STEEL MOMENT CONNECTION WITH ELLIPTICAL REDUCED BEAM SECTION

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STEEL MOMENT CONNECTION WITH ELLIPTICAL REDUCED BEAM SECTION

Seyed Esmaeil MOHAMMADYAN-YASOUJ¹, Fahimeh ESMAEILZADEH², Parham

MEMARZADEH³

ABSTRACT

Development of reduced beam section (RBS) moment connections in the aftermath of the Northridge and Kobe catastrophic earthquakes was to provide highly ductile connections with reliable performance. A new geometry to apply reduced beam section for this type of moment connections is studied in this paper. The elliptical cutting was aimed to increase ductility and energy dissipation of RBS connections. To investigate the nonlinear behavior of RBS connections with elliptical cutting in the beam section, after verification of a Finite Element Model (FEM) with radial cutting based on a previous experimental study, a set of six additional models with and without elliptical cutting were prepared and analyzed. Results of all models were compared and it was confirmed that the elliptical cutting is efficient at improving ductility and energy dissipation of the moment connections.

Keywords: Elliptical cutting; RBS; Moment connection

1. INTRODUCTION

Strengthening the connection and/or weakening the beam framing into the connection are two ideas in order to design seismic resistant steel frames. Accordingly, the concept of Reduced Beam Section (RBS) connection was firstly proposed by Plumier in 1990 and applied by Georgescu in 1996 (Plumier 1990;

Plumier 1996; and Georgescu 1996). Studies on the behavior of RBS beam-to-column connections were widely conducted after the Northridge and Kobe earthquakes. The main goal of RBS was to prevent any sign of plastic deformation or failure at the connection or in its components such as end-plate, column flange, bolts, and welds.

Pachoumis et al. (2009) studied experimental and theoretical models of the RBS moment connection with radius cut under cyclic loading. Results for both models confirmed that the cyclic performance of RBS moment connection is excellent when the plastic hinge is at RBS zone. They suggested readjustment of the geometrical characteristics of the RBS in order to apply it to the European profiles.

As shown in Figure 1, different cutout shapes such as constant, tapered, or radius cut have been suggested to trim the beam flange away from the beam-to-column connection.

1Assistant Professor, Department of Civil Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran, [email protected]

2Postgraduate Student, Department of Civil Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran, [email protected]

3Assistant Professor, Department of Civil Engineering, Najafabad Branch, Islamic Azad University, Najafabad,

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Figure 1. Shapes of reduced beam sections (Pachoumis et al. 2009)

Swati and Gaurang (2014) tested two steel moment connections with and without reduced beam section (RBS) under cyclic loading to study the advantages and usefulness of RBS for Indian profiles.

Experimental tests and the finite element approach were used to compare the results. They observed that due to the RBS application, cracks at the bottom flange weld were prevented.

Sofias et al. (2014) studied two full scale subassemblies of the RBS moment connections with extended bolted end-plate under experimental tests and the finite element analysis approach to investigate EC8, Part 3 key parameters for the design. They used C3D8R and S4R element types to simulate different parts in ABAQUS finite element software and conducted pre-experiment modeling to predict the subassemblies overall behavior and details on the connections moment capacity and the stress-strain progress under load cycles. From the results, they proposed that the "c" parameter of the RBS geometry which is the depth of the flange reduction and the main parameter to reduce cross section strength of the RBS, should be correlated with the ductility level of the steel grade.

Atashzaban et al. (2015) conducted experimentally validation for non-linear finite element models of drilled flange moment connections. They aimed to study the ductility performance of drilled flange moment connections to make them viable alternatives to RBS moment connections in seismic regions.

The drilled flange moment connections were claimed to be easy-to-construct and able to prevent the premature local buckling modes in RBS connections. Accordingly, the effects of design parameters including DF holes configurations and locations were investigated. The results indicated that drilled flange holes are efficiently able to shift the stress concentrations and plastic strain accumulation from the Complete Joint Penetration (CJP) groove weld lines at the column face to the drilled flange area to prevent the premature brittle fracture of the welded joints. Considering the important role of the drilled holes in controlling the non-linear performance of drilled flange moment connections, it was also indicated that increasing the hole diameters from the column face is effective to reduce the maximum equivalent plastic strain (EPEQ) at drilled flange and can reduce EPEQ and Rupture Index (RI) of the CJP groove weld lines. (Atashzaban et al. 2015)

In an analytical study by Rahnavard et el. (2015) used radial and circular cuttings as two approaches to create reduced sections on the beam flanges and proposed a new type of reduced beam section moment connection in which the holes diameter is varied (in a distance from the column face is increasing and then is decreasing). After their analytical study on eight moment connections with different shape of reducing beam flange, they concluded that using varied holes to reduce the beam section, ductility and energy dissipation of the moment connection in comparison to other connections become more.

