Technical Papers
Sep 18, 2024

Design-Oriented Model of Unified Character to Determine Softening–Hardening Stress–Strain Behavior of FRP-Confined Concrete Columns of General Cross Section

Publication: Journal of Composites for Construction
Volume 28, Issue 6

Abstract

Even though many experimental studies have evidenced that fiber-reinforced polymer (FRP)-confined concrete columns under compression might exhibit a postpeak strain-softening response, followed by a hardening behavior (a stress reduction–recovery response), most existing models are only applicable to confined columns developing full hardening behavior. Additionally, their applicability is limited to a certain column cross-sectional shape (circular or noncircular). Therefore, the present study is dedicated to the establishment of a new design-oriented stress–strain model, unified for FRP-confined circular/noncircular concrete columns. For this purpose, first, a new nondimensional confinement stiffness-based index is developed, below which the column response is transformed from a full-hardening behavior (Type A) to a postpeak strain softening–hardening one (Type B). A parabolic-linear stress–strain formulation is proposed for Type A columns by developing a new expression for the calculation of the linear hardening branch’s slope. For the case of Type B, a new methodology is introduced for the simulation of the stress reduction–recovery response beyond the transition zone, whose main elements are calibrated by a large test data set. The dominance degree of the noncircularity effect of the cross section on both Type A and Type B cases was assessed and reflected in the key components of the proposed stress–strain models, based on nonlinear regression analysis. With these considerations, this model could accurately simulate the impact of the noncircularity effect on the stress–strain relationship of Type A and Type B columns, whose predictive performance is validated through a comparative assessment with existing models based on large test stress–strain results.

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Data Availability Statement

All data, models, and codes generated or used during the study appear in the published paper.

Acknowledgments

This study is a part of the project “Sticker—Innovative technique for the structural strengthening based on using CFRP laminates with multifunctional attributes and applied with advanced cement adhesives,” with the reference POCI-01-0247-FEDER-039755. The first author also acknowledges the support provided by the CAIXILHARIA MINIMALISTA project with the reference of “FELLOW_BI/I&D/PIEP/01-2023/2023.” This work was partly financed by FCT/MCTES through national funds (PIDDAC) under the R&D Unit of the Institute for Sustainability and Innovation in Structural Engineering (ISISE), under reference UIDB/04029/2020, and under the Associate Laboratory Advanced Production and Intelligent Systems ARISE under reference LA/P/0112/2020.

Notation

The following symbols are used in this paper:
Ag
total area of a noncircular cross-sectional column;
b
column’s cross-sectional dimension;
deq
diameter of equivalent circular column;
E2
slope of the linear second portion;
E2,0
slope of the softening branch of unconfined concrete;
Ectr
concrete modulus at the transition zone;
Ef
FRP modulus elasticity;
fc
axial stress corresponding to εc;
fc0
compressive strength of unconfined concrete;
fctr
stress at the transition zone;
fci
inflection stress;
fcu
ultimate axial stress;
fc,res
residual stress;
fcII
axial stress at the second stage;
fcIII
axial stress at the third stage;
fc
compressive strength of the standard cylinder;
fl,tr,eq
FRP confinement pressure at the transition stage;
fl,rup
confinement pressure at FRP rupture;
h
longer side of the section;
KL
FRP confinement stiffness;
KL
FRP confinement rigidity threshold;
keff
confinement efficiency factor;
L
column height;
nf
number of FRP layers;
nd1
degree of the polynomial function;
nd2
degree of the parabolic function;
RI
confinement stiffness-based threshold;
Rr
corner radius ratio as 2 r/b;
Rsar
cross-sectional aspect ratio as h/b;
r
corner radius;
tf
nominal thickness of an FRP layer;
α1
polynomial coefficients;
α2
polynomial coefficients;
α3
polynomial coefficients;
αb
calibration factor;
αr
calibration factor;
αsar
calibration factor;
ηε
calibration factor;
η1
calibration factor;
η2
calibration factor;
λ1
term considering stress loss beyond εctr;
λ2
term considering stress recovery portion;
εc
axial strain corresponding to fc;
εc0
axial strain corresponding to fc0;
εci
axial strain at the inflection point;
εci0
axial strain at the inflection point;
εctr
strain at the transition zone;
εcu
ultimate axial strain;
εh,rup
rupture strain of FRP jacket;
ξ1,r
calibration factor;
ξ2,sar
calibration factor;
ξE,r
calibration factor;
ξE,sar
calibration factor;
ξr
calibration factor;
ξε,r
calibration factor;
ξε,sar
calibration factor;
ρK
FRP confinement stiffness index;
ρK
confinement stiffness threshold;
ψf
reduction factor;
ψK
reduction factor; and
ψr
reduction factor.

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Go to Journal of Composites for Construction
Journal of Composites for Construction
Volume 28Issue 6December 2024

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Received: Feb 6, 2024
Accepted: Jul 17, 2024
Published online: Sep 18, 2024
Published in print: Dec 1, 2024
Discussion open until: Feb 18, 2025

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ISISE, IBS, Dept. of Civil Engineering, Univ. of Minho, Azurém, Guimarães 4800-058, Portugal (corresponding author). ORCID: https://orcid.org/0000-0002-8331-2434. Email: [email protected]
Full Professor, ISISE, IBS, Dept. of Civil Engineering, Univ. of Minho, Azurém, Guimarães 4800-058, Portugal. ORCID: https://orcid.org/0000-0003-1528-757X. Email: [email protected]

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