Analysis of Seismic Performance of Steel Moment Connection with Welded Haunch and Cover Plate

Similar documents
Effect of beam dimensions on structural performance of wide beam-column joints

Experiment and Finite-element-method Analysis of Steel Frame Joints Transferring Forces Outside Box Columns

CYCLIC TESTING OF BOLTED CONTINUOUS I-BEAM-TO-HOLLOW SECTION COLUMN CONNECTIONS

Fagà, Bianco, Bolognini, and Nascimbene 3rd fib International Congress

INTERNATIONAL JOURNAL OF CIVIL AND STRUCTURAL ENGINEERING Volume 2, No 2, 2011

THE EXTENDED N2 METHOD IN SEISMIC DESIGN OF STEEL FRAMES CONSIDERING SEMI-RIGID JOINTS

CHAPTER 8 THE DESIGN AND ANALYSIS OF MULTI-STORY BUILDINGS WITH LARGE MOMENT END-PLATE CONNECTIONS 8.1 INTRODUCTION

Seismic evaluation of Hybrid steel frames with different patterns of semi-rigid connection

INTERNATIONAL JOURNAL OF CIVIL AND STRUCTURAL ENGINEERING Volume 2, No 2, 2011

SEISMIC PERFORMANCE OF STEEL FRAMES EQUIPPED WITH BUCKLING RESTRAINED BRACE

SEISMIC BEHAVIOR OF STEEL RIGID FRAME WITH IMPERFECT BRACE MEMBERS

Seismic Evaluation of Steel Moment Resisting Frame Buildings with Different Hysteresis and Stiffness Models

Simi Aboobacker 1 and Nisha Varghese 2

Journal of Asian Scientific Research EVALUATION OF RECTANGULAR CONCRETE-FILLED STEEL-HOLLOW SECTION BEAM-COLUMNS

SEISMIC PERFORMANCE OF CONCRETE TILT-UP BUILDINGS: CURRENT WALL-TO-SLAB CONNECTIONS

Council on Tall Buildings

Reinforced concrete edge beam column slab connections subjected to earthquake loading

Nonlinear Finite Element Modeling & Simulation

Experimental study on seismic behavior of composite concrete and

Experiment of Reinforce Concrete Beams at Different Loading Rates

NON-LINEAR FEM ANALYSIS FOR CES SHEAR WALLS

DESIGN ASPECTS AFFECTING THE SEISMIC BEHAVIOUR OF STEEL MRF BUILDINGS: ANALYSIS OF THREE CASE STUDIES

Cable bracing design in adaptable dual control systems

Seismic Design of Reduced Beam Section (RBS) Steel Moment Connections with Bolted Web Attachment

Available online at ScienceDirect. Procedia Engineering 145 (2016 )

BEHAVIOR OF REINFORCED CONCRETE BEAM WITH OPENING

Study on Beam-to-Column Connection with Viscoelastic Hysteretic Dampers for Seismic Damage Control

Research on the Influence of Infill Walls on Seismic Performance of Masonry Buildings with Bottom Frame-Shear Walls

EVALUATION OF THE NEED FOR WEAK BEAM-STRONG COLUMN DESIGN IN DUAL FRAME-WALL STRUCTURES

Analytical Investigation of Seismic Performance of Exterior RC Beam-Column Joints Rehabilitated with New Scheme

Seismic Performance and Design of Linked Column Frame System (LCF)

Gravity Load Collapse of Reinforced Concrete Columns with Brittle Failure Modes

Fragility Curves for Seismically Retrofitted Concrete Bridges

REVIEW ON SHEAR SLIP OF SHEAR KEYS IN BRIDGES

Design for earthquake-resistent reinforced concrete structural walls

NONLINEAR DYNAMIC RESPONSE OF DISSIPATIVE DEVICES FOR SEISMIC RESISTANT STEEL FRAMES: EXPERIMENTAL BEHAVIOUR AND NUMERICAL SIMULATION

Introducing an Innovative Column Splicing Technique for Steel Structures

The cracking behaviour of reinforced concrete beams under static and dynamic loading

MULTI-LEVEL FORTIFICATION INTENSITIES SEISMIC PERFORMANCE ASSESSMENT FOR REINFORCED CONCRETE FRAME- SHEAR WALL STRUCTURE WITH VISCOUS DAMPERS

Non Linear Analysis of Composite Beam Slab Junction with Shear Connectors using Ansys.16

