Finite Element Modeling of Carbon Fiber-Reinforced Polymer Reinforced Concrete Beams under Elevated Temperatures by ProQuest


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									 ACI STRUCTURAL JOURNAL                                                                              TECHNICAL PAPER
Title no. 105-S64

Finite Element Modeling of Carbon Fiber-Reinforced Polymer
Reinforced Concrete Beams under Elevated Temperatures
by Muhammad Masood Rafi, Ali Nadjai, and Faris Ali

The paper presents details of a three-dimensional finite element       This is due to the fact that reliable methods to determine
(FE) model for the prediction of response of reinforced concrete       residual FRP properties at high temperatures are currently
(RC) beams under an elevated temperature regime. The beams             unavailable. Therefore, the prediction of response of FRP
were reinforced with either steel or fiber-reinforced polymer (FRP)    reinforced structures and validation of theoretical results
bars. Crack formation and propagation were modeled with the
                                                                       against the recorded data are not possible at present.
help of smeared cracks. Changes in the material properties of both
concrete and reinforcing bars at high temperatures have been              This paper presents the details of an FE model and
considered. Constitutive models for the temperature-dependent          compares the analytical and experimental beam behaviors at
material properties of carbon FRP (CFRP) bars and thermal              elevated temperatures. The beams were 120 x 200 mm (5 x 8 in.)
expansion coefficients for both concrete and steel have been           in cross section and were reinforced with carbon FRP
proposed. The effects of tension softening and stiffening have been    (CFRP) or steel bars. A typical midspan cross section of a
included in the model. Excellent convergence and numerical             beam is shown in Fig. 1. The total and span lengths of the
stability of the formulation was found. The models showed good         beam were 2000 and 1750 mm (6.67 and 5.83 ft), respectively.
agreement with the recorded data of temperature and beam               Concrete cover was 20 mm (3/4 in.). FRP bars consisted
strength and stiffness. Analytical concrete stress distribution is     of 9.5 mm (3/8 in.) diameter straight CFRP rods (ff u =
compared in steel and FRP reinforced beams and differences
                                                                       1676 MPa [243 ksi]; Ef = 135.9 GPa [20 × 103 ksi]). Steel bars
are discussed.
                                                                       were 10 mm (3/8 in.) diameter high-strength deformed bars (f y =
Keywords: finite element; modulus; smeared crack; stiffness; stress;
                                                                       530 MPa [77 ksi]; Es = 201 GPa [29 × 103 ksi]). Smooth 6 mm
thermal analysis.                                                      (1/4 in.) diameter closed rectangular stirrups spaced at 100 mm
                                                                       (4 in.) center-to-center were provided. The beams were
                     INTRODUCTION                                      tested simply supported at their ends under a four-point
  The advent of modern computing technology has allowed                static load. A load corresponding to 40% of ultimate
researchers and professionals to carry out in-depth analyses           capacity was applied at the load points that were 400 mm
of complex engineering problems with the help of sophisticated         (1.33 ft) apart. Midspan deflection was monitored using
techniques. The use of finite element modeling (FEM) in                linear variable differential transducers (LVDTs). These were
particular has made the analysis and design of reinforced              placed on the beam top on both sides of its longitudinal center.
concrete (RC) structures a relatively straightforward and              Complete details of the experimental beam testing and
routine exercise. Concrete is essentially a nonlinear material         results can be found in Rafi et al.7 Models for the prediction
and FEM has proved very successful to represent this                   of temperature-dependent material properties of CFRP bars
behavior and to quantify responses of an RC structure in               have been suggested in the study reported in this paper.
areas such as strain development, deflection, load-carrying
capacity, and stress distribution. Significant research has
been conducted to investigate various aspects of the behavior
of fiber-reinforced polymer (FRP) bar reinforced structures.
These efforts have been formulated into a set of design
guidelines.1-3 The research regarding fire resistance of FRP
RC, however, is lacking and further studies have been
suggested by the design codes.1 In particular, analytical
procedures that could accurately determine stress and strain
distribution, both in concrete and FRP bars, and could
provide reliable predictions of the behavior of an FRP-
reinforced structure at high temperatures are unavailable to
date. Among the most serious drawbacks to the development
of such analytical procedures is the lack of sufficient data
into the fire performance of FRP reinforced concrete.
  The study of the behavior of concrete structures at                  Fig. 1—Typical midspan section and positions of thermo-
elevated temperatures is of great practical importance and             couples.
has been a main area of research over the last 25 years. The
researchers have suggested analytical models in order to                 ACI Structural Journal, V. 105, No. 6, November-December 2008.
                                                                         MS No. S-2007-138 received April 17, 2007, and reviewed under Institute publication
study the behavior of steel RC structures under elevated               policies. Copyright © 2008, American Concrete Institute. All rights reserved, including the
temperature environments.4-6 Any such effort, however, has             making of copies unless 
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