DEVELOPMENT OF I-BEAM TO CHS COLUMN MOMENT CONNECTIONS WITH EXTERNAL DIAPHRAGMS FOR SEISMIC

APPLICATIONS

Alireza Bagheri Sabbagh, Tak-Ming Chan

School of Engineering, University of Warwick, Coventry, UK a.bagheri-sabbagh@warwick.ac.uk; t.m.chan@warwick.ac.uk

ABSTRACT

In this paper monotonic FE analysis is used to develop I-beam to CHS column full strength moment connections for earthquake applications. The main components are external diaphragm plates bolted to the beam and welded to the whole circumference of the column to transfer the beam forces to both near and far sides of the column. In the FE models, connector elements are used in places of the bolts to incorporate the connection bolt slip in the analysis. The target performance is to produce large plastic deformation in the beam while the column remains elastic. The web panel zone and other connection components are allowed to partially contribute in the overall inelastic deformation of the connection. Excessive yielding and distortion in the web panel and large stress concentration in the diaphragms in front of the column walls should be avoided as these can lead to weld fracture between the diaphragm plates and the column. Various ring widths for the diaphragm plates were examined and the value designed for the full strength of the beam flanges found to limit the web panel yielding and distortion. In addition, different types of vertical stiffeners are used in the connection region to eliminate the stress concentration in the diaphragms. Two pairs of triangular vertical stiffeners with the length extended to the end of the diaphragm plates provide the required performance. Cyclic FE analysis was also performed and shown that a degree of cyclic deterioration occurs in the moment-rotation behaviour, but similar conclusions as in the monotonic FE analyses can be drawn for the developed connections.

1 INTRODUCTION

The integrity of the common I-beam to H- section column moment connections can be provided by using continuity plates inside the column in front of the beam flanges [1-3]. This well known detailing, however, cannot be easily employed for tubular columns which typically produce higher load resistance in both framing directions than H- section columns. Different configurations for I-beam to tubular column connections have been investigated including through diaphragm, external diaphragm and through plate connections [4-11]. Experimental work on various

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details of I-beam-to-CHS column connections was performed by Alostaz and Schneider to investigate their elastic and inelastic behaviour [5, 6]. They showed that a direct connection to the tubular column wall causes premature flange fracture and severe local distortion on the tube wall [5, 6]. External diaphragm plates (Fig. 1a) have been used to transfer the beam forces around the column [4-9]. It is found that if appropriately designed the inelastic behaviour of the connections equipped with the diaphragm plates can be improved compared with the direct connection [4-9]. Stress concentration and out-of-plane failure deformation in the diaphragm plates as well as large web panel distortion have been reported [5-9] which led to fracture of the plates, welds and columns (Fig. 1b). Shifting the beam away from the face of column [5, 6] and designing the diaphragm ring width for the full strength of the beam flange [9] have been recommended to provide uniform stress flow around the column.

(a) (b)

Fig. 1 (a) Schematic drawing of external diaphragm connections (b) Fractures in

diaphragm plate, weld and column of an external diaphragm connection [6]

In this paper, an evolutionary process for I-beam to CHS column connections is presented by means of FE analysis leads to an optimum ring width for external diaphragm plates. The web panel excessive yielding and deformation need to be avoided. Furthermore, appropriate stiffeners are developed to eliminate stress concentration in the diaphragm plates in front of the column which potentially causes weld fracture between the diaphragm and the column.

In the FE analyses presented in this paper, connector elements are used in places of the bolts representing the slip-bearing action of the connections which found to be highly beneficial to achieve stable hysteretic cycles [12-14]. This method has already been used by Lim and Nethercot [15, 16] for monotonic FEA and by

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Bagheri Sabbagh et al. [17, 18] for both monotonic and cyclic FEA. A more complex method models the body of the bolts and accounts for contact interactions to simulate the slip-bearing action [19-20]. This method can be excessively time consuming especially for cyclic loading analysis and deals with more complicated converging issues compared with the modelling method using connector elements.

2 Design considerations of the I-beam-to-CHS column connections

The connections were designed so as to accommodate plastic hinges in the beam at the location after the connection while the column and connection components remain elastic according to the well known strong-column-weak-beam concept. A degree of inelastic behaviour was allowed in the column web panel [21]. Overstrength and strain hardening factors of 1.25 and 1.1, respectively were used in the design of the connection according to Eurocode 8 [2]. The slip resistance (Rn) of the bolts using AISC Specification [22] was such that no slip occurs in the elastic region up to the plastic moment of the beam. The connection slip, however, was allowed in the inelastic region which in the cyclic loading results in stable hysteresis behaviour [12, 13]. After a few cycles the slip resistances of the bolts degrade significantly mainly due to the reduction of the frictional coefficient and clamping forces of the bolts [12, 13& 18]. This was accounted for both in monotonic and cyclic FEA by assuming 50% reduction in the design slip resistance [13, 18].

