Behavior analysis of bar gaps in welded YT-joints for rolled-steel circular hollow sections

We present a parametric analysis of gap variation between the lap brace and through brace of YT welded joints for rolled-steel circular hollow sections on plane steel structures. Our aim is to investigate the collapse behavior of YT-joints under lap brace axial compression. In particular, we focus on e / d 0 ratios above 0.25 so bending moments can be taken into account during the design. We ﬁnd that joint failure is primarily due to chord wall plastiﬁcation (Mode A) and cross-sectional chord buckling (Mode F) in the region un-derneath the lap brace. Our joint design followed the Limit States Method, and our results were based on a comparative analysis of three diﬀerent methods: an analytical solution derived from a set of international technical norms, an experimental analysis, and numerical modeling using Ansys as calibrated by our experimental results.


INTRODUCTION
The extensive use of steel frame structures is primarily due to the economic advantages of manufacturing steel frames.In this work, we study the strength of connection joints for tubular steel frames as a function of gap length between the lap and through braces of YTjoints.This work extends earlier studies of tubular joints that focused on experimental tests [5], theoretical analyses using the Finite Element Method [2][3][4], and analytical work aimed at developing mathematical expressions of the joint strength [6].

CALCULATION OF CONNECTION RESISTANCE
The YT joint prototype design uses the methodology presented by Wardenier et al. [10] and Packer and Henderson [7].
The Fig. 1 shows forces general scheme using as a limit the maximum capacity of the vertical brace member of the YT joint and the bending moment due the eccentricity was not considered [9].

NOMENCLATURE
A i cross sectional area of member i (i = 0, 1, 2, 3); E modulus of elasticity; E t modulus of elasticity tangent; M 0 bending moment in the chord member; N i axial force applied to member i (i = 0, 1, 2, 3); N * i joint design resistance expressed in terms of axial load in member i; N 0P pre-stressing axial force on the chord; W 0 elastic section modulus of member i (i = 0, 1, 2, 3); d i external diameter of circular hollow section for member i (i = 0, 1, 2, 3); e nodding eccentricity for a connection; f y yield stress; f yi yield stress of member i (i = 0, 1, 2, 3); f 0P pre-stress in chord; f (n ′ ) function which incorporates the chord pre-stress in the joint resistance equation; g gap between the bracings members of a K, N or KT joint, at the face of the chord; g ′ gap divided by chord wall thickness; diameter ratio between bracing on chord; K and N γ ratio of the chord's half diameter to its thickness; ν Poisson's ratio θ included angle between bracing member i (i = 0, 1, 2, 3) and the chord; ϵ maximum specific proportionality strain; f stress; f lp maximum proportionality stress; f r maximum resistance stress; f 1 principal stress 1; f 2 principal stress 2; Table 1 shows the geometric characteristics of the VMB 250 circular hollow sections used in the YT joint.The nominal physical proprieties yield stress (f y ) are equal 250 MPa.

Validity limits
The YT joint meets all geometrical requirements described in the aforementioned references.

A) YT joint parameters
The YT joint parameters are given by Eq. (1) through Eq. ( 5): (1) The stress on the chord, f 0P , depends most critically on the compressing stress.
B) Plastic failure of the chord face (Mode A) Vertical lap brace: Diagonal through brace: C) Punching shear failure of the chord face (Mode B) Vertical lap brace and diagonal through brace are both given by Eq. ( 8):

D) YT Joint Resistance
The joint resistance is the lowest value obtained in items (B) and (C) above.Vertical lap brace: Diagonal through brace: Latin American Journal of Solids and Structures 7(2010) 369 -389 Table 2 presents the results of the calculation.

EXPERIMENTAL PROGRAM
To study the joint, four prototypes constructed from seamless rolled tubes were manufactured by V&M do Brasil.They were called pre-experiment, experiments I, II and III [9].

YT joint prototypes
The dimensions of the prototypes are shown in Fig. 2. The prototypes are fixed by four screws at each end.They were loaded axially at the top of the lap brace.

