Ultimate Strength and Inelastic Behavior of Braced Frame Gusset Plate Connections Charles W. Roeder University of Washington Department of Civil and Environmental Engineering Seattle, WA 98195 Structural Engineers Association of Texas Annual Conference October 30, 2009 Overview of Presentation Introduction - Focus is Seismic Performance Major Research Program on Braced Frame Performance Corner vs. Midspan Gusset Plate Connections Corner Gusset Plate Connection Research Midspan Gusset Plate Connection Research Simulation of Braced Frame Performance Current Design Recommendations Introduction Braced frames are suitable for a wide range of lateral load applications. The focus this work is on seismic performance since this incorporates concerns of nearly all other design applications including wind and blast loading. US Seismic Design Seismic Design in US Relies on Simple elastic analysis methods Small seismic design forces to assure serviceability during small frequent earthquakes Large inelastic deformations during large infrequent earthquakes to assure life safety and collapse prevention Historically Special Moment Resisting Frames (SMRFs) have been primary steel frame system but Special Concentrically Braced Frames (SCBFs) increasingly common in recent years SCBFs are Conceptually Truss Structures Diagonal brace economically provides large strength and stiffness Good for serviceability LS Engineers initially design as a truss with pin joints Real connections are not pins SCBFs are conceptionally very easy to design, but many engineers do not understand their seismic performance Life safety and collapse LS Overview of Seismic Performance of SCBFs 1
Gusset plate connections play a predominant role in braced frame performance because they must develop the required resistance of the brace and the frame while accommodating any required movement or deformation. These connections are focus of this presentation. Brief Overview of Current Seismic Design Method 1. Size brace based on seismic loads 2. Establish plastic capacity in tension and compression P u = R y A g F y (tension) P u = 1.1 R y A g F cr (comp) This practice sometimes leads to misconception that the stiffer and stronger the gusset the better. Brief Overview of Current Seismic Design Method 3. Size brace-gusset welds or bolts for plastic brace capacity φr n > P u (tension) 4. Reinforce Net section of brace? φr n = 0.75 U A n F u > P u (tension) Reinforcement usually required because of large value of P u and the reduction due to φ and U Brief Overview of Current Seismic Design Method (2) 5. Establish Whitmore width Projecting a 30o angle from start to the end of joint. 6. Establish buckling end rotation clearance requirement - typically 2 t p With rectangular gussets this typically results in quite large gussets. 6. Check gusset for buckling and tensile yield Uses area within Whitmore width. Various methods for K and L e. Brief Overview of Current Seismic Design Method 7. Determine equilibrium forces on gusset-beam and gusset-column interfaces based upon expected tensile force Size welds with appropriate resistance factors. 8. Design beam-column connection Great variation bolted or welded with attached or free flanges. Wind load design method is identical except that factored loads are employed and clearance requirement may be neglected. The expected brace forces used in seismic design are typically much larger than the factored loads. 2
Current Designs May Fall Short of Expectations A NEES-SG 4 year multi-institutional research program is in progress to improve understanding and seismic design guidelines for concentrically braced frames. Major Research Program on Braced Frame Performance Researchers from Univ. of California, Berkeley, Univ. of Minnesota, National Center for Research in Earthquake Engineering (NCREE) in Taiwan as well as Univ. Of Washington are engaged in the project. Gussets often very thick and large. Performance often less than than expected. The U. of Washington is lead institution for the research and its focus is on the overall seismic performance of braced frames with a particular emphasis on the influence of gusset plate connections on system performance. Acknowledgements National Science Foundation American Institute of Steel Construction National Center for Research in Earthquake Engineering (NCREE) in Taiwan Nucor Yamato Steel Chaparral Steel Company Columbia Structural Tubing Magnusson Klemencic Associates CANRON Western Constructors Ltd Rutherford and Chekene Dasse Design Inc - Walter P. Moore Many graduate students including Shawn Johnson, Adam Christopulos, David Herman, and Brandon Kutolka Differences Between Corner Gusset Plate and Midspan Beam Gusset Plate Connections 3