A cantilever beam-to-column connection was used with 2m length column and beam (Fig. 2), representing distances between inflection points of an external frame with 4m span under lateral loading. The schematic view and dimensions of the designed connection using standard beam, UB 203×133×30, CHS column, 244×10 and the diaphragm plates are shown in Fig. 2. The diaphragm thickness is 15mm designed for the coupling forces projected to the connection from the overstrength plastic moment in the beam using nominal yield stress of 275MPa. The ring width of the diaphragm plates (w) varies to find out the optimum value as presented in Section 5. A complete ring welded to the column circumference was chosen because in a partial ring, stress concentration at the toes of the weld lines can causes initiation of crack. A web plate with 8mm thickness and 160mm height used to transfer the shear forces to the column.

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w

Fig. 2 Dimensions and section sizes of the investigated I-beam-to-CHS column connections with external diaphragm plates

3 Details of the FE models

FE analysis employing ABAQUS [23] was used for the investigation on the I-beam to CHS column connections with external diaphragms. The boundary conditions, lateral restraints and loading points are shown in Fig. 3a and the connector elements in places of the bolts are shown in Fig. 3b. The lateral restraints were applied at both the top and bottom flanges at the plastic hinge region and loading end of the beams according to the AISC Seismic Provisions [3]. Tie constraints were used for the welded connections between the diaphragm and web plates and the column. Other parameters of the FE models are:

Element type: Shell elements with 8 nodes and reduced integration, S8R, Mesh sizes: 10×10mm for the beam and diaphragm and web plates and 20×20mm for the column, and Material: bi-linear stress-strain behaviour with yielding stress of 275MPa (S275) for the beams and the plates and yielding stress of 355MPa (S355) for the columns, E=210GPa (modulus of elasticity), Es=E/100 (Second modulus) and υ=0.33 (Poisson`s ratio). Kinematic hardening rule was applied to the Von-Mises yielding surface for the cyclic analyses.

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Hinge connections

Lateral restraints in Y direction

Loading points in –Z direction

(a) (b)

Fig. 3 (a) Boundary conditions, lateral restraints and loading points (b) Connector elements

The connector elements from ABAQUS library [23] were a parallel combination (Fig. 4) of a CARTESIAN element for elastic- plastic behaviour and a STOP element for limiting the movement range within the clearance of the bolt holes (±1mm by assuming the bolts at the centre of the holes). The behaviour of the connector elements (Fig. 4) was rigid up to the slip resistance (Rn) of the bolts, movement of the bolts within the tolerances of the bolt holes (±1mm) and rigid bearing hardening. These assumptions were made since the exact positions of the bolts in the holes and therefore contact behaviour are unknown in the actual connection assemblies. This slip-bearing action model has already been used by Shen and Astaneh-Asl [24] and Bagheri Sabbagh et al. [18].

Connector elements

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Fig. 4 Slip-bearing action of the connector elements

4 FE results for development of I-beam-to-CHS column connections with different diaphragm ring widths

An evolutionary process was used for the development of the external diaphragms for the I-beam-to-CHS column connections. Stress distribution and failure deformations of the FE analyses are shown in Fig. 5 and normalised moment-rotation (M/Mp-θ) curves calculated at the plastic hinge location are shown in Fig. 6. Mp is the overstrength plastic moment of the beams (1.25 times the nominal plastic moment). The horizontal portion of the M/Mp-θ curves (Fig. 6) occurred at around 0.5Mp corresponds to the connection slip activated in the FE analyses as discussed previously in Section 2.

The FEA without the external diaphragm plates (direct connection) showed large yielding area and excessive distortion in the column web panel and no yielding in the beam (Figs. 5 and 6, w= 0). By using a diaphragm ring tied to the whole circumference of the column with the width of w= 30mm, a degree of yielding was mobilised in the beam, although the distortion and yielding in the column web panel still took over (Figs. 5 and 6, w= 30). By increasing the ring width from 30mm to 50mm, local buckling occurred in the beam after the connection region and the column web panel contributed less in the overall deformation (Fig. 5, w= 50) than the connection with w= 30mm. Local flange and web buckling in the beam led to strength degradation at around 0.08rad in the moment-rotation curve (Fig. 6, w= 50). The connection with w= 70mm showed even less yielding in the web panel (Fig. 5, w= 70) and strength degradation (Fig. 6, w= 70) due to the beam local buckling initiated earlier (at around 0.07rad) than the connection with w= 50mm.