Instrumentation for tests
In EXPERIMENTS I, II and III, sixteen 5mm electrical resistance KFG-5-120-C1-11 extensometers were used.Their positions are marked EER1 to EER16 in Fig. 3.The EERs were placed on the prototype to measure longitudinal strain, drawing on the work of Fung et al [5].In EXPERIMENT III, 2 rosette gauges and 2 individual extensometers were added (for a total of 24 EERs).Rosette 1 was composed of EER20, EER21 and EER22; rosette 2 was composed of EER17, EER18 and EER19.EER23 and EER24 were placed at the bases of the lap brace and through brace respectively.
In EXPERIMENTS I, II and III, 19 manual reading displacement transducers (TD1 to TD19) and two digital reading displacement transducers (TD20 and TD21) were placed on the prototype as shown in Fig. 4.

Experimental results
The testing methodology used was defined in three stages, as shown below: Stage I. Before starting the test, the prototype was subjected to a cycle of 10 loading of approximately 20% of the estimated collapse loading for the connection, to minimize friction and check the torque of the screws.Based on pre-test the loading was estimated at 50kN.This level of loading is within the elastic limit of the material.The force was applied in small increments and then it was done downloading.for both the case of loading and for unloading.The step load was previously set depending on the stage supposed to loading.At each step of loading, when the pre established loading was reached, expected time to stabilize the transducers and then did the reading.
Stage III.The prototype was loaded to the ultimate state, where the prototype did not offer more resistance, even after he reached the break.Then the prototype was unloaded.
Fig. 5 shows the overall strain of the prototype in EXPERIMENT III, characterized by the development of failure Mode A.
The results presented by extensometers in each EXPERIMENTS I, II and III are similar, are representing the state of tension expected for each region and thus show that the tests were equivalent.
The results of the last loading for each of the tests are shown in Table 3.Two failure modes were observed: plastic failure of the chord face (Mode A) and local buckling of the chord walls (Mode F).

ANALYSIS OF FINITE ELEMENTS
Two numerical models were created in Ansys [1], one using a bilinear stress-strain diagram (BISO -Bilinear Isotropic Hardening) and the other a multilinear (piecewise linear) diagram (MISO -Multilinear Isotropic Hardening).Their results were compared to the experimental tests [9].
Both physical and geometrical non-linearity were considered in the analysis.To implement physical non-linearity, we used the stress-strain diagrams obtained through test-body traction.Test bodies cp1a, cp1b for hollow section of diameter 73mm and cp2a e cp2b for hollow section of diameter 114.3mm [9].
The contour conditions were simulated in Ansys through displacement restrictions.Force was applied in an increasing way, that is, at unit load pitches.
Fig. 6 and Fig. 7 show the stress-strain diagrams of test bodies selected for the numerical analysis.The multilinear model is represented by 26 points (crossed circles), and the bilinear model by two straight lines (triangles).
Table 4 shows data used to represent the material properties of test bodies cp1b and cp2b in the numerical model.Note that the bilinear stress-strain diagram always runs from the origin to the first stress peak (f ), then from this point to the maximum stress (f r ) of the material.
The 26 points to represent the multilinear stress-strain diagram is shown by Table 5.
Figure 6 Experimental, bilinear and multilinear stress-strain diagrams used for test body cp1b, from the through brace and lap brace (ϕ73mm).
Table 4 Data used to represent the bilinear stress-strain diagram with the Ansys software (BISO).
Test Body  The Poisson's ratio was obtained by compression test tube used.The value obtained was ν = 0.3.
The SHELL element was considered most appropriate to represent hollow structures.Specifically, the SHELL181 element was used to generate a mesh for the hollow sections.The SHELL63 element was used for fixation plates.Table 6 shows their characteristics.

