1

Ultimate Strength and Inelastic Behavior of Braced Frame Gusset

Plate ConnectionsCharles W. Roeder

University of WashingtonDepartment of Civil and Environmental Engineering

Seattle, WA 98195Structural Engineers Association of Texas Annual Conference

October 30, 2009

Overview of Presentation

Introduction - Focus is Seismic PerformanceMajor Research Program on Braced Frame Performance– Corner vs. Midspan Gusset Plate Connections

Corner Gusset Plate Connection ResearchMidspan Gusset Plate Connection Research

– Simulation of Braced Frame PerformanceCurrent 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 TrussStructures

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

2

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 compressionPu = Ry Ag Fy (tension)Pu = 1.1 Ry Ag Fcr (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 capacityφRn > Pu (tension)

4. Reinforce Net section of brace?φRn = 0.75 U An Fu > Pu(tension)Reinforcement usually required because of large value of Pu and the reduction due to φ and U

Brief Overview of Current Seismic Design Method (2)

5. Establish Whitmore widthProjecting a 30o angle from start to the end of joint.

6. Establish buckling end rotation clearance requirement - typically 2 tpWith rectangular gussets this typically results in quite large gussets.

6. Check gusset for buckling and tensile yieldUses area within Whitmore width. Various methods for K and Le.

Brief Overview of Current Seismic Design Method

7. Determine equilibrium forces on gusset-beam and gusset-column interfaces based upon expected tensile forceSize welds with appropriate resistance factors.

8. Design beam-column connectionGreat 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.

3

Current Designs May Fall Short of Expectations

Gussets often very thick and large. Performance often less than than expected.

Major Research Program on Braced Frame Performance

A NEES-SG 4 year multi-institutional research program is in progress to improve

understanding and seismic design guidelines for concentrically braced frames.

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.

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.

AcknowledgementsNational Science FoundationAmerican Institute of Steel ConstructionNational Center for Research in Earthquake Engineering (NCREE) in TaiwanNucor Yamato SteelChaparral Steel Company Columbia Structural TubingMagnusson Klemencic AssociatesCANRON Western Constructors LtdRutherford and Chekene Dasse Design Inc - Walter P. MooreMany graduate students including Shawn Johnson, Adam Christopulos, David Herman, and Brandon Kutolka

Differences Between Corner Gusset Plate and Midspan

Beam Gusset Plate Connections

4

Corner Gusset Plate ConnectionsOccur in wide range of bracing systems including diagonal, X-, and V- or chevron bracingProvide good restraint to gusset with support on two edges from beam and columnPotentially difficult to achieve end rotation of brace due inelastic post-buckling deformation

Midspan Gusset Plate Connections

Occur in multi-story X and V- or chevron bracingProvide less restraint to gusset with support on one edge from beamSusceptible to twist or lateral torsional stability of the beamEasier 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

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

Gusset Plate Buckling - Past Experimental Results

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.

5

Prototype StructureTested 27 SCBFs with wide range of gusset connection configurations subjected to cyclic inelastic deformation

UW Experimental Program on gusset plate connections

Out-of-Plane Restraint

Load Beam

Channel Assembly

Axial Force System

Strong Floor

Brace Buckling Important to CBF Behavior

B1 B2 B3

Brace Fracture

Local Pinching Initial Tearing

Tearing Through Brace Wall

Brace Fracture

Widely Distributed Yielding

Yielding in gusset platePlastic hinging and local buckling in beam and column adjacent to gussetDuctile weld tearing -welds are all designed as demand criticalBut large deformation capacity from system if connection properly designed

Specimen HSS-01: Reference Specimen (AISC Design) w/2t Linear Clearance

Inelastic action included– Brace yielding and buckling

Overall failure mode – Fracture of the

gusset plate-to-frame weldsDrift Capacities:

-1.3% to 1.6% (2.9%)

6

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 designFailure 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 connectionsUltimate failure of system due to fracture of brace at plastic hingeDrift range between 1.64% and -1.95% (3.60% total)Bolt fracture at center most bolt onlyPrying 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 multi-story 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 bracesMulti-story X-brace configuration

Relatively good inelastic deformation capacity

7

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 bracesMulti-story X-brace configurationModified 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 storiesGreater inelastic deformation capacity prior to brace fracture with wide flange bracesGood 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

8

Nonlinear FEM Analysis with ANSYS -- Model Description

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

Model Configuration, Elements and Boundary Conditions

Predicted and Measured Force-Displacement Response (HSS-5)

Predicted Response:Brace

Predicted Response:Gusset Plate

-20

-16

-12

-8

-4

0-4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0

Lateral Displacement (in)

Test-HSS 5FEM-HSS 5

Brace Out-of-Plane Displacement

Result of comparisons to 27 test results leads us to have considerable confidence in the analytical predictions.

9

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 elongationComposite slabs and lateral restraint must also be accurately estimate cyclic response

OpenSees models also developed

Accuracy of these models also strongly dependent upon connection modelingFour models shown

Accuracy of OpenSees strongly dependent upon modelsFour 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, andAid in the interpretation and evaluation of test results

10

Proposed Design Procedure Based on Work to Date

Proposed Design Method1) Design beams, columns and braces for required seismic

design forces as with current approach2) Establish expected plastic capacity of brace under tension

(RyAgFy) and compression (1.1 RyAgFcr) 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 < βyield,1RyRyield,1 ........... < βyield,iRyRyield,i (1)

and

Expected Brace Capacity < βfail,1Rfail,1 < βfail,2Rfail,2 … and βyield < βfail (2)

Proposed Design Method (2)4) Size weld joining the tube for the expected tensile force

with β equal to normal weld resistance factor5) 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 30o

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 βof 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 tp

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

11

Limitations of the Method

Intended to achieve the maximum possible ductility from SCBFs with HSS tube bracesMust 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 systemAdditional work is needed and is in progress