SEAONC MINI SEMINAR Gu s s et Pl at e Des i g n Russell Berkowitz Berkowi tz For ore ell / Els Else ess sse er Eng ngin ine eers rs,, Inc Inc..
What We Will Cover
Overview of prominent research and experiments to date Current gusset plate design requirements Limitations of current gusset plate design requirements Recommendations for future research to develop gusset plate design guidance
What We Will Cover
Overview of prominent research and experiments to date Current gusset plate design requirements Limitations of current gusset plate design requirements Recommendations for future research to develop gusset plate design guidance
Gusset Plate Design References
“Seismic Behavior and Design of Gusset Plates”
Abolhassan Astaneh-Asl Steel Tips December 1998
“Brace Frame Gusset Plate Research” Literature Review
Janice Chambers and Christopher Ernst
University of Utah February 2005
“On the Analysis and Design of Bracing Connections”
W.A. Thornton (1991) Proceedings, National Steel Construction Conference
Gusset Plate Design References
“Handbook of Structural Steel Connection Design & Details”
“Handbook of Structural Steel Connection Design & Details”
Tamboli, 1997
Thornton & Kane 1999
AISC
Manual of Steel Construction, 3rd Edition
Seismic Provisions (2002, 2005)
Brace / Gusset Configurations
Astaneh, 1998
Whitmore (1952)
Tested aluminum joints Iso-stress lines obtained by strain gages mounted on gusset plate Plots showed stress trajectories to be along 30° lines with the connected member
Whitmore’s Section
Whitmore, 1952
Whitmore’s Section
Astaneh, 1998
Whitmore (1952)
Distribution of normal and shear stresses along critical sections of gusset do not match beam formulas:
σ = Mc I
τ = VQ It
Maximum normal and shear stresses measured matched beam theory values Location of maximums is different
Bjorhovde & Chakrabarti 1983-88
Six full size steel assemblages
30, 45, 60 angle braces
Monotonic
No frame action
Not applicable to determining interface loads
Used to validate FEM
Bjorhovde & Chakrabarti 1983-88
Bjorhovde & Chakrabarti 1983-88
Rabern and Chakrabarti, 1983
Gross & Cheok (1988)
Used regular frame subassemblages Moment and forces in members showed all members resist lateral loads Gusset failed by buckling when brace was in compression Not monitored for interface forces Predicted prying action failure but frame forces precluded development
Gross & Cheok (1988)
Gross & Cheok, 1988
Cheng et al.
Experiments included frame action
Buckling capacity of gusset 4% - 107% higher with frame action Experimental buckling capacity 63% higher than calculated capacity (using K = 0.65)
Cyclic tests with / without edge stiffeners
Slight increase in compressive capacity with stiffeners
Tapered plate dramatically reduced compressive and energy absorption of gusset plates (46%) Flexibility of tapered gusset caused weld fracture at the boundaries with increasing deformation
Richards et el. , Williams 1986
Most rigorous analytical research to date
Used FEA INELAS and NASTRAN
51 configurations
Frame action considered
Measured fastener behavior modeled into nonlinear FEA to determine gusset interface forces
Richards et el. , Williams 1986
Interface forces largely dependent on:
Plate aspect ratio Brace load Brace angle
Interface forces less dependent on:
