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Deaton aci-fall2010

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Deaton aci-fall2010

  1. 1. Motivation Case Studies of Forensic FEA Conclusions Lessons Learned from Forensic FEA of Failed RC Structures James B. Deaton Lawrence F. Kahn Department of Civil and Environmental Engineering Georgia Institute of Technology ACI Fall Convention – October 25, 2010 Deaton and Kahn Lessons Learned from Forensic FEA of Failed RC Structures
  2. 2. Motivation Case Studies of Forensic FEA Conclusions Motivation – Tools for Structural Analysis Problem Statement Structural failure continues to be a reality because critical limit states are often undetected by engineering analysis. Nonlinear Finite Element Analysis State-of-the-art: Concrete compression crushing, tensile cracking, tension stiffening, steel reinforcement plasticity, steel-concrete bond-slip, geometric nonlinearity, etc. Powerful tool but expensive, time-consuming, and largely unavailable for practicing engineers Deaton and Kahn Lessons Learned from Forensic FEA of Failed RC Structures
  3. 3. Motivation Case Studies of Forensic FEA Conclusions Motivation – Tools for Structural Analysis Linear Elastic Finite Element Analysis Available to every practicing engineer CANNOT describe distribution of force, stress, & displacements at ultimate limit state ... but CAN indicate existence of serious problems Goal of Presentation Demonstrate key practical techniques: 3 case studies of real structural failure Evaluation using linear elastic FEA Features common to all structural engineering software Demonstration of failure to meet key performance criteria Deaton and Kahn Lessons Learned from Forensic FEA of Failed RC Structures
  4. 4. Motivation Case Studies of Forensic FEA Conclusions Parking Structure Shrinkage Cracking Industrial Structure on Non-Uniform Bearing Pedestrian 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
  5. 5. Motivation Case Studies of Forensic FEA Conclusions Parking Structure Shrinkage Cracking Industrial Structure on Non-Uniform Bearing Pedestrian Bridge Collapse Overview of Parking Structure Serviceability Failure 3-story parking deck, 95 meters × 20 meters Extensive early-age cracking of slabs Probable 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
  6. 6. Motivation Case Studies of Forensic FEA Conclusions Parking Structure Shrinkage Cracking Industrial Structure on Non-Uniform Bearing Pedestrian Bridge Collapse Parking Structure Finite Element Model Details Model consisted of ∼24,000 shell elements Loads: Gravity, temperature, shrinkage Graphics of Model Entire Parking Structure: View from North-West Entire Parking Structure: View from North-EastDeaton and Kahn Lessons Learned from Forensic FEA of Failed RC Structures
  7. 7. Motivation Case Studies of Forensic FEA Conclusions Parking Structure Shrinkage Cracking Industrial Structure on Non-Uniform Bearing Pedestrian Bridge Collapse Application of Shrinkage via Temperature Load ∆Tsh = sh α sh = specified shrinkage strain α = coeff. of thermal expansion For sh = 0.0005in in 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 Deaton and Kahn Lessons Learned from Forensic FEA of Failed RC Structures
  8. 8. Motivation Case Studies of Forensic FEA Conclusions Parking Structure Shrinkage Cracking Industrial Structure on Non-Uniform Bearing Pedestrian 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
  9. 9. Motivation Case Studies of Forensic FEA Conclusions Parking Structure Shrinkage Cracking Industrial Structure on Non-Uniform Bearing Pedestrian Bridge Collapse Parking Structure Shrinkage Analysis Conclusions Shrinkage easily incorporated via temperature load in FEA Shrinkage analysis would have suggested: A spacing of expansion joints at 30 meters (vs. 95 meters) Construction sequence that would have reduced restraint Shrinkage 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
  10. 10. Motivation Case Studies of Forensic FEA Conclusions Parking Structure Shrinkage Cracking Industrial Structure on Non-Uniform Bearing Pedestrian 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
  11. 11. Motivation Case Studies of Forensic FEA Conclusions Parking Structure Shrinkage Cracking Industrial Structure on Non-Uniform Bearing Pedestrian Bridge Collapse Overview of Tall Industrial Structure Cylindrical industrial structure on mat foundation Superstructure: 550-ft tall; Mat: 100-ft wide and 8-ft thick Significant displacements occurred during construction Presence of non-uniform geological structure below mat: Superstructure Mat foundation Rock Soil Deaton and Kahn Lessons Learned from Forensic FEA of Failed RC Structures
  12. 12. Motivation Case Studies of Forensic FEA Conclusions Parking Structure Shrinkage Cracking Industrial Structure on Non-Uniform Bearing Pedestrian Bridge Collapse Model Characteristics ∼38,000 shell elements Loads: Gravity, Wind, Seismic P-δ effects neglected Compression-only springs to simulate support Subgrade condition, compare: Uniform subgrade modulus (neglect rock profile) Variable subgrade modulus Deaton and Kahn Lessons Learned from Forensic FEA of Failed RC Structures
