cidect final report 8g-10_06(2of4)
TRANSCRIPT
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SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 5: FE MODELLING OF CONNECTIONS
CHAPTER 5: FE MODELLING OF CONNECTIONS
A total of 13 finite element models were generated and analyzed with the software
package ANSYS 8.1 (Swanson Analysis Systems 2004). The experimental failure mode implied
a fracture of the material under high deformations. This fracture was emulated by the
designation of a maximum equivalent strain which triggered the activation of the “death feature”
of the elements where the stiffness and true stress of an element are reduced to near-zero. The
consideration of large deformations requires the knowledge of a complete material true stress-
strain (Tσ-Tε) curve. Hence, a method to obtain this curve is proposed herein. Once the true
stress-strain curves from the materials were generated, the tests specimens were modelled and
the numerical models verified. In addition to the load-deformation response comparison, the
strain gauge readings from the tests specimens and FE models were compared (load-strain
response).
5.1 Material properties
A multi-linear material Tσ-Tε curve was used to describe the gusset plate, tube and weld
material properties. The generation of the Tσ-Tε curve, based on the engineering stress-strain
(σ-ε) relations with equations (5-1) and (5-2), is suitable prior to the development of necking in
the coupon test.
(5-1)
(5-2)
Afterwards, the stress distribution in the neck region changes from a simple uniaxial to a
complex triaxial case (Aronofsky 1951). In addition, accumulative damage in the material may
lead to the creation of microvoids and microcracks affecting the material internal structure.
Bridgeman (1952) proposed a numerical method for a coupon test with a circular cross-section
which provides an excellent approximation of the stresses and strains in the neck region.
Unfortunately, this method is ineffective for rectangular coupons.
In order to generate the Tσ-Tε curve for a rectangular coupon test in the post-necking
region, several authors have proposed different procedures. Matic (1985) has suggested a
method which describes the change in the tangent modulus of the material versus the absorbed
strain energy density as a hyperbolic function. Shen and Jones (1993) proposed the inclusion of
Tσ σ 1 ε+( )=
Tε 1 ε+( )ln=
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geometric nonuniformities in the models which are calibrated with the initial trace of the coupon
test. Tvergaard (1993) triggered final necking in the models considering the nucleation and
growth of microvoids in the material. Zhang et al.(1999) proposed an equation which describes
the reduction of the coupon’s cross-sectional area and an approximate true average stress
value based on this area. Geltmacher et al. (1999) proposed an algorithm to generate the true
stress-strain curve based on the experimental load-displacement response data and the
specimen shape evolution based on FE models. Khoo (2000) proposed a material model that
considers material dilatation and a continuum damage mechanism under quasi-static loading.
Dumoulin et al. (2003) suggested an original method to determine a true stress-strain curve
based on a tensile coupon test and an image analysis. In most cases, the testing of several
coupons and the measuring of the necking cross-sectional area during the tests is required.
Moreover, FE models of the coupon test are used to verify the correlation between the response
from the numerically-generated curves and the experimental data.
During the laboratory testing of the coupons, the engineering stress-strain relationships
were acquired before the coupon tests developed a neck. Afterwards, the clip gauge was
removed from the coupons, but the load and maximum elongation at rupture were determined
for each coupon test. In order to complete the coupon test Tσ-Tε curve, the method proposed
by Matic (1985) has been adapted to be used herein. Matic’s curve is generated with a starting
point corresponding to a zero plastic strain on the coupon test curve data. In materials exhibiting
a plastic plateau, a better solution is achieved when Matic’s curve starts at the beginning of the
strain-hardening range. The generation of the Tσ-Tε curve in the post-necking region was thus
calculated starting from the necking point (see Figure 5.1), following the change in the tangent
modulus given by Matic’s curve. An interval step of Tε=0.01 was used to generate this curve;
this interval was small enough to capture the Tσ-Tε curve behaviour. The rate of change of the
tangent modulus can be modified and the best rate is determined by an iterative process. For a
generated Tσ-Tε curve of each material, a FE model of the gauge region was analyzed (see
Figure 5.2) and the load-deformation response from the FE model was compared with the
coupon test response data. This process was repeated until the load and displacement at
fracture from the coupon FE model corresponded to the coupon test result. The response
curves for CHS, EHS and gusset plate materials are shown in Figure 5.3 to Figure 5.6.
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The final material property curves used in the FE analyses for all materials are presented
in Figure 5.7. Here the Tσ−Tε uniaxial curves for the two plate materials are very similar as they
exhibited almost identical material properties.
Figure 5.1 Uniaxial Tσ−Tε curve of EHS Figure 5.2 FE model of the gauge region
Figure 5.3 Load-displacement response for CHS
Figure 5.4 Load-displacement response for EHS
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5.2 Connection modelling
In order to simplify the modelling of the connections, symmetric boundary conditions were
applied in the planes of symmetry of the models. This allowed the modelling of only one eighth
of the specimens. In addition to these boundary conditions, the nodes at the tube end were
fixed at the reaction end and the total load acting on the connection was calculated from these
nodes (see Figure 5.8).
Figure 5.5 Load-displacement response for gusset plate (tp= 25 mm)
t
Figure 5.6 Load-displacement response for gusset plate (tp= 32 mm)
t
Figure 5.7 Uniaxial Tσ−Tε curves of materials
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For the meshing process, care was taken to avoid distortions and large aspect ratios in
the elements. The size and number of the elements were always selected to produce elements
with a shape as close to cubic as possible. A gradual change in the mesh size was made from
areas with low stresses to areas with high stresses. A fine mesh was used in areas prone to be
affected by the shear lag phenomenon. Three elements were used through the tube thickness
in all the models. For constructional purposes the slot is typically oversized, hence a small gap
Figure 5.8 Boundary conditions of FE models
Figure 5.9 Gap considered in FE models
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was left between the plate and the tube elements. This ensured that the transmission of the load
was only through the weld (see Figure 5.9). In all the models, the tube material properties were
used for the discretization of the welds.
5.2.1 Element selection
For the FE modelling and analysis of the connections, SOLID45 elements were used
throughout, in the generation of the tube, plate and weld materials. This element is defined by
eight nodes, each node having three translational degrees of freedom, with large deflection and
large strain capabilities. Attempts to use other elements were made. Eight-noded solid elements
with capability for simulating deformations of nearly incompressible elastoplastic materials
(SOLID185) were tried for the modelling, but although these elements enhanced the connection
response they failed to allow distortions in “dead” elements. Twenty-noded solid elements
(SOLID95) were tried with a coarse mesh in the FE models but their CPU time exceeded the
SOLID45 models and lacked any significant improvement.
All the models were analyzed with a fine mesh and a coarser mesh. The use of SOLID95
elements was limited to coarse mesh models due to restrictions in the maximum number of
nodes supported by the software. In general, the coarse mesh models reduced the analysis
time but they were not able to clearly describe the failure modes of the connections.
Furthermore, a comparison between the readings from the strain gauges in test specimens and
the strains in numerical models showed a better agreement for the fine mesh models. The
analysis results for various FE models with different elements are shown in Table 5.1.
5.2.2 Analysis considerations
During the FE analysis of the connections, a nonlinear time step analysis was performed
by applying incremental displacements. This emulates the displacement-control loading
throughout the connection tests. The displacements were applied to the nodes located at the
plate end and nonlinear material properties were considered. Furthermore, the full Newton
Raphson method and frontal equation solver were used. Geometrical non-linearities were taken
into account by allowing large deformations and a uniform reduced integration with hourglass
control was applied. Shape changes (i.e. area, thickness) were considered.
The maximum equivalent strain (εef) used to trigger the activation of the elements’ “death
feature” was obtained by empirical correlations. Initially, all the FE models were analyzed using
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a εef equal to that used during the analysis of the tensile coupon models (approximately 0.9).
However, considerable deformations were needed to generate large strains in the coupons and
trigger the elements’ “death feature”. For this reason, the maximum connection strength and
deformation would over-exceed the experimental results if such εef values were used. This lack
of direct applicability has been related to the difference in the material boundary conditions that
exists between the tensile coupons and the connections. In order to consider the material’s
suppressed necking state that exists in the connections (Salmon and Johnson 1996), all the
connections were analyzed using several εef values and the best correlation between the
experimental and FE analysis results (load-displacement and load-strain responses) was found
using a εef = 0.6.
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a) Maximum load attained in the connection test.
5.3 Evaluation of FE models against experimental results
The accuracy of the FE models was determined by comparing their response with the
result previously acquired during the experimental program. This evaluation was based on their
capacity to reproduce the connection load-deformation response, the maximum load attained, a
Table 5.1 Connection analysis results with different elements used
Connection Type Element used
# of Nodes
# of Elements
Mesh type
Nua) (kN)
NuFE(kN)
Nu/ NuFE
A1SOLID45 16460 12030 Fine
1032978 1.06
SOLID45 7414 5260 Coarse 1010 1.02
SOLID95 18268 3242 Coarse 1005 1.03
A2SOLID45 16406 12030 Fine
11541130 1.02
SOLID45 7414 5260 Coarse 1135 1.02
SOLID95 18268 3242 Coarse 1159 1.00
C1SOLID45 13481 9894 Fine 1107 1083 1.02
SOLID45 5529 3878 Coarse 1216 0.91
SOLID95 15351 2716 Coarse 1215 0.91
C2SOLID45 13481 9894 Fine
11961241 0.96
SOLID45 5529 3878 Coarse 1236 0.97
SOLID95 15351 2716 Coarse 1298 0.92
E1SOLID45 10700 7640 Fine
11091098 1.01
SOLID45 5114 5392 Coarse 1198 0.92
SOLID95 13927 2456 Coarse 1126 0.98
E2SOLID45 10878 7784 Fine
12361186 1.04
SOLID45 5838 4138 Coarse 1218 1.01
SOLID95 15901 2832 Coarse 1205 1.02
E3SOLID45 11243 8036 Fine
13361334 1.00
SOLID45 6352 4495 Coarse 1353 0.99
SOLID95 17774 3158 Coarse 1265 1.05
E4SOLID45 11279 8072 Fine
14001401 1.00
SOLID45 6352 4495 Coarse 1186 1.18
SOLID95 17774 3158 Coarse 1267 1.10
E5SOLID45 11368 8313 Fine
1282
1273 1.01
SOLID45 5522 3676 Coarse 1362 0.94
SOLID95 14320 2536 Coarse 1318 0.97
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comparison between the strain gauge readings in tests specimen and FE models and finally,
their capacity to reproduce correctly the observed failure mechanism. The results of this
evaluation are shown in this section. In addition, the rest of the strain comparison are shown in
Appendix C.
5.3.1 Slotted CHS connection - slot end not filled (Type A)
For the modelling of these connections, the size of the elements was gradually decreased
from the tube end to the slot region and also over the tube circumference. This permitted the
strain distribution to be clearly captured in the critical location and allowed the gradual
propagation of cracking. In general, the FE models reproduced the dimension of the test
specimens as closely as possible and special care was taken during modelling of the weld
region (see Figure 5.10).
FE models A1 and A2
Diameter (D) = 168.3 mm
Tube thickness (t) = 4.8 mm
D/t = 35
Lw/w = 0.66 for connection A1
Lw/w = 0.81 for connection A2
Tube Length (L_tu) = 750 mm
Weld size (al) = 10 mm
The response previously seen during the test specimens was favourably reproduced in
the FE models. In a similar manner, a strain concentration at the slot region induced yielding of
the tube material there, producing change in the connection stiffness and an increase in the
deformations. Afterwards, the tube material carried on straining at the slot region, allowing a
gradual redistribution of strains. For both analyses, the maximum load was near the test value
(see Figure 5.11). Once the first element on the tube cracked, this crack would continue to
propagate thereby affecting the connection stability and stopping the analysis.
Lw
al
Figure 5.10 FE models of connection type A
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The FE models displayed an uneven stress distribution along the connection length, as a
result of shear lag. The use of a short weld length in specimen A1 generated very high stresses
in the base material along the longitudinal welds (see Figure 5.12). In contrast, a longer weld
length (specimen A2) moderated this stress amplification (see Figure 5.13). In addition, a more
uniform stress distribution was found in this second FE model. Unfortunately, this improvement
was not enough to avoid tube fracture at the net section. Moreover, the connection stress
distribution revealed the potential crack path, which consequently would define a tear-out failure
(TO) or a circumferential fracture (CF) failure. For model A1, the stress distribution suggested
both possible paths. On the other hand, the FE model for A2 showed a clear CF path. In
addition, near the attainment of the FE maximum load, ovalitazion of the tube started to take
place in the net section region, as seen previously during the tests.
Figure 5.11 Load - deformation response for specimens and FE models type A
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In general, the FE models favourably reproduced the uneven strain distribution seen
during the tests. The strain distributions along the weld and around the tube circumference were
reproduced reasonably well. In a similar manner to the tests specimens, a strain concentration
at the beginning of the welds (location of SG-5) triggered yielding of the tube material there in
the FE models. The magnitude of the strains during the FE analyses corresponded to those
observed during the tests (see Figures 5.14 and 5.15).
Figure 5.12 Stress distribution (von Mises) at maximum load for FE model A1
Figure 5.13 Stress distribution (von Mises) at maximum load for FE model A2
Figure 5.14 Load-strain response at SG-5 in connection A1
- FE- Lab
Strain (mm/mm)
Figure 5.15 Load-strain response at SG-5 in connection A2
- FE- Lab
Strain (mm/mm)
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The rest of the strain comparisons can be seen in Appendix C. As seen during the tests, a
gradual degradation in the FE model strains (due to distortion of their geometry and crack
propagation) was observed after achievement of the maximum load. In contrast to FE model
A1, the FE model A2 was able to clearly reproduce a CF failure mode. (Once the crack reached
the weld toes in this FE model, it continued spreading around the tube circumference). The
incapacity to clearly reproduce either failure mode (TO and CF) by FE model A1 has been
attributed to a lack of imperfections in the FE models, since it is believed that imperfections may
have defined the crack path during the test. The maximum loads attained by these FE models
are shown in Table 5.2.
5.3.2 Slotted CHS connection - slot end filled (weld return) (Type B)
As explained before, the fabrication of specimens B1 and B2 was made in two stages.
Initially, the plates and the slotted tubes were joined only by longitudinal welds and a slot was
left open between the end of the plate and the tube. Afterwards, the slot was filled with weld
material during fabrication of the weld return. A difference in the failure mode was found
between the test specimens and their corresponding FE models. In the tests, only small
deformations were necessary to develop the ultimate connection capacity and yielding was
concentrated in the weld return region. There, cracks developed in the tube material near the
weld toe and the propagation of these cracks through the tube thickness followed an inclined
plane (see Figure 5.16). This behaviour may be associated with shear yielding in the tube
material. Even though the FE models initially followed the same elastic load-deformation
response, they always had low strains in the weld return region and failure of elements required
large deformations (see Figure 5.17). This discrepancy in the response was believed to be
associated with a lack of residual stresses in the FE models.
Table 5.2 Ultimate capacity for connections type A
Connection Type
Test Load Nux (kN)
FE Analysis Load NuFE (kN) Nux / NuFE
A1 1032 978 1.06A2 1154 1130 1.02
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Several attempts were made to include these initial conditions and modify the FE models‘
behaviour. A FE model introducing an initial change in the weld temperature generated residual
stresses in the weld return region. Although the presence of residual stresses was included, the
connection overall behaviour was not improved. Moreover, the inclusion of initial stresses in
elements located within the heat-affected zone (HAZ) (by means of an input file) had the same
ineffective result. A second FE model including an initial shear strain at all nodes along the weld
toes was generated (see Figure 5.18). Despite this initial strain being minute, the strains
increased rapidly in the elements along the weld toe, hence the failure mode became the same
as for the test specimens. Even though this method improved the response of the models, it
showed inconsistency in a later parametric analysis. There, the FE models constantly repeated
this failure mode but neglected the influence of the weld length on the connection strength.
Finally, considering that connection failure started at the weld return toe region and there the toe
cracking (Stout 1987) had its origin in the HAZ and continued propagating into the base metal, a
new FE model was generated considering the change in strength and ductility of the weld as a
function of the loading angle (Kulak and Grondin 2002) and HAZ. In order to include a change in
the weld properties, the engineering σ-ε curve used for the transverse welds was scaled to
describe the properties of a weld loaded at an orientation of 90° to the weld axis. From this new
data, a Tσ-Tε curve was generated (see Figure 5.19) and this material property was applied to
the elements in the weld return region (loaded at an orientation of 90º to the weld axis).
Figure 5.16 Failure in test specimen B2 Figure 5.17 Initial load - deformation response of FE models
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A fine mesh was generated in front of the weld return and there the HAZ in the tube was
defined by a region having an average width of 1mm (see Figure 5.20). During its generation,
the tube material properties were applied but a low ductility controlled the material fracture. The
reason for this is the change in the ductility of the HAZ which becomes similar to the weld
material due to the merging of the weld and base material. Thus, the maximum strain in the
HAZ was defined to be equivalent to that in the weld oriented at 90º. This low ductility triggered
the creation of cracks in the HAZ modifying the overall connection behaviour to that observed
during the test. In general, the FE models described the first stages of the failure modes but the
analyses would terminate due to excessively high distortion in the “dead” elements in the weld
return region. Moreover, the behaviour of the FE models was the same as the test specimens
(see Figures 5.21 and 5.22). In addition, the FE models had a similar load-deformation
response curve as the tests (see Figure 5.23) and they reached a comparable maximum load
(see Figure 5.3). Finally, a good correlation can be appreciated between the strain gauge
readings of the specimens and FE models on Appendix C.
