Advancing Steel and Concrete

Bridge Technology

Manual For Finite Element

Analysis

Presentation to T-5

July 2012

John M. Kulicki

Task Team

• FHWA

– Dr. Brian D. Kozy, PE

– Mr. Reggie Holt

• Prime – ALTSS Center, Lehigh University

– Dr. Richard Sause, PE

– Dr. Chad Kusko

• Task Leader – Modjeski and Masters, Inc

– Dr. John Kulicki, PE

– Dr Thomas Murphy, PE

Objectives and Approach

• Provide greater consistency in application

of FEA to bridge structures

– Raise the level of basic understanding to

encourage wider application of FEA

– Avoid blunders

– Understand behavior

– Introduce economies

Refined Analysis Tasks

• Deliverables are a manual of refined

analysis, AASHTO LRFD provisions, and

example (benchmark) problems.

• Spread across Task 1 and Task 2.

How?

• Produce instructional manual over two Tasks

• Task 1 – first 7 sections and examples

– Application basics

– Not material specific

– bridge type specific guidelines for steel and

concrete

– Proposed Spec changes to more directly use

results of FEA

How?

• Task 2 – 7 more advanced sections and

benchmark examples

• 2 Phases

How?

• Keep flexible

• Encourage initiative and creativity

• Avoid deep mathematics

• Concentrate on application

• Don’t overwhelm with too much “Big

Bridge Stuff”

• Avoid software specifics to extent possible

– try to stay generic

1. Refined Methods of Analysis in

AASHTO LRFD (T1)

• FEA as one refined method of analysis

permitted by LRFD

• 1D, 2D grid vs. 3D FEA compared

• Areas in LRFD where refined methods are

suggested/permitted (which are FEA

applicable)

• Compatibility of analysis and specification

provisions

2. Fundamentals of FEA (T1)

• General capabilities of modern software –

not a commercial

• Typical input and output

• Shape functions and degrees of freedom

• Typical element families and usage

• Handling torsion – and warping in

particular

2. Fundamentals of FEA (continued)

• Boundary conditions

• Substructuring

3. Meshing (T1)

• How many elements?

• What type – selection guides?

• Auto mesh generators

4. Model Verification (T1)

• Model and software verification

• Learning the software

• Vetting the design process

• Retrofitting bridges

• Examples – results of incorrect BC’s Posit ive Moment - S10N 0.5L - BF Stresses

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8

Lusas St ress (Ksi)

Fie

ld S

tre

ss (

Ksi

)

Case 5

Case 6

Case 7

Case 8

Field=Lusas

Linear

(Field=Lusas)

Live Load Moment in Exterior Box Girder

-10000

-8000

-6000

-4000

-2000

0

2000

4000

6000

8000

0 200 400 600 800 1000

Distance (ft)

Mo

men

t (k

-ft)

5. Evaluation of Stresses with

Shell Elements (T1)

• Integrating stresses

• Effective flange width

• Automatic slicing

• Staged loading/construction and stress

evaluation

6. Live Load Application (T1)

• What does AASHTO LRFD require?

• When is more required?

• How is live load modeled?

• How does program go from wheels to

nodes?

• Verifying automated

loaders

7. Composite Section Analysis (T1)

• Effective flange widths

• Red Herrings (axial forces in bending

members)

8. Examples

• Comparison of 1D, 2D and 3D analyses

for load distribution

– Steel bridges

– Concrete bridges

– Guidance on when refined analysis is

beneficial or needed

9. Concrete Bridges (T2)

• Modeling creep and shrinkage

• Made continuous for live load

• Secondary PT effects

• Linear elastic analysis vs. cracked

concrete material

• See staging elsewhere

-0.07

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0 0 200 400 600 800 1000

Time (days)

Dis

pla

cem

en

t (i

nc

hes)

10. Prestressing and Post-tensioning (T2)

• Is prestressing a resistance or a load?

• Service vs. ultimate

• Applying P/T in an FEA – trajectory or

equivalent loads

11. Steel Bridges (T2)

• Handling mixed materials

• Cross-frames and diaphragms

• Picking the geometric positioning and

associated modeling issues

• Layover

• Deck construction

• Staged construction

• Hot spot fatigue analysis

13. Steel Bridges (continued)

• Initial imperfections, e.g. web flatness

• Camber

• Distortion-Induced Fatigue - stiffness vs.

flexibility – modeling issues

12. Steel Connections (T2)

• Actual stress distributions vs. typical

design assumptions vs. FEA

• Localized yielding and redistribution

13. Stability Analysis (T2)

• Imperfections and initial stresses, e.g.

residual stresses

• What the design equations account for

and what is typically modeled.

14. Nonlinear Considerations (T2)

• When is nonlinear analysis required?

• Material

• Geometric

• Combined

• Lift-off, i.e. changed boundary conditions

during analysis

• Slip-stick

15. Dynamic Analysis (T2)

• Look to Seismic Guide Spec and current

provisions

• Mass and stiffness modeling

– Mass moment of inertia

• How many modes are enough?

• Using the mass participation percentage

• Time history, modal (spectral) analysis

• Special requirements for seismic analysis

of girder bridges

16. Examples (T2)

• Curved multi-beam bridge – static and

dynamic analysis

• Stability example

• Time-dependent

example

Schedule

2011 2012 2013 2014 Estimated

Subtask # Subtask Description O N D J F M A M J J A S O N D J F M A M J J A S O N D J F M

Completi

on

1.1 Summary of FEA Fundamentals 15%

1.2 Protocols for Refined Analysis 10%

1.3 Advanced Topics 0%

1.4 Verification 10%

1.5 Manual Sections 10%

1.6 Examples 0%