Research Result Presentation...Research Result Presentation Evaluation of Reserve Shear Capacity of Bridge Pier Caps Using the Deep Beam Theory Presented by: Pappu Baniya Introduction

Research Result PresentationEvaluation of Reserve Shear Capacity of Bridge Pier

Caps Using the Deep Beam Theory

Presented by: Pappu BaniyaAnish Sharma

Dr. Serhan Guner

Outline

2

• Introduction

• Objectives & Methodology

• Overview of STM‐CAP

• Verification with CAST

• Nonlinear FEM

• Training Session

• Conclusion

Pappu Baniya (15 min)

Anish Sharma (6 min)

Pappu Baniya (18 min)

Serhan Guner (12 min)

Serhan Guner (2 min)

Introduction

3

• Pier caps transfer the load from girder to piers

• In Ohio: 28,000 bridges• In the U.S.: 600,000 bridges

GirderGirder

Pier Cap

Column

Pier Cap

Column

Girders Girder Load

Introduction

4

• Sectional Method

Source: Wikimedia

Critical Sections

Beam

Shear Force Diagram

Bending Moment Diagram

Problem Statement

5

Overloaded pier cap

• Most of the bridge pier caps are found to be overloaded.

• Limited funding for repair and rehabilitation.

Problem Statement

6

Objective

• Determine a practical and accurate analysis methodology for bridge pier caps.

• Develop a solution algorithm/computer program based on the suitable method STM‐CAP.

• Verify the developed solution procedure.

• Compare the results with nonlinear FEM and sectional analysis method.

7

• Kani performed shear tests in 1964.

Literature Review

8

Shear S

tren

gth / f c’

Shear‐Span Ratio (𝑎/𝑑)

ExperimentStrut and Tie MethodSectional Method

Pier cap

Centroid of tension reinforcement d

a2a1

R2R1

P

Solution ApproachBeam

Slender Beam Deep Beam

Depth Shear Span‐to‐Depth Ratio (a/d) <2.0

9

Sectional Method Nonlinear AnalysisStrut‐and‐Tie Method

R1 R2 R3

D D D D D D D D D D DD

Width of D‐ region =h

h

• Strut and Tie Model (STM)

Methodology

10

R1 R2 R3

• Conceptual truss model to give a definite load‐path.

Methodology

11

• Elements of STM– Struts– Ties– Nodes

P

R1 R2

Tension Tie

Compressive strutNode

Element Nature RepresentsStrut Compression Member ConcreteTie Tension Member ReinforcementNode Connection (Joint) Concrete

Methodology

12

Ties TensionFor Rebar & Stirrup

Struts CompressionFor Concrete

NodesGirder Loads

StrutTie

Tie

Tie

Columns

Methodology• STM is complex for daily design and analysis.

– Engineers unfamiliar with the STM– No checks for invalid/inefficient model– Iterative process: significant time for each model

• Explored innovative strategies to reduce the complexity to a level sim. to the sectionalmethod.

• Developed STM‐CAP (Strut and Tie Method forpier CAPs)

13

STM‐CAP• About 16 modules and 5,000 lines of code.• Embedded into spreadsheet.

14

Overview of STM‐CAP

START

Input Geometry Details

Input Factored Load Details (girder load, girder spacing)

Deep or Slender?(a/d ratio)

Bridge NamePID No.

Centerline

C1 C2CenterlineA1 A3

P1=331 k P3=331 k

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START

Input Geometry Details

Input Factored Load Details (girder load, girder spacing)

Input Reinforcement Details(Area and centroid of longitudinal rebar,

area and spacing of stirrup)

Deep (a/d < 2.0)Input Material Properties

(f’c, fy, rebar diameter, stirrup bar area)

Input Resistance Factors(ϕc, ϕs, node multiplier)

Deep or Slender?(a/d ratio)

Bottom bar Layer 1: 7 nos. #9Total Area: 7 in2Centroid: 4 in

Top bar Layer 1: 7 nos. #10Layer 2: 4 nos. #10Total Area: 13.97 in2Centroid: 5.95 in

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• Strut and Tie Method (STM)

• Capacities as per Section 5.8.2 of AASHTO LRFD 2017.


17

331 261 70 70 261 331

TieStrut

Node

Node number

Overview of STM‐CAPUtilization Ratio = Force/Capacity

18


19


20

Model 1 Model 2

Model 3 Model 4

• Very fast modeling and analysis time.• Teaches user how to perform strut‐and‐tie analysis.• More accurate capacity predictions.


21

If >1.0: flexure overloadIf >1.0: shear overload

If >1.0: compression overload

• Determines the overload type and its location.

CAST Verification

22

STM‐CAP

0.76

0.71

0.420.69

0.13

0.48 0.410.1 0.14

CAST0.75

0.70

0.69 0.41 0.48 0.41 0.09

0.13

0.14

• Eight pier caps were modeled with STM‐CAP and CAST.

