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

OUTLINE Problem introduction Research significance Literature review Numerical model Validation Conclusions

PROBLEM INTRODUCTION Predicting fire behavior Reinforced concrete Circular columns P

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

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

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

NUMERICAL MODEL

DISCRETIZATION segment

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

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

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

M-K RELATIONSHIPS P = Papplied P segment

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

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

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

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

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

CASE STUDY Temperature (C) Time (min)

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

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