Corner Gusset Plate Connections Occur in wide range of bracing systems including diagonal, X-, and V- or chevron bracing Provide good restraint to gusset with support on two edges from beam and column Potentially difficult to achieve end rotation of brace due inelastic postbuckling deformation Midspan Gusset Plate Connections Occur in multi-story X and V- or chevron bracing Provide less restraint to gusset with support on one edge from beam Susceptible to twist or lateral torsional stability of the beam Easier to achieve end rotation of brace due inelastic post-buckling deformation Corner Gusset Plate Connection Research Extensive past research on connections and large body of current research on CBF systems Gusset Plate Buckling - Past Experimental Results Prior Corner Gusset Plate Research Research from a number of sources but the majority of test results are research at University of Alberta in 1990 s and early 2000 s Brown Edge Buckling Model Modified Thornton Buckling Current Gusset Plate Connection Research - Motivated by observation that simple connection tests provide indications of connection performance but do not reflect full implications of gusset plate connection design on system performance. 4
Prototype Structure UW Experimental Program on gusset plate connections Tested 27 SCBFs with wide range of gusset connection configurations subjected to cyclic inelastic deformation Channel Assembly Brace Buckling Important to CBF Behavior Out-of-Plane Restraint B1 B2 B3 Load Beam Axial Force System Strong Floor Brace Fracture Widely Distributed Yielding Specimen HSS-01: Reference Specimen (AISC Design) w/2t Linear Clearance Local Pinching Tearing Through Brace Wall Initial Tearing Brace Fracture Yielding in gusset plate Plastic hinging and local buckling in beam and column adjacent to gusset Ductile weld tearing - welds are all designed as demand critical But large deformation capacity from system if connection properly designed Inelastic action included Brace yielding and buckling Overall failure mode Fracture of the gusset plate-to-frame welds Drift Capacities: -1.3% to 1.6% (2.9%) 5
Elliptical clearance model developed to produce more compact gussets and improved seismic performance. Current design methods imply that bigger (stronger) are better - but One connections with very conservative design and other with a balance design Failure Mode: Brace Fracture Drift Capacities: 3/8 = 3.1% to 1.7% (4.8%) 7/8 = -1.5% to 1.0% (2.5%) Significant Reduction in drift capacity for brace in compression 3/8 Plate 7/8 Plate w/ Large Beam Bolted End Plate Connections (HSS-21) Generally behaved well but well below the best of welded connections Ultimate failure of system due to fracture of brace at plastic hinge Drift range between 1.64% and -1.95% (3.60% total) Bolt fracture at center most bolt only Prying of column flanges noted at outer most bolts of endplate connection Midspan Gusset Plate Connection Research Midspan Gussets occur is chevron (V- or inverted V-braced sytems) multi-story X-braced and similar systems. Typically require a multistory test specimen. Experiments Performed at NCREE Three full-scale 2-story steel frames tested at NCREE under cyclic inelastic deformation Rectangular gussets with HSS tubular braces Rectangular gussets with wide flange braces Tapered gussets with HSS tubular braces Multi-story X-brace configuration Relatively good inelastic deformation capacity 6
Wide Flange Braces Provide Greater Ductility and Deformation Capacity but Place Greater Demand on Connections Full-Scale 3-Story Frames also tests at NCREE Two full-scale 3-story steel frames tested at NCREE under cyclic inelastic deformation Rectangular gussets with HSS tubular braces Rectangular gussets with wide flange braces Multi-story X-brace configuration Modified midspan gusset plate clearance criteria using a 6tp horizontal clearance zone Inelastic Performance Very Good for Frame and Connections -HSS 3-Story test 3-Story Test with Wide Flange Braces Completed March 28, 2009 Reasonable distribution of inelastic deformation between 3 stories Greater inelastic deformation capacity prior to brace fracture with wide flange braces Good performance from both midspan and corner gusset plate connections NCREE Tests Show that 8tp Horizontal Clearance Method Provides Best Performance Engineers must predict the stiffness, resistance and deformation capacity of braced frames. - Simulation of braced frame performance 7
Nonlinear FEM Analysis with ANSYS -- Model Description Model Configuration, Elements and Boundary Conditions Predicted and Measured Force- Displacement Response (HSS-5) Each component was modeled using shell elements. Steel response was modeled using a cyclic, bi-linear kinematic-hardening constitutive model. Shear tab was modeled explicitly. Shear stiffness of individual bolts modeled using concentrated springs. Very important to achieving good comparison with experiments Model did not include capabilities to model weld tearing and fracture. Fine mesh in critical areas, but coarser mesh in less critical areas to achieve more rapid convergence Predicted Response: Brace Predicted Response: Gusset Plate Brace Out-of-Plane Displacement 0-4.5-4 -3.5-3 -2.5-2 -1.5-1 -0.5 0-4 -8-12 -16 Lateral Displacement (in) Test-HSS 5 FEM-HSS 5-20 Result of comparisons to 27 test results leads us to have considerable confidence in the analytical predictions. 8
