on the use of the ec3 and aisi specifications to estimate the ultimate load of cfrp-strengthened...

ARTICLE IN PRESS

Thin-Walled Structures 47 (2009) 1102–1111

Contents lists available at ScienceDirect

Thin-Walled Structures

0263-82

doi:10.1

� Corr

E-m

journal homepage: www.elsevier.com/locate/tws

On the use of the EC3 and AISI specifications to estimate the ultimate load ofCFRP-strengthened cold-formed steel lipped channel columns

Nuno Silvestre a, Dinar Camotim a,�, Ben Young b

a Department of Civil Engineering and Architecture, IST/ICIST, Technical University of Lisbon, Portugalb Department of Civil Engineering, The University of Hong Kong, Hong Kong

a r t i c l e i n f o

Available online 25 December 2008

Keywords:

Cold-formed steel columns

CFRP-strengthening

Local buckling

Distortional buckling

Flexural–torsional buckling

Ultimate strength

Design approach

31/$ - see front matter & 2008 Elsevier Ltd. A

016/j.tws.2008.10.013

esponding author. Fax: +351218497650.

ail address: [email protected] (D. Cam

a b s t r a c t

This paper summarises an investigation carried out to predict the structural behaviour of CFRP-

strengthened cold-formed steel lipped channel columns�more specifically, it addresses the applic-

ability of the provisions of Eurocode 3 (EC3) and the AISI Specification (AISI-DSM, direct strength

method), both developed for cold-formed steel members, to estimate their load-carrying capacity. It is

worth noting that EC3 and AISI-DSM adopt different approaches to perform this task: while the former

is based on the ‘‘effective width’’ concept, the latter may adopt the ‘‘Direct Strength Method’’. First, the

most relevant aspects related to the experimental and numerical investigations carried out to obtain

‘‘exact’’ column collapse loads are briefly presented. Then, an extensive numerical study is performed,

which is intended to evaluate the benefits of CFRP-strengthening for different CFRP ply configurations,

number of CFRP plies and steel yield stresses. After proposing different methodologies to extend the

application of the EC3 and AISI-DSM design provisions to CFRP-strengthened cold-formed steel

columns, the estimates provided by them are compared with the experimental values. On the basis of

these comparisons, some concluding remarks are drawn concerning the merits and shortcomings of

extending the domain of application of the current EC3 and AISI-DSM design approaches, so that they

may cover also CFRP-strengthened lipped channel columns.

& 2008 Elsevier Ltd. All rights reserved.

1. Introduction

Carbon fibre reinforced plastic (CFRP) composite materialshave been increasingly employed in the construction industry,mainly in applications dealing with structural strengthening andrepair [1]. They are ideally suited for this purpose, due to acombination of (i) very high stiffness-to-weight and strength-to-weight ratios and (ii) an excellent durability in aggressiveenvironments. Indeed, it has been shown, both analytically andexperimentally, that the addition of externally bonded FRPcomposites significantly improves the performance of a structuralmember, namely its stiffness, load-carrying capacity, durabilityand fatigue behaviour under cyclic loadings. In the last few years,several investigations (both experimental and numerical) werecarried out to evaluate the benefits of CFRP-strengthening steelstructures [2–18] — very recently, an interesting and comprehen-sive state-of-the-art review of FRP-strengthening of steel struc-tures was published by Zhao and Zhang [19]. As far as strength isconcerned, the failure of CFRP-strengthened cold-formed steelmembers may stem from (i) local, distortional or global buckling

ll rights reserved.

otim).

of the steel-CFRP member, (ii) rupture or debonding of the CFRPsheets or (iii) a combination of both. Thus, a rational (safe andeconomical) design of CFRP-strengthened cold-formed steelmembers must be preceded by studies addressing all the abovepotential failure mechanisms.

Previous experimental and numerical investigations carriedout by the authors [20–22] made it possible to assess the load-carrying capacity of several cold-formed steel lipped channelcolumns strengthened by means of sheets made of carbon fibrereinforced polymers (CFRP-strengthened columns). Short and longfixed cold-formed lipped channel columns were tested — thespecimens were (i) brake-pressed from high strength steel sheetswith nominal yield stresses equal to 450 and 550 MPa and (ii)strengthened by means of carbon fibre sheets (CFRPS) glued atdifferent locations of the member outer surfaces (web, flanges orlips) and having either longitudinally or transversally orientedfibres. The results obtained from the experimental programconsisted of non-linear equilibrium paths (applied load vs. axialshortening) and ultimate load values. Since most column failuresstemmed from local-plate and/or distortional buckling effects, theexperimental results were used to validate numerical analysesbased on a shell finite element model, carried out in the codeABAQUS [23] and adopting a linear-elastic/perfectly-plastic consti-tutive law to describe the steel material behaviour.

