evaluation of deteriorated gusset platessp.bridges.transportation.org/documents/2014 scobs... ·...
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SOLUTIONS FOR THE BUILT WORLD
Evaluation of Existing Gusset Plates
Columbus, Ohio
June 24, 2014
Jonathan C. McGormley, S.E. Principal
Wiss, Janney, Elstner Associates, Inc.
AASHTO T-18
Partially funded by IDOT to evaluate impact of 2013 MBE on load ratings of existing gusset plates
On going since I-35W collapse investigation identified gusset plate design deficiency
Experience obtained through the load rating of numerous gusset plates throughout the country
Review of NCHRP Project 12-84
Independent capacity check of more than 175 NCHRP gusset plate simulations (focused on evaluation of compression and shear)
Proposed changes to 2013 MBE
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WJE Study
2013 AASHTO MBE Replaces FHWA Guide “ Load Rating Guidance and
Examples For Bolted and Riveted Gusset Plates in Truss
Bridges”
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Fasteners
Compression
Whitmore – Lmid
“Partial Shear Plane”
Tension
Block Shear
Vertical Shear
Horizontal Shear
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Gusset Plate Design Limit States
Revised
New
Revised
Revised
Revisions to global “shear” based checks
Vertical Shear
Horizontal Shear
The 0.74 value of Ω was proven to be excessively conservative
Actual value varies depending on combination of moment and shear; which is why WJE uses a variable value based actual state of stress at the location of interest
2013 MBE uses constant value of 0.88
WJE variable value typically ranges between 0.85 and 0.95
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Comments on Shear Changes in MBE
Revisions to Whitmore compression check
Compression
– Whitmore-Lmid
Use centerline L value on Whitmore section rather than average of center and end values (makes effective L longer)
Use K = 0.5 rather than 1.2 (makes effective L shorter)
Fits NCHRP experimental and simulation data better
Still highly variable results
Substantial unconservatism at times
Substantial conservatism at times
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Comments on Compression Changes in MBE
New “Partial Shear” check
Compression
– “Partial Shear Plane”
Added to “cover” cases where Whitmore-Lmid is unconservative
Requires only one simple calculation
Does the intended job
Gives highly variable results
Is very conservative at times
Does not mitigate the highly conservative Whitmore-Lmid cases
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Comments on Compression Changes in MBE
Changes are an improvement
New approach can be very conservative at times
Conservatism not very expensive in new designs
Few hundred pounds of added steel per connection
Conservatism can be very expensive when evaluating existing connections
Few hundred pounds of added steel per connection
Thousands of dollars of installation costs (even tens of thousands) per connection
Load posting until retrofit in place
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Comments on Evaluation Changes in MBE
Cost for additional analytical effort is typically far less than the cost to repair or replace gusset plates
Even if repairs are required, additional analyses help to reduce costs by considering the contributions of all existing elements
Underestimating gusset plate capacity has significant effect on load ratings
e.g., a 10% underestimation in capacity could result in a 30% reduction
in rating under very common dead and live load conditions
Therefore, even a small improvement in capacity calculation can result in big changes in rating values (and big cost savings)
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Impact of Conservatism
Much more accurate – yet still reasonable - capacities can be obtained without resorting to sophisticated FE models
It is especially worthwhile to sharpen the pencil when either the Whitmore Lmid or Partial Shear check provides a less than acceptable load rating
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Next Step in Evaluation Process
Changes to MBE
Primarily affects Commentary and expands the
Commentary to recommend use of more rigorous
analyses when ratings using MBE equations indicate
insufficient capacity
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Recognize that the MBE checks are conservative
Recommend to Rating Engineer that an unacceptable load rating should lead to more rigorous analysis before repairs/posting are required
Additional analysis not limited to just FEM
Approach also applies to deterioration
Worked example problems referenced
Approval requested for AASHTO T-18 Ballot Item 5
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Changes to MBE
Basic Corner Check A first-principles analytical approach utilizing fundamental
steel design theory to conservatively calculate gusset
plate limit state capacities at critical cross sections
including those affected by deterioration.
