MotivationCase Studies of Forensic FEA

Conclusions

Lessons Learned from ForensicFEA of Failed RC Structures

James B. Deaton Lawrence F. Kahn

Department of Civil and Environmental EngineeringGeorgia Institute of Technology

ACI Fall Convention – October 25, 2010

Deaton and Kahn Lessons Learned from Forensic FEA of Failed RC Structures

MotivationCase Studies of Forensic FEA

Conclusions

Motivation – Tools for Structural Analysis

Problem StatementStructural failure continues to be a reality because critical limitstates are often undetected by engineering analysis.

Nonlinear Finite Element AnalysisState-of-the-art: Concrete compression crushing, tensilecracking, tension stiffening, steel reinforcement plasticity,steel-concrete bond-slip, geometric nonlinearity, etc.Powerful tool but expensive, time-consuming, and largelyunavailable for practicing engineers

Deaton and Kahn Lessons Learned from Forensic FEA of Failed RC Structures

MotivationCase Studies of Forensic FEA

Conclusions

Motivation – Tools for Structural Analysis

Linear Elastic Finite Element AnalysisAvailable to every practicing engineerCANNOT describe distribution of force, stress, &displacements at ultimate limit state ... butCAN indicate existence of serious problems

Goal of PresentationDemonstrate key practical techniques:

3 case studies of real structural failureEvaluation using linear elastic FEAFeatures common to all structural engineering softwareDemonstration of failure to meet key performance criteria

Deaton and Kahn Lessons Learned from Forensic FEA of Failed RC Structures

MotivationCase Studies of Forensic FEA

Conclusions

Parking Structure Shrinkage CrackingIndustrial Structure on Non-Uniform BearingPedestrian Bridge Collapse

Parking Structure Shrinkage Cracking

Case Study # 1:

Parking Structure Shrinkage Cracking

Deaton and Kahn Lessons Learned from Forensic FEA of Failed RC Structures

MotivationCase Studies of Forensic FEA

Conclusions

Parking Structure Shrinkage CrackingIndustrial Structure on Non-Uniform BearingPedestrian Bridge Collapse

Overview of Parking Structure Serviceability Failure

3-story parking deck, 95 meters × 20 metersExtensive early-age cracking of slabsProbable cause of cracking: shrinkage

High w/c ratio + no expansion joints

Representative photograph:

Deaton and Kahn Lessons Learned from Forensic FEA of Failed RC Structures

MotivationCase Studies of Forensic FEA

Conclusions

Parking Structure Shrinkage CrackingIndustrial Structure on Non-Uniform BearingPedestrian Bridge Collapse

Parking Structure Finite Element Model Details

Model consisted of ∼24,000 shell elementsLoads: Gravity, temperature, shrinkage

Graphics of Model Entire Parking Structure: View from North-West

Entire Parking Structure: View from North-East

Deaton and Kahn Lessons Learned from Forensic FEA of Failed RC Structures

MotivationCase Studies of Forensic FEA

Conclusions

Parking Structure Shrinkage CrackingIndustrial Structure on Non-Uniform BearingPedestrian Bridge Collapse

Application of Shrinkage via Temperature Load

∆Tsh =εsh

α

εsh = specified shrinkage strain

α = coeff. of thermal expansion

For εsh = 0.0005 inin and α = 5.5× 10−6/◦F ⇒ ∆Tsh = −90.9◦F

Investigation of Stresses Due to Shrinkage The purpose of the following results was to demonstrate the stress conditions within the Floor 1 slab during the combined loading of Self-Weight and Shrinkage, and to evaluate several possible measure which could relieve this stress.. Case 1: Shrinkage Analysis – Replace fixed joints with rollers to assess unrestrained shrinkage of structure. Shrinkage loading is only loading condition applied. Displacement Graphic (Red = deformed, Blue = undeformed):

Maximum displacement as shown in above graphic: x-displacement = 0.04732 meters y-displacement = 0.009382 meters Expected displacements: x-displacement expected = 94.6 meters * 0.0005 shrinkage strain = 0.0473 meters y-displacement expected = 18.78 meters * 0.0005 shrinkage strain = 0.00939 meters

Deaton and Kahn Lessons Learned from Forensic FEA of Failed RC Structures

MotivationCase Studies of Forensic FEA

Conclusions

Parking Structure Shrinkage CrackingIndustrial Structure on Non-Uniform BearingPedestrian Bridge Collapse

Investigate Means of Relieving High Slab Stresses

Case 3: Shrinkage Analysis – All North/South walls removed Abstract: Under shrinkage conditions only, if all the North/South walls are removed, is the stress due to shrinkage relieved such that we can claim that the proximate cause of cracking is the stiffness provided by these walls? Conclusion: Removal of N-S walls does not seem to relieve the shrinkage stress. SXX TOP Due to Shrinkage Only – A-M:

SYY TOP Due to Shrinkage Only – A-M:

