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Frontiers of Structural and Civil Engineering

Front. Struct. Civ. Eng.    2019, Vol. 13 Issue (1) : 81-91
Deflection behavior of a prestressed concrete beam reinforced with carbon fibers at elevated temperatures
Mohammed FARUQI(), Mohammed Sheroz KHAN
Department of Civil and Architectural Engineering, Texas A&M University—Kingsville, Texas, USA
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Fiber reinforced polymer(FRP) have unique advantages like high strength to weight ratio, excellent corrosion resistance, improving deformability and cost effectiveness. These advantages have gained wide acceptance in civil engineering applications. FRP tendons for prestressing applications are emerging as one of the most promising technologies in the civil engineering industry. However, the behavior of such members under the influence of elevated temperatures is still unknown. The knowledge and application of this could lead to a cost effective and practical considerations in fire safety design. Therefore, this study examines the deflection behavior of the carbon fiber reinforced polymer(CFRP) prestressed concrete beam at elevated temperatures. In this article, an analytical model is developed which integrates the temperature dependent changes of effective modulus of FRP in predicting the deflection behavior of CFRP prestressed concrete beams within the range of practical temperatures. This model is compared with a finite element mode (FEM) of a simply supported concrete beam prestressed with CFRP subjected to practical elevated temperatures. In addition, comparison is also made with an indirect reference to the real behavior of the material. The results of the model correlated reasonably with the finite element model and the real behavior. Finally, a practical application is provided.

Keywords FRP      CFRP      concrete      elevated temperatures      deflections      prestress     
Corresponding Authors: Mohammed FARUQI   
Online First Date: 09 April 2018    Issue Date: 04 January 2019
 Cite this article:   
Mohammed FARUQI,Mohammed Sheroz KHAN. Deflection behavior of a prestressed concrete beam reinforced with carbon fibers at elevated temperatures[J]. Front. Struct. Civ. Eng., 2019, 13(1): 81-91.
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Mohammed FARUQI
Mohammed Sheroz KHAN
Fig.1  Eccentricity and the prestress force
Fig.2  Beam geometry modeled in Solidworks. (a) front view; (b) isometric view
Fig.3  Tension reinforcements modeled in Solidworks. (a) front view; and (b) isometric view
Fig.4  Geometry of assembled beam modeled in Solidworks. (a) front view; and (b) isometric view
Material Density (kg/m3) Efrp (kN/mm2) ν
CFRP 1470 386.05 0.3
Concrete 2400 29.725 0.2
Tab.1  Material Properties
Fig.5  Modeled beam in ANSYS. (a) front view; and (b) isometric view
Fig.6  Meshing of the model beam. (a) front view; and (b) isometric view
Fig.7  Steady-state thermal analysis. (a) front view; and (b) isometric view
Fig.8  Static structural analysis
Fig.9  Deflection of the model beam simulated in ANSYS
Temperature (°C) Deflection (mm)
Analytical model Finite element model
200 30.72 34.50
250 34.56 38.59
275 38.80 43.18
300 42.69 44.24
325 50.47 47.94
350 59.30 52.25
Tab.2  Comparison of analytical and finite element model
Fig.10  Simply supported beam
Fig.11  Cross section and the area of the transformed section
Ap ,frp= Area of prestressed tension reinforcement
Ac= Area of concrete
b= Width of the beam
c1 = Distance of centroid from top surface
c2 = Distance of centroid from bottom surface
d= Depth of beam
de = Effective depth
dl= Change in length
dT= Change in temperature
e= Eccentricity
E= Modulus of elasticity
Ec= Young’s modulus of concrete
Ef = Young’s modulus of fiber
Em = Young’s modulus of matrix
Ef rp = Young’s modulus of FRP
Ep ,frp = Effective modulus of prestressed FRP system
Ep ,frp@ T°C = Young’s modulus of prestressed FRP composite at elevated temperatures
f1 = Concrete stresses at top surface
f2 = Concrete stresses at bottom surface
fc = Compressive strength of concrete
fp s = Stress in the prestressed system
fr = Modulus of rupture
I= Moment of inertia
Ic r = Cracking moment of inertia
Ie = Effective moment of inertia
Ig = Gross moment of inertia
Ks = Support conditions of the system
L= Span of the beam
l= Original length
M= Moment
Mo= Mid-span moment due to dead load
Ma = Applied moment
Mc r = Cracking moment
ML = Mid-span moment due to live load
P= Prestress force
Pe = Effective prestress force
Pi = Initial prestress force
r= Strength reduction factor due to elevated temperature
r2= Radius of gyration
RA = Reaction at support
RB = Reaction at support
S1 = Section modulus at top fiber
S2= Section modulus at bottom fiber
Tf rp = Temperature at which the deflecton is calculated
Vf = Volume fraction of fiber
Vm = Volume fraction of matrix
w= Uniformly distributed superimposed load
wL = Live load acting on the beam
wo = Dead load acting on the beam
W= Self weight of the beam
x= Distance of NA from top surface
yt = Distance from center of gravity of beam to extreme fibers
αc = CFRP expansion per degree temperature of variation
αf = Coefficient of thermal expansion of fiber
αm = Coefficient of thermal expansion of matrix
αL = Coefficient of thermal expansion of frp composite in longitudinal direction
Δa = Deflection from ANSY
ΔT = Deflection due to elevated temperature
η = Modular ratio
σ = Stress
? = Strain
?h = Strain in concrete due to shrinkage
φe t = Shrinkage curvature due to elevated temperatures
ϕ= Deflection constant
v= Poisson’s ratio
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