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Compression “Corner” Tension “Corner”
Middle Chunk
A “corner” is the smallest piece of plate that contains all of a member’s fasteners
LV
LH
𝜎𝑉𝑀 = 𝜎2 + 3𝜏2 ≤ 𝐹𝑦
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von Mises Yield Criterion
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θ°
θv°
θH°
WP
PH
VH
PV
VV
Basic Corner Check
Lv/2
LH/2
Pn
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Basic Corner Check
θ°
θv°
θH°
WP
PH
VH
PV
VV
Select minimum section
Require resultant forces to pass through work point
Determine forces on most critical surface using Von Mises (assume moment = 0)
Forces on other surface as required to make overall resultant align with member
Calculate capacity (Pn) using VV, PV, VH, and PH
Repeat for tension corner
Pn
Fasteners
Compression
Whitmore – Lmid
Partial Shear
Corner Checks
Tension
Block Shear
Vertical Shear
Horizontal Shear
Considerations:
Basic Corner Check provides more accurate picture of yield state at end of compression member than Partial Shear check, yet is still conservative
By checking buckling, BCC takes into consideration slenderness checks of Whitmore
If BCC has lowest capacity, carry out Refined Corner Check
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Gusset Plate Limit States – First Step in Improving Analysis
Gusset Plate Evaluation Guide 7 example problems highlighting benefits of more rigorous
analysis.
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Gusset Plate Evaluation Guide
Example 1: Noncompact gusset plate with short vertical buckling length
Example 2: Noncompact gusset plate with long vertical buckling length (4 member)
Example 3: Noncompact with medium vertical buckling length
Example 4: Noncompact gusset plate with long vertical buckling length (5 member)
Example 5: Compact chamfered gusset plate with short vertical buckling length
Example 6: Noncompact gusset plate with medium vertical buckling length and deterioration
Example 7: Compact end node gusset plate
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Gusset Plate Evaluation Guide
Examples show that substantial increases in capacity can be obtained through more rigorous analysis
Additional analysis can help identify locations requiring retrofit
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Gusset Plate Evaluation Guide
When AASHTO equations indicate a deficiency, additional analysis should be used to further refine capacity before recommending repairs/replacement
The Basic Corner Check and Refined Corner Check are two first-principals based analytical procedures that maximize the plate capacity over the smallest “corner” that incorporates a member’s fasteners
Deterioration can be accounted for using the BCC or RCC by checking affected cross sections
Deterioration calculations should consider the commonly recognized strain hardening behavior, e.g. net section, when appropriate
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Conclusions
Questions? Thank You
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Refined Corner Check
Select minimum section
Remove constraint that both surface resultants must pass through WP (allows small reductions in Vv and/or VH and commensurate large increases in Pv and/or PH)**
Significant increase in Pn can be realized
However, remaining sections of plate must be checked for associated demands
Requires iterative approach in order to optimize Pn without overstressing plate
θ°
WP
PH
VH
PV
VV
ePH
ePV
eVH eVV
Pn
** recall: Fy = [σ2 + 3τ 2]1/2
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Refined Corner Check – Middle Chunk
Section between comp. and tension corners
Requires concurrent forces (i.e., make sure all member loads consistent with comp. force)
Tension member surfaces can carry moment (they are not “maxed out” by V and P)
Calculate available MT and resulting MQ, PQ and VQ
Check the Q surface to see if it can handle the resulting demands
PC=PV
VC=VV PT
VT
VQ
A B
Q
C
MT
MQ
PQ
MC
