CIDECT Final Report 8G-10_06(2of4)

5-1

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=

5-2


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

5-5


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

5-6


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

5-7


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.

5-8


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


12361186 1.04

SOLID45 5838 4138 Coarse 1218 1.01

SOLID95 15901 2832 Coarse 1205 1.02


13361334 1.00

SOLID45 6352 4495 Coarse 1353 0.99

SOLID95 17774 3158 Coarse 1265 1.05


14001401 1.00

SOLID45 6352 4495 Coarse 1186 1.18

SOLID95 17774 3158 Coarse 1267 1.10


1282

1273 1.01

SOLID45 5522 3676 Coarse 1362 0.94

SOLID95 14320 2536 Coarse 1318 0.97

5-9


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

5-10


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

5-11


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)

5-12


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

5-13


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

5-14


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)


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

5-15


Figure 5.20 Materials in FE models type B

Figure 5.21 Failure mode in FE model B1 and test specimen

5-16


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.

5-17


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


Davg/t = 28

Lw/w = 0.62 for connection E1




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

5-18


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

5-19


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


5-20


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



Davg/t = 28

Lw/w = 0.79



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)


- FE- Lab

Strain (mm/mm)

Lw

al

Figure 5.30 FE models of connection type E5

5-21


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

5-22


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.



- FE- Lab

Strain (mm/mm)

5-23


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



D/t = 35

Lw/w = 0.68 for connection C1

Lw/w = 0.81 for connection C2


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)



E5 1282 1113 1273 1.01 1.15

Lw

al

Figure 5.34 FE models of connection type C

5-24


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


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


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)


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


FE models E3 and E4



Davg/t = 28





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


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


E3 1336 984 1348 0.99 1.36E4 1400 1078 1413 0.99 1.30

5-29


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


- FE- Lab

Strain (mm/mm)


- FE- Lab

Strain (mm/mm)

5-30


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



D/t = 35

Lw/w = 0.86 for connection A3C



Lw

al

Figure 5.46 FE model of connection type A3C

5-31


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


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)


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


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



D/t = 35

Lw/w = 0.84 for connection C3C



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


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)


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


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


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'


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.


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


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


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⁄


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.


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


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)


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.


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


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


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'


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


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


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.


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.


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


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


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


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

)


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≥


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.


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


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


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


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)


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.


.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


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


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


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


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


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


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.


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)


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


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≤ ≤ ≥ ≥


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)


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)


≥

≥

≥

25 Dt---- 40≤ ≤≥

≥ ≥

≥20 D

t---- 25<≤

≥ ≥

≥

25 Dt---- 40≤ ≤0.6 Lw w⁄ 0.8≤ ≤ ≥

≥

≥20 D

t---- 25<≤

≥ ≥


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


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


CIDECT Final Report 8G-10_06(2of4)

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