SEISMIC EFFECTS ON COUPLED SHEAR WALL STRUCTURE BY COUPLING BEAMS WITH SIDE BOLTED STEEL PLATES

Seismic Reinforcement of Existing Masonry Structure On Conceptual Design

Effect of FRP strengthening on the behavior of shear walls with opening

THE BEHAVIOR OF TWO MASONRY INFILLED FRAMES: A NUMERICAL STUDY

INHERENT DUCTILITY OF REINFORCED CONCRETE SHEAR WALLS WITH NON-SEISMIC DETAILING

Modeling of Coupled Nonlinear Shear and Flexural Responses in Medium-Rise RC Walls

NONLINEAR FINITE ELEMENT ANALYSIS OF SHALLOW REINFORCED CONCRETE BEAMS USING SOLID65 ELEMENT

Tests on Seismic Behavior of Pre-cast Shear Walls with Vertical Reinforcements Spliced by Two Different Grout Ways

Analysis of Shear Wall Transfer Beam Structure LEI KA HOU

Shaking Table Test of Controlled Rocking Reinforced Concrete Frames

NONLINEAR FINITE ELEMENT ANALYSIS OF NON- SEISMICALLY DETAILED INTERIOR RC BEAM-COLUMN CONNECTION UNDER REVERSED CYCLIC LOAD

Nonlinear Analysis of Reinforced Concrete Column with ANSYS

Overview of Presentation. SCBFs are Conceptually Truss Structures

EVALUATION OF LAMINATED HOLLOW CIRCULAR ELASTOMERIC RUBBER BEARING

Original Publication: International Journal of High-Rise Buildings Volume 1 Number 3

On Improved Performance Of Eccentrically Braced Frames With Replaceable Shear Link

Experimental investigation of the use of CFRP grid for shear strengthening of RC beams

NON-LINEAR FINITE ELEMENT MODELING OF RC FRAME-MASONRY WALL INTERACTION UNDER CYCLIC LOADINGS

22. DESIGN OF STEEL BRACED FRAMES Eccentrically Braced Steel Frames

Nonlinear Redundancy Analysis of Truss Bridges

REHABILITATION OF RC BUILDINGS USING STRUCTURAL WALLS

MIDAS Training Series

A new ductile approach design of joints assembled with screw connectors

ASSESSMENT OF SEISMIC BEHAVIOR OF ECCENTRICALLY BRACED FRAME WITH DOUBLE VERTICAL LINK (DV-EBF) ABSTRACT

SHAKE TABLE TESTING OF BRIDGE REINFORCED CONCRETE COLUMNS UNDER COMBINED ACTIONS

Structural Engineering

Cold-Formed Steel Special Bolted Moment Frames: Cyclic Testing and Numerical Modeling of Moment Connections

RELIABILITY OF SEISMIC LINKS IN ECCENTRICALLY BRACED STEEL FRAMES

Seismic performance of skew bridge with friction type rubber bearings

Design check of BRBF system according to Eurocode 8 Use of pushover analysis

PORTAL FRAMES 1.0 INTRODUCTION

ANALYTICAL AND EXPERIMENTAL STUDIES ON SEISMIC BEHAVIOR OF DEEP COLUMN-TO-BEAM WELDED REDUCED BEAM SECTION MOMENT CONNECTIONS

Seismic Analysis and Design of Vertically Irregular RC Building Frames

EVALUATION OF THE SEISMIC BEHAVIOR OF PRECAST CONCRETE BUILDINGS WITH ENERGY DISSIPATING DEVICES

Experimental Behavior of Concrete Cylinders Confined with CFRP Composites

Modelling of RC moment resisting frames with precast-prestressed flooring system

Inelastic Versus Elastic Displacement-Based Intensity Measures for Seismic Analysis

ANALYTICAL STUDIES OF A FULL-SCALE STEEL BUILDING SHAKEN TO COLLAPSE

Numerical Behavior Study of Short Link, Intermediate Link and Long Link in Eccentrically Braced Frame Steel Structure

SEISMIC EVALUATION OF HIGH RISE STEEL STRUCTURES WITH AND WITHOUT BRACING

SEISMIC VULNERABILITY ASSESSMENT OF STEEL PIPE SUPPORT STRUCTURES

INNOVATIVE DESIGN AND TESTING OF A SEISMIC RETROFITTED STEEL DECK TRUSS BRIDGE

Advance Design Bracing members design according to Eurocode 3

Seismic Performance of Reinforced Concrete Eccentric Beam-Column Connections with Floor Slabs