  13. 13. Motivation Case Studies of Forensic FEA Conclusions Parking Structure Shrinkage Cracking Industrial Structure on Non-Uniform Bearing Pedestrian Bridge Collapse Response Increase: Uniform vs. Variable Subgrade Response Gravity+Wind Tip Lateral Displacement ∼73% increase Foundation Settlement Displacement ∼46% increase Area of steel required by Wood & Armer ∼58% increase Shear force through foundation section ∼395% increase Deaton and Kahn Lessons Learned from Forensic FEA of Failed RC Structures
  14. 14. Motivation Case Studies of Forensic FEA Conclusions Parking Structure Shrinkage Cracking Industrial Structure on Non-Uniform Bearing Pedestrian Bridge Collapse Vertical Displacements in Mat Foundation Gravity Alone Max uplift: 0.15 in. Max settlement: 1.91 in. Gravity + Wind Max uplift: 1.80 in. Max settlement: 3.74 in. Deaton and Kahn Lessons Learned from Forensic FEA of Failed RC Structures
  15. 15. Motivation Case Studies of Forensic FEA Conclusions Parking Structure Shrinkage Cracking Industrial Structure on Non-Uniform Bearing Pedestrian Bridge Collapse Lateral Displacement at Top of Structure Max Lateral Displacement Gravity: 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
  16. 16. Motivation Case Studies of Forensic FEA Conclusions Parking Structure Shrinkage Cracking Industrial Structure on Non-Uniform Bearing Pedestrian Bridge Collapse Pedestrian Bridge Collapse Case Study # 3: Pedestrian Bridge Collapse Deaton and Kahn Lessons Learned from Forensic FEA of Failed RC Structures
  17. 17. Motivation Case Studies of Forensic FEA Conclusions Parking Structure Shrinkage Cracking Industrial Structure on Non-Uniform Bearing Pedestrian Bridge Collapse Pedestrian Bridge Collapse Bridge collapse during placement of concrete deck in 2002 52 meter long, single steel tub girder bridge Failure mode: global lateral torsional buckling FEA conducted for Dr. Donald White at Georgia Tech mm thick, and are located throughout the length of the girder at the same locations as all K-diaph 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 so the exception of a 0.5 m2 (5.27 ft2 ) square ventilation opening located in the center of the diaphra Vertical bearing stiffeners are provided on each side of this ventilation opening, and are welded t the interior and exterior sides of the end diaphragm. Each bearing stiffener has the cross-sectiona dimensions of 175mm x 14mm. A transverse flange of dimensions 250mm x 14 mm is provided the top of each end diaphragm. The bridge was supported on both ends by elastomeric bearings. The North end is fixed both transverse and longitudinal translation, while the South end is an expansion elastomeric bea which restrains transverse displacement but allows for slight longitudinal translation by way of a 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 0.7 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 34 which corresponds to a yield stress, fy, of 50 ksi. The Young’s modulus of the steel was taken to 29000 ksi. The concrete is specified to have a compressive strength, fc’, 21 MPa, or 3000 psi, an assumed to be normal weight concrete with a density of 150 pcf. Figure 2: General Cross-SectionalGeometry of the Marcy Pedestrian Bridge Deaton and Kahn Lessons Learned from Forensic FEA of Failed RC Structures
  18. 18. Motivation Case Studies of Forensic FEA Conclusions Parking Structure Shrinkage Cracking Industrial Structure on Non-Uniform Bearing Pedestrian Bridge Collapse Pedestrian Bridge Finite Element Model Use FEA to investigate stability of structure Model details: ∼22,000 elements Assume weight (but not stiffness) of concrete Deaton and Kahn Lessons Learned from Forensic FEA of Failed RC Structures
  19. 19. Motivation Case Studies of Forensic FEA Conclusions Parking Structure Shrinkage Cracking Industrial Structure on Non-Uniform Bearing Pedestrian Bridge Collapse Stability During Placement of Deck Concrete Goal: Determine when placement of deck causes instability For each load combination SW Steel + LC1−LC9, perform elastic stability analysis & compute buckling load multiplier. SW Steel Slab LC1 Slab LC2 Slab LC3 Slab LC4 Slab LC5 Slab LC6 Slab LC7 Slab LC8 Slab 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/Pcr P/Pcr = 1.0 LC2 LC3 LC4 LC5 LC6 LC7 LC8 LC9 ~68% of concrete deck placed Deaton and Kahn Lessons Learned from Forensic FEA of Failed RC Structures
  20. 20. Motivation Case Studies of Forensic FEA Conclusions Parking Structure Shrinkage Cracking Industrial Structure on Non-Uniform Bearing Pedestrian Bridge Collapse Global Lateral Torsional Buckling Confirmed Instability occurs when deck was placed over 2/3 of length Buckling mode shape matches observed failure mode If only considered LC9 (full deck), limit state was identified Deaton and Kahn Lessons Learned from Forensic FEA of Failed RC Structures
  21. 21. Motivation Case Studies of Forensic FEA Conclusions Conclusions Linear elastic FEA points to failure modes not captured in simplified analyses Straightforward and inexpensive to generate Commonly ignored structural behaviors can be modeled: Shrinkage Non-uniform bearing conditions Evaluation of structural stability Construction sequence While approximate, analysis contributes significant value to design and construction process. Deaton and Kahn Lessons Learned from Forensic FEA of Failed RC Structures
  22. 22. Motivation Case Studies of Forensic FEA Conclusions Thank You Contact: http://bendeaton.me Deaton and Kahn Lessons Learned from Forensic FEA of Failed RC Structures

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