Table 5.3 Ultimate capacity for connections type B
Connection TypeTest Load Nux (kN)
FE Analysis Load NuFE (kN) Nux / NuFE
B1 1087 1080 1.01B2 1211 1216 1.00
Displacement1e-6mm Displacement
1e-6mm
Figure 5.18 Application of initial strain Figure 5.19 Tσ-Tε curves of fillet welds
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Figure 5.20 Materials in FE models type B
Figure 5.21 Failure mode in FE model B1 and test specimen
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5.3.3 Slotted EHS connection - slot end not filled (gusset plate oriented to give a large
eccentricity)
For the modelling of these connections, the size of the elements was gradually decreased
from the tube end to the slot region, and also around the tube circumference. This permitted
Figure 5.22 Failure mode in FE model B2 and test specimen
Figure 5.23 Load-deformation response for test specimens and FE models.
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the strain distribution and the gradual propagation of material cracking to be captured in the
critical region (see Figure 5.24).
FE models E1 and E2
Diameter (D1) = 220 mm
Tube thickness (t) = 5.9 mm
Davg/t = 28
Lw/w = 0.62 for connection E1
Lw/w = 0.78 for connection E2
Tube Length (L_tu) = 1000 mm
Weld size (al) = 14 mm
Initially, these FE models had an elastic response equivalent to their test specimen
counterparts (E1 and E2). The FE models had a lower connection yield load than the tests (see
Figure 5.25), followed by a gradual load increase as well as a large plastic deformation. The
reason for this difference (between tests specimens and FE models) is likely due to occasional
oversizing of the welds during their fabrication process, as a was result of low welding control.
This weld oversizing elevated the test specimens ultimate strength as it slightly reduced the
strain concentration at the slot region, thus delaying the onset of material yielding there. In
contrast, the FE models were not able to reproduce this behaviour as each represented only a
quarter of the connection and they had a uniform weld size.
al
Lw
Figure 5.24 FE models of connections type E1 and E2
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In the course of the FE analyses, the end of the elastic response was followed by a
transition region that is similar to the transition seen in test specimens E3, E4 and E5 before the
attainment of a yield plateau. Unfortunately, the strain concentration at the slot region of these
FE models prevented the attainment of this plateau, and it triggered the fracture (or "death") of
the elements at the slot region. Even though the weld length of these FE models was similar to
that in test specimen E3, E4 and E5, the large eccentricity in these connections negatively
affected their behaviour. A check of the distortion limit in the tube cross-section was performed
herein, considering D2 (the minor dimension) as the tube diameter, at the end of each time step.
(An ultimate load distortion limit of 3% of the tube outer dimension has been advocated by Lu et
al. (1994) and is now widely used for tubular structures). For both FE models, this limit (0.03D2)
was only exceeded by FE model E2. Despite this, the variation between the load corresponding
to this limit and the maximum load barely exceeded 2%.
At the maximum load, the uneven stress distribution in the FE models demonstrated the
influence of shear lag on the behaviour of these connections. In addition to the characteristic
stress distribution due to shear lag, the use of a short weld length (in FE model E1) produced a
Figure 5.25 Load - deformation response for specimens and FE models E1 and E2
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high stress concentration in the tube base material all along the parallel welds (see Figure
5.26). On the other hand, an increase in Lw (see Figure 5.27) decreased the magnitude of the
stresses along the parallel welds and just a stress concentration at the slot region. In a similar
manner to the test specimens, distortion of the tube cross-section was restrained by the gusset
plate and the large distortion of FE model E2 is due to the gradual formation of a neck in the slot
region. The connection stress distribution suggested a CF failure for both FE models and a
further TO failure for model E1. However, once the crack started its propagation in model E1,
rotation of the end part of the EHS led to a CF failure, as also observed during the test.
The FE models favourably reproduced the uneven strain distribution and strain magnitude
along the welds and around the tube circumference that was observed in the test (see Figures
5.28 and 5.29). Further FE vs test strain comparisons are given in Appendix C. The maximum
loads attained for these FE models are shown in Table 5.4.
Table 5.4 Ultimate capacity for connections E1 and E2
Connection Type
Test Load Nux (kN)
Distortion Limit LoadFE Analysis NuFE-D (kN)
FE Analysis Ultimate Load
NuFE (kN)Nux / NuFE Nux / NuFE-D
E1 1109 - 1098 1.01 -E2 1236 1174 1186 1.04 1.05
Figure 5.26 Stress distribution (von Mises) at maximum load for FE model E1
Figure 5.27 Stress distribution (von Mises) at maximum load for FE model E2
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5.3.4 Slotted EHS connection - slot end not filled (gusset plate oriented to give small
eccentricity)
For this FE model, the element size was gradually decreased from the tube edges to the
slot region and a large number of elements were used in front of the weld start (see Figure
5.30).
FE model E5
Diameter (D2) = 110 mm
Tube thickness (t) = 5.9 mm
Davg/t = 28
Lw/w = 0.79
Tube Length (L_tu) = 1000 mm
Weld size (al) = 15 mm
As observed in test specimen E5, the reduction of the connection eccentricity improved
the load transfer from the EHS to the gusset plate and reduced the strain concentration at the
slot region, in the FE model. In a similar manner to specimens E1 and E2, uneven oversizing of
Figure 5.28 Load-strain response at SG-5 in connection E1
- FE- Lab
Strain (mm/mm)
Figure 5.29 Load-strain response at SG-5 in connection E2
- FE- Lab
Strain (mm/mm)
Lw
al
Figure 5.30 FE models of connection type E5
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the welds was also done during fabrication of this test specimen. This resulted in a connection
overstrength that the FE model was not able to duplicate. Despite this, the response of the FE
model favourably emulated the trend of its test counterpart. Moreover, the FE model
displacement marking the transition from a yield plateau to the hardening region was close to
that of the test specimen. Beyond this point, the FE model continued to achieve larger
displacements until tube fracture started (at a load level near the test result). Based on this, it is
possible to infer that the maximum connection strength is principally determined by the relative
weld length (Lw). Nevertheless, the weld size can affect the strain concentration at the slot
region which may impact the overall connection behaviour (see Figure 5.31).
In order to determine the distortion in the tube cross-section geometry, the change of the
EHS small dimension (D2) was measured at the end of each time step. In general, the tube
material (in the small dimension) tended to move towards the gusset plate. This caused the
distortion limit to be reached during the transition from the elastic response to a yield plateau.
Even though there was a considerable difference between the connection displacement at the
maximum connection strength and at the distortion limit, there was only a difference of 11%
between their corresponding loads. It appears that, once the distortion limit was exceeded,
Figure 5.31 Load - deformation response for specimens and FE model E5
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ovalization in the tube cross-section slowly increased until the tube material fractured. In
addition, the demand at the slot region was relaxed as the deformation was re-distributed from
the connection region to the tube mid-length.
At the maximum load, the stress distribution confirmed the presence of shear lag since
the load transfer was mainly concentrated at the slot region, resulting in the fracture of the EHS
there. This phenomenon produced an uneven stress distribution along the weld that was more
marked here than for the rest of the FE models. The ovalization of the slot region, which started
at a relatively early stage, became more visible near the attainment of the maximum load and
continued to increase rapidly after this point (see Figure 5.32). In general, the FE model
favourably reproduced the strain distributions along the weld and around the tube
circumference. Furthermore, the strain gauge readings at the weld start (SG-5) correlated very
well (see Figure 5.33). Further FE vs. test strain comparisons are given in Appendix C.
The connection stress distribution at the maximum load showed the path that the crack
would follow at a later stage (see Figure 5.32). The failure mode in this FE model corresponded
to that seen during the test (CF). The maximum loads attained for this FE model and also at the
distortion limit are shown in Table 5.5.
Figure 5.32 Stress distribution (von Mises) at maximum load for FE model E5
Figure 5.33 Load-strain response at SG-5 in connection E5
- FE- Lab
Strain (mm/mm)
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5.3.5 Slotted gusset plate to tube connections in tension
5.3.5.1 Slotted gusset plate to CHS connection (Type C)
For these FE models, the elements size was gradually decreased from the tube edges to
the region in front of the start of the welds. In addition, a large number of elements was used at
the inner corner of the gusset plate (see Figure 5.34). This region proved its importance when
the bowing outwards started there, as a consequence of the gusset plate yielding.
FE models C1 and C2
Diameter (D) = 168.3 mm
Tube thickness (t) = 4.8 mm
D/t = 35
Lw/w = 0.68 for connection C1
Lw/w = 0.81 for connection C2
Tube Length (L_tu) = 750 mm
Weld size (al) = 14 mm (in both models)
The load-deformation response previously seen during the testing of specimens C1 and
C2 was closely replicated by the FE models (see Figure 5.35). In addition, the FE models were
capable of reproducing this response even near the maximum load, despite the large
deformations in the CHS and the gusset plate. Beyond the elastic response, the bowing
outwards of the gusset plate started to increase the distortion of the tube shape. In order to
determine the significance of this distortion, the change in the tube cross-section was computed
at the end of each time-step and then compared with a distortion limit of 3% of the tube
diameter (D). For both FE models, the attainment of this limit occurred at an early stage of the
connection plastic response. Therefore, the use of a limit on the distortion of the tube cross-
Table 5.5 Ultimate capacity for connections type E5
Connection Type
Test Load Nux (kN)
Distortion Limit Load FE Analysis
NuFE-D (kN)
FE Analysis Ultimate Load
NuFE (kN)Nux / NuFE Nux / NuFE-D
E5 1282 1113 1273 1.01 1.15
Lw
al
Figure 5.34 FE models of connection type C
5-24
SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 5: FE MODELLING OF CONNECTIONS
section at the ultimate limit state, to determine the connections ultimate capacity, may be more
reasonable rather than just a maximum load approach (see Figure 5.35).
The lack of a slot improved the load transfer from the tube to the gusset plate and
enhanced the connection stress distribution, especially in front of the gusset plate (see Figures
5.36 and 5.37). Because of this, both FE models displayed similar stress distributions, despite
having a big difference in their intensity.
Figure 5.35 Load - deformation response for specimens and FE models type C
5-25
SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 5: FE MODELLING OF CONNECTIONS
This difference in stress magnitude is the result of an interaction between the weld length
and the bowing of the gusset plate. The stress distributions in the gusset plates (see Figures
5.36 and 5.37) again confirmed the presence of shear lag, causing a stress concentration at the
inner corners of the gusset plate and hence plate yielding there and bowing of the gusset plate.
This interaction has been studied further in a subsequent parametric analysis. At the maximum
load, the connection stress distribution revealed the potential crack path which eventually
became a circumferential fracture (CF) for both FE models. Tube ovalization began at an early
stage of the plastic response and continued increasing until it was very prominent at the
maximum load.
Despite the two connections in each test specimen being fabricated alike connection
failure did not always take place at the end where the strain gauges were installed. Since this
was the case for both of these test specimens, the comparison of strain readings from the test
specimens and the FE models has showed some variations. Nevertheless, the general trend
followed by the FE models has always corresponded to that exhibited by the test specimens
(see Figures 5.38 and 5.39). In addition, the uneven strain distribution along the weld and
around the tube circumference was reproduced reasonably well by the FE models. Further FE
vs. test strain comparisons are given in Appendix C.
Figure 5.36 Stress distribution (von Mises) at maximum load for FE model C1
Figure 5.37 Stress distribution (von Mises) at maximum load for FE model C2
5-26
SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 5: FE MODELLING OF CONNECTIONS
The progressive deformation of the FE models was mainly created by the bowing of the
gusset plate, particularly after the attainment of the maximum load when cracks propagated.
Once cracking reached the weld toes it continued around the tube circumference. The
maximum load attained for these FE models is shown in Table 5.6.
5.3.5.2 Slotted gusset plate to EHS (gusset plate oriented to give a large eccentricity)
Since the bowing outward of the gusset plate affected the behaviour of this connection
type, as previously seen for connections type C, the element size was gradually decreased from
the tube edges to the region in front of the weld start and also to the inner corner of the gusset
plate (see Figure 5.40).
Table 5.6 Ultimate capacity for connections type C
Connection Type
Test Load Nux (kN)
Distortion Limit LoadFE Analysis NuFE-D (kN)
FE Analysis Ultimate Load
NuFE (kN)Nux / NuFE
Nux / NuFE-D
C1 1107 858 1081 1.02 1.29C2 1196 902 1235 0.95 1.32
Figure 5.38 Load-strain response at SG-5 in connection C1
- FE
- Lab
Strain (mm/mm)
Figure 5.39 Load-strain response at SG-5 in connection C2
- FE- Lab
Strain (mm/mm)
5-27
SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 5: FE MODELLING OF CONNECTIONS
FE models E3 and E4
Diameter (D1) = 220 mm
Tube thickness (t) = 5.9 mm
Davg/t = 28
Lw/w = 0.62 for connection E3
Lw/w = 0.74 for connection E4
Tube Length (L_tu) = 1000 mm
Weld size (al) = 15 mm
In a similar manner to the slotted EHS connections, the welds were unevenly over-sized
during fabrication of these test specimens. Once again, this provided these connections with
some over-strength that the FE models did not emulate (because of uniform weld sizing being
used). This resulted in a lower proportional limit and a lower connection yield load, in the FE
models (see Figure 5.41).
al
Lw
Figure 5.40 FE models of connections E3 and E4
Figure 5.41 Load - deformation response for specimens and FE models E3 and E4
5-28
SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 5: FE MODELLING OF CONNECTIONS
Nevertheless, the FE models did reproduce the overall response of the test specimens.
In a similar manner (to connections type C), the bowing outwards of the gusset plate increased
the distortion of the tube cross-section and eventually induced fracture of the tube material at
the weld start. A check on the tube cross-section distortion (using D2 as the tube diameter),
performed at the end of each time-step, revealed the attainment of this deformation limit
(0.03D2) at a relatively small displacement, for both FE models. As a result, the difference
between the maximum load and the load at this ultimate deformation limit was at least 30% (see
Table 5.7).
As seen in the FE models C1 and C2, the lack of a slot improved the stress distribution as
the load in the tube in front of the gusset plate could be transferred directly to the weld.
Analogous to the tests, shear lag in the gusset plate encouraged the attainment of the yield
strain in the elements located at the inner corners. This encouraged bowing of the gusset plate,
which increased the element strain at the weld start and triggered element fracture ("death")
there. The EHS connections have exhibited a different stiffness for the gusset plate orientation
relative to each axis and the greatest deformation occurs when gusset plate is oriented to give a
large eccentricity. At the maximum load, FE model E4 (having the longer weld) showed a better
stress distribution than FE model E3 (especially at the inner corners of the gusset plate). This
decreased the gusset plate deformations and consequently the tube cross-section distortion
(see Figures 5.42 and 5.43).
Table 5.7 Ultimate capacity for connections type E3 and E4
Connection Type
Test Load Nux (kN)
Distortion LimitsFE Analysis NuFE-D (kN)
FE Analysis Load
NuFE (kN)Nux / NuFE Nux / NuFE-D
E3 1336 984 1348 0.99 1.36E4 1400 1078 1413 0.99 1.30
5-29
SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 5: FE MODELLING OF CONNECTIONS
Moreover, the stress distribution in the FE models revealed the potential crack path, which
eventually became CF for both models. In general, the uneven strain distribution along the
welds and around the tube circumference was reproduced reasonably well for these FE models.
Similarly, the change in strain at the beginning of the welds (location SG-5) in the FE models
reflected that observed during the tests (see Figures 5.44 and 5.45).
Figure 5.42 Stress distribution (von Mises) at maximum load on FE model E3
Figure 5.43 Stress distribution (von Mises) at maximum load on FE model E4
Figure 5.44 Load-strain response at SG-5 in connection E3
- FE- Lab
Strain (mm/mm)
Figure 5.45 Load-strain response at SG-5 in connection E4
- FE- Lab
Strain (mm/mm)
5-30
SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 5: FE MODELLING OF CONNECTIONS
Further FE vs. test strain comparisons are given in Appendix C. The maximum load
attained for these FE models is shown on Table 5.7.
5.3.6 Connections under compression load
In a similar manner to the tension tests, a progressive application of compression
displacement was made at the gusset plate end. However, an additional lateral displacement (in
the x-axis direction of the FE models) was applied to emulate the gradual out-of-straightness
seen during the tests. In order to study the behaviour of connections under these compression
loading conditions, a quarter of each test specimen was modelled. The governing failure mode
for this loading condition corresponded to local buckling of the tube (LB). Nevertheless, the
factors responsible for this failure mode varied since they were determined by the connection
type. The results of these analyses are presented in this section.
5.3.6.1 Slotted CHS to gusset plate connection - slot end not filled
The element size in FE model A3C was progressively decreased from the tube ends to
the slot region. In order to determine the need to use contact elements herein, the distance
between the gusset plate and the tube wall (defining the slot end) was reviewed at the end of
each time step. The FE analysis results showed that the maximum load occurred before contact
of the gusset plate and the CHS wall at the end of the slot. As a result, contact elements were
not required. Moreover, this FE model was able to clearly capture the strain distribution at the
slot and the formation of a buckle there, before the open slot length was reduced to zero.