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Refined Corner Check – Middle Chunk
If Q surface is overstressed, different combinations of PC, VC, VT, PT, MT must be used
If analysis shows members can carry significant moments, then it may be possible to remove the constraint that member resultants must pass through WP
Once a combination of forces is identified that does not overload the plate sections, calculate Pn using the compression corner resultants
PC=PV
VC=VV PT
VT
VQ
A B
Q
C
MT
MQ
PQ
MC
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Examples of BCC and RCC using FHWA specimen P5-C-WV (0.5)
Ultimate Compression Member Load (P): Per FHWA FE model: 1890 k Per Partial Shear check: 1218 k Per Whitmore-Lmid: 2461 k WJE Basic Corner Check: 1483 k Since BCC < Whitmore-Lmid; use RCC WJE Refined Corner Check: 1775 k WJE Pn = 1745 k AASHTO Pn= 1218 k
P
Since connection is so compact, not surprising FE load significantly higher; as FE modeling accounted for strain-hardening, which was significant in this case
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Examples of BCC and RCC using FHWA specimen E1-U-307SS-WV(0.5)
Ultimate Compression Member Load (P): Per FHWA FE model: 974 k Per Partial Shear check: 632 k Per Whitmore-Lmid: 797 k WJE Basic Corner Check: 779 k Since BCC < Whitmore -Lmid; use RCC WJE Refined Corner Check: 890 k WJE Pn = 797 k (limited by WLmid)
AASHTO Pn = 632 k
P
In this case, RCC gives much better value than WLmid; however, this is not always the case, so must stick with WLmid value if less than RCC value
ID#G-T-wwwxyz-a
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FHWA Experimental Program
Bolt Type: A307 or A490
Standoff Distance: S=Short L=Long
Free Edge Distance: S=Short L=Long
Thickness: 1/8s of an inch
Test Sequence
Truss: W=Warren WV=Warren w/ Vert. P=Pratt
Test #
GP=Test E=Experimental P=Parametric
Geometry: C=Chamfered U=Unchamfered
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Buckling Modified Basic Corner Check
This is FHWA case P5-U-WV; for which the WLmid value is much lower than the BCC value; indicating buckling may be an issue. We could use the WLmid value, but it is very conservative in such cases.
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Buckling Modified Basic Corner Check
Calculate the length of each “span” as the clear spacing along the span centerline. Calculate the effective length (KL) using K = 1.0 for the shorter span; and K = 0.5 for the longer span Calculate critical compressive stress (FCR) for maximum KL Repeat BCC, limiting the principal stress on the critical surface to FCR instead of allowing von Mises Fy
LH
LV
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Example of Buckling Modified BCC using FHWA P5-U-WV (0.438)
P
Ultimate Compression Member Load (P): Per FHWA FE model: 1350 k Per Partial Shear check: 1216 k Per Whitmore-Lmid: 1010 k WJE Basic Corner Check: 1518 k Since BCC > Whitmore -Lmid; use BMBCC WJE BMBCC: 1128 k WJE Pn = 1128 k AASHTO Pn = 1010 k
If BCC had not been modified to account for stability, would have had to stick with lower WLmid value.
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WJE Approach vs. MBE Procedure
Sim. Pn (t=0.4375”) = 817 k Sim. Pn (t=0.5”) = 974 k Sim. Pn (t=0.625”) = 1,369 k
All E1-WV-307SS Connections
500
600
700
800
900
1,000
1,100
1,200
0.250 0.375 0.500 0.625 0.750
Cap
acit
y [k
ips]
Gusset Plate Thickness [in.]
Whit.Lmid
PS
HS
BCC
RCC
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WJE Approach vs. MBE Procedure
Sim. Pn (t=0.375”) = 1,050 k Sim. Pn (t=0.4”) = 1,170 k Sim. Pn (t=0.4375”) = 1,350 k Sim. Pn (t=0.5”) = 1,635 k Sim. Pn (t=0.625”) = 2,145 k
All P5U-WV-NP Connections
500
1,000
1,500
2,000
2,500
3,000
0.250 0.375 0.500 0.625 0.750
Cap
acit
y [k
ips]
Gusset Plate Thickness [in.]
Whit.Lmid
PS
HS
BCC
RCC
BMCC
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WJE Approach vs. MBE Procedure
500
1,000
1,500
2,000
2,500
3,000
3,500
0.250 0.375 0.500 0.625 0.750
Cap
acit
y [k
ips]
Gusset Plate Thickness [in.]