Strengthening of infilled RC frames by CFRP

This point intends to acquaint the reader with some of the basic concepts of the earthquake engineer:

Design of large scale wind turbine towers in seismic areas

RESILIENT INFRASTRUCTURE June 1 4, 2016

Seismic Evaluation and Retrofit of Beam- Column Joints of Mid-America Bridges Part 2: Steel Sheet and Plate Retrofit

Study of an Optimum Design Method for Links

EXPERIMENTAL STUDY OF THE DEFORMATION CAPACITY OF STRUCTURAL MASONRY

STUDY ON MODELING OF STEEL RIGID FRAME BRIDGE FOR DYNAMIC ELASTO-PLASTIC ANALYSIS

Original Publication: International Journal of High-Rise Buildings Volume 5 Number 3

optimal design of frp retrofitting for seismic resistant rc frames C. Chisari 1, C. Bedon 2 1

Behaviour of Concrete Filled Rectangular Steel Tube Column

Study on Nonlinear Static Analysis of R/C Frames Retrofitted With Steel Plate Shear Wall

ULTIMATE LOAD-CARRYING CAPACITY OF SELF-ANCHORED CONCRETE SUSPENSION BRIDGE

International Conference on Mechanics and Civil Engineering (ICMCE 2014)

FATIGUE ANALYSIS OF A NOTCHED CANTILEVER BEAM USING ANSYS WORKBENCH. N. Sinan Köksal, Arif Kayapunar and Mehmet Çevik

THE BEHAVIOR OF ECCENTRICALLY BRACED FRAMES WITH SHORT LINKS

Transcription:

Research Journal of Applied Sciences, Engineering and Technology 4(14): 2199-224, 212 ISSN: 24-7467 Maxwell Scientific Organization, 212 Submitted: March 1, 212 Accepted: April 4, 212 Published: July 15, 212 Analysis of Seismic Performance of Steel Moment Connection with Welded Haunch and Cover Plate Sun Yuping and Jiang Dingwei School of Civil Engineering, LanZhou University of Technology, LanZhou 735, China Abstract: In this study, a new connection joint of cover-plate-haunch connection was brought forward on the basis of improving haunch connection and cover plate connection. This kind of connection joint not only overcomes the shortcomings that bilateral haunch connections affect the flatness of floor and the interior appearance, but also strengthens the connection performance. ABAQUS finite element software is used to study node stress, plastic zone distribution, ultimate bearing capacity and hysteretic behavior. The result of new model is compared with past model. The results indicate that the new connection can effectively reduce stress concentration on butt weld of the joint, make the plastic hinge away from the connection and lower the possibility of brittle fracture. The ultimate bearing capacity of new connection can be increased 23% than normal connection, equivalent viscous damping coefficient and ductility factor is respectively.321 and 4.6, therefore the new connection is theoretically feasible and practical in application as well as excellent performance in earthquakes and the ideal energy dissipation. Key words:cover-plate-haunch connection, ductility factor, energy dissipation, equivalent viscous damping coefficient, haunch connection, hysteretic behavior, plastic hinge INTRODUCTION 1994 Northbridge earthquake happened in the California of USA and 1995 Kobe earthquake happened in Japan, great amounts of rigid connections of steel frame damaged. The most common form of damage occurred in the interface of the welding zone between beam and column flange. Post-earthquake many researchers (Chen et al., 26) about the traditional nodes were carried out by domestic and foreign scholars and the design concept of make the plastic hinge away from the connection was presented (Wang, 26). It could improved stress states on connection of welding seam base on the plastic hinge shift away from the surface of column and also avoided serious brittle fracturing in the welding zone. (Yu et al., 26) gives the experimental study on full-scale steel beam-to-column moment connections. It is worth mentioning two methods to make the plastic hinge away from the connection. One is base on reinforced joints, such as set up cover plate, slab used as stiffening rib in beam flange of joint, enlarge the section of beam flange, haunch and so on. The other one is using reduced beam section connection, which is weakening partial of the beam flange or web, such as dogbone connections and using long slot bore in beam web. By more than decade research (Sun et al., 21), have demonstrated that those change can improve the seismic performance of steel connections in different ways. (Sun et al., 21) analyses the seismic consideration and fracture-resistance of beam-to-column web rigid connections for steel moment frames. (Lin et al., 23) gives the theorem proving based on the extension rule. (Mahin, 1998) shows the lessons from damage to steel buildings during the northridge earthquake. There have two forms for haunch connection: unilateral haunch and bilateral haunch of the beam-column connection. Unilateral haunch connection could relief weld stress concentration at haunch side of flange, while stress at the other side of beam flange is larger than normal connection. The main reasons of this phenomenon are that neutral axis move to haunch side of unilateral haunch connection. So it will result brittle fractures easily at nonhaunch side of flange. We could realize relocation of plastic hinge in bilateral haunch connection, which can reduce weld stress focus and better than unilateral haunch connection, as well as a good seismic behavior was shown. However, in practical engineering, some steel frame have high requirement, haunch in upper side of beam lead to floor unevenness and visage will be affected. Three connection models were created in this paper: normal connection, unilateral haunch connection, the connection with cover plate on top flange and haunch on lower flange. All models using box column and H-beam. And using finite element software ABAQUS to discuss node stress, plastic zone distribution, ultimate bearing capacity and hysteretic behavior in this study. METHODOLOGY Establish finite element model: Geometry model: According to the suggestions in Literature (Yu and Qian, 26), we should prefer to use Corresponding Author: Sun Yuping, School of Civil Engineering, LanZhou University of Technology, LanZhou 735, China 2199