In the present study, elliptical cutting is proposed as a new geometry to apply reduced beam section for RBS moment connection. The elliptical cutting was aimed to increase ductility and energy dissipation of RBS connections. To investigate the nonlinear behavior of RBS connections with elliptical cutting in the beam section, after verification of a finite element model with radial cutting based on a previous experimental study, a set of four additional models with and without elliptical cutting were prepared, analyzed, and compared.

2. METHODOLOGY

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2.1 Creation and Verification of Finite Element Models

In order to prepare the theoretical models, a finite element model of an experimental steel moment connection with RBS was created based on a previous study by Swati and Gaurang (2014). They considered steel moment connections with and without RBS then tested a set of two subassemblies experimentally and created their finite element models to study the advantages and usefulness of RBS for Indian profiles under cyclic loading. The test setup and details of the subassembly used for verification are shown in Figure 2. Geometrical properties of the column and beam with RBS based on the reference study for verification are presented in Table 1 and Figure 2.

Figure 2. Test setup and subassemblies for the verification study (Swati and Gaurang 2014) Table 1. Details of the reference model for verification (Swati and Gaurang 2014)

Member Profile d ࢚࢝ bf ࢚ࢌ RBS parameters

a b c R

Column WPB150 162 8 154 11.5 - - - -

Beam NPB200 200 5.6 100 8.5 60 160 25 140.5

Notes: All dimensions are in mm; d represents the depth; ݐ௪ represents thickness of the web; bf represents the flange width; and a, b, c, and R is are parameters as shown in Figure 3 for RBS moment connection

Figure. 3. Parameters for radius cut in RBS moment connection

A theoretical model was created in ABAQUS finite element software. Geometrical and material nonlinearity was considered. The nonlinear material properties were defined based on Table 2.

Table 2. Material properties (Swati and Gaurang 2014) Section ࡲ_࢟ (MPa) ࡲ_࢛ (MPa) ࣇ ࡱ (MPa)

NPB200 330 484 0.3 ʹ ൈ ͳͲ^ହ

WPB150 334 486 0.3 ʹ ൈ ͳͲ^ହ

Notes: ܨ௬represents yielding stress; ݂௨ represents ultimate strength; ߥ represents poisson´s ratio; and ܧ represents modulus of elasticity.

The beam and column parts were modelled using four noded thin shell elements (element S4R). Tie

ܴ ൌͶܿ^ଶ൅ ܾ^ଶ ͺܿ

Column

Beam

ܽ ܾ ܿ

ݏ ܾ_௙

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constraint was used to define the interactions between the beam and column parts at column face.

As shown in Table 3, the cyclic loading protocol with displacement amplitude was considered according to SAC (1996) loading protocol. In the experimental model, the applied loading history was until load step #7, but the next steps shown in this table are for investigation of later models after verification process.

Table 3. Loading history

Load step # 1 2 3 4 5 6 7 8 9

Number of cycles (n) 6 6 6 4 2 2 2 2 2

Interstory drift angle

(radians) 0.00375 0.005 0.0075 0.01 0.015 0.02 0.03 0.04 0.05 Beam tip displacement

(mm) ±3.75 ±5 ±7.5 ±10 ±15 ±20 ±30 ±40 ±50

Different parameters such as material modeling and mesh size at different regions were considered to prepare a verified model based on the reference model until interstory drift angle of 0.03 radians. In the reference model, Von Mises stress values at column web in the connection zone and at RBS area at 0.03 radians were 313 to 358 MPa and 313 to 403 MPa, respectively. Results of six selected models in Table 4 and Figures 4 and 5, show that models with trilinear material modeling and mesh size of either 10 mm or 20 mm at different regions that showed no flange buckling, have the minimum difference of stress values with the reference model.