Direction of force (tension vs. compression) Bracing configuration Beam and column properties Gusset fasteners (bolted vs. welded) Brace eccentricity
Richards et el. , Williams 1986
Frame action
“beam and column load the gusset, equally as much as the brace” Pinching occurs , frame angle changes Brace in tension buckles gusset
Direction of forces align with brace with increased loading 1.4 connection factor
Richards et el. , Williams 1986
Williams, 1986
Richards et el. , Williams 1986
Williams, 1986
Richards et el. , Williams 1986
Williams, 1986
Richards et el. , Williams 1986
Williams, 1986
Berkeley BRB Tests, 2002
Lopez et al. 2002
Berkeley BRB Tests, 2002
Test 1
Yielding at brace-to-column gusset plates
Yielding at column base
Yielding at beam-column moment connection
Test 2
CP welds at gusset - col. initiated crack at 1.7% , 2” long at 2.6% drift Free edge of gusset buckled at 2.6% drift when brace was in tension
Berkeley BRB Tests, 2002
Aiken et al. 2002
Berkeley BRB Tests, 2002
Lopez et al. 2002
Observed Seismic Performance of Gusset Plates Satisfactory performance in general A few cases of gusset failure have been reported:
Mexico City, Northridge, Kobe Earthquakes Observed failure modes Fracture of welds Buckling of gusset plate Net section fracture of gusset plate or brace Most of these failures are related to non-ductile design and poor detailing
Observed Seismic Performance
Astaneh, 1998
Current Gusset Design (SCBF)
AISC Seismic Provisions (2002)
Tensile strength of bracing connection
Ry AgFy
Maximum force that can be delivered by structure
Flexural strength of bracing connection
In-Plane Buckling = 1.1RyMp
Out-of-Plane Buckling
Connection must be able to accommodate inelastic rotations associated with post-buckling deformations Design compressive strength at least Fcr Ag
Current Gusset Design
Astaneh recommends the following hierarchy for gusset design failure modes
Astaneh, 1998
Out-of -Plane Brace Buckling
Astaneh, 1998
Out-of -Plane Brace Buckling
Hinges at brace midpoint and in gussets Provide min. “2t” to allow rotation in gusset max “4t”
Astaneh, 1986
Out-of -Plane Brace Buckling
Astaneh, 1998
Limit States at Brace – Gusset Connection
Astaneh, 1998
Limit States at Brace – Gusset Connection
Block shear failure
Bolt tear through on the gusset
Calculate using AISC Eq. J4-3
Calculated using AISC Eq. J3-2
Strength of Bolts or Welds
Limit States at Brace – Gusset Connection
Astaneh, 1991
Tension Yielding and Net Section Fracture of Whitmore’s Area
Tension Yielding is the most desirable mode of gusset failure
Py = AgwFy
Net Section Fracture is the least desirable
Astaneh suggests: suggests: φ Pn ≥ φ (1.1R yP y )
Pn = A nwFu
Buckling of Gusset Plate
Astaneh, 1998
Buckling of Gusset Plate
Yamamoto et al. 1988
Buckling of Gusset Plate
Pseudo-Column Buckling Approach
Equivalent Strip or Thornton Method
Applies buckling compressive stress over Whitmore’s area
Buckling of Gusset Plate
Astaneh, 1998
Buckling of Gusset Plate
Use AISC column equations for Fcr Kl Fy λ c = E r π Fcr = (0.658 )Fy
λ c ≤ 1.5
⎡ .877 ⎤ Fcr = ⎢ 2 ⎥ Fy ⎣ λ c ⎦
λ c > 1.5
λ c2
Buckling of Gusset Plate
L=
Average of l1, l2, l3
Longest one-inch wide strip
Longest of l1, l2, l3
Buckling of Gusset Plate
What “K” value to use for buckling length?