FE model A3C
Diameter (D) = 168.3 mm
Tube thickness (t) = 4.8 mm
D/t = 35
Lw/w = 0.86 for connection A3C
Tube Length (L_tu) = 750 mm
Weld size (al) = 10 mm
Lw
al
Figure 5.46 FE model of connection type A3C
5-31
SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 5: FE MODELLING OF CONNECTIONS
In the same way as for the tension tests, the load transfer from the tube to the gusset
plate produced a strain concentration at the slot region. Because of this, the elements close to
the slot region experienced a progressive major strain increase meanwhile the rest of the tube
remained at small strain values. This strain concentration triggered the formation of local
buckling near the beginning of the welds and marked the change in the connection stiffness.
This initial small buckle continued to grow as the load increased, up to attainment of the
maximum load. Beyond this point, distortion of the connection persisted but the load decreased
gradually (see Figure 5.47). Finally, the FE analysis stopped due to numerical solution problems
associated with excessive distortion of elements at the slot region. Nevertheless, considerable
deformation had taken place in the connection by this stage and the load at this point
corresponded to approximately 80% of the maximum load.
At the maximum load, the FE model displayed an uneven (von Mises) stress distribution
in the connection region. This suggested that the weld length would also influence the intensity
of the shear lag under compression loading (see Figure 5.48), but no other connection was
tested to verify this. Only a slight ovalization of the tube cross-section was observed since the
main deformation was located at the slot region. To generate a buckle of the entire net cross-
Figure 5.47 Load - deformation response for specimen and FE A3C
FE
5-32
SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 5: FE MODELLING OF CONNECTIONS
section large deformations were required. The attainment of the suggested distortion limit
(0.03D) required a displacement of 6.9 mm in this FE model, which corresponds to 153% of the
value required to attain the maximum load (4.5 mm). The FE model favourably reproduced the
strain distributions along the welds and around the tube circumference. Moreover, the strain
gauge readings at the beginning of the weld (location SG-5) compared very well with the FE
strains (see Figure 5.49). Further FE vs. test strain comparison are given in Appendix C. The
maximum load attained for this FE model is shown in Table 5.8.
5.3.6.2 Slotted gusset plate to CHS connection
The element size, in FE model C3C was progressively decreased from the tube ends to
the beginning of the welds. In addition, similar modelling was done at the inner corner of the
gusset plate where a large number of elements were used (see Figure 5.50). The requirement
to use contact elements was avoided in this FE model too, since the distance between the
gusset plate edge and the tube surface (the more critical zone of contact) showed insignificant
variations for at least 80% of the FE analysis (which also included the attainment of the
Table 5.8 Ultimate capacity for connection A3CConnection
TypeTest Load Nux (kN)
FE Analysis Load NuFE (kN) Nux / NuFE
A3C -1145 -1067 1.07
Figure 5.48 Stress distribution (von Mises) at maximum load of FE model A3C
Figure 5.49 Load-strain response at SG-5 in connection A3C
- FE
- Lab
5-33
SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 5: FE MODELLING OF CONNECTIONS
maximum load). This is due to the restriction on deformation imposed by the welds, since they
were fabricated close to the critical point.
FE models C3C
Diameter (D) = 168.3 mm
Tube thickness (t) = 4.8 mm
D/t = 35
Lw/w = 0.84 for connection C3C
Tube Length (L_tu) = 750 mm
Weld size (al) = 14 mm
In a similar manner to the tension test, the presence of shear lag (which was affected by
the weld length) was found to influence the behaviour of this connection under compression
load. In general, the load-deformation response for the FE model followed that of the test
specimen (see Figure 5.51).
Lw
al
Figure 5.50 FE models of connection type C in
Figure 5.51 Load - deformation response for specimen and FE model C3C
FE
Deformation Limit (0.03D)
5-34
SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 5: FE MODELLING OF CONNECTIONS
Moreover, the FE model reproduced the strain concentration (induced by shear lag) at the
beginning of the welds and at the inner corners of the gusset plate (see Figure 5.52). Close to
the end of the elastic response, the gusset plate started to bow inwards exacerbating the tube's
local stability and negatively affecting the connection behaviour. Despite this, the connection
load continued to increase while this distortion and a local buckle, in front of the weld start
position, grew slowly. During this FE analysis, the ultimate load distortion limit (0.03D) was
exceeded near the attainment of the maximum load. Beyond this limit the stability of the
connection was compromised and the tube cross-section distortion continued at an increasingly
rapid rate until local bucking (LB) failure.
The FE model displayed an uneven stress distribution in the connection region (see
Figure 5.52), but lack of a slot did enhance the stress distribution there. The FE models
favourably reproduced the strain distribution along the welds and around the tube
circumference. Moreover, the strain readings at the beginning of the welds (location SG-5)
correlated well (see Figure 5.53). Further FE vs. test strain comparison are given in Appendix C.
The maximum load attained for this FE model is shown in Table 5.9.
Table 5.9 Ultimate capacity for connection C3C
Connection TypeTest Load Nux (kN)
FE Analysis Load NuFE (kN) Nux / NuFE
C3C -869 800 1.09
Figure 5.52 Stress distribution (von Mises) at maximum load on FE model
(MPa)
Figure 5.53 Load-strain response at SG-5 in connection C3C
- FE
- Lab
5-35
SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 5: FE MODELLING OF CONNECTIONS
5.4 Summary of Chapter 5
A method has been suggested herein to generate a complete true stress-strain curve,
including the necking phase, when rectangular tensile coupon tests are used to determine the
material properties. In general, the FE models employed here have described the load-
deformation response and stress distribution acting in the connections, and were capable of
reproducing the failure modes of the test specimens. Moreover, a good agreement was
generally found between strain readings from test specimens and FE models. In a similar
manner to the test specimens, the shear lag phenomenon had a prime influence on the
behaviour of these FE models. Finally, these FE models have shown the possible need for
imposition of an ultimate deformation limit on the tube cross-section, for some connection types.
6-1CHAPTER 6: PARAMETRIC FINITE ELEMENT ANALYSIS
In the previous section, the FE models demonstrated their capacity to reproduce the load-
displacement response, the strain distribution at various loads and the failure mode for the test
specimens. Hence, a parametric analysis was undertaken using these FE models to study the
influence of parameters such as: the weld length (Lw), eccentricity reduced by half the gusset
plate thickness ( ) and the tube diameter-to-thickness ratio (D/t), on the connection strength. In
total a further 756 FE connections have been modelled during this research phase.
During this parametric analysis, the dimensioning of gusset plates and weld legs was
made so as to avoid failure modes other than Tear Out Failure (TO) or Circumferential Tensile
Fracture (CF) of the tubes. However, this dimensioning stayed within practical design limits in
an attempt to reasonably reproduce the compatibility of deformations existing between the
gusset plate, welds and tube under real design conditions. Moreover, the material properties
used throughout these analyses corresponded to the properties used previously during the
modelling of the specimens, as these were deemed to be realistic. During the tests it was
observed how the weld length influenced the overall connection behaviour and, depending on
this length, the failure mode in the connections varied from TO to CF. Considering this, FE
models were generated using Lw/w ratios ranging from 0.40 to 1.50. Applying this range of
values, the FE models were able to reproduce pure TO failure, a combination of TO and CF, CF
influenced by the shear lag phenomenon and pure CF without shear lag. In addition to this,
using a CHS with a diameter (D) of 180mm, and an EHS with an average diameter (Davg) of 165
mm, several D/t and Davg/t ratios were used in the generation of these FE models. These ratios
covered the range that would be found in practice: 45, 40, 35, 30, 25, 20 and 15. The
specimens tested previously in the laboratory are within the bounds of these ratios.
6.1 Parametric analysis results of slotted CHS connection - slot end not filled
Failure of this connection type was mainly governed by the growth of a crack in the tube
material near the start of the weld. Afterwards, the crack path followed during its propagation
was influenced by the weld length. In most cases, material cracking initiated near the weld
(where a high strain concentration takes place). However, in connections having a weld length
sufficient to develop their full strength, the location of this point was influenced by the tube
x'
SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 6: PARAMETRIC FINITE ELEMENT ANALYSIS
6-2thickness. For tubes with a large D/t ratio tube cracking started close to the weld, but a gradual
transition from this point to the slot end was observed as D/t decreased.
In order to determine the efficiency of the net cross-sectional area of the CHS, the
connection strength (NuFE) calculated during the parametric analysis has been normalized with
respect to AnFu. Furthermore, for comparison with current code or specification
recommendations, all resistance factors and partial safety factors have been set equal to unity
during this normalization (even though AISC (2005) and CSA (2001) prescribe different values).
The results from the parametric analysis show a gradual transition between the failure and
CF. The existence of this transition had been suggested before during the test of specimen A1.
There, the combination of both failure modes suggested that the occurrence of either failure
mode depended on the weld length (see Figure 6.1) and small variations produced during the
weld fabrication.
FE model A1 showed this combination of failure modes at an early stage. Once fracture
occurred on the net area in tension (for block failure), the strain distribution showed the
possibility of crack propagation by either following a TO failure or CF failure. However, the FE
analysis typically stopped at this post-ultimate stage. In general, the transition between these
Figure 6.1 Combined TO and CF failure of specimen and FE model A1
SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 6: PARAMETRIC FINITE ELEMENT ANALYSIS
6-3failure modes for the FE models exhibited this trait and the transition occurred at a ratio of Lw/w
near 0.75 (as indicated on Figure 6.2). However, a lower ratio was found for FE models with a
low D/t ratio, which suggests the existence of a correlation between these two parameters.
For FE models with a Lw/w ratio ranging from 0.40 to 0.80, TO failure was found to be the
governing failure mode. During the analyses, a combination of TO failure and weld material
failure (WM) was found in several FE models with a small D/t ratio. In order to prevent weld
material failure, their weld leg length (al) was increased. This produced an increase in the
connection strength as a result of the increase in the net area in tension during block failure.
Despite this connection “over-strength”, all the resulting FE analysis results followed the trend
suggested for the block failure formulae. The prediction for a tube with D/t=45 is shown in
Figure 6.2.
Even though some variation occurred during the calculation of the connection strength for
the lower Lw/w ratios, the overall results suggest that the full efficiency of the net cross-sectional
area can be developed if a ratio of Lw/w 1.0 is utilized. In Figure 6.2, the FE results are
compared with the formulae currently used to design this connection type. The design
provisions of AISC (2005) recommend the use of a variable efficiency factor for Lw/D ratios <1.3
but for Lw/D 1.3 AISC deems that the full section capacity can be achieved. The FE parametric
results support this latter rule. However, a considerable variation between the parametric
analysis results and AISC took place for Lw/D ratios <1.3. In general, the use of improved the
AISC prediction. Nevertheless, this variable efficiency factor is only applicable in the range of
Lw/w ratios from 0.75 to 0.91 because the TO failure mode governs for smaller Lw/w ratios.
AISC gives no bounds on the tear out (TO) failure mode check so this would always be
performed in conjunction with the circumferential tensile fracture (CF) check. The efficiency
factor (as can be seen in Figure 6.2) recommended by AISC, for application to the CF limit state
check, provides a better solution than CSA (2001) and Packer and Henderson (1997).
Even though the FE models with a Lw/w ratio >1.0 developed the full efficiency (100% of
AnFu) of their net cross-sectional area (see Figure 6.2), the governing failure mode continued to
be net section fracture at the connection. The strains in the tube material away from the
connection remained in the elastic range and the overall deformation was concentrated at the
≥
≥
x'
SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 6: PARAMETRIC FINITE ELEMENT ANALYSIS
6-4slot region (see Figure 6.1). The reason for this behaviour has been attributed to the high Fy/Fu
ratio of the tube material. (The same tube material properties were used in the FE parametric
analysis as established for the verified FE model, which in turn were based on the test
specimens. This high Fy/Fu ratio is thought to be representative of the modern cold-formed tube
material properties). On FE models showing a Lw/w ratio >1.0, this high ratio produced an
average AnFu/AgFy ratio near 0.96. Generally, the presence of a low ratio will impede the
possibility of developing the gross-section tensile yield strength (see Figure 6.3), thus confining
the member deformation to the slot region. While this is still acceptable for statically-loaded
connections it has important implications for these connections under cyclic (seismic) loading.
The results from these parametric analyses are shown in Table 6.1, where the results from FE
models with a failure mode throughout the weld metal (WM) or a combined mode involving the
weld (TO-WM and CF-WM) have been excluded.
Finally, the FE models type A developed the full effective net cross-sectional area before
they exhibited excessive distortion of the tube geometry. However, once material cracking
started a rapid distortion of the tube geometry would still occur.
SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 6: PARAMETRIC FINITE ELEMENT ANALYSIS
5
6-5
Figure 6.2 Parametric analysis results and experimental results for connection type A (NuFE/AnFu)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.
Lw/w
Nu
FE/A
nF
u
D/t=15D/t=20D/t=25D/t=30D/t=35D/t=40D/t=45LabCSA (2001)AISC (2005)AISC (2005) x'Predicted TO_Table 2.2Packer & Henderson (1997)
A1
A2
TO Failure
CF
Shear
Lag
Present
CF
1.3 Lw / D
TO Predicted
for D/t = 45
Figure 6.3 Parametric analysis results and experimental results for connection type A (NuFE/AgFy)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5
Lw/w
Nu
FE
/AgF
y
D/t=15
D/t=20
D/t=25
D/t=30
D/t=35
D/t=40
D/t=45
LAB
A1A2
TO Failure
CF
Shear Lag
Present
CF
SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 6: PARAMETRIC FINITE ELEMENT ANALYSIS
6-6
Tabl
e 6.
1 P
aram
etric
ana
lysi
s re
sults
for c
onne
ctio
n ty
pe A
0.57
0.77
0.83
0.92
1.01
1.05
1.10
1.13
1.16
1.19
1.23
1.27
1.31
1.43
1.79
2.11
Lw
/D
ThD
/t0.
400.
540.
590.
650.
710.
740.
770.
800.
820.
840.
870.
900.
921.
011.
261.