Whit.Lmid
PS
HS
BCC
RCC
Sim. Pn (t=0.375”) = 1,305 k Sim. Pn (t=0.4”) = 1,410 k Sim. Pn (t=0.4375”) = 1,590 k Sim.Pn (t=0.5”) = 1,890 k Sim. Pn (t=0.625”) = 2,475 k
All P5C-WV-NP Connections
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WJE Approach vs. AASHTO Procedure
Sim. Pn (t=0.375”) = 1,514 k Sim. Pn (t=0.4375”) = 1,853 k Sim. Pn (t=0.5”) = 2,215 k Sim. Pn (t=0.625”) = 2,915 k
1,000
1,500
2,000
2,500
3,000
3,500
4,000
0.250 0.375 0.500 0.625 0.750C
apac
ity
[kip
s]
Gusset Plate Thickness [in.]
Whit.Lmid
PS
HS
BCC
RCC
All P6C-WV-NP connections
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WJE Approach vs. AASHTO Procedure
Most E and P Connections
0.0
0.5
1.0
1.5
2.0
2.5
0 10 20 30 40 50 60 70 80 90 100 110 120 130
Pro
fess
ion
al F
acto
r
Gusset Number
Whit.Lmid
HS
PS
BCC
RCC
BMCC
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WJE Approach vs. MBE Procedure
Professional Factors – Controlling Checks
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
0 10 20 30 40 50 60 70 80 90 100 110 120 130
Pro
fess
ion
al F
act
or
Gusset Number
AASHTO - Whit.Lmid
AASHTO - HS
AASHTO - PS
WJE - Whit.Lmid
WJE - HS
WJE - BCC
WJE - RCC
WJE - BMCC
As-Designed (kips/plate)
446 Partial Shear
530 Basic Corner Check
651 Whitmore-Lmid
718 Fastener
831 Horizontal Shear
1200 Vertical Shear
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Case Study Example – Additional Analysis
Controls initially
Since BCC < WLmid, use RCC subject to upper limit of WLmid
As-Designed (kips/plate)
446 Partial Shear
530 Basic Corner Check
651 Whitmore-Lmid
704 Refined Corner Check
718 Fastener
831 Horizontal Shear
1200 Vertical Shear
Reliable capacity = 651k
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Case Study Example – Additional Analysis
Controls
HS-20 Inventory Load Rating
0.85 Partial Shear
1.21 Basic Corner Check
1.73 Whitmore-Lmid
1.96 Refined Corner Check
2.02 Fastener
2.51 Horizontal Shear
4.09 Vertical Shear
HS-20 IR = 1.73
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Case Study Example – Additional Analysis
Controls
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Case Study Example – Additional Analysis
Note that this is a support node
Vertical forces in webs do not balance
Vertical web forces must pass through horizontal shear zone to be resolved at bearing; which must be accounted for in HS check
This condition was not evaluated in NCHRP study
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Case Study Example – FEM
Deterioration Need to evaluate effects of deterioration on gusset plate
capacity by considering limit states that may have been
made critical by the deterioration
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Type of distress
Location of distress
Average or minimum?
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Considerations for Deterioration
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Common narrow horizontal band of section loss
≈ 1 ½ in.