R

RnRigid‐plastic

Stop

+1mm‐1mmhole`s centre

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w= 0 w=30mm

Failure deformations

w= 50mm w= 70mm

Failure deformations

w= 90mm w= 110mm

Fig. 5 Failure deformations and Von-Mises stress contours of the I-beam-to-CHS column connections with different diaphragm ring widths (w=0, 30, 50, 70, 90 and

110mm)

Web panel yielding at the peak load 

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Fig. 6 Moment-rotation curves of the I-beam-to-CHS column connections with different diaphragm ring widths (w=0, 30, 50, 70, 90 and 110mm)

The failure deformations and moment rotation curves of the connections with w=90 and 110mm were close to those of the connection with w=70mm (Figs. 5 and 6). Increasing the diaphragm ring width, however, reduced the yielding region in the web panel (shown in Fig. 5, w=90 and 110mm) which in the connection with w= 110mm was nearly vanished. The diaphragm plate with w= 90mm showed a degree of yielding in the web panel which is acceptable according to the current design codes [1-3; 22] discussed by El-Tawil et al [21], therefore in this case assumed as the optimum diaphragm width. The diaphragm width of w= 90mm also meets the design criteria proposed by Wang et al. [9] to resist full strength of the beam flanges.

In all the FE analyses presented in this section for different diaphragm widths (w= 0, 30, 50, 70, 90 and 110mm), stress concentration occurred in the diaphragm plates in front of the column face. This potentially leads to weld fracture between the diaphragm and the column as well as local buckling in the diaphragm plates (reported by other researchers [5-9]). This stress concentration cannot be eliminated in the compressive diaphragm either by increasing the diaphragm thickness from 15mm to 20mm or the material yielding strength from 275MPa to 355MPa (Fig. 7). The reason can be second order effects in the compressive diaphragm which can be intensified by initiation of the beam local buckling and large deformations. This phenomenon is addressed in the next section.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.02 0.04 0.06 0.08 0.1

M/M

p

θ (rad)

No ring

w=30mm

w=50mm

w=70mm

w=90mm

w=110mm

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Diaphragm thickness= 20mm Diaphragm strength= 355MPa

Fig. 7 Stress concentration in the diaphragm plates with increased thickness from 15mm to 20mm and the material strength from 275MPa to 355MPa

5 FE results for development of I-beam-to-CHS column connections with different diaphragm stiffeners

Different configurations of vertical stiffeners tied to the external diaphragms (with w= 90mm) and the column were examined to minimise the stress concentration in the diaphragm plates (Fig. 8). Firstly, the stiffeners inside the connection were used between the diaphragm plates which have less architectural impact than the outside stiffeners on top of the diaphragm plates. In the model equipped with 100mm length vertical stiffeners (Fig. 8, St1), the stress concentration initiated at the tip of the stiffeners in the compressive diaphragm and propagated towards the face of the column at the larger load increments. By extending the vertical stiffeners further inside the connection (Fig. 8, St2), similar stress concentration was observed. The stress concentration also occurred in the compressive diaphragm plate in the connection with separated pairs of vertical stiffeners (with 50mm height) extended to the end of connection for each of the diaphragm plates (Fig. 8, St3). The stress concentration, however, is minimised by using the same vertical stiffeners as St3, but placed outside of the connection on top of the diaphragm plates (Fig. 8, St4). The reason is higher connection stiffness provided by using outside stiffeners and consequently less second order effects in the diaphragm plates. By using a more effective triangular shape for the outside vertical stiffeners with 100mm height in front of the column (Fig. 8, St5), the stress concentration was completely removed in front of the column in the compressive diaphragm, although a degree of yielding appeared at the toe of the tension diaphragm. The reason is excessive transverse deformation of the diaphragm plates by increasing the stiffness of the connection. By trimming the stiffeners (Fig. 8, St6) the stress concentration again initiated at the tip of the stiffeners and propagated at the larger load increments similar to the behaviour of the connections with St1 and St2. Therefore, using the vertical stiffeners with the

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shorter length than the whole connection length should be avoided in this type of connections.

