 1.54 499.1 1.20 611.6 0.98
Average 1.49 1.06 1.45 1.15 0.96 C1-457R3 Exceeded 371.6 487.7 690.1 553.4 --- 755.8 --- 559.3 --- 676.9 --- 801.5 --- D2-457L Exceeded 371.6 487.7 684.5 540.6 --- 769.4 --- 564.2 --- 742.5 --- 851.4 ---
Note: All resistance factors are taken as 1.0. The units of forces are in kN.
41
Cope
Bolted connection Welded connection
Figure. 1 Schematic of a bolted or welded connection on a coped beam
42
Cope
Cope
Potential block of web material tearing off
Welded end connection
Potential block of web material tearing off
Bolted end connection
Figure. 2 Potential block shear failure in a coped beam
weld
Note: The block shear failure generally consists of shear yielding on the gross area of the shear face and tensile rupture along the net area of the tension face
Potential block shear failure mode
Potential block shear failure mode
43
Figure. 3 Block shear model of failure identified by Birkemoe and Gilmor (1978)
Rupture SurfaceB
B
A A
44
Figure 4 Block shear model proposed by Ricles and Yura (1983)
0.6Fy
Fu
45
c
dc
TB
twD
b b'
a
p
ss
Figure 5 Schematics of the test specimen
46
Note: All dimensions are in millimeters
Figure 6 Overall design dimensions of the test specimens
Beam E (UB 356x171x67)
356PE2
356TE1
Details of typical clip angle
26 Dia. holes for M24 bolt
Details of A1 clip angle
47
A1-406r3 A2-406r2 B1-406t B2-406r1
C1-457R3 C2-457T D1-457R1 D2-457L
E1-356T E2-356P
Note: All dimensions are in millimeters
Figure 7 Connection details of all of the test specimens
48
Figure 8 Schematic of the test setup
Test Beam
3300mm2700mm
Lateral BracingApplied Load (P)
Reaction (Q)
L
D
Support
Roller Assemblies
Load Cell (890kN)
Supporting Column
Test Beam
Hydraulic Cylinder (890 kN)
Bracing Column
Lateral Bracing
Test Frame
Concrete Strong Floor
Roller Assemblies Load Cell
(330kN)
Test Connection
Stub Support
Lateral Bracing
Beam L (mm) A 510 B 510 C 600 D 600 E 550
49
LVDT 3
LVDT 2 LVDT 1
LVDT 8 (lateral)
LVD
T 7LV
DT 6
LVDT 5
LVDT 4
Applied Load (P)
Reaction (Q)
Figure 9 Layout of LVDTs
50
Figure 10 Layout of strain gauges
20
19
24
141516
1 2 3 4 5 67
8 910
111213
2517
23
(Back side)18
26
Applied Load (P)
Reaction (Q)
51
(a) Specimen B2
(b) Specimen C1
(c) Specimen C2
(d) Specimen D1
52
(e) Specimen E1
Figure 11 Photos of failed specimens B2, C1, C2, D1, and E1
53
(a) Specimen A1
(b) Specimen B2
Figure 12 Photos of the buckled shapes of specimens A1 and B1
Top flange Beam web
buckled
Clip angle Bottom flange
54
0
100
200
300
400
500
600
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Deflection, δ (mm)
App
lied
Load
, P (k
N)
B1-406tA2-406r2
A1-406r3 B2-406r1
P
Figure 13 Applied load vs. load point deflection curves for specimens A1, A2, B1, and B2
55
Figure 14 Longitudinal strain distribution along the tension area for specimen E1
0
200
400
600
800
1000
1200
1400
1600
0 10 20 30 40 50 60 70 80 90 100 110 120
Distance from beam end (mm)St
rain
(mic
ro s
trai
n)
Test P=70kN
Test P=183kN
Wel
ded
Ang
le E
dge,
a=5
0mm
1 2 3 4 5Strain gauge #1
Strain gauge #5
56
0
20
40
60
80
100
120
140
160
180
0 500 1000 1500 2000
Strain (micro strain)
Dis
tanc
e fr
om to
p ed
ge o
f bea
m w
eb (m
m)
Test P=70kN
Test P=183kN
Figure 15 Shear strain distribution along the shear area for specimen E1
Clip angles
7 6
5
8 9 10
11 12 13
57
0
20
40
60
80
100
120
140
160
180
200
220
-1000 -900 -800 -700 -600 -500 -400 -300 -200 -100 0 100 200 300 400
Strain (micro strain)
Dis
tanc
e fr
om to
p ed
ge o
f bea
m w
eb (m
m)
Test P=70kN
Test P=183kN
Figure 16 Flexural strain distribution along the shear area for specimen E1
7 6
5
8 9 10
11 12 13
58
Figure 17 Load vs. web deformation curves for specimens C1 and D1 (aspect ratio
series 2)
0
100
200
300
400
500
600
700
800
0 1 2 3 4 5 6 7 8 9 10 11 12
Web Deformation, ∆1-∆2 (mm)
Con
nect
ion
Rea
ctio
n, Q
(kN
)
D1-457R1C1-457R3
Q
C1-457R3 D1-457R1
b’ b’
a a
b’/a = 1.6 b’/a = 3.8
100 150
59
Figure 18 Reaction versus web deformation curves for the shear area series
0
100
200
300
400
500
600
700
800
0 1 2 3 4 5 6 7 8 9 10 11 12
Web Deformation, ∆1-∆2 (mm)
Con
nect
ion
Rea
ctio
n, Q
(kN
)
C2-457T
C1-457R3
Q
C1-457R3 C2-457T
100 100
60
Figure 19 Reaction versus web deformation curves for the web thickness and beam depth series
0
100
200
300
400
500
600
700
0 1 2 3 4 5 6 7 8 9 10 11 12
Web Deformation, ∆1-∆2 (mm)
Con
nect
ion
Rea
ctio
n, Q
(kN
)
C2-457T
E1-356T
B1-406t (Modified)
Q
C2-457TB1-406t E1-356T
404
50
100 100
100
120 120
120
50 50
61
Figure 20 Reaction vs. web deformation curves for cope length series
0
100
200
300
400
500
600
700
800
0 1 2 3 4 5 6 7 8 9 10 11 12
Web Deformation, ∆1-∆2 (mm)
Con
nect
ion
Rea
ctio
n, Q
(kN
)
D1-457R1D2-457L Q
D1-457R1 D2-457L
120 120
90 90