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Check reduced section for HS, using FU on reduced section
Just like you would check the similarly reduced section along the row of fastener holes immediately below (Section A-A)
A′ A′
A A
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Deterioration creates potentially critical new “corners”
No deterioration “corner”
Potentially critical new “corner”
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Corner Check and Deterioration
θ°
θv°
θH°
WP
PH
VH
PV
VV
θ°
θv°
θH°
WP
PH
VH
PV
VV
V, P and associated location change based on reduced section
θH changes to fit location of deterioration
In narrow corroded zones, use teff = tmeasured x Fu/Fy ≤ torig
One reason why corroded L11 was less critical than undamaged U10 in I-35W Bridge
Pn Pn
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Common localized area of section loss
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Corner Check and Deterioration
θ°
θv°
θH°
WP
PH
VH
PV
VV
θ°
θv°
θH°
WP
PH
VH
PV
VV
Pn Pn
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Examples of BCC and RCC using FHWA specimen P14-U-C1-W(0.5)
P
Section loss specimen
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Examples of BCC and RCC using FHWA specimen P14-U-C1-W(0.5)
P
Section loss specimen
WJE “Corner”
VV
VH
PV
PH
WP’s for corner forces no longer at midpoint due to shift in CG of plate section caused by corrosion Magnitudes of P and V forces reduced due to corrosion
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Examples of BCC and RCC using FHWA specimen P14-U-C1-W(0.5)
Ultimate Compression Member Load (P): Per FHWA FE model: 1316 k Per Partial Shear check: 838 k Per Whitmore-Lmid: 1334 k WJE Basic Corner Check: 1150 k Since BCC < Whitmore-Lmid; use RCC WJE Refined Corner Check: 1317 k WJE Horiz. Shear Check: 1230k Pn = 1230k
P
Partial Shear check is so low because it essentially assumes that all surfaces surrounding the compression member are in a similar condition as the critical surface (i.e., it doesn’t take into account the better conditions on the other surface)
Controls
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WJE Approach vs. AASHTO Procedure
500
1,000
1,500
2,000
2,500
3,000
0 0.5 1 1.5 2 2.5
Cap
acit
y [k
ips]
Gusset Plate
Whit.Lmid
PS
HS
BCC
RCC
Uncorroded Corroded
Sim. Pn (t=0.5” Uncorroded) = 1,652 k Sim. Pn (t=0.5” Corroded) = 1,316 k
P14-U-C1/2-W-INF corroded connections
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Examples of BCC and RCC using FHWA specimen P14-U-C1-W(0.5)
Very high strains and associated strain hardening in deteriorated zone
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Gusset Plate Example – Additional Analysis
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Gusset Plate Example – Additional Analysis
With Deterioration (kips/plate)
260 Partial Shear
340 Basic Corner Check
428 Horizontal Shear
439 Whitmore-Lmid
503 Refined Corner Check
718 Fastener
1067 Vertical Shear
Pn = 428 k
A A
Corner
Horizontal Shear
P
Controls
When AASHTO equations indicate a deficiency, additional analysis should be used to further refine capacity before recommending repairs/replacement
The Basic Corner Check and Refined Corner Check are two first-principals based analytical procedures that maximize the plate capacity over the smallest “corner” that incorporates a member’s fasteners
Deterioration can be accounted for using the BCC or RCC by checking affected cross sections
Deterioration calculations should consider the commonly recognized strain hardening behavior, e.g. net section, when appropriate
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Conclusions
…Except as specified herein, a load rating analysis of main truss member gusset plates and their connections shall be conducted according to the provisions of Articles 6A.6.12.6.1 through 6A.6.12.6.9. Alternatively, a load rating analysis may be performed according to the provisions of Article 6A.6.12.6.11.
In situations where gusset plate capacity is controlled by buckling (i.e. Partial Shear or Whitmore) a more refined analysis is warranted.
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Proposed AASHTO MBE Modifications 6A.6.12.6-Gusset Plates
…These provisions are based on the findings from NCHRP Project 21-84 (NCHRP, 2013), and supersede the 2009 FHWA Guidelines for gusset-plate load ratings. …
As shown in NCHRP, 2013, the gusset plate compression checks, i.e. Partial Shear and Whitmore, can be very conservative, frequently underestimating plate capacity by more than 25 percent and in one case underestimating plate capacity by more than 40 percent. When evaluating existing gusset plates, the cost of being conservative is much higher than when designing new plates. Therefore, in situations where the governing checks are known to have substantial conservatism, more accurate estimates of gusset plate capacity is warranted.