Table 4. Trial models for material modeling and mesh study

Model

#

Material properties

Mesh size (mm) Von Mises stress (MPa) Connection

zone

Other Flange buckling

At column web in the

connection zone At RBS

1 bilinear 20 20 No 307-334 307-334

2 bilinear 10 10 No 294-324 324-355

3 bilinear 10 20 Yes 317-346 317-346

4 trilinear 10 20 Yes 242-282 443-484

5 trilinear 10 10 No 322-363 363-443

6 trilinear 20 20 No 322-363 363-443

Figure 4. Von Mises stress values (a) model #8 in ABAQUS; and (b) reference model in ANSYS (Swati and Gaurang 2014)

(a) (b)

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Figure 5. Load-displacement behavior (a) model #8; and (b) reference for verification (Swati and Gaurang 2014) 2.2 Selection of the Final models

After load application was increased to upper than 0.03 radians, even with continuity and doubler web plates, lateral torsional or local buckling was observed in the models. Therefore, new sections were designed to create the models for parametric study. Geometrical properties of the new sections are shown in Tables 5 and 6. Material properties of ST37 shown in Table 7, were considered for the final models with new sections.

Table 5. Dimensions of designed sections

Section h ࢈ࢌ ࢚࢝ ࢚ࢌ ࡭ ࢆ

Beam 200 200 9 15 7800 233325

Column 360 300 12.5 22.5 18000 359756

Notes: h represents section height (mm); ܾ௙ represents flange width (mm); ݐ௪ represents web thickness (mm); ݐ௙

represents flange thickness (mm); ܣ represents section area (mm²); and ܼ represents the plastic section modulus (mm).

Table 6. Dimensions of stiffener and doubler plates

Plate ࢒ ࢈ ࢚

Stiffener 360 120 10

Doubler 400 360 15

Notes: ݈ represents plate length (mm); ܾ represents plate width (mm); and ݐ represents plate thickness (mm).

Table 7. Material properties for the final models

Section ࡲ࢟ (MPa) ࡲ࢛ (MPa) ࢿ࢟ ࢿ࢛ ࣇ ࡱ (MPa)

Beam, column, stiffener

and doubler 240 370 0.0012 0.2 0.3 ʹ ൈ ͳͲ^ହ

Notes: ܨ_௬represents yielding stress; ݂_௨ represents ultimate strength; ߝ_௬ represents yielding strain; ߝ_௨ represents ultimate strain; ߥ represents Poisson’s ratio; and ܧ represents modulus of elasticity.

For moment frame beams with RBS connections based on radius cut, FEMA 350 (2000) recommends RBS parameters according to Equations 1, 2, 3, and 4 as in the following:

ܽ ؆ ሺͲǤͷ െ ͲǤ͹ͷሻܾ௙ (1)

ܾ ؆ ሺͲǤ͸ͷ െ ͲǤͺͷሻ݀௕ (2)

ܿ ؆ ሺͲǤʹ െ ͲǤʹͷሻܾ௙ (3)

(a) (b)

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ܴ ൌͶܿ^ଶ൅ ܾ^ଶ ͺܿ

(4)

Parameters for circularly and elliptically drilled cut to create RBS moment connections are shown in Figures 6 and 7. The final models are designated in Table 8. In this table, parameter ݀௕ is the beam depth and to have a comparison between models, the values for ܽǡ ܾǡand ܿ are almost the average of proposed values by FEMA 350 except those that are separately defined. In Table 8, SMR represents the steel moment resisting frame with normal beam; ܴܤܾܵ௔௩Ǥܿ௔௩Ǥ represents the steel moment resisting frame considering the average values recommended by FEMA 350 to create radius cut in the beam flange; ܦܨܥܾ௔௩Ǥܿ௔௩Ǥ represents the steel moment resisting frame considering the average values recommended by FEMA 350 to create circularly drilled cut in the beam flange; ܦܨܧܾ௔௩Ǥܿ௔௩Ǥ represents the steel moment resisting frame considering the average values recommended by FEMA 350 to create elliptically drilled cut in the beam flange; ܦܨܧܾ௘ܿ௔௩Ǥ represents the steel moment resisting frame considering an effective value of b less than recommendation by FEMA 350 and the average of recommended values for c by this code to create elliptically drilled cut in the beam flange; and ܦܨܧܾ௘ܿ௘

represents the steel moment resisting frame considering effective values of b and c less than recommendation by FEMA 350.

