1. Nikhil Keshav Raut Michigan State University
A Numerical Model for Predicting the Fire Behavior of Circular Reinforced Concrete Columns
Nikhil Keshav Raut
Michigan State University

2. OUTLINE Problem introduction Research significance Literature review
Numerical model
Validation
Conclusions

3. PROBLEM INTRODUCTION Predicting fire behavior Reinforced concrete
Circular columns P

4. RESEARCH SIGNIFICANCE
Circular columns widely used
Simulating behavior under
realistic fire
Loading
Restraint
failure conditions
Parametric studies
Design guidelines

5. STATE-OF-THE-ART Limited fire tests on circular columns
No separate guidelines in codes – ACI 216.1
Standard fire exposure
Limited sample size

6. LEVELS OF MODELING Level of Analysis Conventional Methods
Macroscopic FEM
Microscopic FEM
Too complex
Results are difficult to interpret
No spalling models
Currently, lack of 3D material properties
Sectional analysis
Too simplistic
Not rational
Does not account for:
- spalling
- Failure criteria
- High temperature material properties
Sectional analysis used for predicting global response
Most factors can be incorporated
Simpler than microscopic FEM
Easy to interpret results
Computationally effective

7. NUMERICAL MODEL

8. DISCRETIZATION
segment

9. Fire Scenario Standard Fire Scenarios Realistic Fires
Effect of sprinklers can be incorporated
Standard Fires (ASTM E119 & ASTM 1529) incorporated
Two Design Fires Incorporated.
300
600
900
1200
1500 60
120
180
240
Time (min)
ASTM E119 fire
Hydrocarbon fire
Fire I
Fire II

10. Cross Sectional Details
THERMAL ANALYSIS
Heat Conduction Equation:
FEM is used to calculate the
temperature distribution in
the column cross section
Boundary Condition
Cross Sectional Details
Discritization

11. STRENGTH ANALYSIS Discritization (Thermal) Cross Sectional Details
Discritization (Structural)

12. M-K RELATIONSHIPS
P = Papplied P
segment

13. STRUCTURAL ANALYSIS Second order Nonlinear Structural Analysis
[F] = [K] [Δ]
where:
[K] = secant stiffness matrix,
EI (flexural rigidity) is calculated from the M-Ψ relationships generated earlier
Calculate strains from displacements.
Check failure
If not failed → Increment time
Repeat till failure occurs.
Compute deflections and internal moments at each time step. M  1 EI
Secant rigidity (EI) of a column segment

14. MATRIX FORMULATION From moment curvature relationship
segment
From moment curvature relationship M  1 EI
Secant rigidity (EI) of a column segment
secant stiffness matrix for a segment
Average axial stiffness from all elements
Where n = number of elements

15. VALIDATION Lie T.T. and Woolerton J.L. (1988) test column (III14)
48 mm
P = 1431 KN
3.8 m
fy = 414 MPa
f’c = 39.3 MPa
6  25 mm
356 mm dia
 10 mm stirrups
Cross Section
Elevation

16. VALIDATION – TEMPERATURE
Critical temperature limit for rebars = 593 C
Temperature (C)
Time (min)

17. VALIDATION – DEFLECTION
Axial Deformation (mm)
Time (min)

18. CASE STUDY
Temperature (C)
Time (min)

19. CONCLUSIONS Numerical models can be used to predict
behavior of circular columns
Design fires, loadings and various failure
criteria can be incorporated
Can be used for parametric studies to
develop design guidelines

20. THANK YOU