Theoretical Analysis and Design of Prestressed CFRP-Reinforced Steel Columns
Publication: Journal of Composites for Construction
Volume 26, Issue 3
Abstract
This paper theoretically analyzes the symmetrical global buckling behavior of imperfect prestressed carbon fiber-reinforced polymer (CFRP) laminate-reinforced steel columns (PCRSCs) with two hinged supports under axial and eccentric compression loadings. First, the causes of the buckling of the component are revealed; either the steel yields or the CFRP becomes slack. Therefore, four buckling cases are found, and a theoretical calculation method for the buckling capacity is established. On this basis, a theoretical calculation method for the optimal CFRP initial prestressing force and maximum buckling capacity is built from physical explanations. The results of the theoretical method fit well with the test and finite-element results. Finally, a design method of PCRSCs is proposed for engineering applications, followed by a design example, by which the optimal reinforcing efficiency is realized.
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Data Availability Statement
All data, models, and code generated or used during the study appear in the published article.
Acknowledgments
This research was supported by the National Key Research and Development Program of China (Grant No. 2019YFF0301503), the National Natural Science Foundation of China (Grant Nos. U2106219 and 52108227), the Institute for Guo Qiang, Tsinghua University (Grant No. 2019GQG1004), and the Shanghai Sailing Program (Grant No. 21YF1419500).
Notation
The following symbols are used in this paper:
- Aca
- cross-sectional area of the cross arm or prestressing chair;
- Ae
- half-length of the major axis of the ellipse;
- AP
- cross-sectional area of CFRP;
- As
- cross-sectional area of steel;
- a
- (final) supporting length;
- amax
- maximum supporting length considering space limitations;
- amix
- (final) supporting length that makes the symmetric and antisymmetric buckling capacities equivalent;
- a0
- initial supporting length;
- B
- bending stiffness of the steel column;
- Bca
- bending stiffness of the cross arm or prestressing chair;
- Be
- half-length of the minor axis of the ellipse;
- bca
- width of the prestressing chair;
- bP
- CFRP width;
- bs
- width of the I-section;
- bspace
- width for the space of the bolts and other components in the prestressing chair and anchorage;
- bx
- distance from the center of the CFRP to the center of the bolt in the prestressing chair;
- C11
- coefficient for calculating Pb;
- D
- quantity for calculating Pb;
- Eca
- elastic modulus of the cross arm or prestressing chair;
- EP
- elastic modulus of CFRP;
- Es
- elastic modulus of steel;
- e
- eccentricity of compressive external loading;
- f
- design strength of steel;
- fP
- CFRP strength;
- fy
- yield point of steel;
- hs
- height of the I-section;
- Ica
- moment of inertia of the cross arm or prestressing chair;
- IP
- moment of inertia of CFRP;
- Is
- moment of inertia of steel;
- Kca
- axial stiffness of the cross arm or prestressing chair;
- Kla
- spring stiffness;
- Kla,1
- spring stiffness before the concave-side CFRP becomes slack;
- Kla,2
- spring stiffness after the concave-side CFRP becomes slack;
- KP
- axial stiffness of the steel stay or CFRP;
- Ks
- axial stiffness of the steel column;
- k
- a coefficient affected by initial imperfection vom;
- L
- steel column length;
- La
- length of anchorage;
- Lp
- CFRP length;
- LP,0
- initial CFRP length;
- M
- sum of the external bending moments of the steel section;
- m
- average value;
- N
- additional vertical compression force;
- P
- external compression force;
- Pb
- buckling capacity;
- Pb,FEM
- buckling capacity according to the FEM;
- Pb,H
- buckling capacity of the ideal prestressed stayed column (Hafez et al. 1979);
- Pb,TH
- buckling capacity using the theory of this paper;
- Pb,TH,i
- buckling capacity calculated by Buckling case i in this paper (i = 0, 1, 2, and 3);
- Pb,max,d
- design value of Pb,max,TH, which is ϕcPb,max,TH;
- Pb,max,FEM
- maximum buckling capacity according to the FEM;
- Pb,max,TH
- maximum buckling capacity according to the theory of this paper;
- Pb,test
- buckling capacity from the test;
- PE
- Euler buckling load;
- Pmax
- maximum theoretical buckling capacity;
- Pn
- required compressive bearing capacity;
- Pt
- external force at the moment when both sides of the CFRPs become slack in the compressive deformation phase or at the moment when both sides of the CFRPs come under tension;
- R
- diameter of the thread bolt;
- r
- radius of the gyration of the steel section;
- S
- horizontal supporting force;
- Sl
- horizontal force provided by the CFRP on the left side;
- Sr
- horizontal force provided by the CFRP on the right side;
- Ti
- initial CFRP prestressing force;
- Tl
- left side initial CFRP prestressing force;
- Tmax,d
- maximum design prestressing force considering the CFRP strength and maximum prestressing force that can be achieved with no prestressing machine;
- Tmin,H
- minimum effective prestressing force (Hafez et al. 1979);
- Topt
- optimal initial CFRP prestressing force;
- Topt,FEM
- optimal initial CFRP prestressing force according to the FEM;
- Topt,H
- optimal initial CFRP prestressing force (Hafez et al. 1979);
- Topt,TH
- optimal initial CFRP prestressing force according to the theory of this paper;
- Tr
- right side initial CFRP prestressing force;
- T23b
- initial CFRP prestressing force corresponding to the boundary of Buckling cases 2 and 3;
- T23b,d
- design value of T23b;
- tca
- thickness of the prestressing chair;
- tP
- CFRP thickness;
- tsf
- thickness of the I-section steel flange;
- tsw
- thickness of the I-section steel web;
- vom
- initial imperfection at the midspan of the steel column after prestressing the CFRP;
- vom,0
- initial imperfection at the midspan of the steel column before prestressing the CFRP;
- Ws
- steel cross section modulus;
- α
- angle between the CFRP and the longitudinal axis of the steel column;
- α1, α2, α3
- coefficients for calculating φ;
- ΔTc
- reduction in the CFRP prestressing force caused by Δy;
- ΔTe
- change in the CFRP force caused by the lateral displacement Δx;
- Δx
- lateral displacement of the steel column;
- Δx,1
- midspan lateral displacement at the moment when both sides of the CFRPs become slack in the compressive deformation phase;
- Δx,2
- midspan lateral displacement at the moment when both sides of the CFRPs come under tension;
- Δx,M
- lateral deformation due to column end rotation caused by the bending moment under eccentric compression;
- Δx,y
- lateral deformation of the midspan generated by Δy;
- Δy
- axial displacement of the steel column;
- Δy,2
- axial displacement of the steel column at the moment when both sides of the CFRPs come under tension;
- Δy,c
- axial displacement generated by the axial compression of the material;
- Δy,x
- axial displacement of the end generated by Δx;
- η
- reduction factor;
- γ
- coefficient of the section plastic development;
- σ
- mean square error;
- λ
- slenderness of the pure steel column;
- λn
- regularized slenderness of the pure steel column;
- φ
- stability coefficient of the pure steel column;
- φs,TH
- stability coefficient of PCRSC according to the theory of this paper;
- φs,opt,TH
- optimal value of φs,TH; and
- ϕc
- reduction factor in design.
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History
Received: Sep 27, 2021
Accepted: Jan 10, 2022
Published online: Mar 28, 2022
Published in print: Jun 1, 2022
Discussion open until: Aug 28, 2022
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