49L
w/w
A1-
0A
1-1
A1-
2A
B1-
1A
1-22
AB
1-2
AB
1-3
A1-
3A
B1-
4A
1-31
AB
1-5
AB
1-6
A1-
32A
1-4
A1-
5A
1-6
FEm
odel
515
647
686
747
802
830
853
866
881
889
902
909
911
914
915
914
NuF
Elo
ad(k
N)
TOTO
TOTO
TOTO
-CF
TO-C
FTO
-CF
CF
CF
CF
CF
CF
CF
CF
CF
Failu
rem
ode
0.54
0.67
0.72
0.78
0.84
0.87
0.89
0.90
0.92
0.93
0.94
0.95
0.95
0.95
0.95
0.95
NuF
E/A
gF
y
0.55
0.69
0.74
0.80
0.86
0.89
0.92
0.93
0.95
0.95
0.97
0.98
0.98
0.98
0.98
0.98
NuF
E/A
nF
u
A2-
0A
2-1
A2-
2A
B2-
1A
2-22
AB
2-2
AB
2-3
A2-
3A
B2-
4A
2-31
AB
2-5
AB
2-6
A2-
32A
2-4
A2-
5A
2-6
FEm
odel
583
735
779
848
911
941
965
979
995
1004
1017
1022
1023
1026
1027
1027
NuF
Elo
ad(k
N)
TOTO
TOTO
TOTO
-CF
TO-C
FTO
-CF
CF
CF
CF
CF
CF
CF
CF
CF
Failu
rem
ode
0.54
0.68
0.72
0.79
0.85
0.87
0.90
0.91
0.92
0.93
0.95
0.95
0.95
0.95
0.95
0.95
NuF
E/A
gF y
0.56
0.70
0.75
0.81
0.87
0.90
0.92
0.94
0.95
0.96
0.97
0.98
0.98
0.98
0.98
0.98
NuF
E/A
nF u
A3-
0A
3-1
A3-
2A
B3-
1A
3-22
AB
3-2
AB
3-3
A3-
3A
B3-
4A
3-31
AB
3-5
AB
3-6
A3-
32A
3-4
A3-
5A
3-6
FEm
odel
668
846
898
979
1050
1082
1108
1124
1140
1150
1162
1167
1168
1169
1170
1170
NuF
Elo
ad(k
N)
TOTO
TOTO
TO-C
FTO
-CF
TO-C
FTO
-CF
CF
CF
CF
CF
CF
CF
CF
CF
Failu
rem
ode
0.55
0.69
0.73
0.80
0.86
0.88
0.90
0.92
0.93
0.94
0.95
0.95
0.95
0.95
0.96
0.96
NuF
E/A
gF
y
0.56
0.71
0.76
0.82
0.88
0.91
0.93
0.95
0.96
0.97
0.98
0.98
0.98
0.98
0.98
0.98
NuF
E/A
nF
u
A4-
0A
4-1
A4-
2A
B4-
1A
4-22
AB
4-2
AB
4-3
A4-
3A
B4-
4A
4-31
AB
4-5
AB
4-6
A4-
32A
4-4
A4-
5A
4-6
FEm
odel
753
970
1031
1131
1219
1256
1292
1310
1330
1339
1352
1356
1357
1358
1359
1360
NuF
Elo
ad(k
N)
TOTO
TOTO
TO-C
FTO
-CF
TO-C
FTO
-CF
CF
CF
CF
CF
CF
CF
CF
CF
Failu
rem
ode
0.53
0.68
0.72
0.80
0.86
0.88
0.91
0.92
0.94
0.94
0.95
0.95
0.95
0.95
0.96
0.96
NuF
E/A
gFy
0.55
0.70
0.75
0.82
0.88
0.91
0.94
0.95
0.96
0.97
0.98
0.98
0.98
0.98
0.99
0.99
NuF
E/A
nFu
A7-
0A
7-1
A7-
2A
B7-
1A
7-3
AB
7-2
AB
7-3
A7-
4A
B7-
4A
7-5
AB
7-5
AB
7-6
A7-
6A
7-7
A7-
8A
7-9
FEm
odel
1026
1283
1355
1464
1542
1572
1600
1604
1612
1618
1623
1623
1622
1623
1623
1624
NuF
Elo
ad(k
N)
TOTO
TOTO
TOTO
-CF
CF
CF
CF
CF
CF
CF
CF
CF
CF
CF
Failu
rem
ode
0.61
0.76
0.80
0.86
0.91
0.93
0.94
0.95
0.95
0.95
0.96
0.96
0.96
0.96
0.96
0.96
NuF
E/A
gF
y
0.62
0.78
0.83
0.89
0.94
0.96
0.97
0.98
0.98
0.99
0.99
0.99
0.99
0.99
0.99
0.99
NuF
E/A
nF
u
A5-
0A
5-1
A5-
2A
B5-
1A
5-22
AB
5-2
AB
5-3
A5-
3A
B5-
4A
5-31
AB
5-5
AB
5-6
A5-
32A
5-4
A5-
5A
5-6
FEm
odel
1632
1726
1854
1957
1989
2004
2010
2010
2011
2011
2011
2011
2009
2010
2010
NuF
Elo
ad(k
N)
TO-W
MTO
TOTO
-CF
TO-C
FC
FC
FC
FC
FC
FC
FC
FC
FC
FC
FC
FFa
ilure
mod
e
0.78
0.82
0.88
0.93
0.95
0.96
0.96
0.96
0.96
0.96
0.96
0.96
0.96
0.96
0.96
NuF
E/A
gFy
0.80
0.85
0.91
0.96
0.98
0.99
0.99
0.99
0.99
0.99
0.99
0.99
0.99
0.99
0.99
NuF
E/A
nFu
A6-
0A
6-1
A6-
2A
B6-
1A
6-22
AB
6-2
AB
6-3
A6-
3A
B6-
4A
6-31
AB
6-5
AB
6-6
A6-
32A
6-4
A6-
5A
6-6
FEm
odel
2633
2643
2641
2636
2639
2639
2639
2633
2635
2635
NuF
Elo
ad(k
N)
WM
WM
WM
WM
WM
-CF
WM
-CF
CF
CF
CF
CF
CF
CF
CF
CF
CF
CF
Failu
rem
ode
0.96
0.96
0.96
0.96
0.96
0.96
0.96
0.96
0.96
0.96
NuF
E/A
gF
y
0.99
1.00
1.00
0.99
1.00
1.00
1.00
0.99
0.99
0.99
NuF
E/A
nF
u
6.72
8.40
11.2
0
45 40 35 30 25 20 15
3.73
4.20
4.80
5.60
SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 6: PARAMETRIC FINITE ELEMENT ANALYSIS
6-76.2 Parametric analysis results of slotted CHS connection - slot end filled (weld return)
The behaviour of this connection type was governed by the formation of a crack in the
weld return region. The formation and subsequent propagation of this crack was triggered by a
strain concentration at this location which is in turn dependant on the weld length. Despite the
initial reduction of the tube cross-sectional area due to the presence of the slot, the fabrication
of the weld return compensated for the lost material, thus eliminating a possible failure through
the net cross-sectional area. More importantly, the tensile stress area became equal to the
gross cross-sectional area (An=Ag). The connection strength (NuFE) has been normalized with
respect to AnFu in Figure 6.4, where it can be seen that the maximum strength achieved was
still only about 0.95 AnFu (where An=Ag), even for very large Lw/w values. Even though a net
section fracture was avoided here, either TO or CF failure through the gross area remained as
possible failure modes, with the latter being influenced by the shear lag phenomenon in a small
parametric range. The transition between TO and CF occurred for FE models having Lw/w
ratios ranging from 0.70 to 0.80. Moreover, this transition and the achievement of the full
efficiency of the gross cross-sectional area were influenced by the D/t ratio. The elimination of
the shear lag phenomenon was observed for FE models having a small D/t ratio and a Lw/w
ratio close to 0.80, but larger Lw/w values applied for thinner tubes. The vertical lines on Figure
6.4 show only the lower limits for these transitions.
The AISC's efficiency factor of 1.0 for connections with ratios agrees with the
parametric analysis results. However, an important variation took place for ratios <1.3. In
that range, a sudden drop in the connection efficiency is given by the AISC specification
whereas there is a gradual change shown by the FE models. The efficiency factors
recommended by CSA (2001) and Packer and Henderson (1997) are excessively conservative.
Gross cross-sectional area yielding was achieved for FE models having Lw/w > 1.0 (see
Figure 6.5). However, the amount of deformation sustained by the tubes was limited and their
failure was determined by cracking in the weld return region. This behaviour has been attributed
to the initial fabrication conditions of the specimens and the influence is included in the FE
models. The fabrication of the weld return considerably affected the behaviour of this region,
diminishing its capacity to sustain considerable strains, which would in turn allow the tube to
undergo large deformations and encourage the formation of a neck away from the connection.
Lw D⁄ 1.3≥
Lw D⁄
SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 6: PARAMETRIC FINITE ELEMENT ANALYSIS
6-8Furthermore, this low ductility precipitates the occurrence of TO failure. Because of this, the
predictions for TO failure from design provisions always exceeded the FE analysis results.
Thus, it is considered that a fabrication process which avoids slot-filling, with the associated
heat concentration in this region, would improve the connection behaviour. The results from
these parametric analyses are shown in Table 6.2, where the results from FE models with a
failure mode throughout the weld metal (WM) or a combined mode involving the weld (TO-WM
and CF-WM) have been excluded.
SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 6: PARAMETRIC FINITE ELEMENT ANALYSIS
5
6-9
Figure 6.4 Parametric analysis results and experimental results for connection type B (NuFE/AnFu)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.
Lw/w
Nu
FE/A
nF
u
(An=Ag)
D/t=15
D/t=20
D/t=25
D/t=30
D/t=35
D/t=40
D/t=45
Lab
CSA(2001)
AISC(2005)
AISC(2005) x'
Predicted TO_Table 2.2
Packer & Henderson (1997)
B1
B2
CF
Shear
Lag
Present
CF
TO Failure
TO Predicted
for D/t = 45
1.3 L w / D
Figure 6.5 Parametric analysis results and experimental results for connection type B (NuFE/AgFy)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5
Lw/w
Nu
FE
/AgF
y
D/t=15
D/t=20
D/t=25
D/t=30
D/t=35
D/t=40
D/t=45
Lab
B1 B2
TO Failure
CF
Shear
Lag
Present
CF
SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 6: PARAMETRIC FINITE ELEMENT ANALYSIS
6-10
Tabl
e 6.
2 P
aram
etric
ana
lysi
s re
sults
for c
onne
ctio
n ty
pe B
0.57
0.77
0.83
0.89
0.95
1.01
1.07
1.13
1.13
1.19
1.25
1.31
1.43
1.79
2.11
Lw/D
thic
knes
sD
/t0.
400.
540.
590.
630.
670.
710.
750.
800.
800.
840.
880.
921.
011.
261.
49LW
/w
B1-
0B
1-1
B1-
2B
B1-
1B
B1-
2B
1-3
BB
1-3
BB
1-4
B1-
4B
1-5
BB
1-5
B1-
6B
1-7
B1-
8B
1-9
FEm
odel
578
709
746
783
819
852
884
913
913
932
947
956
964
970
972
NuF
Elo
ad(k
N)
TOTO
TOTO
TO-C
FTO
-CF
TO-C
FTO
-CF
TO-C
FC
FC
FC
FC
FC
FC
FFa
ilure
mod
e
0.60
0.74
0.78
0.82
0.85
0.89
0.92
0.95
0.95
0.97
0.99
1.00
1.01
1.01
1.01
NuF
E/A
gFy
0.56
0.68
0.72
0.75
0.79
0.82
0.85
0.88
0.88
0.90
0.91
0.92
0.93
0.93
0.93
NuF
E/A
nF
B2-
0B
2-1
B2-
2B
B2-
1B
B2-
2B
2-3
BB
2-3
BB
2-4
B2-
4B
2-5
BB
2-5
B2-
6B
2-7
B2-
8B
2-9
FEm
odel
648
798
840
881
922
959
996
1030
1030
1052
1070
1077
1086
1092
1094
NuF
Elo
ad(k
N)
TOTO
TOTO
TOTO
TO-C
FTO
-CF
TO-C
FC
FC
FC
FC
FC
FC
FFa
ilure
mod
e
0.60
0.74
0.78
0.82
0.86
0.89
0.93
0.96
0.96
0.98
0.99
1.00
1.01
1.02
1.02
NuF
E/A
gFy
0.56
0.68
0.72
0.76
0.79
0.82
0.85
0.88
0.88
0.90
0.92
0.92
0.93
0.94
0.94
NuF
E/A
nFu
ng
(A=A
)
B3-
0B
3-1
B3-
2B
B3-
1B
B3-
2B
3-3
BB
3-3
BB
3-4
B3-
4B
3-5
BB
3-5
B3-
6B
3-7
B3-
8B
3-9
FEm
odel
740
910
962
1008
1057
1099
1139
1179
1179
1207
1224
1229
1241
1246
1248
NU
FElo
ad(k
N)
TOTO
TOTO
TOTO
TO-C
FTO
-CF
TO-C
FC
FC
FC
FC
FC
FC
FFa
ilure
mod
e
0.60
0.74
0.79
0.82
0.86
0.90
0.93
0.96
0.96
0.99
1.00
1.00
1.01
1.02
1.02
NuF
E/A
gFy
0.56
0.69
0.72
0.76
0.80
0.83
0.86
0.89
0.89
0.91
0.92
0.93
0.93
0.94
0.94
NuF
E/A
nFu
ng
(A=A
)
B4-
0B
4-1
B4-
2B
B4-
1B
B4-
2B
4-3
BB
4-3
BB
4-4
B4-
4B
4-5
BB
4-5
B4-
6B
4-7
B4-
8B
4-9
FEm
odel
858
1060
1121
1177
1232
1285
1336
1373
1374
1408
1428
1437
1445
1449
1452
NuF
Elo
ad(k
N)
TOTO
TOTO
TOTO
TO-C
FTO
-CF
TO-C
FC
FC
FC
FC
FC
FC
FFa
ilure
mod
e
0.60
0.75
0.79
0.83
0.87
0.90
0.94
0.97
0.97
0.99
1.00
1.01
1.02
1.02
1.02
NuF
E/A
gFy
0.56
0.69
0.73
0.76
0.80
0.83
0.87
0.89
0.89
0.91
0.93
0.93
0.94
0.94
0.94
NuF
E/A
nFu
ng
(A=A
)
B5-
0B
5-1
B5-
2B
B5-
1B
B5-
2B
5-3
BB
5-3
BB
5-4
B5-
4B
5-5
BB
5-5
B5-
6B
5-7
B5-
8B
5-9
FEm
odel
1067
1346
1419
1488
1557
1621
1673
1709
1709
1729
1734
1739
1735
1740
1746
NuF
Elo
ad(k
N)
TOTO
TOTO
TOTO
TOTO
-CF
CF
CF
CF
CF
CF
CF
Failu
rem
ode
0.63
0.79
0.84
0.88
0.92
0.96
0.99
1.01
1.01
1.02
1.02
1.03
1.02
1.03
1.03
NuF
E/A
gFy
0.58
0.73
0.77
0.81
0.85
0.88
0.91
0.93
0.93
0.94
0.94
0.95
0.94
0.95
0.95
NuF
E/A
nFu
ng
(A=A
)
B6-
0B
6-1
B6-
2B
B6-
1B
B6-
2B
6-3
BB
6-3
BB
6-4
B6-
4B
6-5
BB
6-5
B6-
6B
6-7
B6-
8B
6-9
FEm
odel
1288
1685
1779
1869
1958
2044
2107
2122
2121
2146
2150
2152
2150
2150
2166
NuF
Elo
ad(k
N)
TO-W
FTO
TOTO
TOTO
-CF
TO-C
FTO
-CF
CF
CF
CF
CF
CF
CF
CF
Failu
rem
ode
0.61
0.80
0.85
0.89
0.93
0.98
1.01
1.01
1.01
1.02
1.03
1.03
1.03
1.03
1.03
NuF
E/A
gFy
0.57
0.74
0.78
0.82
0.86
0.90
0.93
0.93
0.93
0.94
0.95
0.95
0.95
0.95
0.95
NuF
E/A
nFu
ng
(A=A
)
B7-
0B
7-1
B7-
2B
B7-
1B
B7-
2B
7-3
BB
7-3
BB
7-4
B7-
4B
7-5
BB
7-5
B7-
6B
7-7
B7-
8B
7-9
FEm
odel
2801
2811
2805
2818
NuF
Elo
ad(k
N)
TO-W
FW
FW
FW
FW
FW
F-C
FW
F-C
FW
F-C
FW
F-C
FW
F-C
FW
F-C
FC
FC
FC
FC
FFa
ilure
mod
e
1.02
1.02
1.02
1.03
NuF
E/A
gFy
0.94
0.94
0.94
0.95
NuF
E/A
nFu
ng
(A=A
)
3.73
45
4.20
40
4.80
35
5.60
30
11.2
015
6.72
25
8.40
20
un
g(A
=A)
SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 6: PARAMETRIC FINITE ELEMENT ANALYSIS
6-116.3 Parametric analysis results of slotted EHS connection - slot end not filled (gusset
plate oriented to give a large eccentricity)
In the presentation of the results of these analyses, the average of the larger and smaller
dimension of the EHS was considered as the "tube diameter" (Davg). For the connection type
E1, the region defining the transition between TO failure and CF showed a wide range. Here,
the transition occurred for Lw/w ratios from 0.60 to 0.80 depending on the tube Davg /t ratio. In
order to avoid confusion about the presence of either failure mode, only the lower limit of this
transition is shown in Figures 6.6 and 6.7. In several FE models the use of small D/t ratios
stimulated the presence of WM failure, but an increase in their weld leg length generated similar
results as previously seen for connections type-A. Furthermore, the TO failure predicted by
design provisions is shown here. The parametric analysis results normalized with respect to
their AnFu (Figure 6.6) show a gradual increase in the net cross-sectional area efficiency, but
only a maximum of 94% of AnFu was achieved here despite the use of large Lw/w ratios.
However, the normalization of connection strength (NuFE) with respect to AgFy showed the
achievement of the gross-section yield capacity for these connections (see Figure 6.7) for high
Lw/w ratios.
This behaviour of these connections can likely be attributed to the fact that the FE models
had an average AnFu/AgFy ratio close to 1.09. In most cases, when this ratio is greater than one
it encourages gross-section yielding to occur before net-section fracture. The parametric
analysis results and current design rules are compared in Figures 6.6 and 6.7. In order to
include the AISC (2005) in this comparison, the average dimension of the EHS (Davg) was
considered as its diameter (D). The use of this dimension provided somewhat better results
than using the larger or smaller axis dimension but none of the formulae followed the trend
described by the parametric analysis results. The results from these parametric analyses are
shown in Table 6.3.
SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 6: PARAMETRIC FINITE ELEMENT ANALYSIS
u)
y)
6-12
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6
Lw /w
Nu
FE/A
nF u
D /t=15avg
D /t=20avg
D /t=25avg
D /t=30avg
D /t=35avg
D /t=40avg
D /t=45avg
LabCSA(2001)AISC(2005)_Davg
AISC(2005)_D x'avg
Predicted TO_Table 2.2Packer & Henderson (1997)
E1
E2
TO
Failure
CF
Shear Lag
Present
1.3 L / Dw avg
CF
TO Predicted
for D / t =45avg
Figure 6.6 Parametric analysis results and experimental results for connection type E1 (NuFE/AnF
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6
Lw/w
Nu
FE
/AgF
y
D /t=15avg
D /t=20avg
D /t=25avg
D /t=30avg
D /t=35avg
D /t=40avg
D /t=45avg
Lab
E1
E2
TO
Failure
CF
Shear Lag
Present
CF
Figure 6.7 Parametric analysis results and experimental results for connection type E1 (NuFE/AgF
SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 6: PARAMETRIC FINITE ELEMENT ANALYSIS
6-13
0.42
0.55
0.70
0.77
0.83
0.89
0.95
1.01
1.07
1.13
1.19
1.31
1.43
1.79
2.11
Lw/D
ThD
avg/t
0.30
0.40
0.50
0.56
0.60
0.64
0.68
0.73
0.77
0.81
0.85
0.94
1.03
1.28
1.52
Lw/w
EB
1-1
EB
1-2
EB
1-3
E1-
1E
1-2
EB
1-4
EB
1-5
E1-
3E
B1-
6E
1-4
E1-
5E
1-6
E1-
7E
1-8
E1-
9FE
mod
el
430
503
580
611
636
665
687
703
723
733
745
769
782
782
782
NuF
Elo
ad(k
N)
TOTO
TOTO
TOTO
TOTO
TO-C
FTO
-CF
CF
CF
CF
CF
CF
Failu
rem
ode
0.55
0.64
0.74
0.78
0.81
0.85
0.88
0.90
0.92
0.94
0.95
0.98
1.00
1.00
1.00
NuF
E/A
gFy
0.50
0.59
0.68
0.72
0.75
0.78
0.81
0.82
0.85
0.86
0.87
0.90
0.92
0.92
0.92
NuF
E/A
nFu
EB
2-1
EB
2-2
EB
2-3
E2-
1E
2-2
EB
2-4
EB
2-5
E2-
3E
B2-
6E
2-4
E2-
5E
2-6
E2-
7E
2-8
E2-
9FE
mod
el
482
565
653
687
717
748
773
791
815
826
844
873
883
883
883
NuF
Elo
ad(k
N)
TOTO
TOTO
TOTO
TOTO
CF
CF
CF
CF
CF
CF
CF
Failu
rem
ode
0.55
0.64
0.74
0.78
0.82
0.85
0.88
0.90
0.93
0.94
0.96
0.99
1.01
1.01
1.01
NuF
E/A
gFy
0.50
0.59
0.68
0.72
0.75
0.78
0.81
0.83
0.85
0.86
0.88
0.91
0.92
0.92
0.92
NuF
E/A
nFu
EB
3-1
EB
3-2
EB
3-3
E3-
1E
3-2
EB
3-4
EB
3-5
E3-
3E
B3-
6E
3-4
E3-
5E
3-6
E3-
7E
3-8
E3-
9FE
mod
el
548
645
743
785
818
853
880
897
929
944
961
994
1005
1002
1003
NuF
Elo
ad(k
N)
TOTO
TOTO
TOTO
TOTO
TO-C
FTO
-CF
CF
CF
CF
CF
CF
Failu
rem
ode
0.55
0.65
0.74
0.79
0.82
0.85
0.88
0.90
0.93
0.94
0.96
0.99
1.01
1.00
1.00
NuF
E/A
gFy
0.50
0.59
0.68
0.72
0.75
0.78
0.81
0.82
0.85
0.87
0.88
0.91
0.92
0.92
0.92
NuF
E/A
nFu
EB
4-1
EB
4-2
EB
4-3
E4-
1E
4-2
EB
4-4
EB
4-5
E4-
3E
B4-
6E
4-4
E4-
5E
4-6
E4-
7E
4-8
E4-
9FE
mod
el
633
750
866
914
955
996
1029
1053
1071
1102
1120
1153
1167
1167
1167
NuF
Elo
ad(k
N)
TOTO
TOTO
TOTO
TO-C
FTO
-CF
TO-C
FC
FC
FC
FC
FC
FC
FFa
ilure
mod
e
0.55
0.65
0.75
0.79
0.82
0.86
0.89
0.91
0.92
0.95
0.96
0.99
1.01
1.01
1.01
NuF
E/A
gFy
0.50
0.59
0.69
0.72
0.76
0.79
0.82
0.83
0.85
0.87
0.89
0.91
0.92
0.92
0.92
NuF
E/A
nFu
EB
5-1
EB
5-2
EB
5-3
E5-
1E
5-2
EB
5-4
EB
5-5
E5-
3E
B5-
6E
5-4
E5-
5E
5-6
E5-
7E
5-8
E5-
9FE
mod
el
784
923
1061
1121
1163
1212
1254
1286
1303
1333
1354
1389
1391
1392
1393
NuF
Elo
ad(k
N)
TOTO
TOTO
TOTO
-CF
TO-C
FTO
-CF
CF
CF
CF
CF
CF
CF
CF
Failu
rem
ode
0.57
0.67
0.77
0.81
0.84
0.88
0.91
0.93
0.94
0.96
0.98
1.00
1.01
1.01
1.01
NuF
E/A
gFy
0.52
0.61
0.71
0.75
0.77
0.81
0.83
0.86
0.87
0.89
0.90
0.92
0.93
0.93
0.93
NuF
E/A
nFu
EB
6-1
EB
6-2
EB
6-3
E6-
1E
6-2
EB
6-4
EB
6-5
E6-
3E
B6-
6E
6-4
E6-
5E
6-6
E6-
7E
6-8
E6-
9FE
mod
el
945
1131
1307
1382
1441
1476
1524
1593
1610
1631
1679
1728
1731
1730
1732
NuF
Elo
ad(k
N)
TOTO
TOTO
TOTO
-CF
TO-C
FTO
-CF
CF
CF
CF
CF
CF
CF
CF
Failu
rem
ode
0.55
0.66
0.76
0.81
0.84
0.86
0.89
0.93
0.94
0.95
0.98
1.01
1.01
1.01
1.01
NuF
E/A
gFy
0.51
0.61
0.70
0.74
0.78
0.80
0.82
0.86
0.87
0.88
0.90
0.93
0.93
0.93
0.93
NuF
E/A
nFu
EB
7-1
EB
7-2
EB
7-3
E7-
1E
7-2
EB
7-4
EB
7-5
E7-
3E
7-4
E7-
6E
7-7
E7-
8E
7-9
FEm
odel
1212
1514
1766
1881
1964
2041
2106
2145
2225
2254
2269
2265
2273
NuF
Elo
ad(k
N)
TOTO
TOTO
TO-C
FC
FC
FC
FC
FC
FC
FC
FC
FFa
ilure
mod
e
0.54
0.68
0.79
0.84
0.88
0.91
0.94
0.96
0.99
1.01
1.01
1.01
1.01
NuF
E/A
gFy
0.50
0.62
0.73
0.78
0.81
0.84
0.87
0.89
0.92
0.93
0.94
0.93
0.94
NuF
E/A
nFu
11.0
015
6.60
25
8.25
20
4.71
35
5.50
30
3.67
45
4.13
40
Tabl
e 6.
3 P
aram
etric
ana
lysi
s re
sults
for c
onne
ctio
n ty
pe E
1
SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 6: PARAMETRIC FINITE ELEMENT ANALYSIS
6-146.4 Parametric analysis results of slotted EHS connection - slot end not filled (gusset
plate oriented to give small eccentricity)
In general, connection types E1 and E5 showed similarities in their results. However, the
change in gusset plate orientation and the resulting minor eccentricity ( ) associated with type
E5 positively improved the overall response of these FE models. The region defining the
transition between TO failure and CF was reduced to a Lw/w ratio near to 0.70 (see Figure 6.8),
but a lower Lw/w ratio was found for thick tubes. In general, the net cross-sectional area
efficiency achieved for these FE models did not surpass the value reached for the type E1 (0.94
AnFu). However, the normalization of the connection strength (NuFE) with respect to AgFy
showed an average increase of 3% over their E1 counterparts (see Figure 6.9), and uniform
gross-section yielding took place over the tube length before net-section fracture. Moreover, this
advantageous behaviour started with FE models having a ratio of Lw/w > 0.80. For FE models
with Lw/w > 1.00 the shear lag phenomenon seems to have no more influence on the
connection efficiency and the inability to attain the full efficiency is related to the tube shape.
The use of Davg for the AISC design provision for this connection type approximately agrees
with the end of the shear lag influence, although the range of influence of the shear lag is not
well defined. The application of rather than is an improvement relative to the numerical
results too.
Even though the governing failure mode for low Lw/w ratios was TO failure, the strain
distribution for these FE models showed a small combination with the CF. This has been
associated with the low for this connection which enhanced the distribution of the force
between the tube and the gusset plate. Because of this, the connection efficiency of FE models
in this low Lw/w range always exceeded the predicted of TO capacity, according to design
provisions. The results from these parametric analyses are shown in Table 6.4, where the
results from FE models with a failure mode throughout the weld metal (WM) have been
excluded.
x'
x' x
x'
SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 6: PARAMETRIC FINITE ELEMENT ANALYSIS
u)
y)
6-15
Figure 6.8 Parametric analysis results and experimental results for connection type E5 (NuFE/AnF
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6
Lw/w
Nu
FE/A
nF
u
D /t=15avg
D /t=20avg
D /t=25avg
D /t=30avg
D /t=35avg
D /t=40avg
D /t=45avg
LabCSA(2001)AISC(2005)_Davg
AISC(2005)_D x'avg
Predicted TO_Table 2.2Packer & Henderson (1997)
E5
CF
Shear Lag
Present
TO failure
1.3 Lw/ Davg
CF
TO Predicted
for D / t = 45avg
Figure 6.9 Parametric analysis results and experimental results for connection type E5 (NuFE/AgF
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6
Lw/w
Nu
FE/A
gF
y
D /t=15avg
D /t=20avg
D /t=25avg
D /t=30avg
D /t=35avg
D /t=40avg
D /t=45avg
Lab
TO failure
CF
CF
Shear Lag
Present
E5
SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 6: PARAMETRIC FINITE ELEMENT ANALYSIS
6-16
Tabl
e 6.
4 P
aram
etric
ana
lysi
s re
sults
for c
onne
ctio
n ty
pe E
5
0.42
0.56
0.69
0.77
0.83
0.89
0.95
1.01
1.13
1.19
1.31
1.43
1.79
2.11
Lw/D
Th
Dav
g/t
0.30
0.40
0.50
0.56
0.60
0.64
0.68
0.73
0.81
0.85
0.94
1.03
1.28
1.52
Lw/w
EB
51-1
EB
51-2
EB
51-3
E51
-1E
51-2
EB
51-4
EB
51-5
E51
-3E
51-4
E51
-5E
51-6
E51
-7E
51-8
E51
-9F
Em
odel
454
551
635
684
711
736
754
776
790
796
796
796
796
797
NuF
Elo
ad(k
N)
TOTO
TOTO
TOTO
TOTO
-CF
CF
CF
CF
CF
CF
CF
Fai
lure
mod
e
0.58
0.70
0.81
0.87
0.91
0.94
0.96
0.99
1.01
1.02
1.02
1.02
1.02
1.02
NuF
E/A
gF y
0.52
0.64
0.73
0.79
0.82
0.85
0.87
0.89
0.91
0.92
0.92
0.92
0.92
0.92
NuF
E/A
nF u
EB
52-1
EB
52-2
EB
52-3
E52
-1E
52-2
EB
52-4
EB
52-5
E52
-3E
52-4
E52
-5E
52-6
E52
-7E
52-8
E52
-9F
Em
odel
507
611
704
761
796
825
846
867
890
895
897
894
895
895
NuF
Elo
ad(k
N)
TOTO
TOTO
TOTO
TOTO
-CF
CF
CF
CF
CF
CF
CF
Fai
lure
mod
e
0.58
0.70
0.80
0.87
0.91
0.94
0.96
0.99
1.01
1.02
1.02
1.02
1.02
1.02
NuF
E/A
gF y
0.52
0.63
0.72
0.78
0.82
0.85
0.87
0.89
0.91
0.92
0.92
0.92
0.92
0.92
NuF
E/A
nF u
EB
53-1
EB
53-2
EB
53-3
E53
-1E
53-2
EB
53-4
EB
53-5
E53
-3E
53-4
E53
-5E
53-6
E53
-7E
53-8
E53
-9F
Em
odel
561
684
791
858
897
931
957
981
1009
1022
1017
1019
1020
1021
NuF
Elo
ad(k
N)
TOTO
TOTO
TOTO
TOTO
-CF
CF
CF
CF
CF
CF
CF
Fai
lure
mod
e
0.56
0.68
0.79
0.86
0.90
0.93
0.96
0.98
1.01
1.02
1.02
1.02
1.02
1.02
NuF
E/A
gF
y
0.51
0.62
0.72
0.78
0.81
0.84
0.87
0.89
0.91
0.92
0.92
0.92
0.92
0.92
NuF
E/A
nF
u
EB
54-1
EB
54-2
EB
54-3
E54
-1E
54-2
EB
54-4
EB
54-5
E54
-3E
54-4
E54
-5E
54-6
E54
-7E
54-8
E54
-9F
Em
odel
620
784
906
978
1028
1072
1104
1112
1166
1182
1194
1192
1191
1192
NuF
Elo
ad(k
N)
TOTO
TOTO
TOTO
TOTO
-CF
CF
CF
CF
CF
CF
CF
Fai
lure
mod
e
0.53
0.68
0.78
0.84
0.89
0.92
0.95
0.96
1.00
1.02
1.03
1.03
1.03
1.03
NuF
E/A
gF y
0.48
0.61
0.71
0.76
0.80
0.84
0.86
0.87
0.91
0.92
0.93
0.93
0.93
0.93
NuF
E/A
nF u
EB
55-1
EB
55-2
EB
55-3
E55
-1E
55-2
EB
55-4
EB
55-5
E55
-3E
55-4
E55
-5E
55-6
E55
-7E
55-8
E55
-9F
Em
odel
827
1020
1190
1289
1325
1370
1384
1393
1419
1419
1415
1415
1416
1419
NuF
Elo
ad(k
N)
TOTO
TOTO
TO-C
FC
FC
FC
FC
FC
FC
FC
FC
FC
FF
ailu
rem
ode
0.60
0.74
0.86
0.93
0.96
0.99
1.00
1.01
1.03
1.03
1.02
1.02
1.02
1.03
NuF
E/A
gF y
0.54
0.67
0.78
0.84
0.87
0.90
0.91
0.91
0.93
0.93
0.93
0.93
0.93
0.93
NuF
E/A
nF u
EB
56-1
EB
56-2
EB
56-3
E56
-1E
56-2
EB
56-4
EB
56-5
E56
-3E
56-4
E56
-5E
56-6
E56
-7E
56-8
E56
-9F
Em
odel
955
1208
1436
1563
1625
1664
1702
1769
1744
1767
1767
1767
1773
1766
NuF
Elo
ad(k
N)
TOTO
TOTO
-CF
CF
CF
CF
CF
CF
CF
CF
CF
CF
CF
Fai
lure
mod
e
0.56
0.71
0.84
0.91
0.95
0.97
0.99
1.03
1.02
1.03
1.03
1.03
1.04
1.03
NuF
E/A
gF y
0.51
0.64
0.76
0.83
0.86
0.88
0.90
0.94
0.93
0.94
0.94
0.94
0.94
0.94
NuF
E/A
nF u
E57
-3E
57-4
E57
-5E
57-6
E57
-7E
57-8
E57
-9F
Em
odel
2218
2231
2255
2300
2315
2350
2349
NuF
Elo
ad(k
N)
WF
WF
WF
WF
WF
WF
WF
CF
CF
CF
CF
CF
CF
CF
Fai
lure
mod
e
0.99
1.00
1.01
1.03
1.03
1.05
1.05
NuF
E/A
gF y
0.90
0.91
0.92
0.94
0.94
0.96
0.96
NuF
E/A
nF u
11.0
015
6.60
25
8.25
20
4.71
35
5.50
30
3.67
45
4.13
40
SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 6: PARAMETRIC FINITE ELEMENT ANALYSIS
6-17A clear tendency of the tube material to align with the line of action of the force was
observed for this connection type E5. This created a distortion of the tube geometry exceeding
the maximum limit proposed in the previous section (3% distortion of the tube cross-section)
prior to maximum load capacity being attained. Because of this distortion, a difference of 10%
was observed between the connection ultimate strength and the load corresponding to this
deformation limit. This contrasted with the FE models type E1, where the gusset plate
orientation in the connection provided a supplementary stiffness which helped the tube avoid
excessive distortion.
6.5 Slotted gusset plate to tube connection in tension
The possibility of avoiding a reduction in the tube gross cross-sectional area is the
principal advantage of this connection type. Because of this, the tube's net area can be
considered equal to the gross cross-sectional area (An=Ag), thus reducing the risk of a brittle
fracture in the connection. However, a strain concentration in the weld region tends to trigger
the growth of a crack, introducing an undesirable failure mechanism. Even though this strain
concentration is basically determined by the connection weld length, the influence of additional
factors such as the gusset plate dimensions and tube shape have been found in the course of
this parametric analysis. Hence, a detailed explanation for each connection configuration
follows.
6.5.1 Parametric analysis results of slotted gusset plate to CHS connection
Test results and the FE connection tensile strength (NuFE) normalized with respect to
AnFu (where An=Ag) are shown in Figure 6.10. For FE models with low Lw/w ratios the
connection strength was principally controlled by TO failure and the connection strengths were
close to the values predicted by design provisions. This has been related to the influence of the
gusset plate deformation which increases the strains in the weld region. Nevertheless, this
effect diminishes as the Lw/w ratio decreases.
The transition between this failure mode and CF failure occurred in FE models at Lw/
w=0.70. For Lw/w ratios between 0.7 and 1.0 the connection strength was limited by shear lag
and bowing out of the gusset plate. This interaction dictated the magnitude of the strains in the
weld region and thus the material cracking there.
SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 6: PARAMETRIC FINITE ELEMENT ANALYSIS
6-18For Lw/w >1.0 cracking in the weld region disappeared at ultimate load allowing the
formation of a neck at the tube mid-length (see Figures 6.10 and 6.11). This shows that the
gradual reduction of strains in the weld region allows large deformations away from the
connection region. Despite the generation of a neck for long connections, the ultimate
connection strength never exceeded 96% of AnFu. This is because of the excessive element
deformations associated with necking, which terminated the numerical solution procedure
prematurely during the FE analysis.
