deaton aci-fall2010
TRANSCRIPT
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