Top: σt = 2600 psi · Bottom: σt = 2800 psi

Case 2: Shrinkage Analysis – All elements North of Column Line G inactivated. Abstract: Under shrinkage conditions only, if all elements North of Column Line G are inactivated, is the stress due to shrinkage relieved such that we can claim that the proximate cause of cracking is the lack of an expansion joint? Conclusion: Expansion joint at G does not seem to relieve the shrinkage stress. SXX TOP Due to Shrinkage Only – A-G:

SYY TOP Due to Shrinkage Only – A-G:

Top: σt = 1660 psi · Bottom: σt = 1968 psi

Case 4: Shrinkage Analysis – All elements North of G and South of C inactivated. Abstract: Under shrinkage conditions only, if all elements North of Column Line G and South of C are inactivated, is the stress due to shrinkage relieved such that we can claim that the proximate cause of cracking is the lack of an expansion joint at C and G? Conclusion: Shrinkage stress relieved by approximately ! (compare SXX top). SXX TOP Due to Shrinkage Only – C-G:

SYY TOP Due to Shrinkage Only – C-G:

Top: σt = 715 psi · Bottom: σt = 845 psi

Relieve shrinkage stress ∼3.5x by adding expansion joints

Deaton and Kahn Lessons Learned from Forensic FEA of Failed RC Structures

MotivationCase Studies of Forensic FEA

Conclusions

Parking Structure Shrinkage CrackingIndustrial Structure on Non-Uniform BearingPedestrian Bridge Collapse

Parking Structure Shrinkage Analysis Conclusions

Shrinkage easily incorporated via temperature load in FEAShrinkage analysis would have suggested:

A spacing of expansion joints at 30 meters (vs. 95 meters)Construction sequence that would have reduced restraintShrinkage performance criteria in mix designGraphics of Model

Entire Parking Structure: View from North-West

Entire Parking Structure: View from North-East

Deaton and Kahn Lessons Learned from Forensic FEA of Failed RC Structures

MotivationCase Studies of Forensic FEA

Conclusions

Parking Structure Shrinkage CrackingIndustrial Structure on Non-Uniform BearingPedestrian Bridge Collapse

Industrial Structure on Non-Uniform Bearing

Case Study # 2:

Industrial Structure on Non-Uniform Bearing

Deaton and Kahn Lessons Learned from Forensic FEA of Failed RC Structures

MotivationCase Studies of Forensic FEA

Conclusions

Parking Structure Shrinkage CrackingIndustrial Structure on Non-Uniform BearingPedestrian Bridge Collapse

Overview of Tall Industrial Structure

Cylindrical industrial structure on mat foundationSuperstructure: 550-ft tall; Mat: 100-ft wide and 8-ft thickSignificant displacements occurred during constructionPresence of non-uniform geological structure below mat:

Superstructure

Mat foundation

Rock Soil

Deaton and Kahn Lessons Learned from Forensic FEA of Failed RC Structures

MotivationCase Studies of Forensic FEA

Conclusions

Parking Structure Shrinkage CrackingIndustrial Structure on Non-Uniform BearingPedestrian Bridge Collapse

Model Characteristics

∼38,000 shell elementsLoads: Gravity, Wind, SeismicP-δ effects neglectedCompression-only springs tosimulate supportSubgrade condition, compare:

Uniform subgrade modulus(neglect rock profile)Variable subgrade modulus

Deaton and Kahn Lessons Learned from Forensic FEA of Failed RC Structures

MotivationCase Studies of Forensic FEA

Conclusions

Parking Structure Shrinkage CrackingIndustrial Structure on Non-Uniform BearingPedestrian Bridge Collapse

Response Increase: Uniform vs. Variable Subgrade

Response Gravity+WindTip Lateral Displacement ∼73% increaseFoundation Settlement Displacement ∼46% increaseArea of steel required by Wood & Armer ∼58% increaseShear force through foundation section ∼395% increase

Comparison of shear contours here!Deaton and Kahn Lessons Learned from Forensic FEA of Failed RC Structures

MotivationCase Studies of Forensic FEA

Conclusions

Parking Structure Shrinkage CrackingIndustrial Structure on Non-Uniform BearingPedestrian Bridge Collapse

Vertical Displacements in Mat Foundation

Gravity AloneMax uplift: 0.15 in.Max settlement: 1.91 in.

Gravity + WindMax uplift: 1.80 in.Max settlement: 3.74 in.

Deaton and Kahn Lessons Learned from Forensic FEA of Failed RC Structures

MotivationCase Studies of Forensic FEA

Conclusions

Parking Structure Shrinkage CrackingIndustrial Structure on Non-Uniform BearingPedestrian Bridge Collapse

Lateral Displacement at Top of Structure

Max Lateral DisplacementGravity: 11.5 in.Gravity + Wind: 34.8 in.