In most cases, the attainment of the connection ultimate capacity was associated with
surpassing the tube's distortion limit. Figure 6.12 shows how the smallest difference occurs for
connections having thick tubes and this difference is within 20% for tubes with a D/t ratio of 15
and 20. Moreover, a gradual increase in the connection strength can be appreciated when the
load at this distortion limit is normalized with respect to AnFu (see Figure 6.13) where a linear
variation is evident. The results from these parametric analyses are shown in Table 6.5 and
Table 6.6, where the results from FE models with a failure mode throughout the weld metal
(WM) have been excluded.
SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 6: PARAMETRIC FINITE ELEMENT ANALYSIS
u)5
y)
6-19
Figure 6.10 Parametric analysis results and experimental results for connection type C (NuFE/AnF
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.
Lw/w
Nu
FE/A
nF
u
(An=Ag)
D/t=15D/t=20D/t=25D/t=30D/t=35D/t=40D/t=45LabCSA (2001)AISC(2005)AISC(2005) x'Predicted TO_Table 2.2Packer & Henderson (1997)
C1
C2
Tension
Failure
Shear Lag
Present
Tension Failure:
Necking
TO Failure
1.3 Lw/ D
TO Predicted
for D/t=45
Figure 6.11 Parametric analysis results and experimental results for connection type C (NuFE/AgF
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5
Lw/w
Nu
FE
/AgF
y
D/t=15
D/t=20
D/t=25
D/t=30
D/t=35
D/t=40
D/t=45
Lab
C1
C2
TO Failure
Tension
Failure
Shear Lag
Present
Tension Failure:
Necking
SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 6: PARAMETRIC FINITE ELEMENT ANALYSIS
6-20
0.57
0.67
0.77
0.83
0.89
0.95
1.01
1.07
1.13
1.19
1.25
1.31
1.43
1.79
2.11
Lw
/D
ThD
/t0.
400.
470.
540.
590.
630.
670.
710.
750.
800.
840.
880.
921.
011.
261.
49L w
/w
C1-
1C
B1-
1C
1-2
C1-
3C
B1-
2C
B1-
3C
1-4
CB
1-4
C1-
5C
1-6
CB
1-5
C1-
7C
1-8
C1-
9C
1-10
FEm
odel
708
764
812
842
873
901
933
966
990
998
998
998
998
998
998
NuF
Elo
ad(k
N)
TOTO
TOTO
TOTO
-CF
TO-C
FC
FC
FC
FC
FC
FC
FN
EC
KN
EC
KFa
ilure
mod
e
0.74
0.80
0.85
0.88
0.91
0.94
0.97
1.01
1.03
1.04
1.04
1.04
1.04
1.04
1.04
NuF
E/A
gFy
0.68
0.73
0.78
0.81
0.84
0.87
0.90
0.93
0.95
0.96
0.96
0.96
0.96
0.96
0.96
NuF
E/A
nFu
C2-
1C
B2-
1C
2-2
C2-
3C
B2-
2C
B2-
3C
2-4
CB
2-4
C2-
5C
2-6
CB
2-5
C2-
7C
2-8
C2-
9C
2-10
FEm
odel
784
843
897
928
959
992
1029
1061
1092
1118
1120
1120
1120
1121
1121
NuF
Elo
ad(k
N)
TOTO
TOTO
-CF
TO-C
FTO
-CF
CF
CF
CF
CF
CF
CF
CF
NE
CK
NE
CK
Failu
rem
ode
0.73
0.78
0.83
0.86
0.89
0.92
0.96
0.99
1.02
1.04
1.04
1.04
1.04
1.04
1.04
NuF
E/A
gFy
0.67
0.72
0.77
0.80
0.82
0.85
0.88
0.91
0.94
0.96
0.96
0.96
0.96
0.96
0.96
NuF
E/A
nFu
C3-
1C
B3-
1C
3-2
C3-
3C
B3-
2C
B3-
3C
3-4
CB
4-3
C3-
5C
3-6
CB
4-3
C3-
7C
3-8
C3-
9C
3-10
FEm
odel
885
945
1005
1041
1073
1106
1147
1184
1226
1260
1275
1275
1275
1276
1276
NuF
Elo
ad(k
N)
TOTO
TOTO
TO-C
FTO
-CF
TO-C
FC
FC
FC
FC
FC
F-N
EC
KN
EC
KN
EC
KN
EC
KFa
ilure
mod
e
0.72
0.77
0.82
0.85
0.88
0.90
0.94
0.97
1.00
1.03
1.04
1.04
1.04
1.04
1.04
NuF
E/A
gFy
0.67
0.71
0.76
0.78
0.81
0.83
0.86
0.89
0.92
0.95
0.96
0.96
0.96
0.96
0.96
NuF
E/A
nFu
C4-
1C
B4-
1C
4-2
C4-
3C
B4-
2C
B4-
3C
4-4
CB
4-4
C4-
5C
4-6
CB
4-5
C4-
7C
4-8
C4-
9C
4-10
FEm
odel
1007
1073
1148
1183
1210
1259
1301
1338
1385
1424
1461
1479
1480
1481
1481
NuF
Elo
ad(k
N)
TOTO
TOTO
TOC
FC
FC
FC
FC
FC
FC
FC
F-N
EC
KN
EC
KN
EC
KFa
ilure
mod
e
0.71
0.75
0.81
0.83
0.85
0.89
0.91
0.94
0.97
1.00
1.03
1.04
1.04
1.04
1.04
NuF
E/A
gFy
0.65
0.70
0.74
0.77
0.78
0.82
0.84
0.87
0.90
0.92
0.95
0.96
0.96
0.96
0.96
NuF
E/A
nFu
C5-
1C
B5-
1C
5-2
C5-
3C
B5-
2C
B5-
3C
5-4
CB
5-4
C5-
5C
5-6
CB
5-5
C5-
7C
5-8
C5-
9C
5-10
FEm
odel
1315
1405
1483
1529
1578
1626
1675
1726
1763
1766
1766
1766
1767
1767
1768
NuF
Elo
ad(k
N)
TOTO
TOTO
TO-C
FC
FC
FC
FC
FC
FC
FC
FN
EC
KN
EC
KN
EC
KFa
ilure
mod
e
0.78
0.83
0.88
0.90
0.93
0.96
0.99
1.02
1.04
1.04
1.04
1.04
1.04
1.04
1.04
NuF
E/A
gFy
0.72
0.76
0.81
0.83
0.86
0.88
0.91
0.94
0.96
0.96
0.96
0.96
0.96
0.96
0.96
NuF
E/A
nFu
CB
6-1
C6-
2C
6-3
CB
6-2
CB
6-3
C6-
4C
B6-
4C
6-5
C6-
6C
B6-
5C
6-7
C6-
8C
6-9
C6-
10FE
mod
el
1817
1930
1989
2060
2115
2174
2182
2185
2186
2186
2186
2186
2187
2188
NuF
Elo
ad(k
N)
WF
TOTO
TOTO
-CF
TO-C
FTO
-CF
CF
CF
CF
CF
CF
NE
CK
NE
CK
NE
CK
Failu
rem
ode
0.87
0.92
0.95
0.98
1.01
1.04
1.04
1.04
1.04
1.04
1.04
1.04
1.04
1.04
NuF
E/A
gFy
0.80
0.85
0.87
0.91
0.93
0.96
0.96
0.96
0.96
0.96
0.96
0.96
0.96
0.96
NuF
E/A
nFu
CB
7-3
C7-
4C
B7-
4C
7-5
C7-
6C
B7-
5C
7-7
C7-
8C
7-9
C7-
10FE
mod
el
2647
2719
2784
2840
2862
2863
2864
2864
2865
2866
NuF
Elo
ad(k
N)
WF
WF
WF
WF
WF
CF
CF
CF
CF
CF
CF
CF
CF
NE
CK
NE
CK
Failu
rem
ode
0.96
0.99
1.01
1.03
1.04
1.04
1.04
1.04
1.04
1.04
NuF
E/A
gFy
0.89
0.91
0.93
0.95
0.96
0.96
0.96
0.96
0.96
0.96
NuF
E/A
nFu
11.2
015
6.72
25
8.40
20
4.80
35
5.60
30
3.73
45
4.20
40
Tabl
e 6.
5 P
aram
etric
ana
lysi
s re
sults
for c
onne
ctio
n ty
pe C
SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 6: PARAMETRIC FINITE ELEMENT ANALYSIS
1
1
1
1
1
6-21
Figure 6.12 Ratio of maximum load to load at the suggested distortion limit (connection type C)
.0
.1
.2
.3
.4
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5
L /w
uFE
uFE-D
w
@ maxN /
N
D/t=15
D/t=20
D/t=25
D/t=30
D/t=35
D/t=40
D/t=45
TO Failure
Tension
Failure
Shear Lag
Present
Neck
Figure 6.13 Parametric analysis results: load at distortion limit for connection type C (NuFE/AnFu)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5
L /w w
NU
FE
-D/A
nF
u
( An=Ag)
D/t=15
D/t=20
D/t=25
D/t=30
D/t=35
D/t=40
D/t=45
Tension
Failure
Shear Lag
Present
Tension Failure:
Necking
TO Failure
SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 6: PARAMETRIC FINITE ELEMENT ANALYSIS
6-22
0.57
0.67
0.77
0.83
0.89
0.95
1.01
1.07
1.13
1.19
1.25
1.31
1.43
1.79
2.11
Lw/D
ThD
/t0.
400.
470.
540.
590.
630.
670.
710.
750.
800.
840.
880.
921.
011.
261.
49Lw
/w
C1-
1C
B1-
1C
1-2
C1-
3C
B1-
2C
B1-
3C
1-4
CB
1-4
C1-
5C
1-6
CB
1-5
C1-
7C
1-8
C1-
9C
1-10
FEm
odel
676
671
692
695
696
698
706
723
731
726
745
748
769
805
846
Nlo
ad(k
N)
uFE
TOTO
TOTO
TOTO
-CF
TO-C
FC
FC
FC
FC
FC
FC
FN
EC
KN
EC
KFa
ilure
mod
e
0.70
0.70
0.72
0.72
0.73
0.73
0.74
0.75
0.76
0.76
0.78
0.78
0.80
0.84
0.88
NuF
E/A
gF
0.65
0.65
0.67
0.67
0.67
0.67
0.68
0.70
0.70
0.70
0.72
0.72
0.74
0.77
0.81
y
NuF
E/A
nuF
C2-
1C
B2-
1C
2-2
C2-
3C
B2-
2C
B2-
3C
2-4
CB
2-4
C2-
5C
2-6
CB
2-5
C2-
7C
2-8
C2-
9C
2-10
FEm
odel
716
723
746
753
766
771
774
789
799
813
820
821
847
913
961
Nlo
ad(k
N)
uFE
TOTO
TOTO
-CF
TO-C
FTO
-CF
CF
CF
CF
CF
CF
CF
CF
NE
CK
NE
CK
Failu
rem
ode
0.67
0.67
0.69
0.70
0.71
0.72
0.72
0.73
0.74
0.76
0.76
0.76
0.79
0.85
0.89
NuF
E/A
gF
0.61
0.62
0.64
0.65
0.66
0.66
0.66
0.68
0.68
0.70
0.70
0.70
0.73
0.78
0.82
y
NuF
E/A
nuF
C3-
1C
B3-
1C
3-2
C3-
3C
B3-
2C
B3-
3C
3-4
CB
4-3
C3-
5C
3-6
CB
4-3
C3-
7C
3-8
C3-
9C
3-10
FEm
odel
799
820
845
850
866
880
884
900
919
918
940
950
980
1054
1109
Nlo
ad(k
N)
uFE
TOTO
TOTO
TO-C
FTO
-CF
TO-C
FC
FC
FC
FC
FC
F-N
EC
KN
EC
KN
EC
KN
EC
KFa
ilure
mod
e
0.65
0.67
0.69
0.69
0.71
0.72
0.72
0.73
0.75
0.75
0.77
0.78
0.80
0.86
0.91
NuF
E/A
gyF
0.60
0.62
0.64
0.64
0.65
0.66
0.67
0.68
0.69
0.69
0.71
0.72
0.74
0.79
0.83
NuF
E/A
nuF
C4-
1C
B4-
1C
4-2
C4-
3C
B4-
2C
B4-
3C
4-4
CB
4-4
C4-
5C
4-6
CB
4-5
C4-
7C
4-8
C4-
9C
4-10
FEm
odel
993
953
982
989
1005
1017
1040
1048
1081
1101
1100
1112
1147
1232
1313
Nlo
ad(k
N)
uFE
TOTO
TOTO
TOC
FC
FC
FC
FC
FC
FC
FC
F-N
EC
KN
EC
KN
EC
KFa
ilure
mod
e
0.70
0.67
0.69
0.70
0.71
0.72
0.73
0.74
0.76
0.77
0.77
0.78
0.81
0.87
0.92
NuF
E/A
gF
0.64
0.62
0.64
0.64
0.65
0.66
0.67
0.68
0.70
0.71
0.71
0.72
0.74
0.80
0.85
y
NuF
E/A
nuF
C5-
1C
B5-
1C
5-2
C5-
3C
B5-
2C
B5-
3C
5-4
CB
5-4
C5-
5C
5-6
CB
5-5
C5-
7C
5-8
C5-
9C
5-10
FEm
odel
1216
1250
1272
1287
1309
1333
1347
1369
1376
1396
1429
1433
1469
1582
1660
Nlo
ad(k
N)
uFE
TOTO
TOTO
TO-C
FC
FC
FC
FC
FC
FC
FC
FN
EC
KN
EC
KN
EC
KFa
ilure
mod
e
0.72
0.74
0.75
0.76
0.77
0.79
0.79
0.81
0.81
0.82
0.84
0.85
0.87
0.93
0.98
NuF
E/A
gyF
0.66
0.68
0.69
0.70
0.71
0.73
0.73
0.74
0.75
0.76
0.78
0.78
0.80
0.86
0.90
NuF
E/A
nuF
CB
6-1
C6-
2C
6-3
CB
6-2
CB
6-3
C6-
4C
B6-
4C
6-5
C6-
6C
B6-
5C
6-7
C6-
8C
6-9
C6-
10FE
mod
el
1680
1729
1753
1782
1806
1828
1855
1880
1891
1925
1945
1983
2105
2176
Nlo
ad(k
N)
uFE
WF
TOTO
TOTO
-CF
TO-C
FTO
-CF
CF
CF
CF
CF
CF
NE
CK
NE
CK
NE
CK
Failu
rem
ode
0.80
0.82
0.84
0.85
0.86
0.87
0.88
0.90
0.90
0.92
0.93
0.95
1.00
1.04
NuF
E/A
gyF
0.74
0.76
0.77
0.78
0.79
0.80
0.82
0.83
0.83
0.85
0.86
0.87
0.93
0.96
NuF
E/A
nuF
CB
7-3
C7-
4C
B7-
4C
7-5
C7-
6C
B7-
5C
7-7
C7-
8C
7-9
C7-
10FE
mod
el
2287
2322
2366
2399
2459
2480
2510
2571
2728
2820
Nlo
ad(k
N)
uFE
WF
WF
WF
WF
WF
CF
CF
CF
CF
CF
CF
CF
CF
NE
CK
NE
CK
Failu
rem
ode
0.83
0.85
0.86
0.87
0.90
0.90
0.91
0.94
0.99
1.03
NuF
E/A
gyF
0.77
0.78
0.79
0.81
0.83
0.83
0.84
0.86
0.92
0.95
NuF
E/A
nuF
11.2
015
6.72
25
8.40
20
4.80
35
5.60
30
3.73
45
4.20
40
ble
6.6
Par
amet
ric a
naly
sis
resu
lts fo
r con
nect
ion
type
C a
t a d
isto
rtion
lim
it (0
.03D
)
SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 6: PARAMETRIC FINITE ELEMENT ANALYSIS
6-236.5.2 Parametric analysis results of slotted gusset plate to EHS connection (gusset plate
oriented to give a large eccentricity)
Figures 6.14 shows the connection tensile strength (NuFE) determined in this parametric
analysis (and the test results for specimens E3 and E4), normalized with respect to AnFu (where
An=Ag). This normalization provides a correlation with the efficiency factors recommended in
current design codes/guides. Here, the best estimation of the trend is provided again by the
AISC efficiency factor and the use of improves this correlation. However, the maximum
efficiency achieved by the FE results only reaches 0.96 AnFu. This phenomenon (the inability of
these elliptical tubes to reach 100% of AnFu) was also observed for slotted EHS gusset plate
connections with similar EHS orientation. (see type E1, section 6.3, and the discussion of
material properties).
The failure mode for FE models with Lw/w<0.60 was governed principally by TO failure.
Nevertheless, a combination with weld metal failure took place for tubes with a low Davg/t ratio.
The transition between TO failure and CF failure occurred in a good number of FE models
having Lw/w=0.60, but lower values were found for thicker tubes. For FE models with low Lw/w
ratios the connection strength surpassed the prediction from design provisions for TO failure. A
similar behaviour has been observed previously for connection type E5. However, the use of
more FE-generated parametric data in this region is necessary to provide a clearer picture.
