Evaluation of Deteriorated Gusset Platessp.bridges.transportation.org/Documents/2014 SCOBS... · This is FHWA case P5-U-WV; for which the WL mid value is much lower than the BCC value;

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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

Solutions for the Built World Page 2

WJE Study

2013 AASHTO MBE Replaces FHWA Guide “ Load Rating Guidance and

Examples For Bolted and Riveted Gusset Plates in Truss

Bridges”


Fasteners

Compression

Whitmore – Lmid

“Partial Shear Plane”

Tension

Block Shear

Vertical Shear

Horizontal Shear


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


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


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


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


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)


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


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


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


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.




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


von Mises Yield Criterion


θ°

θv°

θH°

WP

PH

VH

PV

VV

Basic Corner Check

Lv/2

LH/2

Pn


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


Gusset Plate Limit States – First Step in Improving Analysis

Gusset Plate Evaluation Guide 7 example problems highlighting benefits of more rigorous

analysis.



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



Examples show that substantial increases in capacity can be obtained through more rigorous analysis

Additional analysis can help identify locations requiring retrofit



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


Conclusions

Questions? Thank You



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


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


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


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


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


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


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.


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


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.


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



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]


Whit.Lmid

PS

HS

BCC

RCC

BMCC



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]


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


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]


Whit.Lmid

PS

HS

BCC

RCC

All P6C-WV-NP connections



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



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


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


651 Whitmore-Lmid

704 Refined Corner Check

718 Fastener


1200 Vertical Shear

Reliable capacity = 651k



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



Controls



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


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


Type of distress

Location of distress

Average or minimum?


Considerations for Deterioration



Common narrow horizontal band of section loss

≈ 1 ½ in.


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


Deterioration creates potentially critical new “corners”

No deterioration “corner”

Potentially critical new “corner”


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



Common localized area of section loss


Corner Check and Deterioration

θ°

θv°

θH°

WP

PH

VH

PV

VV

θ°

θv°

θH°

WP

PH

VH

PV

VV

Pn Pn



Examples of BCC and RCC using FHWA specimen P14-U-C1-W(0.5)

P

Section loss specimen



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



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



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



Very high strains and associated strain hardening in deteriorated zone


Gusset Plate Example – Additional Analysis


Gusset Plate Example – Additional Analysis

With Deterioration (kips/plate)

260 Partial 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


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.


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.


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.


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.


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



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.



Thank You Questions?


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


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


Experimental Program

Peak load

4% equivalent plastic strain

0.2 inch fastener shear displacement


Parametric Study

Failure Criteria

Plate thickness

Mill-to-bear

Material strength

Chamfer

Shingle plates

Edge stiffening

Corrosion

Studied Parameters


Repairing Deterioration


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


Design of Repair Elements