Values from 0.5 – 1.2 have been proposed
K = 0.65 (0.45 for double) often used
Consistently conservative
K = 1.2 proposed by Brown (1988) and Astaneh (1998)
Tests indicating possibility of end of bracing member moving out of plane
Gusset Plate Buckling Limit State
Not been accurately modeled by pseudo-column buckling approach
Highly variable compared to test results
Consistently conservative
Buckling capacity strongly dependent on frame action effects Local gusset plate research needed to produce more accurate methods of predicting buckling
Gusset Plate Edge Buckling
Astaneh, 1998
Gusset Plate Edge Buckling
Astaneh, 1991
Edge Stiffeners
AASHTO (1997)
This has been around for years for steel bridge trusses
L fg t
< 2.0 E
Fy
Brown (1988)
Formula proposed to prevent edge buckling prior to gusset yielding
L fg
t
< 0.83 E
Fy
Adequate for monotonic loading
Edge Stiffeners
Astaneh 1998
Gussets showed edge buckling when Brown criteria satisfied during cyclic tests Limit Lfg / t to the point where Fcr / Fmax is reduced significantly Proposed criteria to prevent cycling free edge buckling prior to reaching maximum compression capacity
L fg t
< 0.75 E
Fy
Edge Stiffeners
Little experimental research published on the effects of stiffeners Four tests with 3/8” and 1/4” plates
3/8” plate showed 15% - 19% increase in buckling capacity, only 2% for ¼” plate Strain measurements showed more force going through stiffeners than gusset plate Energy absorption increased in compression
FEA shows no increase in peak capacity, but post-buckling capacity was increased
Gusset Plate Interface Forces
Astaneh, 1998
Interface Connection Models
Astaneh, 1998
Gusset Plate Interface Loads
Models are based on load paths dictated by the designer Lower Bound Theorem Limit Analysis
Determine force distribution in equilibrium with applied load If no forces in structure exceed yield criteria, loads will not likely lead to collapse
Interface Connection Models
KISS Model (Thornton 1991)
Thornton, 1991
Interface Connection Models
AISC Model (AISC 1984)
Thornton, 1991
Interface Connection Models
Ricker Model
Thornton, 1991
Interface Connection Models
Modified Richard Method (Williams 1986)
Thornton, 1991
Interface Connection Models
Thornton Model – Uniform Force Method
Thornton, 1991
Interface Connection Models
Thornton UFM
Richard Method
Comprehensive Offers approximate value to capture frame action effects and a way to incorporate into design
Captures frame action effects Based on empirical evidence Not applicable for column web connections
AISC-LRFD 3rd ed. Manual
Recommends use of UFM
AISC Uniform Force Method
AISC UFM Special Case 1
AISC UFM Special Case 2
AISC UFM Special Case 3
Design Criteria for Gusset Plates at Interface with Beam / Column
Astaneh check for “critical sections” 2
(N / φNY ) + M / φMP + (V / φ VY )4 ≤ 1.0
Chambers and Ernst
Determine von Mises and the maximum principal stresses considering shear and normal stresses Von Mises stress < 0.9Fy
σ e = σ + σ − σ xσ y + 3τ xy 2 x
2 y
Maximum principal stress < 0.75 Fu
Gusset Connection to Beam / Col
The 1.4 “Ductility Factor” in AISC 3 rd Ed.
Connection must be designed for the larger of the peak stress or 1.4 x average stress Originated from figures by Williams and Richards FEA showed ratio max / ave fastener force and the ratio min / ave fastener force Handbook of Structural Steel Connections (1997) Hewitt and Thornton (2004) reviewed plots and suggest ductility factor should be 1.25
Gusset Connection to Beam / Col
Hewitt & Thornton, 2004
Gusset Connection to Beam / Col
FEA shows resultant connector forces on welds are not longitudinal
Resistance of weldements up to 50% stronger when not loaded longitudinally Consider vector direction of forces on welds for design Use eq. A-J2-1 of AISC 3 rd ed.
Frame Action
Traditional approach assumes lateral loads resisted by diagonal braces Large rotational restraint provided by gusset connection
Frame providing bending resistance
Braces loaded in bending
Semi-rigid, forces at joint strongly dependent on connection rigidity Welded connections approach fixed condition
Frame Action
Frame Action
Richards uses F-∆ relationships to approximate M-θ
PRCONN program uses results of nonlinear FEA to develop M-θ relationships
Research needed to develop M-θ equations for braced frame connections
Detailing to Reduce Frame Action Effects
Detailing to Reduce Frame Action Effects
Research Recommendations
Research Recommendations
Development of moment-rotation curves for semi-rigid strong and weak axis connection Local response of connections must incorporate realistic rigidity of connection Shears, axial forces and moments on local connection determined from global gusset research results Local gusset plate connection research to determine load distribution through connections
Research Recommendations
Local gusset plate research to track peak stress values and locations at connections This will help with determining and designing for individual connector design loads