In an attempt to reduce the numbers of factors interacting here, three gusset plate
dimensions were used. For FE models with Davg/t ratios ranging from 25 to 45, gusset plates
with similar dimensions were used. The results from this group showed that, in addition to the
shear lag phenomenon, an increase in the tube thickness had a negative influence on the
connection efficiency (as was also seen during the connection type C analysis). For FE models
with Davg/t ratios of 15 and 20, an increase in the gusset plate dimensions enhanced their
efficiency. However, the presence of the shear lag phenomenon always limited this
improvement. Finally, for ratios Lw/w 1.1 the presence of the shear lag phenomenon was
effectively diminished.
As a general rule, the FE models having were able to achieve the tube gross
cross-sectional area yield strength (see Figures 6.15). Moreover, the tube deformation forced
x'
≥
Lw w⁄ 0.60≥
SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 6: PARAMETRIC FINITE ELEMENT ANALYSIS
6-24the tube material into the strain hardening region. This occurred particularly for the FE models
with a large connection weld length. Despite the fact that the formation of a crack in the weld
region always defined the connection failure mechanism (since the EHS were unable to develop
a neck), it is important to note that the tube deformation at failure resulted in a stress of 1.2Fy
over the entire tube length (see Figures 6.15). For the FE models with a Lw/w ratio ranging from
0.60 to 1.1, the connection efficiency was defined by several factors: the strain concentration in
the weld region (due to the presence of shear lag); the amount of distortion of the tube geometry
(and its detrimental effect on the connection strength); gusset plate yielding due to bowing
outwards; and the tube Davg/t ratio.
In the course of this parametric analysis, a considerable difference was found to occur
between the maximum load and the load corresponding to the distortion limit. (The latter was
taken as a deformation of 3% of the smaller dimension of the EHS). Figure 6.16 shows the
variation of these differences and, more importantly, it indicates how the largest difference takes
place in the region with a strong shear lag presence. For the group of FE models having a Davg/
t ratio between 25 and 45, the principal reason for the distortion is associated with bowing of the
gusset plate. For FE models with Davg/t ratios of 15 and 20, the use of larger gusset plates
increased the connection stiffness, however this still did not eliminate the large distortion of the
tube shape. Based on these results, one could suggest that the use of a distortion limit to
predict the connection ultimate capacity might be more appropriate than the maximum load
approach. Furthermore, if one used an ultimate deformation limit corresponding to 3% of the
larger dimension of the EHS, this deformation limit would still govern. For increasing values of
Lw/w, a gradual increase in the connection strength can be appreciated when the load at this
distortion limit is normalized with respect to AnFu (see Figure 6.17), for most of the Lw/w range.
The results from these parametric analyses are shown in Table 6.7 and Table 6.8, where the
results from FE models with a failure mode throughout the weld metal (WM) have been
excluded.
SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 6: PARAMETRIC FINITE ELEMENT ANALYSIS
6-25
Figure 6.14 Parametric analysis results and experimental results, connection type E3 (NuFE/AnFu)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6
Lw/w
Nu
FE
/AnF
u
(An=Ag)
D /t=15avg
D /t=20avg
D /t=25avg
D /t=30avg
D /t=35avg
D /t=40avg
D /t=45avg
LabCSA(2001)AISC(2005)_DavgAISC(2005)_Davg x'Predicted TO_Table 2.2Packer & Henderson (1997)
TO Failure
E3
E4
Tension Failure
Shear Lag
Present
1.3 Lw / Davg
TO Predicted
for D / t = 45avg
Tension Failure
Figure 6.15 Parametric analysis results and experimental results, connection type E3 (NuFE/AgFy)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6
Lw/w
Nu
FE/A
gF
y
D /t=15avg
D /t=20avg
D /t=25avg
D /t=30avg
D /t=35avg
D /t=40avg
D /t=45avg
Lab
TO Failure
E3 E4
Tension Failure
Shear Lag
Present
Tension Failure
SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 6: PARAMETRIC FINITE ELEMENT ANALYSIS
6-26
Tabl
e 6.
7 P
aram
etric
ana
lysi
s re
sults
for c
onne
ctio
n ty
pe E
3
0.30
0.54
0.65
0.77
0.83
0.92
1.01
1.07
1.13
1.19
1.25
1.31
1.43
1.79
2.11
Lw/D
ThD
avg/
t0.
220.
390.
470.
560.
600.
670.
730.
780.
820.
860.
910.
951.
031.
291.
53L
w/w
BE
31-1
E31
-1B
E31
-2E
31-2
E31
-3B
E31
-3E
31-4
BE
31-4
E31
-5E
31-6
BE
31-5
E31
-7E
31-8
E31
-9E
31-1
0FE
mod
el
557
700
764
824
850
892
901
926
944
944
944
944
946
946
NuF
Elo
ad(k
N)
TOTO
TOTO
TO-C
FC
FC
FC
FC
FC
FC
FC
FC
FC
FFa
ilure
mod
e
0.71
0.89
0.98
1.05
1.09
1.14
1.15
1.18
1.21
1.21
1.21
1.21
1.21
1.21
NuF
E/A
gF y
0.57
0.71
0.78
0.84
0.86
0.91
0.91
0.94
0.96
0.96
0.96
0.96
0.96
0.96
NuF
E/A
nF u
BE
32-1
E32
-1B
E32
-2E
32-2
E32
-3B
E32
-3E
32-4
BE
32-4
E32
-5E
32-6
BE
32-5
E32
-7E
32-8
E32
-9E
32-1
0FE
mod
el
623
788
861
924
952
993
1027
1042
1053
1059
1059
1059
1059
1061
1061
NuF
Elo
ad(k
N)
TOTO
TOTO
-CF
CF
CF
CF
CF
CF
CF
CF
CF
CF
CF
CF
Failu
rem
ode
0.80
0.90
0.98
1.05
1.08
1.13
1.17
1.19
1.20
1.21
1.21
1.21
1.21
1.21
1.21
NuF
E/A
gF y
0.63
0.71
0.78
0.84
0.86
0.90
0.93
0.94
0.95
0.96
0.96
0.96
0.96
0.96
0.96
NuF
E/A
nF u
BE
33-1
E33
-1B
E33
-2E
33-2
E33
-3B
E33
-3E
33-4
BE
33-4
E33
-5E
33-6
BE
33-5
E33
-7E
33-8
E33
-9E
33-1
0FE
mod
el
670
895
972
1035
1063
1103
1143
1164
1179
1193
1203
1201
1203
1204
1204
NuF
Elo
ad(k
N)
TOTO
TOTO
-CF
CF
CF
CF
CF
CF
CF
CF
CF
CF
CF
CF
Failu
rem
ode
0.67
0.90
0.97
1.04
1.06
1.10
1.14
1.16
1.18
1.19
1.20
1.20
1.20
1.20
1.20
NuF
E/A
gF y
0.53
0.71
0.77
0.82
0.85
0.88
0.91
0.93
0.94
0.95
0.96
0.95
0.96
0.96
0.96
NuF
E/A
nF u
BE
34-1
E34
-1B
E34
-2E
34-2
E34
-3B
E34
-3E
34-4
BE
34-4
E34
-5E
34-6
BE
34-5
E34
-7E
34-8
E34
-9E
34-1
0FE
mod
el
727
1025
1106
1174
1206
1244
1285
1310
1335
1355
1372
1386
1397
1397
1398
NuF
Elo
ad(k
N)
TOTO
TOTO
-CF
TO-C
FC
FC
FC
FC
FC
FC
FC
FC
FC
FC
FFa
ilure
mod
e
0.73
0.88
0.95
1.01
1.04
1.07
1.11
1.13
1.15
1.17
1.18
1.19
1.20
1.20
1.20
NuF
E/A
gF y
0.58
0.70
0.76
0.80
0.83
0.85
0.88
0.90
0.91
0.93
0.94
0.95
0.96
0.96
0.96
NuF
E/A
nF u
E35
-1B
E35
-2E
35-2
E35
-3B
E35
-3E
35-4
BE
35-4
E35
-5E
35-6
BE
35-5
E35
-7E
35-8
E35
-9E
35-1
0FE
mod
el
1191
1278
1354
1376
1439
1477
1519
1534
1559
1584
1615
1649
1663
1664
NuF
Elo
ad(k
N)
WM
TOTO
TOTO
-CF
CF
CF
CF
CF
CF
CF
CF
CF
CF
CF
Failu
rem
ode
0.86
0.92
0.98
0.99
1.04
1.07
1.10
1.11
1.13
1.15
1.17
1.19
1.20
1.20
NuF
E/A
gF y
0.68
0.73
0.78
0.79
0.83
0.85
0.87
0.88
0.90
0.91
0.93
0.95
0.96
0.96
NuF
E/A
nF u
E36
-1B
E36
-2E
36-2
E36
-3B
E36
-3E
36-4
BE
36-4
E36
-5E
36-6
BE
36-5
E36
-7E
36-8
E36
-9E
36-1
0FE
mod
el
1582
1664
1787
1827
1887
1946
1984
2038
2065
2063
2066
2070
2081
2081
NuF
Elo
ad(k
N)
WM
TOTO
TO-C
FC
FC
FC
FC
FC
FC
FC
FC
FC
FC
FC
FFa
ilure
mod
e
0.92
0.97
1.04
1.07
1.10
1.14
1.16
1.19
1.21
1.21
1.21
1.21
1.22
1.22
NuF
E/A
gF y
0.73
0.77
0.83
0.85
0.88
0.90
0.92
0.95
0.96
0.96
0.96
0.96
0.97
0.97
NuF
E/A
nF u
BE
37-2
E37
-2E
37-3
BE
37-3
E37
-4B
E37
-4E
37-5
E37
-6B
E37
-5E
37-7
E37
-8E
37-9
E37
-10
FEm
odel
2056
2234
2302
2368
2443
2489
2542
2579
2606
2623
2676
2686
2684
NuF
Elo
ad(k
N)
WM
WM
TOTO
-CF
CF
CF
CF
CF
CF
CF
CF
CF
CF
CF
CF
Failu
rem
ode
0.92
1.00
1.03
1.06
1.09
1.11
1.13
1.15
1.16
1.17
1.19
1.20
1.20
NuF
E/A
gF y
0.73
0.79
0.82
0.84
0.87
0.88
0.90
0.91
0.92
0.93
0.95
0.95
0.95
NuF
E/A
nF u
11.0
015
6.60
25
8.25
20
4.71
35
5.50
30
3.67
45
4.13
40
SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 6: PARAMETRIC FINITE ELEMENT ANALYSIS
1
1
1
1
1
1
1
1
1
6
6-27
Figure 6.16 Ratio of the maximum load to load at suggested distortion limit, connection type E3
.00
.05
.10
.15
.20
.25
.30
.35
.40
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6
Lw/w
NuFE @ max/ NuFE-D
Davg/t=15
Davg/t=20
Davg/t=25
Davg/t=30
Davg/t=35
Davg/t=40
Davg/t=45
TO Failure Tension Failure
Shear Lag
Present
Tension Failure
Figure 6.17 Parametric analysis results, load at distortion limit, connection type E3 (NuFE/AnFu)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.
Lw/w
NU
FE
-D/A
nF
u
(Ag=An)
D /t=15avg
Davg/t=20
Davg/t=25
Davg/t=30
Davg/t=35
Davg/t=40
Davg/t=45
TO Failure
Tension Failure
Shear Lag
Present
Tension Failure
SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 6: PARAMETRIC FINITE ELEMENT ANALYSIS
6-28
0.30
0.54
0.65
0.77
0.83
0.92
1.01
1.07
1.13
1.19
1.25
1.31
1.43
1.79
2.11
Lw/D
ThD
avg/
t0.
220.
390.
470.
560.
600.
670.
730.
780.
820.
860.
910.
951.
031.
291.
53L w
/w
BE31
-1E3
1-1
BE31
-2E3
1-2
E31-
3BE
31-3
E31-
4BE
31-4
E31-
5E3
1-6
BE31
-5E3
1-7
E31-
8E3
1-9
E31-
10FE
mod
el
538
636
680
739
754
789
823
836
830
830
827
823
807
754
Nlo
ad(k
N)
uFE
TOTO
TOTO
TO-C
FC
FC
FC
FC
FC
FC
FC
FC
FC
FFa
ilure
mod
e
0.69
0.81
0.87
0.94
0.96
1.01
1.05
1.07
1.06
1.06
1.06
1.05
1.03
0.96
N/A
F
0.55
0.65
0.69
0.75
0.77
0.80
0.84
0.85
0.84
0.84
0.84
0.84
0.82
0.77
uFE
gy
N/A
F
BE32
-1E3
2-1
BE32
-2E3
2-2
E32-
3BE
32-3
E32-
4BE
32-4
E32-
5E3
2-6
BE32
-5E3
2-7
E32-
8E3
2-9
E32-
10FE
mod
el
uFE
nu
563
678
725
792
828
841
846
848
849
849
849
849
849
848
833
Nlo
ad(k
N)
uFE
TOTO
TOTO
-CF
CF
CF
CF
CF
CF
CF
CF
CF
CF
CF
CF
Failu
rem
ode
0.64
0.77
0.83
0.90
0.94
0.96
0.96
0.97
0.97
0.97
0.97
0.97
0.97
0.97
0.95
N/A
F
0.51
0.61
0.66
0.72
0.75
0.76
0.77
0.77
0.77
0.77
0.77
0.77
0.77
0.77
0.75
uFE
gy
N/A
F
BE33
-1E3
3-1
BE33
-2E3
3-2
E33-
3BE
33-3
E33-
4BE
33-4
E33-
5E3
3-6
BE33
-5E3
3-7
E33-
8E3
3-9
E33-
10FE
mod
el
uFE
nu
646
773
828
879
895
910
923
925
930
934
938
942
939
941
920
Nlo
ad(k
N)
uFE
TOTO
TOTO
-CF
CF
CF
CF
CF
CF
CF
CF
CF
CF
CF
CF
Failu
rem
ode
0.65
0.77
0.83
0.88
0.90
0.91
0.92
0.93
0.93
0.93
0.94
0.94
0.94
0.94
0.92
N/A
F
0.51
0.61
0.66
0.70
0.71
0.72
0.73
0.74
0.74
0.74
0.75
0.75
0.75
0.75
0.73
uFE
gy
N/A
F
BE34
-1E3
4-1
BE34
-2E3
4-2
E34-
3BE
34-3
E34-
4BE
34-4
E34-
5E3
4-6
BE34
-5E3
4-7
E34-
8E3
4-9
E34-
10FE
mod
el
uFE
nu
899
900
942
969
982
1000
1016
1010
1022
1031
1026
1046
1059
1073
1046
Nlo
ad(k
N)
uFE
TOTO
TOTO
-CF
TO-C
FC
FC
FC
FC
FC
FC
FC
FC
FC
FC
FFa
ilure
mod
e
0.77
0.78
0.81
0.83
0.85
0.86
0.88
0.87
0.88
0.89
0.88
0.90
0.91
0.92
0.90
N/A
F
0.62
0.62
0.65
0.66
0.67
0.68
0.70
0.69
0.70
0.71
0.70
0.72
0.73
0.73
0.72
uFE
gy
N/A
F
E35-
1BE
35-2
E35-
2E3
5-3
BE35
-3E3
5-4
BE35
-4E3
5-5
E35-
6BE
35-5
E35-
7E3
5-8
E35-
9E3
5-10
FEm
odel
uFE
nu
1029
1056
1085
1096
1122
1126
1138
1154
1150
1178
1172
1190
1247
1218
Nlo
ad(k
N)
uFE
WM
TOTO
TOTO
-CF
CF
CF
CF
CF
CF
CF
CF
CF
CF
CF
Failu
rem
ode
0.74
0.76
0.78
0.79
0.81
0.81
0.82
0.83
0.83
0.85
0.85
0.86
0.90
0.88
N/A
F
0.59
0.61
0.62
0.63
0.64
0.65
0.65
0.66
0.66
0.68
0.67
0.68
0.72
0.70
uFE
gy
N/A
F
E36-
1BE
36-2
E36-
2E3
6-3
BE36
-3E3
6-4
BE36
-4E3
6-5
E36-
6BE
36-5
E36-
7E3
6-8
E36-
9E3
6-10
FEm
odel
uFE
nu
1353
1387
1422
1436
1444
1469
1488
1522
1516
1529
1543
1568
1619
1593
Nlo
ad(k
N)
uFE
WM
TOTO
TO-C
FC
FC
FC
FC
FC
FC
FC
FC
FC
FC
FC
FFa
ilure
mod
e
0.79
0.81
0.83
0.84
0.84
0.86
0.87
0.89
0.89
0.89
0.90
0.92
0.95
0.93
N/A
F
0.63
0.64
0.66
0.67
0.67
0.68
0.69
0.71
0.70
0.71
0.72
0.73
0.75
0.74
uFE
gy
N/A
F
BE37
-2E3
7-2
E37-
3BE
37-3
E37-
4BE
37-4
E37-
5E3
7-6
BE37
-5E3
7-7
E37-
8E3
7-9
E37-
10FE
mod
el
uFE
nu
1692
1740
1764
1797
1830
1865
1881
1905
1940
1951
1990
2078
2070
Nlo
ad(k
N)
uFE
WM
WM
TOTO
-CF
CF
CF
CF
CF
CF
CF
CF
CF
CF
CF
CF
Failu
rem
ode
0.75
0.78
0.79
0.80
0.82
0.83
0.84
0.85
0.87
0.87
0.89
0.93
0.92
N/A
F
0.60
0.62
0.63
0.64
0.65
0.66
0.67
0.68
0.69
0.69
0.71
0.74
0.73
uFE
gy
N/A
F
11.0
015
uFE
nu
8.25
20
6.60
25
4.71
35
5.50
30
3.67
45
4.13
40
Tabl
e 6.