www.sciencedirect.com/science/journal/twst

www.elsevier.com/locate/tws

dx.doi.org/10.1016/j.tws.2008.10.013

mailto:[email protected]

ARTICLE IN PRESS

Nomenclature

As, Ac gross section steel and CFRPS areasbeff wall effective widthbw, bf, bl web, flange and lip widthsd1, d2, e0 local, distortional and global imperfection amplitudesE, n Young’s modulus and Poisson’s ratiof1 elastic stress at the CFRPS when the steel yieldsfy steel yield stressfc CFRPS ultimate stressL column lengthP1 first yield loadPExp, Pu experimental and numerical ultimate loadsPE critical global buckling loadPL, PD, PFT local, distortional and flexural–torsional buckling

loadsPnL, PnD, PnE nominal strengths for the local/global, distortional

and global failures

Pu.ap ultimate load estimatePy squash loadts, tc,, t steel sheet, CFRPS and wall (t ¼ tc+ts) thickness values(–)S, (–)L related to short and long columns(–)s, (–)c, (–)r related to the steel sheet, CFRPS and resinw global buckling reduction factorwd distortional buckling reduction factoref elongation after fracturely cross-section strain when the steel yieldsl global slendernessld distortional slendernesslp wall (local) slendernessr wall effective width reduction factors0.2 0.2% proof stresssL wall local buckling stresssD cross-section distortional buckling stresssu ultimate tensile stress

N. Silvestre et al. / Thin-Walled Structures 47 (2009) 1102–1111 1103

The main objective of this work is to assess whether theprovisions of Eurocode 3 Part 1.3 [24–26] and the AISI Specifica-tion [27,28], which were developed specifically for cold-formedsteel member design, can also be used to estimate the ultimatestrength of the above CFRP-strengthened cold-formed steel lippedchannel columns. Note that EC3 and AISI adopt differentapproaches to perform this task: while the EC3 provisions arebased on the ‘‘effective width’’ concept, the AISI-DSM, directstrength method ones involve the application of the ‘‘DirectStrength Method’’ [29]. In particular, the authors propose amethodology to extend the domain of application of theseprovisions to cover CFRP-strengthened cold-formed steel lippedchannel columns, which is subsequently validated and calibratedthrough comparisons between EC3/AISI ultimate load estimatesand experimental values. On the basis of these comparisons, itbecomes possible to draw some relevant conclusions concerningthe merits and shortcomings of this novel (extended) use the twocurrent EC3 and AISI-DSM design approaches.

2. Overview of previous experimental and numericalinvestigations

The authors have recently carried out experimental andnumerical investigations on the load-carrying capacity of CFRP-strengthened cold-formed steel lipped channel columns, whichhave already been reported [20–22] and will be overviewed in thissection. The tests were conducted on fixed-ended cold-formedsteel lipped channel columns strengthened by means of CFRPSglued to their outer surfaces (web, flanges and/or lips) and withthe fibres oriented either longitudinally or transversally — forreference purposes, a few bare steel columns were also tested. Thespecimens were brake-pressed from high strength zinc-coatedgrades G450 and G550 structural steel sheets (i) with nominal0.2% proof (yield) stresses equal to 450 and 550 MPa and (ii)conforming to the Australian Standard AS 1397 [30]. All thecolumn specimens had nominal web width bw ¼ 125 mm, flangewidth bf ¼ 102 mm and lip width bl ¼ 14 mm and the testprogram comprised two test series: (i) one involving 9 shortcolumns (L ¼ 600 mm) made of G550 steel sheets with nominalthicknesses ts ¼ 1.0 mm and (ii) the other consisting of 10 longercolumns (L ¼ 2200 mm) made of G450 steel sheets with nominalthicknesses ts ¼ 1.5 mm. The specimen labelling provides infor-mation about the test series and the location and orientation ofthe CFRPS: (i) the first letter states whether the specimen belongs

to the short (S) or long (L) column test series, (ii) the followingletters indicate if the specimen has no strengthening (NIL), CFRPSlocated in the web (W), CFRPS located in the web and flanges (WF)or CFRPS located in the web, flanges and lips (WFL), and (iii) thenumbers specify whether the CFRPS are oriented longitudinally(0) or transversally (90). Finally, the letter ‘‘R’’ identifies a repeatedtest.