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Proposed AASHTO MBE Modifications C6A.6.12.6-Gusset Plates
A refined simulation analysis using the finite element method may be employed to determine the nominal resistance of a gusset-plate connection at the strength limit state in lieu of satisfying the requirements specified in Articles 6A.6.12.6.6 through 6A.6.12.6.9….
If a load rating conducted in accordance with Articles 6A.6.12.6.6 through 6A.6.12.6.9 indicates an unacceptable load rating and the limiting capacity is based on any of the following: compression (i.e. Partial Shear, Whitmore) or a deteriorated condition, then a more refined analysis should be performed. Any more rigorous analysis must be consistent with a rational application of established engineering principles.
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Proposed AASHTO MBE Modifications 6A.6.12.6.11-Refined Analysis
The necessary fidelity of the model is dependent upon the failure mode under investigation. For instance, simple planar shell finite element models of single gusset plates have been successfully used to identify the nominal shear resistance of gusset-plate connections…..
Because the basic compression checks comprise empirical fit of a wide-range of conditions, significant improvements in accuracy can be provided by explicitly considering the flow of forces through the plate and the capacities of the sections resisting those forces. An example of such an approach is illustrated in Figure X.
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Proposed AASHTO MBE Modifications C6A.6.12.6.11-Refined Analysis
In this approach the following assumptions and constraints are made:
Failure surfaces represent minimum section that includes all member fasteners
Forces act at centroid of respective section surfaces
Surfaces can carry no moment
Combination and normal and shear forces limited by von Mises stress criterion
Resultant of each section forces pass through nodal work point
Resultant of all section forces must align with member
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Proposed AASHTO MBE Modifications C6A.6.12.6.11-Refined Analysis
Subject to the limitations of other checks, this approach provides more accurate estimate of capacity when compared to the partial shear check.
Since this method is generally conservative, it can be further refined by removing certain constraints. For example, it is not essential for the resultants of the section forces to pass through the work point, nor is it necessary for the failure sections to carry no moment. Provided that there is adequate capacity in other areas of the gusset plate, these constraints can be eliminated. If they are eliminated the other sections of the plate must be evaluated for the corresponding demands. All other checks, i.e. horizontal shear, block shear, etc. still apply. Refer to WJE reference for examples demonstrating this approach.
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Proposed AASHTO MBE Modifications C6A.6.12.6.11-Refined Analysis
Thank You Questions?
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Guidelines for the Load and Resistance Factor Design and Rating of
Riveted and Bolted Gusset-Plate Connections for Steel Bridges
FHWA Tested 12 full-scale gusset plate connections to assess the limit states of shear, buckling, and corrosion
Georgia Tech utilized 212 finite element models calibrated to experimental test results to complete a parametric study
Computer simulations used to determine failure load and resulting limit state professional factors
Study resulted in the development of new AASHTO provisions replacing FHWA Guide
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NCHRP Project 12-84
Test frame created to accommodate five members with diagonals oriented at 45 degrees
Phase 1 testing focused on shear along Section A-A and buckling of gusset plate compression zone
Stand-off distance and free edge length varied
All buckling failures were side-sway
Phase 2 testing used same geometries and investigated effects of corrosion and use of retrofit shingle plates and edge stiffening
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Experimental Program
Peak load
4% equivalent plastic strain
0.2 inch fastener shear displacement
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Parametric Study
Failure Criteria
Plate thickness
Mill-to-bear
Material strength
Chamfer
Shingle plates
Edge stiffening
Corrosion
Studied Parameters
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Repairing Deterioration
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Repairing Deterioration
Inside plate fabricated to bear on end of compression member along this surface (did not have to take out rivets so as to connect to compression member)
Use angles, plates or other shapes to transfer forces “around” deteriorated areas (i.e., localized deterioration does not require whole new plates)
Transfer compression forces from member to reinforcement plates via bearing when possible, to limit the amount of fasteners that must be removed at one time
Mobilize new load paths when available, to limit the amount of fasteners that must be removed at one time
Take advantage of existing elements that cross critical failure planes
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Design of Repair Elements