Figure 6. Parameters for circularly drilled cut in RBS moment connection

Figure 7. Parameters for elliptically drilled cut in RBS moment connection Table 8. Properties of beams in the final models

Model name Beam reduced flange parameters ሺ࢓࢓ሻ

ࢇ ൌ ૙Ǥ ૟૞࢈ࢌ ࢈ ൌ ૙Ǥ ૠ૞ࢊ࢈ ࢉ ൌ ૙Ǥ ૛૛૞࢈ࢌ ࢉࢋൌ ૙Ǥ ૚࢈ࢌ ࢊࢉ࢏࢘ࢉ࢒ࢋ࢙ ࢈ࢋൌ ૙Ǥ ૝૞ࢊ࢈

SMR - - - -

ܴܤܾܵ௔௩Ǥܿ௔௩Ǥ ͳ͵Ͳ ͳͷͲ Ͷͷ - - -

ܦܨܥܾ௔௩Ǥܿ௔௩Ǥ ͳ͵Ͳ 150 45 - ݀ଵൌ ͵ʹǤͷǢ݀ଶ

ൌ ͶͷǢ݀ଷൌ ͵ʹǤͷ

-

ܦܨܧܾ௔௩Ǥܿ௔௩Ǥ ͳ͵Ͳ 150 45 - - -

ܦܨܧܾ௘ܿ௔௩Ǥ 130 - 45 - - 90

ܦܨܧܾ௘ܿ௘ 130 - - 30 - 90

3. RESULTS AND DISCUSSION

Maximum decrease in the connection strength at 0.04 radians interstory drift (0.01 radians for elastic behavior and 0.03 radians for plastic behavior) is limited to 20% of section plastic moment (ܯ௣) (AISC

Column

Beam

ܽ ^ܾ

ܿ

ܾ௙

Column

Beam

ܽ ܾ

ܿ

ܾ௙

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2002). To compare the results of all models in terms of their strength and rotational behavior, 3D graphical models and their ܯ െ ߠ curves are shown in Figures 8 to 13 and Table 8 presents extra data on the strength, ductility, and energy dissipation of the models.

In SMR which was a steel moment resisting connection with no RBS, the maximum values of Vone Mises stress is at column face and therefore, failure of welding is possible.

Figure 8. Model ܵܯܴ (a) Vone Mises stress; (b) Equivalent plastic strain; (c) M-! curve

Von Mises stress criterion for ܴܤܾܵ௔௩Ǥܿ௔௩Ǥ which was steel moment resisting connection with radius cut show that stress concentration is at RBS area and therefore, failure at connection zone is almost impossible.

Figure 9. Model ܴܤܾܵ௔௩Ǥܿ௔௩Ǥ (a) Vone Mises stress; (b) Equivalent plastic strain; (c) M-! curve The maximum value of stress in ܦܨܥܾ_௔௩Ǥܿ_௔௩Ǥ which was steel moment resisting connection with circularly drilled cut show that stress concentration is in the RBS area.

(a) (b) (c)

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Figure 10. Model ܦܨܥܾ௔௩Ǥܿ௔௩Ǥ (a) Vone Mises stress; (b) Equivalent plastic strain; (c) M-! curve For model ܦܨܧܾ௔௩Ǥܿ௔௩Ǥ which was steel moment resisting connection with elliptically drilled cut, stress concentration is in the RBS area and appearance of plastic hinge is going to be far from the column face, but local buckling at beam flange results in strength reduction of the connection. This local buckling may be due to the higher cutting area in this model in comparison to the values by FEMA 350.

Figure 11. Model ܦܨܧܾ௔௩Ǥܿ௔௩Ǥ (a) Vone Mises stress; (b) Equivalent plastic strain; (c) M-! curve To prevent local buckling at beam flange in the RBS area by decreasing cutting area, model ܦܨܧܾ௘ܿ௔௩Ǥ

in which b was less than the minimum value suggested by FEMA 350, was considered.

(a) (b) (c)

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Figure 12. Model ܦܨܧܾ_௘ܿ_௔௩Ǥ (a) Vone Mises stress; (b) Equivalent plastic strain; (c) M-! curve

Reduction of RBS length in ܦܨܧܾ௘ܿ௔௩Ǥ in comparison to other models that was to reduce the RBS area removed the local buckling of the flange beam and increased connection strength. In this model, energy dissipation and ductility was improved in comparison to the model with radius cut. Less energy dissipation and strength of ܦܨܧܾ௘ܿ௔௩Ǥ in comparison to ܦܨܥܾ௔௩Ǥܿ௔௩Ǥ seemed to be due to the higher RBS area.