Contributions to Drift∼81.8%⇒ Rigid body rotation∼18.2%⇒ Flexure

Deaton and Kahn Lessons Learned from Forensic FEA of Failed RC Structures

MotivationCase Studies of Forensic FEA

Conclusions

Parking Structure Shrinkage CrackingIndustrial Structure on Non-Uniform BearingPedestrian Bridge Collapse

Pedestrian Bridge Collapse

Case Study # 3:

Pedestrian Bridge Collapse

Deaton and Kahn Lessons Learned from Forensic FEA of Failed RC Structures

MotivationCase Studies of Forensic FEA

Conclusions

Parking Structure Shrinkage CrackingIndustrial Structure on Non-Uniform BearingPedestrian Bridge Collapse

Pedestrian Bridge Collapse

Bridge collapse during placement of concrete deck in 200252 meter long, single steel tub girder bridgeFailure mode: global lateral torsional bucklingFEA conducted for Dr. Donald White at Georgia Tech

Page 4 of 16

mm thick, and are located throughout the length of the girder at the same locations as all K-diaphragms

and transverse struts. This, as well, is illustrated in Figure 3

Closed end diaphragms are provided at both ends of the girder. These diaphragms are solid with

the exception of a 0.5 m2 (5.27 ft2) square ventilation opening located in the center of the diaphragm.

Vertical bearing stiffeners are provided on each side of this ventilation opening, and are welded to both

the interior and exterior sides of the end diaphragm. Each bearing stiffener has the cross-sectional

dimensions of 175mm x 14mm. A transverse flange of dimensions 250mm x 14 mm is provided along

the top of each end diaphragm.

The bridge was supported on both ends by elastomeric bearings. The North end is fixed against

both transverse and longitudinal translation, while the South end is an expansion elastomeric bearing,

which restrains transverse displacement but allows for slight longitudinal translation by way of a slotted

hole during typical expansion that an exposed bridge will experience.

It should be noted that the actual structure was fabricated with a maximum camber of 0.75

meters, or slightly less than 30”, or approximately 1.4% of the length of the girder.

The steel specified in the General Notes of the design drawings is ASTM A709 Grade 345W,

which corresponds to a yield stress, fy, of 50 ksi. The Young’s modulus of the steel was taken to be

29000 ksi. The concrete is specified to have a compressive strength, fc’, 21 MPa, or 3000 psi, and is

assumed to be normal weight concrete with a density of 150 pcf.

Figure 2: General Cross-Sectional Geometry of the Marcy Pedestrian Bridge

Deaton and Kahn Lessons Learned from Forensic FEA of Failed RC Structures

MotivationCase Studies of Forensic FEA

Conclusions

Parking Structure Shrinkage CrackingIndustrial Structure on Non-Uniform BearingPedestrian Bridge Collapse

Pedestrian Bridge Finite Element Model

Use FEA to investigate stability of structureModel details: ∼22,000 elementsAssume weight (but not stiffness) of concrete

Deaton and Kahn Lessons Learned from Forensic FEA of Failed RC Structures

MotivationCase Studies of Forensic FEA

Conclusions

Parking Structure Shrinkage CrackingIndustrial Structure on Non-Uniform BearingPedestrian Bridge Collapse

Stability During Placement of Deck Concrete

Goal: Determine when placement of deck causes instabilityFor each load combination SW Steel + LC1−LC9, performelastic stability analysis & compute buckling load multiplier.

SW Steel

Slab LC1Slab LC2Slab LC3Slab LC4Slab LC5Slab LC6Slab LC7Slab LC8Slab LC9

+

10 0.2 0.4 0.6 0.8

1.2

0

0.2

0.4

0.6

0.8

1

Fraction of Concrete Deck Placed

P/Pc

r

P/Pcr = 1.0

LC2

LC3

LC4

LC5

LC6LC7

LC8 LC9

~68% of concrete deck placed

Deaton and Kahn Lessons Learned from Forensic FEA of Failed RC Structures

MotivationCase Studies of Forensic FEA

Conclusions

Parking Structure Shrinkage CrackingIndustrial Structure on Non-Uniform BearingPedestrian Bridge Collapse

Global Lateral Torsional Buckling Confirmed

Instability occurs when deck was placed over 2/3 of lengthBuckling mode shape matches observed failure modeIf only considered LC9 (full deck), limit state was identified

Deaton and Kahn Lessons Learned from Forensic FEA of Failed RC Structures

MotivationCase Studies of Forensic FEA

Conclusions

Conclusions

Linear elastic FEA points to failure modes not captured insimplified analysesStraightforward and inexpensive to generateCommonly ignored structural behaviors can be modeled:

ShrinkageNon-uniform bearing conditionsEvaluation of structural stabilityConstruction sequence

While approximate, analysis contributes significant value todesign and construction process.

Deaton and Kahn Lessons Learned from Forensic FEA of Failed RC Structures

MotivationCase Studies of Forensic FEA

Conclusions

Thank YouContact: http://bendeaton.me

Deaton and Kahn Lessons Learned from Forensic FEA of Failed RC Structures