Res. J. Appl. Sci. Eng. Technol., 4(14): 2199-224, 212 3 18 Path 3 3 22 (a) and specimen 1 mm Path 3 9 15 (b) WH specimen Fig. 3: Stress-strain curve of Q345 steel 1 mm 15 9 Fig. 1: Geometry of specimens (unit: mm) Stress (MPa ) 6 5 4 3 2 1.5.1.15.2.25.3 Strain Fig. 2: Stress-strain curve of Q345 steel weld ladder cover plate on top flange and haunch on lower flange to analysis beam-column connection of steel frame. We created three connection models in this paper: normal box column-h beam connection (BASE specimen), haunch on lower flange connection ( specimen), cover plate on top flange and haunch on lower flange connection (WH specimen). Comparison and analysis will be made to the last specimen and the other two specimens. The geometries of analysis utilized in this research consisted of HW3 6 box column connected to HM22 5. The length of beam is 18 mm and column high is 3 mm. Model shape and geometry size as shown in Fig. 1. Fig. 4: Mesh of moments Material properties: All members using Q345 steel, The elastic modulus and Posson s ratio are assumed as E = 22, MPa and n =.3. Von Mises yield criterion by used and multiple alignment equivalent strengthen stressstrain curve as shown in Fig. 2. Material defect and the effect of weld residual stress were not considered during analysis. Mesh generation and loading law: Figure 3 shows the stress-strain curve of Q345 steel. The models are analyzed using ABAQUS, as shown in Fig. 4. The finite element model utilized in this study is reduced integration element C3D8R. The element is defined by eight nodes having three degrees of freedom at each node. The upper end of column is hinge and applied 1 MPa pressure on it. The bottom of column is consolidation to bear upper pressure. During the process of analysis, loading procedure divided into uniaxial loading (impose.3 radian vertical displacement at the end of beam) and cyclic loading. Cyclic loading displacement curve apply on the free end of beam as shown in Fig. 5. 22