Analtical Results Extended to Multi-Story Frames Developed models for initiation of cracking at gusset welds and fracture of the brace based upon Equivalent Plastic Strain Analtical Results Extended to Multi-Story Frames Analysis of multi-story systems clearly shows different behavior of midspan gusset plates. First they are more susceptible to lateral stability issues due to lateral support and twist of the brace. End rotation models don t work the same as for corner gusset plates. For Good Accuracy Detailed FEM Models Require: Careful modeling of both gusset plate and beam-column connections Including modeling of bolt deformation and bolt hole elongation Composite slabs and lateral restraint must also be accurately estimate cyclic response OpenSees models also developed Accuracy of these models also strongly dependent upon connection modeling Four models shown Accuracy of OpenSees strongly dependent upon models Four analysis from 4 models shown a) Pinned braces severely underestimate resistance. b) Rigid brace connections overestimate resistance and stiffness c) Rigid links for gusset with pinned braces stiff significantly underestimate resistance d) Rigid links with spring stiffness provide best estimate These models have been used to aid in the design of Six 2- and 3-story frames to: Estimate strains and deformations prior to testing to finalize design issues, Predict the response of the braced frames prior to testing, and Aid in the interpretation and evaluation of test results 9
Proposed Design Procedure Based on Work to Date Proposed Design Method 1) Design beams, columns and braces for required seismic design forces as with current approach 2) Establish expected plastic capacity of brace under tension (R y A g F y ) and compression (1.1 R y A g F cr ) as currently done. Effective length of brace can be taken as true length 3) For connection design, propose a balance procedure to assure good seismic performance rather than current forced based method. Expected Brace Capacity < β yield,1 R y R yield, 1...... < β yield,i R y R yield, i (1) and Expected Brace Capacity < β fail, 1 R fail, 1 < β fail, 2 R fail, 2 and β yield < β fail (2) Proposed Design Method (2) 4) Size weld joining the tube for the expected tensile force with β equal to normal weld resistance factor 5) Check the net section of the brace at tip of the slot. Use the expected tensile yield force of the brace and the expected tensile capacity of the net section with β of 0.9. Note that analysis and experiments suggest that net section fracture is controlled by the limit if flexible connections are employed. However, net section fractures have been noted primarily with overly stiff, strong connections. 6) Based upon the weld length and tube diameter check block shear of the gusset plate with β of 0.85 Proposed Design Method (3) 8) Establish the Whitmore width by the 30 o projected angle method as currently used. 9) Establish the dimensions of corner gusset plates with the elliptical clearance model with an 8t clearance This can be done graphically or by an approximate equation developed in research 10) Establish the dimensions of midspan gusset plates with 6tp linear (horizontal) clearance Proposed Design Method (4) 11) Use these dimensions and Whitmore width to check gusset for buckling, tensile yield and tensile net section fracture. - Use average gusset length and K of 0.65 for corner gussets - Use average gusset length and K of 1.2 for midspan gussets - More conservative K (> 1) needed for midspan gussets - For tensile yield compare the expected tensile yield of the plate to the expected tensile capacity of the brace with a β of 0.9 - For tensile fracture compare the nominal ultimate tensile capacity of the plate to the expected yield capacity of the brace with a β of 0.85. Proposed Design Method (5) 12) Size the welds joining gusset plate to the beam and column to develop the full plastic capacity of the gusset plate -- not the expected tensile capacity of the brace CJP welds of matching weld metal achieve this Fillet welds of matching metal on both sides of the gusset must be slightly larger than t p 13) The beam-to-column connection must use full CJP welds to join the beam flanges to the column 14) The resulting gusset plate should be stiff and strong enough to support full loads but should not have any extra stiffness or resistance 10
Limitations of the Method Intended to achieve the maximum possible ductility from SCBFs with HSS tube braces Must design the connection to have adequate stiffness and resistance but not excess stiffness and resistance - Overly conservative connection design reduces the expected performance of the system Additional work is needed and is in progress 11