The material properties of the cold-formed steel columns wereobtained through tensile coupon tests — the measured values aregiven next, for the short and long columns (nominal 0.2% proofstresses s0.2.S ¼ 550 MPa and s0.2.L ¼ 450 MPa): (i) static 0.2%proof stresses s0.2.S ¼ 610 MPa and s0.2.L ¼ 521 MPa, (ii) Young’smoduli ES ¼ 207 GPa and EL ¼ 218 GPa, (iii) static tensile strengthssu.S ¼ 626 MPa and su.L ¼ 546 MPa and (iv) elongations afterfracture ef.S ¼ 9.2% and ef.L ¼ 11.4%. As for the CFRPS thickness andmaterial properties, the values provided by the fabricators wereadopted: (i) thickness tc ¼ 0.11 mm, (ii) tensile strengthsu.c ¼ 4200 MPa, (iii) tensile modulus Ec ¼ 235 GPa and (iv)elongation after fracture ef.c ¼ 1.8%. Moreover, the (single) CFRPSwere attached to the outer surfaces of the zinc-coated cold-formed steel columns by means of an epoxy resin with tensilestrength and modulus equal to su.r ¼ 30 MPa and Er ¼ 3.5 GPa —

after attaching the CFRPS, the specimens were completely curedfor a period of seven days.

All the experimental ultimate strength values (PExp) obtained,concerning the short (S1) and long (L1) specimens with andwithout CFRPS strengthening, are given in Tables 1 and 2. Itshould be noted that all (short and long) column failures were dueto the distortional buckling or local-plate/distortional interactivebuckling. Then, the excessive column wall deformations,caused by the buckling-triggered collapse, also originate theoccurrence of CFRPS debonding in the post-failure stages. Inorder to assess the reliability of the experimental set-up andprocedure, three tests were repeated — the differences betweenthe ultimate strengths determined for each pair of (supposedly)identical specimens were 1.3% (S1-WF-90), 1.8% (L1-NIL) and 1.7%(L1-WFL-0). More detailed information about the test programcarried out can be found in Refs. [20,22].

The finite element code ABAQUS [23] was used to simulate thenon-linear behaviour and estimate the load-carrying capacity ofthe cold-formed steel lipped channel columns with and withoutCFRPS strengthening. All columns were discretised into finemeshes of S4R shell finite elements (four-node elements withreduced integration) and the rounded corners were not taken intoaccount in the modelling. In order to simulate the column fixed

ARTICLE IN PRESS

Table 2Buckling and experimental/numerical ultimate loads of the long columns L1.

Column Experimental-P (kN) Numerical-P (kN) Pu/PExp

PExp Gain (%) PD Gain (%) PL Gain (%) Pu Gain (%)

L1-NIL 85.2 – 84.4 – 84.5 – 89.0 – 1.045

L1-NIL-R 86.7 1.8 1.027

L1-F-0 90.1 5.8 84.7 0.4 87.8 3.9 91.8 3.2 1.019

L1-W-0 95.5 12.1 86.5 2.5 85.6 1.3 94.3 6.0 0.987

L1-WF-0 98.6 15.7 86.7 2.7 88.9 5.2 98.4 10.6 0.998

L1-WFL-0 102.1 19.8 88.3 4.6 89.3 5.7 102.5 15.2 1.004

L1-WFL-0-R 100.4 17.8 1.021

L1-F-90 92.6 8.7 85.5 1.3 86.9 2.8 93.7 5.3 1.012

L1-W-90 88.1 3.4 89.0 5.5 87.2 3.2 93.5 5.1 1.061

L1-WF-90 100.9 18.4 90.3 7.0 89.6 6.0 99.8 12.1 0.989

L1-WFL-90 – – 90.5 7.2 89.7 6.2 107.0 20.2 –

Mean 1.016

Standard Deviation 0.024

Table 1Buckling and experimental/numerical ultimate loads of the short columns S1.

Column Experimental-P (kN) Numerical–P (kN)a Pu/PExp

PExp Gain (%) PL Gain (%) Pu Gain (%)

S1-NIL 54.9 – 26.8 – 55.9 – 1.018

S1-F-0 56.0 2.0 28.5 6.3 57.4 2.7 1.025

S1-W-0 55.9 1.8 27.6 3.0 57.3 2.5 1.025

S1-WF-0 60.2 9.7 29.2 9.0 62.8 12.3 1.043

S1-WFL-0 61.4 11.8 29.5 10.1 63.4 13.4 1.026

S1-F-90 56.4 2.7 27.9 4.1 56.8 1.6 1.007

S1-W-90 55.6 1.3 28.0 4.5 56.3 0.7 1.013

S1-WF-90 63.2 15.1 29.3 9.3 61.4 9.8 0.972

S1-WF-90-R 62.4 13.7 0.984

S1-WFL-90 – – 29.4 9.7 62.3 11.5 –

Mean 1.012

Standard Deviation 0.022

a The distortional buckling loads of the short columns are PDE130 kN.