8 P
aram
etric
ana
lysi
s re
sults
for c
onne
ctio
n ty
pe E
3 at
a d
isto
rtion
lim
it (0
.03
D2)
SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 6: PARAMETRIC FINITE ELEMENT ANALYSIS
6-296.6 Connections under compression load
6.6.1 Parametric analysis results of slotted CHS connection - slot end not filled
The maximum load of the connections fabricated with a slotted tube was governed by the
failure mode of local buckling in the tube slot region. The formation of this local buckle was
influenced by the tube D/t ratio and the strain concentration at the beginning of the weld, the
latter being due to the presence of shear lag. For a short weld length, the shear lag
phenomenon increased the strain concentration at the beginning of the weld, thus provoking the
premature formation of a buckle, and on occasions the failure of the weld material. On the other
hand, a large weld length diminished the strain concentration and allowed a local bucking failure
of the entire cross-section at the slot region (see Figure 6.18).
In order to describe the connection behaviour on a common basis, the connection
strength (NuFE) calculated during the parametric analyses (and the test result for specimen
A3C) has been normalized with respect to AgFy in Figure 6.19.
For FE models with Lw/w<0.92, the connection behaviour can be described by a
combination of several factors. The strain concentration taking place in front of the weld region
triggered the formation of a buckle affecting the tube geometry there. In most cases, the load
necessary to produce this buckle was not enough to modify the geometry of the entire cross-
section. In general terms, the Lw/w ratio determined the strain concentration at the weld region
and the D/t ratio determined the connection's ability to redistribute these strains to the entire
cross-section, which could improve the efficiency factor. For FE models having Lw/w> 0.92, the
maximum efficiency was determined only by the tube D/t ratio and the length of the slot (lsl),
because the shear lag phenomenon had no influence.
SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 6: PARAMETRIC FINITE ELEMENT ANALYSIS
.3
6-30
Figure 6.18 Local buckling of FE models with a slotted tube, for short and long welds
Figure 6.19 Parametric analysis results and experimental result, connection type A under compression (NuFE/AgFy)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1
Nu
FE
/AgF
y
D/t=15
D/t=20
D/t=25
D/t=30
D/t=35
D/t=40
D/t=45
Lab
A3CShear Lag
Phenomenon
Present
Lw/w
Local buckling of
Eentire cross-section
SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 6: PARAMETRIC FINITE ELEMENT ANALYSIS
6-31In the course of these analyses, the slot length (lsl) was set to be equal to the thickness of
the gusset plate (tp). However, to establish the importance of the slot size on the connection
efficiency, the length of the slot was increased in several FE models with a ratio of Lw/w= 0.92.
In Figure 6.20 the connection efficiency for the most representative D/t ratios decreases as the
ratio of lsl/tp increases. A maximum slot length of three times the thickness of the gusset plate
has been considered here, as this dimension was expected to be within the construction
tolerances commonly found in practice. Even with the use of a large slot, the maximum
decrease in connection efficiency did not exceed 10% in all cases, relative to the short slot
case.
In most of the FE models, the maximum load was close to the tube distortion limit load
and once this limit was exceeded rapid distortion of the tube shape governed the tube
behaviour. So no significant difference between the maximum load and the load corresponding
to the distortion limit was found. The results from these parametric analyses are shown in
Table 6.9, where the results from FE models with a failure mode throughout the weld metal
(WM) have been excluded.
Figure 6.20 Local buckling of FE models with a slotted tube, for short and long slot lengths
SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 6: PARAMETRIC FINITE ELEMENT ANALYSIS
6-32
6.6.2 Parametric analysis results of slotted gusset plate to CHS connection
For FE models of connections fabricated with a slotted gusset plate, the failure mode of
local buckling of the tube gross cross-sectional area (see Figure 6.21) was influenced by
several factors: a strain concentration at the beginning of the weld (due to shear lag) which was
determined by the Lw/w ratio; the bowing inwards of the gusset plate exacerbating the tube's
local stability which is related to the plate's flexural stiffness and load applied; and the tube
thickness which defines the D/t ratio and hence the tube local buckling load. In order to describe
the behaviour of these connections on a common basis, the connection strength (NuFE) has
been normalized with respect to AgFy (see Figure 6.22). The D/t ratios for the CHS used in this
parametric analysis always corresponded to at least a Class 3 section (CSA 2001).
In an attempt to reduce the number of parameters having an influence on the FE models'
behaviour, a constant plate moment of inertia at the slot region was tried throughout this
Table 6.9 Parametric analysis results for connection type A3C
0.57 0.77 0.83 1.01 1.13 1.19 1.31 1.43 1.79 L w /D
Th D/t 0.40 0.54 0.59 0.71 0.80 0.84 0.92 1.01 1.26 L w /w
CA1-0 CA1-1 CA1-2 CA1-3 CA1-4 CA1-5 CA1-6 CA1-7 CA1-8 FE model
482 604 636 732 791 808 823 827 829 NuFE load (kN)
0.50 0.63 0.66 0.76 0.82 0.84 0.86 0.86 0.86 NuFE /AgFy
CA2-0 CA2-1 CA2-2 CA2-4 CA2-5 CA2-6 CA2-7 CA2-8 FE model
551 687 724 900 931 947 950 949 NuFE load (kN)
0.51 0.64 0.67 0.84 0.87 0.88 0.88 0.88 NuFE /AgFy
CA3-0 CA3-1 CA3-2 CA3-3 CA3-4 CA3-5 CA3-6 CA3-7 CA3-8 FE model
630 794 838 967 1043 1076 1101 1102 1101 NuFE load (kN)
0.51 0.65 0.68 0.79 0.85 0.88 0.90 0.90 0.90 NuFE /AgFy
CA4-0 CA4-1 CA4-2 CA4-3 CA4-4 CA4-5 CA4-6 CA4-7 CA4-8 FE model
777 975 1028 1182 1263 1293 1310 1309 1306 NuFE load (kN)
0.55 0.69 0.72 0.83 0.89 0.91 0.92 0.92 0.92 NuFE /AgFy
CA5-0 CA5-1 CA5-2 CA5-3 CA5-4 CA5-5 CA5-6 CA5-7 CA5-8 FE model
894 1144 1212 1417 1522 1557 1592 1595 1593 NuFE load (kN)
0.53 0.68 0.72 0.84 0.90 0.92 0.94 0.94 0.94 NuFE /AgFy
CA6-3 CA6-4 CA6-5 CA6-6 CA6-7 CA6-8 FE model
WF WF WF 1816 1958 1998 2044 2051 2053 NuFE load (kN)
0.87 0.93 0.95 0.98 0.98 0.98 NuFE /AgFy
CA7-5 CA7-6 CA7-7 CA7-8 FE model
WF WF WF WF WF 2647 2730 2760 2772 NuFE load (kN)
0.96 0.99 1.01 1.01 NuFE /Ag Fy
11.20 15
6.72 25
8.40 20
4.80 35
5.60 30
3.73 45
4.20 40
SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 6: PARAMETRIC FINITE ELEMENT ANALYSIS
6-33parametric analysis. However, this was possible only for FE models with D/t ratios from 25 to 45
(Plate1). With FE models having a thicker tube, the presence of out-of-plane gusset plate
buckling required an increase in the plate dimensions (Plates 2 and 3). Due to these
differences, the FE analysis results are collated according to their plate properties.
For FE models with low Lw/w ratios and high D/t ratios (using Plate 1), the efficiency was
determined predominantly by the tube thickness. For thin tubes, the (low) load necessary to
produce tube local bucking induces only a slight deformation on the gusset plate, hence
reducing the effect of plate bowing on the connection efficiency. On the other hand, the local
bucking load associated with thicker tubes produces considerable deformation of the gusset
plate, amplifying the effect of plate bowing on the connection efficiency. Figure 6.22 shows a
gradual diminution of the variation between the efficiencies of the tubes using Plate 1 with
increasing Lw/w.
For FE models with larger plates (Plates 2 and 3), a clear increase in the gross cross-
sectional area efficiency was shown. However, these showed a similar rate of change in
connection efficiency as the Plate 1 group. Figure 6.22 indicates that the factors affecting the
connection efficiency continue to be present even for large weld lengths.
Throughout these analyses, a check of the tube cross-section ultimate strength distortion
limit (3%D) was made. In most cases the maximum load occurred after surpassing this
distortion limit. Once this limit was exceeded, rapid distortion of the tube geometry took place,
limiting much increase of the load beyond this limit. As a result of this, the ratio of the maximum
load to the load corresponding to this distortion limit never exceeded 1.06. The results from
these parametric analyses are shown in Table 6.10, where the results from FE models with a
failure mode throughout the weld metal (WM) have been excluded.
SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 6: PARAMETRIC FINITE ELEMENT ANALYSIS
6-34
Figure 6.21 Local buckling of FE models with a slotted gusset plate, for short and long welds
Figure 6.22 Parametric analysis results and experimental result, connection type C under compression (NuFE/AgFy)
SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 6: PARAMETRIC FINITE ELEMENT ANALYSIS
6-35
6.7 Weld design
Figure 6.23 shows the theoretical relationship between a Weld Material (WM) failure and
a Tear-Out (TO) failure with the fillet weld leg length (al) in slotted CHS connections. (Here al
was normalized with respect to the tube thickness (t) and all resistance factors were set to 1.0).
According to this figure, the shear strength of the weld will gradually increase as al is
augmented, resulting in a change in the governing failure mechanism (from a WM to a TO
failure). Even though this figure suggests that an al equivalent to t may prevent the presence of
a WM failure in the connection, a further parametric analysis (with 90 FE models of slotted CHS
connections considering several al values, Lw/w ratios and D/t ratios) has suggested that this
assumption may be incorrect.
Table 6.10 Parametric analysis results for connection type C3C
SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 6: PARAMETRIC FINITE ELEMENT ANALYSIS
6-36
As a result of the stress concentration at the beginning of the welds, it is expected that the
tube material will yield there and then fracture. However, it has been found that this stress
concentration can also induce weld yielding there (which will result in a subsequent WM failure)
for connections with al/t ratios barely exceeding 1.0. Therefore, based on these analyses, it is
suggested to use an al 1.7t and 1.5t for slotted CHS connections with and without a weld
return respectively, when a TO failure is expected (i.e for ratios Lw/w < 0.7). On the other hand,
as the Lw/w ratio increases and the failure mechanism changes from a TO to a CF failure, the
decrease in the magnitude of the stress concentration at the beginning of the weld will allow one
to use a smaller al. Thus, al 1.5t is conservative for ratios Lw/w 0.7 (i.e. when a CF failure is
expected).
For slotted gusset plate to CHS connections, a further analysis of 45 FE models has
suggested the use of al 2t for connections with ratios Lw/w < 0.60 (where the TO failure
governs). For the region marking the transition from a TO to a CF failure (i.e for ratios
), al 1.7t is suggested and al 1.5t may be used for ratios Lw/w > 0.8.
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80
2.00
2.20
0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00
l
AX
wu
/(A
F+
0.6
AF
)n
tu
nv
yTear-Out failure
Weld Material failure
a / t
Figure 6.23 Theoretical influence of the al/t ratio in the governing failure mechanism of a slotted CHS connection (without weld return)
≥
≥ ≥
≥
0.6 Lw w⁄ 0.8≤ ≤ ≥ ≥
SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 6: PARAMETRIC FINITE ELEMENT ANALYSIS
6-37The range of validity of all these recommendations corresponds to connections with D/t
ratios ranging from 25 to 40. For connections with D/t=20, the use of al 2.5t is recommended
for ratios Lw/w < 0.8 and al 2t for larger ratios. For thicker tubes, the use of an alternative
welding procedure is recommended, especially for connections with ratios Lw/w < 0.8. All these
recommendations are summarized in Table 6.11 and Table 6.12.
It must be borne in mind that the above fillet weld size recommendations are independent
of resistance factors being applied, to both the weld design model and the tear-out design
model.
Table 6.11 Recommended weld size for slotted CHS connections
Suggested weld leg length Range of validity
Lw/w < 0.7al 1.7t (without a weld return)
al 1.5t (with weld return)
Lw/w 0.7 al 1.5t (both details)
Lw/w < 0.8 al 2.5t (both details)
Lw/w 0.8 al 2.0t (both details)
Table 6.12 Recommended weld size for slotted gusset plate to CHS connections
Suggested weld leg length Range of validity
Lw/w < 0.6 al 2t
al 1.7t
Lw/w > 0.8 al 1.5t
Lw/w < 0.8 al 2.5t (both details)
Lw/w 0.8 al 2.0t (both details)
≥
≥
≥
25 Dt---- 40≤ ≤≥
≥ ≥
≥20 D
t---- 25<≤
≥ ≥
≥
25 Dt---- 40≤ ≤0.6 Lw w⁄ 0.8≤ ≤ ≥
≥
≥20 D
t---- 25<≤
≥ ≥
SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 6: PARAMETRIC FINITE ELEMENT ANALYSIS
6-386.8 Summary of Chapter 6
In this chapter, the FE models showed a gradual transition between the failure modes of
"block shear" tear-out and circumferential tensile fracture, with a continual monotonic increase
in the connection capacity as the weld length increased. The transition point between these
failure modes depended on factors such as: the connection type, the weld length, the tube
diameter-to-thickness ratio and the connection eccentricity. This gradual transition between
failure modes is in contrast to the behaviour given by design models in current specifications,
since these specifications do not consider a gradual change between these limit states.
For the slotted CHS connections, the use of a weld length-to-distance between welds
ratio of Lw/w > 1.0 allowed the attainment of 100% efficiency of the tube net area (AnFu).
However, it was not possible to develop the gross-section yield strength of these tubes because
of their low AnFu/AgFy ratio, and only 96% of AgFy was attained. The efficiency for the slotted
EHS connections was limited to 94% of the tube net area (AnFu). Nevertheless, these were able
to attain the gross-section yield strength (100% AgFy) because of a higher AnFu/AgFy ratio. In
general, the CHS showed better behaviour than the EHS, since the distortion of their shape
mostly occurred near attainment of connection ultimate strength and the value had only a
small influence on their behaviour. Unfortunately, for both tubes large strains always took place
in the slot region, even with the use of long welds. The inclusion of a weld return provides the
possibility to eliminate net area fracture and transfer this deformation away from the connection.
In general this objective was accomplished for connections with a weld return, as they were
capable of attaining their gross-section yield strength (100% of AgFy). However, the initial
fabrication conditions that were included in the FE models always had a negative effect on the
behaviour of connections with a weld return, thus limiting the overall tube deformations. This
limited the tube net area efficiency to 95% of AnFu, where An=Ag, for this connection type.
In slotted gusset plate to CHS connections loaded in tension, with Lw/w >1.0, the
decrease in strain concentration at the weld region allowed the creation of a neck away from the
connection. However, the associated deformations in the tube cross-section shape suggest the
imposition of a distortion limit. On the other hand, for slotted gusset plate to EHS connections
brittle fracture continued to be the principal failure mechanism, even with long weld lengths.
These connections only attained a net cross-sectional area efficiency of 96% of AnFu, (where
x
SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 6: PARAMETRIC FINITE ELEMENT ANALYSIS
6-39An=Ag), but were capable of exceeding the gross-section yield strength and promoting strain-
hardening of the tube material, reaching capacities of 1.2 AgFy. In addition, the level of distortion
for slotted gusset plate to EHS connections was similar to that for their CHS counterparts.
For the connections loaded under compression, the parametric analysis results have
shown the possibility to diminish the influence of shear lag on slotted CHS connections with a
ratio of Lw/w > 0.92. The gross-cross sectional area efficiency here ranged from 86% to 100% of
AgFy. This range is due to the net area cross-sectional properties at the slot region. (Results
were normalized with respect to Ag because this is a compression case). The behaviour of the
slotted gusset plate to CHS connection type was less promising and also confirmed the
negative effect of gusset plate deformation prevalent with this connection type. However, from
these analyses it can be noted that the use of a large gusset plate (with a large moment of
inertia) can improve the gross cross-sectional area efficiency, as the FE models with a larger
gusset plate reached an efficiency close to 100% of AgFy.
For connections under quasi-static tension loading, the current design provisions for
"block shear" tear out and circumferential tension fracture have been evaluated against the
experimental research and parametric analysis results. For the treatment of shear lag, the
American Specification (AISC 2005) provides the closest solution to the trend followed by these
results. Furthermore, the accuracy of this design method can be improved by reducing the
eccentricity of the half connection, , by half of the gusset plate thickness (i.e., by using =
-tp/2). Despite this improvement this preferred model is still over-conservative and not
representative of the true connection behaviour. Against block shear failure, the Canadian (CSA
2001) and American (AISC 2005) specifications use the same design model. However their
application range is not clear and the parametric results have shown that this application range
can vary depending on several factors. Based on all these results, a new design methodology is
provided in the next chapter of this Report.
Since the stress concentration taking place at the beginning of the weld can also affect the
weld behaviour and, more importantly, lead to a weld material failure, it was decided to also
provide a series of recommendations to dimension the fillet size for CHS connection details.
x x' x
SLOTTED END CONNECTIONS TO HOLLOW SECTIONS, CH 6: PARAMETRIC FINITE ELEMENT ANALYSIS