Res. J. Appl. Sci. Eng. Technol., 4(14): 2199-224, 212 Diplacement (mm) 1 87.5 6 3-3 -6-87.5-1 Along web height (mm) 15 1 5-5 -1-15 4 8 12 16 2 24 WH Time increment Fig. 5: Cyclic loading displacement curve apply on the free end of beam 1 2 3 4 Von mises stress (MPa) Fig. 6: The Von Mises stress of web THE RESULT OF FINITE ELEMENT ANALYSE Node stress: For whole analysis the stress distribution of connections, the Von Mises stress distribution along the three stress path ( to Path 3) of beam top flange and 5 mm away from column under on.3 radian vertical displacement imposed at the free end of beam were analyzed and compared. Figure 6 showed Von Mises stress distribution of beam web along the distance of 5 mm away from column flange. In Fig. 6, web stress of each specimen present small at the middle and large at the ends. The stress of BASE specimen is symmetric distribution along the direction of web and neutral axis located at middle of web. The web stress at haunch side of specimen is smaller than BASE specimen. The maximum stress appeared at the other side of haunch flange and the stress value higher than the edge of haunch side obviously. The minimum stress value of specimen located at 9.3 mm offset from the central of the beam web. It indicates that neutral axis of web shift down after haunch. The web stress in cover plate side of WH is slightly larger than the stress in haunch side. It is not obvious that the neutral axis of web to shift down and almost locate at the median of web. The Von Mises stress distribution along width direction of beam upper flange in the joint () shown 28 Mises stress (MPa ) Mises stress (MPa) WH 4 375 35 325 3 275 25 225 2-1 -75-5 -25 25 5 75 1 Fig. 7: The Von Mises stress of path 1 Mises stress (MPa) 356 WH 354 352 35 348 346 344 342 34 338 336-75 -5-25 25 5 75 Fig. 8: The Von Mises stress of path 2 4 35 3 25 2 15 1 5 WH.5 1. 1.5 2. Fig. 9: The Von Mises stress of path 3 The Von Mises stress distribution along width direction of beam upper flange in the joint () shown as Fig. 7. In actual engineering, we usually assume that the stress is uniform distribution along beam flange. However, in Fig. 7, we can observe that stress distribution of beam flange is uneven and the shape is similar to W, the stress values are higher at the ends and the central of flange than other area. The maximum Mises stress value occurs at the ends of flange, which is explained by the effect of different flange width in contact region of beamcolumn. Further observation in Fig. 7, the stress of different points in upper flange of BASE and specimen is larger than yield stress of steel. Due to the neutral axis of web to shift down after haunch, the stress of different 221

Res. J. Appl. Sci. Eng. Technol., 4(14): 2199-224, 212 Fig. 1: The Von Mises stress of path 1 points in upper flange of specimen was slightly larger than those in BASE. The results indicate that beam flange at tension side even in a more insecure situation after haunch. However, the stress of upper flange in elastic stage during the whole loading process when cover plate at upper flange in specimen. The results indicate that cover plate in upper flange of specimen can effectively decrease stress value in weld zone of connection. Figure 8 showed Von Mises stress distribution along width direction of beam upper flange in the joint (). Obviously, we can observe that the stress value was high in the medium and low in the ends along width direction of each specimen. The stress value of flange was in elastic state during the whole loading process except for middle part in flange of BASE specimen, while the flange of WH specimen entered the plastic state. Figure 9 showed Von Mises stress distribution along length direction of beam upper flange (Path 3). We can observe stress is monotonically decreasing along length direction of beam flange in BASE and and stress curve of haunch connection had a horizontal line around the end of haunch plate, which is explained by stiffness difference of flange at the end of haunch plate. Stress peak present to beam flange near weld region for BASE and, while stress maximum shift out from the cover plate region of flange when cover plate on the upper flange of haunch connection. So it can ease the stress concentration near weld. The appearance and development of the plastic hinges: In order to get the moir interferometry images and the Von Mises stress distribution, we imposed.3 radian vertical displacement at the end of beam. The moir interferometry images showed in Fig. 1. All specimens are local yield. Firstly, for normal connection, plastic deformation appeared in the ends of flange near weld. With loading displacement increasing, plastic region extending toward the central and upper flange and lower flange on the beam-to-column connections reach plastic yield. Then plastic region was extending toward the central of web from in junction of flange with web. Finally, plastic hinge formed at the node junction of beam-to-column, as showed in (Fig. 1a). During the whole loading process of haunch connection, the region of beam flange from weld to the end of haunch was in elastic state. Plasticity deformation area formed firstly at bottom flange near the external end of haunch where the maximum stress value appeared. With the loading displacement is increasing, plastic region extending toward the central of web from in junction of flange with web. However, stress in upper flange slightly larger than those in normal connection 222