N. Silvestre et al. / Thin-Walled Structures 47 (2009) 1102–11111104

support conditions, rigid plates (modelled by means of three-noderigid elements R3D3) were attached to the column end sectionsand their centroidal translations and rotations were prevented —

only the axial translation of one end section was left free, in orderto enable the application of the compressive load. The short andlong column meshes involved 15�10 mm2 (length–width) and30�10 mm2 finite elements, which correspond to (i) 1462 and2250 elements, (ii) 1505 and 2625 nodes, and (iii) 8622 and15,342 degrees of freedom, respectively. Moreover, the numericalanalyses were based on (i) the mean measured values of the cross-section dimensions (ii) the nominal lengths L ¼ 600 mm and2200 mm, (iii) the nominal steel elastic constants and yieldstresses, and (iv) the CFRPS material properties provided by thefabricators. The CFRPS-strengthened walls were modelled asdouble-ply plates: one steel plate and one CFRPS ply. Initially,column bifurcation analyses to evaluate the buckling loads andidentify the corresponding buckling modes. These analysesshowed that (i) the short columns buckle in five half-wave localmodes and (ii) the long columns buckle in three half-wavedistortional modes. These ABAQUS buckling analyses provided thebuckling load values given in Table 1 — PL and PD, for local anddistortional buckling.

The initial geometrical imperfections were incorporated inthe post-buckling analysis through the a priori definition of

a linear combination of normalised buckling mode shapes.Since no column initial geometric imperfections were measured,the criterion adopted to select the appropriate imperfection toinclude in a particular test simulation was the ‘‘closeness’’between the initial portions of the experimental and numericalequilibrium paths P(u). The imperfection amplitudes yielded bythis approach were found to agree fairly well with the onesobtained by adopting the methodology proposed by Schafer andPekoz [31]. For long columns (L1), local and distortionalimperfection amplitudes similar to d1 ¼ 0.66ts (type 1) andd2 ¼ 1.55ts (type 2) were included in the analyses — thesevalues correspond to a cumulative distribution functionP(Dod) ¼ 0.75. For short columns (S1), local-plate imperfectionamplitudes similar to d1 ¼ 1.98ts (type 1) were mainly considered— this value is associated with P(Dod) ¼ 0.96. In order toreproduce the experimental procedure as closely as possible,the following measures were taken: (i) the non-linear numericalanalyses were carried out by means of an incremental–iterative procedure with an arc-length control strategy, (ii) axialdisplacements were imposed at the column free end sectionand (iii) the applied load was deemed equal to the reactiveforce at the other (fixed) column end section. More detailedinformation about these numerical analyses was reported inRefs. [21,22].

ARTICLE IN PRESS


All the numerical ultimate strength values (Pu) obtained,concerning the short (S1) and long (L1) specimens with andwithout CFRPS strengthening, are given in Tables 1 and 2. Theobservation of these experimental and numerical results promptsthe following remarks:

(i)

TablColu

S2-N

S2-F

S2-W

S2-W

S2-W

S2-F

S2-W

S2-W

S2-W

TablColu

S2-N

S2-F

S2-W

S2-W

S2-W

In both the short and long columns, the ultimate loadincreases due to CFRP-strengthening and detected by thenumerical analyses are quite similar to those found in thecourse of the experimental investigation — Tables 1 and 2make it possible to quantify this similarity.

(ii)
The numerical ultimate load values (Pu) compare fairly wellwith the experimental ones (PExp). Indeed, the mean andstandard deviation values of the Pu/PExp ratio read 1.012 and0.022 (short columns) and 1.016 and 0.024 (long columns) —
moreover, the maximum differences are 4.3% (short columns)and 6.1% (long columns). These facts illustrate the accuracy ofthe proposed numerical model, which was used to performthe parametric study presented in the next section.