COMPARISON BETWEEN EXPERIMENTAL TEST RESULTS AND NUMERICAL MODEL RESULTS
The experimental tests and numerical models can be compared on the basis of strains obtained by the extensometers [9].For the rosettes, comparisons between theory and experiment can be made between the principal stresses.
Fig. 8 show the principal stresses f 1 measured at rosette 1 in EXPERIMENT III and the numerical models.

RESULTS FOR THE EFFECT OF GAP LENGTH ON YT-JOINT STRENGTH
The principal stresses "f 1 " for each gap size are shown in Figs. 9 through 14.For all models, the largest stresses were observed on the chord at the joint intersection.Our models show that the stress distributions between the lap brace and through brace are indeed influenced by the gap size.As seen in Fig. 15, varying gap sizes from the "GAP10.33"to "GAP110" models produces approximately twice the principal stress "f 1 " for the same load of 100kN.
For each model, the respective yield load was then determined based on a yield strength of σ e = 0.33 GPa, as defined by a tensile test [8].Table 8 shows the yield load for each of the new models.As the gap size increases, the yield load of the joint decreases, which translates into a smaller load supported on the top of the lap brace.Hence the larger the gap size, the smaller the load transfer efficiency between the braces.

NUMERICAL ANSYS ANALYSIS OF DIMENSION LOAD VERSUS YIELD LOAD
We designed the tubular YT-joint specimen using values presented by CIDECT [10] and Packer and Henderson [7].This gave a dimension load of 137 kN with 100% efficiency on the top of the lap brace and 82% efficiency for the through brace (Item 2).Note that we did not take bending moments into consideration during the design calculations since e/d 0 =0.25.Recall that the Mode A failure depends on the gap length.The dimension loads for each  of the new models were calculated in the same way as before, except that we took bending moments into consideration since e/d 0 > 0.25.We compared the results with the yield loads supplied by Ansys, and our results are presented in Fig. 20.
Table 9 shows the values of dimension load, yield load and the percent difference between them.

CONCLUSIONS
We found that variation in gap lengths do not alter the principal failure mode for YT-joints.The principal failure modes are due to wall chord plastification (Mode A) and chord buckling (Mode F) regardless of the gap length.For gap lengths between g=10.33 mm and g=110 mm, the percent difference between the dimension load and the yield load decreases as the gap length increases.For gap values up to g=70 mm, the yield load of the numerical model is above the dimension load, implying that such designs are safe.For gap lengths greater than g=70 mm, the yield load falls short of the dimension load, implying that such designs are unsafe and the existing formulations of such joint designs should be reexamined.

LatinFigure 1
Figure 1 Forces general scheme of YT joint.

Figure 3
Figure 3 Positioning of the extensometers on the YT joint prototype.

Figure 4
Figure 4 Positioning of the DTs on the YT joint prototype.

Figure 5
Figure 5 Overall strain of the prototype for EXPERIMENT III.

Figure 8
Figure 8 Principal stress f 1 measured at rosette 1 in EXPERIMENT III and the numerical models.

Figure 15
Figure 15 Principal stress "f 1 " for our numeric models.

8. 1
Failure modesThe predominant failure modes for "GAP30" through "GAP110" are shown in Figs.16 through 19, respectively.This shows that the main failure mechanisms are due to chord wall plastification (Mode A) and chord buckling (Mode F).

Figure 16
Figure 16 Plastic failure due to chord wall plastification in model "GAP30".

Figure 18
Figure 18 Plastic failure due to chord wall plastification in model "GAP110".
Figure 20 Dimension load and yield load.

Table 1
Physical and geometrical characteristics.

Table 2
Results of the calculation procedure.

Table 3
Last loading to EXPERIMENTS I, II and III.

Table 5
Data used to represent the multilinear stress-strain diagram with the Ansys software (MISO).

Table 6
Characteristics of elements.

Table 7
Gap lengths, eccentricities and e/d 0 ratios of models studied in this work.

Table 8
Yield load for our numeric models.

Table 9
Dimension load, yield load and percent difference between them.