In model ܦܨܧܾ_௘ܿ_௘, decrease of RBS area by reducing cutting depth in the beam flange improved the final strength, energy dissipation, but due to the decrease in the RBS areas the plastic hinge may extend to the connection zone.

Figure 13. Model ܦܨܧܾ௘ܿ௘ (a) Vone Mises stress; (b) Equivalent plastic strain; (c) M-! curve Table 8. Moment-rotational behavior and energy dissipation of the final models Model

name

ࡹ_࢟

ሺ࢑ࡺǡ ࢓ሻ ࡹ_࢛

ሺ࢑ࡺǡ ࢓ሻ ીܡൈ ૚૙^૜

ሺܚ܉܌ሻ ી܎ൈ ૚૙^૜

ሺܚ܉܌ሻ ࣆ Energy Desi.

ሺ࢑ࡺǤ ࢓ሻ

SMR 155 239 11 50 4.5 127

ܴܤܾܵ௔௩Ǥܿ௔௩Ǥ 120 180 10 50 5 114

ܦܨܥܾ௔௩Ǥܿ௔௩Ǥ 120 182 10 50 5 117

ܦܨܧܾ௔௩Ǥܿ௔௩Ǥ 110 150 9 50 5.55 103

(a) (b) (c)

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ܦܨܧܾ௘ܿ௘ 140 210 10 50 5 126 4. CONCLUSIONS

Different steel moment connection with radius, circularly drilled, and elliptically drilled cut on the beam flanges to create RBS and without RBS were modeled and compared to investigate RBS reduce beam section using elliptical cutting as a new method. Analytical study on these models provides the following findings:

· While the model without RBS showed stress concentration at column face in the welding all final models with radius cut, circularly drilled cut, and elliptically drilled cut satisfied the AISC criterion to provide connection strength at 0.04 radians higher than the 0.8 of the section plastic moment.

· Considering the appropriate dimensions to have similar values of cutting area, models with circularly and elliptically drilled cut in comparison to the models with radius cut have more ductility and energy dissipation capacity.

· Once RBS length and depth (b and c) in RBS models with elliptically drilled cut are reduced in order to decrease the cutting area to prevent the local buckling in the beam flange, the stress concentration may move to the column face. Since, an average value of FEMA 350 recommendations was utilized for RBS distance from the column face or a in all RBS models, a higher value of a may prevent stress concentration in the connection zone.

5. REFERENCES

American Institute of Steel Construction (AISC). (2002). Seismic provisions for structural steel buildings.

American Institute of Steel Construction.

Atashzaban, A., Hajirasouliha, I., Jazany, R. A., & Izadinia, M. (2015). Optimum drilled flange moment resisting connections for seismic regions. Journal of Constructional Steel Research, 112, 325-338.

FEMA350.Recommendedseismic design criteria fornewsteel moment-frame buildings. Washington (DC), 2000.

Georgescu D. Recent developments in theoretical and experimental results on steel structures. Seismic resistant braced frames. Costruzioni Metall 1996;1: 39–52.

Pachoumis, D. T., Galoussis, E. G., Kalfas, C. N., & Christitsas, A. D. (2009). Reduced beam section moment connections subjected to cyclic loading: Experimental analysis and FEM simulation. Engineering Structures, 31(1), 216-223.

Plumier A.Newidea for safe structure in seismic zone. In: Proceedings of IABSE symposium on mixed structures including new materials. 1990. p. 431–36.

Plumier A. Reduced beam sections; a safety concept for structures in seismic zones. Bul Stiint Univ Politeh Timis"

(Romania) 1996;41(2):46–59.

Rahnavard, R., Hassanipour, A., & Siahpolo, N. (2015). Analytical study on new types of reduced beam section moment connections affecting cyclic behavior. Case Studies in Structural Engineering, 3, 33-51.

Sofias, C. E., Kalfas, C. N., & Pachoumis, D. T. (2014). Experimental and FEM analysis of reduced beam section moment endplate connections under cyclic loading. Engineering Structures, 59, 320-329.

Swati, A. K., & Gaurang, V. (2014). Study of steel moment connection with and without reduced beam section.

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Venture, S. J. (1996). Experimental investigations of beam-column subassemblages. Rep. No. SAC-96-01, Parts I and II.