• CAST (Computer Aided Strut‐and‐Tie)– Research‐based, general purpose strut‐and‐tie software.– Uses ACI formulations (modified for AASHTO).

Nonlinear FEM Modeling & Verification

23

VecTor2

• 2D continuum finite element model.• Based on Modified Compression Field Theory (Vecchio and

Collins, 1986 at the University of Toronto)• Smeared rotating crack model.• Many second order material behaviors.

• More realistic simulation of behavior of the deep cap beams.• How conservative strut and tie method is than the nonlinear

FEM.

Nonlinear FEM Modeling

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• Existing Cap Beam


25

• Existing Cap Beam• Nonlinear FE Model

DL+LL DL+LL DL+LL

Beam: 0.7% stirrupsBeam: 0.3% stirrupsBeam: 0.1% stirrupsColumnConcrete Cover


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Determination of Utilization Ratios

Stresses at failure load

Critical region marked

Same region marked at factored load

gAverage stresses at each region at factored load

Utilization Ratio

Divided by capacity

0.25 0.24

0.39 0.28 0.11

0.37 0.04

0.03


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Comparison of Utilization Ratios

Utilization ratios are 40% on average of STM.Failure behavior matches well.

(0.37) (0.04)

(0.03)

(0.39) (0.28) (0.24) (0.11)

STM‐AASHTONonlinear FEM

Governing Member


28

•Nonlinear FEM capacities are much higher than STM.•Nonlinear FEM’s modeling and analysis time is significantly higher.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 0.5 1 1.5 2 2.5 3 3.5

Util

izat

ion

Rat

io

Shear Span-Depth Ratio (a/d)

• Not an appropriate method for deep pier caps.

Comparison with Sectional Method

29

C

C

A

A

B

B

D

D

Comparison with Sectional Method

30

0

0.2

0.4

0.6

0.8

1

1.2

0 0.5 1 1.5 2 2.5 3 3.5

Utilization Ra

tio

Shear Span‐Depth Ratio (a/d)

Sectional MethodSTM‐CAP (Optimized)Nonlinear FEM

Training Session

Conclusion

32

• Developed a specialized STM tool for pier cap, STM‐CAP.– Uses VBA coding to provide a graphical solution.– Permits quick and easy optimization.– Teaches users the correct use of STM.– Runs very fast (modeling + analysis time).– Helps with load rating as well as rehabilitation decisions.

• Validated the accuracy of STM‐CAP.• Demonstrated that the sectional method underestimates the shear capacity of deep pier caps (up to 3 times).

• Accuracy: NLFEA > STM‐CAP > Sectional Method Time: STM‐CAP ≈ Sectional Method <<< NLFEA.

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Review PanelMs. Andrea Parks, PEMr. Matthew Blythe, PEMs. Michelle Lucas

Acknowledgements

Pappu Baniya (MS Student)[email protected]

Anish Sharma (MS Student)[email protected]

Dr. Serhan Guner (Assistant Professor)[email protected]


35

36

Benefits

• Right funding →Right place

Cost Saving

Reduced Congestion

Reduced Safety Risk

Second Order Properties considered in VT2

37

Nonlinear FEM Verification


38

•Capacity from Nonlinear FEM are consistently higher than STM(AASTHO)

•Modeling and Analysis time is significantly higher.•STM‐CAP predicts similar behavior in less time and best for dailyanalysis.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 0.5 1 1.5 2 2.5 3 3.5

Util

izat

ion

ratio

Shear span-to-depth ratio (a/d)


39

•Capacity from Nonlinear FEM are consistently higher than STM(AASTHO)

•Modeling and Analysis time is significantly higher.•STM‐CAP predicts similar behavior in less time and best for dailyanalysis.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 0.5 1 1.5 2 2.5 3 3.5

Util

izat

ion

ratio

Shear span-to-depth ratio (a/d)

• Strut and tie model is based on lower bound theorem.Nonlinear FEM simulates till ultimate failure.

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0

400

800

1200

1600

2000

2400

2800

3200

0 2 4 6 8 10

Loa

d (k

ips)

Displacement (mm)

Failure point

DifferenceFirst yield point


41

Higher capacity from Nonlinear FEM but took more analysis time than STM‐CAP.


42

Comparison of Utilization RatiosSTM‐CAPNonlinear FEM

Utilization ratios are 40% on average of STM‐CAP.Behavior matches.

The Final Report and Fact Sheet can be found at: http://www.dot.state.oh.us/Divisions/Planning/SPR/Research/reportsandplans/Pages/default.aspx

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Research Result Presentation...Research Result Presentation Evaluation of Reserve Shear Capacity of Bridge Pier Caps Using the Deep Beam Theory Presented by: Pappu Baniya Introduction

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