St1 St2

St3 St4

St5 St6

Fig. 8 Stress concentration in the diaphragms of the connections with different vertical stiffeners connected to the diaphragm plates and the column

Initiation of stress concentration

Initiation of stress concentration

Propagation of stress concentration

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The moment-rotation curves of the connections with all the examined stiffeners (Fig. 9, St1-6) are similar to that of the connection without stiffener. The strength degradation starts at around 0.07rad due to local buckling in the beam after the connection region. The slip resistance load level was increased by increasing the connection stiffness (Fig. 9, St1-6). The moment-rotation curves of the connections using St5 and with w=70, 90 and 110mm (shown by dashed lines in Fig. 9) are very close to each other. The stress concentration in the connections with St5, w=70 and 110mm was also removed in the compressive diaphragms in front of the column similar to the connection with St5, w=90mm (Fig. 8, St5). The connection with triangular stiffeners (St5) can be assumed as optimum in this case.

Fig. 9 Moment-rotation curves of the I-beam-to-CHS column connections with different vertical stiffeners

6 Cyclic FE results for the developed connection configurations

Cyclic loading applied to the FE models using w= 70 and 90mm diaphragm plates with and without the optimum vertical stiffeners, St5, examined in the previous section. In the cyclic FEA, surface to surface contact was used between the diaphragm plates and the beam flanges to avoid their penetration during the buckling deformation. The cyclic moment-rotation curves as well as the monotonic curves are shown in Figs. 10a and b. It is evident that the strength degradation occurred earlier in the cyclic curves than the monotonic curves (Fig. 10) due to the cyclic deterioration effect. The deterioration is even sharper in the cyclic FEA with w= 70mm than that of the FEA with w=90mm (Fig. 10a). Similar to the results obtained in the monotonic FE analyses (presented in the previous sections) it can

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.02 0.04 0.06 0.08 0.1

M/M

p

θ (rad)

without stiffener

St1

St2

St3

St4

St5, w=70

St5,w=90

St5, w=110

St6

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be concluded that: (i) web and flange buckling after the connection region (Fig. 11) is the main reason for the strength degradation, (ii) the connection using w= 90mm showed less web panel yielding than the connection with w= 70mm and (iii) the use of vertical stiffeners St5, eliminated the stress concentration in the diaphragms in front of the column face.

(a) Without vertical stiffeners

(b) With vertical stiffeners St5

Fig. 10 Cyclic and monotonic moment-rotation curves of the connections using w= 70 and 90mm (a) without vertical stiffeners and (b) with St5

‐1.4‐1.2‐1

‐0.8‐0.6‐0.4‐0.2

00.20.40.60.81

1.21.4

‐0.1 ‐0.06 ‐0.02 0.02 0.06 0.1

M/M

p

θ (rad)

monotonic, w=70

cyclic, w=70mm

monotonic, w=90

cyclic, w=90

‐1.4‐1.2‐1

‐0.8‐0.6‐0.4‐0.2

00.20.40.60.81

1.21.4

‐0.08 ‐0.04 0 0.04 0.08

M/M

p

θ (rad)

monotonic, w=70

monotonic, w=90

cyclic, w=70

cyclic, w=90

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(a) (b)

Fig. 11 Failure deformations and Von-Mises stress contours for the cyclic FE analyses of the connections using (a) w= 90mm and (b) w= 90mm with St5

7 CONCLUSIONS

Optimum configurations for I-beam-to-CHS column moment resisting connections with external diaphragm plates were developed using monotonic FE analysis. Two types of connection failure were eliminated: web panel distortion and stress concentration in the diaphragm plates.

A full ring welded to the column as external diaphragm plates is needed to reduce excessive yielding and distortion in the web panel zone. By designing the total ring width for the full strength of the beam flanges (w= 90mm in this study) slight yielding occurred in the web panel zone which is acceptable according to the current design codes.

Two pairs of triangular vertical stiffeners found to eliminate the stress concentration in the diaphragm plates in front of the column face. These stiffeners were welded to the column face and to the top of the diaphragms outside the connection and extended to the end of the diaphragms (St5 in this study).

Cyclic FEA also performed and confirmed the results achieved in the monotonic FEA. Cyclic deterioration effect caused earlier strength degradation in the developed connections (using w= 70 and 90mm with or without St5).

ACKNOWLEDGEMENTS

The authors are grateful to the Engineering and Physical Science Research Council (EP/1020489/1) for the project funding and Dr José Miguel Castro from University of Porto for his technical support.

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