Res. J. Appl. Sci. Eng. Technol., 4(14): 2199-224, 212 Force Force Force 125 1 75 5 25-1 -75-5 -25-25 25 5 75 1-5 -75-1 -125 Displacement 125 1 75 5 25-1 -75-5 -25-25 25 5 75 1-5 -75-1 -125 Displacement 125 1 75 5 25-1 -75-5 -25-25 25 5 75 1-5 -75-1 -125 Displacement Fig. 11: Load-displacement hysteretic loops apply on free end of beam which can explained by neutral axis offset toward the haunch side. The top flange of butt weld yield firstly and the formation process of plastic area was the same as normal connection. Plastic hinge of haunch connection formed initially on flange near the external end of haunch side in theory, while in actual engineering, top flange yield firstly due to the existence of weld defect and residual stress which lead to occur potential safety hazard easily. So we would attach importance to it. Plastic deformation of the bottom flange of coverplate-haunch connection is the same as haunch connection. For upper flange, the coverage area with Table 1: Result of the members Equivalent viscous Ductility Ultimate bearing Specimen damping coefficient factor capacity (KN) BASE.261 3.63 97.3.298 3.97 19 WH.321 4.6 12 cover plate was in elastic state where stiffness increased. Firstly, plasticity deformation area formed at top flange near the external end of cover plate. Then, with the load is increasing, plastic region extending toward the ends of flange and the central of web. Finally, plastic hinge formed at the top flange and the bottom near. So coverplate-haunch connection could be controlled the plastic hinge position on beam effectively. Hysteretic behavior: Figure 11 showed loaddisplacement hysteretic loops at free end of beam. With cyclic displacement increasing, all specimen share the almost same shape and curve slope decreases continuously until attain the extreme limit loading. The beam-to-column connections form has great effect on hysteretic loops, in which the hysteretic loops of coverplate-haunch connection is the plumpest, haunch connection is the second and normal connection is the poorest. The results indicate that cover-plate-haunch connection with best energy dissipation ability than other two connections. According to the requirements of Specificating of Testing Methods for Earthquake Resistant Building, energy dissipation coefficient and equivalent viscous damping coefficient are the key factors to affect the antiearthquake performance of a building. The more the hysteretic curve is full, the larger the nergy dissipation coefficient and equivalent viscous damping coefficient, as well the better energy dissipation capacity of specimen was shown and the better the seismic behavior. Energy dissipation capacity is defined by the difference between the absorbed energy under loading and released energy under unloading after one control cycle. Ductility performance is defined by the ratio of maximum deformation in certain load to limit deformation in elastic stage. Table 1 showed the ultimate bearing capacity, equivalent viscous damping coefficient and ductility factor of the members. The results indicate that the ultimate bearing capacity of haunch connection can be increased 12% than normal connection and cover-platehaunch connection can be increased 23%. The equivalent viscous damping coefficient of normal connection is.261 and ductility factor is smaller than 4, which means energy dissipation capacity is lower. Therefore, it has poor seismic performance. The equivalent viscous damping coefficient of haunch connection is.298 and ductility factor is close to 4, so its seismic performance is good. The equivalent viscous damping coefficient of cover-plate-haunch connection is the largest among three 223

Res. J. Appl. Sci. Eng. Technol., 4(14): 2199-224, 212 members and ductility factor is larger than 4 which have excellent performance in earthquakes and the ideal ductility. CONCLUSION connection, the hysteretic loops is plump, so it has excellent performance in earthquakes and the ideal ductility. REFERENCES C C C The triaxial stress condition was complicated on butt weld of normal connection, sensitive to welding defect and result brittle fractures easily. It had obvious effect to decrease the stress of bottom flange at the welding seam for haunch connection, while that inability to top flange. Cover-plate-haunch connection can effectively decrease the stress at the welding seam, reduce stress focus and avoid to brittle fractures. The stiffness increased at the joint for cover-platehaunch connection, which makes the stress of beam section at weld zone less than other area. So nonwelded region yielded first and achieve the goal of outer moving of plastic hinge. The ultimate bearing capacity of cover-plate-haunch connection can be increased 23% than normal connection, equivalent viscous damping coefficient and ductility factor is respectively.321 and 4.6, larger than normal connection and haunch Chen, C.C., C.C. Lin and C.H. Lin, 26. Ductile moment connections used in steel column-tree moment-resisting frames. J. Constr. Steel Res., 62: 793-81. Lin, H., J.G. Sun and Y.M. Zhang, 23. Theorem proving based on the extension rule. J. Autom. Reasoning, 31(1): 11-21. Mahin, S.A., 1998. Lessons from damage to steel buildings during the northridge earthquake. Eng. Struct., 2(4-6): 261-27. Sun, Y., X. Wen and H. Li, 21. Seismic Behavior Analysis of Reinforced Connection and Fracture- Resistance Design. Appraisal Repairs and Maintenance of Structures, pp: 1585-159. Wang, Y., 26. Study and progress of plastic hinge outside-moving of new ductile connections of steel frame. J. Qingdao Technol. Univ., pp: 1-6. Yu, H., J. Qian, Y. Feng, D. Hai, L. Jianhua and L. Yueming, 26. Experimental study on full-scale steel beam-to-column moment connections. Earthq. Eng. Vib., 4(2): 311-323. 224