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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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