3. Parametric study

In addition to columns S1 and L1, let us now use the validatedfinite element numerical model to perform a set of buckling andpost-buckling analyses of additional CFRP-strengthened lippedchannel cold-formed steel columns with several cross-sectiongeometries, steel yield stresses and CFRP-strengthening config-urations. In order to analyse the influence of CFRP-strengtheningon the load-carrying capacity of columns failing in local,distortional and global buckling modes, three different columnfamilies were investigated — their geometries are defined by:

(i)

em

-

-

em

-

S2: bw ¼ 100 mm, bf ¼ 50 mm, bl ¼ 10 mm, ts ¼ 1 mm,L ¼ 600 mm (short columns).

(ii)
L2: bw ¼ 100 mm, bf ¼ 100 mm, bl ¼ 10 mm, ts ¼ 2 mm,L ¼ 1800 mm (long columns).
3n S2 buckling and ultimate loads, for fy ¼ 250 and 550 MPa (1 CFRPS).

PL (kN) Gain (%) fy ¼ 250 MPa fy ¼ 550 MPa

Pu (kN) Gain (%) Pu (kN) Gain (%)

IL 23.3 – 35.7 – 58.4 –

0 24.6 5.7 37.6 5.2 60.0 2.7

-0 24.3 4.4 36.5 2.3 60.6 3.7

F-0 25.6 10.0 38.9 9.0 62.6 7.2

FL-0 25.9 11.1 39.4 10.4 63.4 8.5

90 24.2 3.9 36.2 1.3 61.1 2.6

-90 24.7 6.1 36.4 1.9 59.9 3.8

F-90 25.7 10.3 37.5 5.0 60.6 4.3

FL-90 25.8 10.7 37.9 6.1 60.6 4.6

4n S2-0 buckling and ultimate loads, for 1, 2 and 3 CFRPS (fy ¼ 250 MPa).

1 CFRPS 2 CFRPS

PL (kN) Gain (%) Pu (kN) Gain (%) PL (kN) Gain (

IL 23.3 – 35.7 – 23.3 –

0 24.6 5.7 37.6 5.2 26.0 11.5

-0 24.3 4.4 36.5 2.3 25.4 9.1

F-0 25.6 10.0 38.9 9.0 28.0 20.2

FL-0 25.9 11.1 39.4 10.4 28.5 22.4

(iii)

%)

TableColum

L2-N

L2-F-

L2-W

L2-W

L2-W

L2-F-

L2-W

L2-W

L2-W

VL: bw ¼ 100 mm, bf ¼ 80 mm, bl ¼ 10 mm, ts ¼ 2.5 mm,L ¼ 3000 mm (very long columns).

All steel (E ¼ 210 GPa, n ¼ 0.3) columns are fixed and areconcentrically loaded. The CFRP-strengthening configurationsconsidered are NIL, F-0, W-0, WF-0, WFL-0, F-90, W-90, WF-90and WFL-90, and they may be associated with various numbers ofCFRPS (tc ¼ 0.11 mm each). Regardless of the CFRP-strengtheningconfiguration adopted, columns S2, L2 and VL always buckled in(i) seven half-wave local, (ii) three half-wave distortional and(iii) single-wave flexural–torsional critical modes, respectively —

in the non-linear analyses, the initial geometric imperfectionsexhibit these critical buckling mode shapes. The initial imperfec-tion amplitudes for columns S2 and L2 were selected by using theapproach proposed by Schafer and Pekoz [31]: while theimperfection amplitude d1 ¼ 1.98ts (type 1) was considered forthe S2 columns (value associated with a cumulative distributionfunction P(Dod) ¼ 0.96), the imperfection amplitude d2 ¼ 1.55ts

(type 2) was adopted for the L2 columns (corresponding to acumulative distribution function P(Dod) ¼ 0.75) — it is worthnoting that the distortional imperfection shape adopted for the L2column exhibited a mid-span half-wave with the flanges movingoutwards. Regarding the columns VL, an initial imperfectionamplitude equal to e0 ¼ L/250 was considered, which is pre-scribed by EC3 for lipped channel columns and corresponds to thedesign curve b (EC3-1-3). Additionally, the columns VL were alsoanalysed using a lower imperfection amplitude e0 ¼ L/1000, avalue often adopted in global post-buckling analyses [32–34]. Thecritical buckling (Pc ¼ PL, PD, PFT) and ultimate (Pu) loads obtainedby means of shell finite element analyses (FEAs) are presented inTables 3–8. Tables 3 (column S2 with a single CFRPS), 5 (columnL2 with two CFRPS) and 7 (column VL with three CFRPS) show thePc and Pu values for two different steel yield stress values (fy ¼ 250and 550 MPa). On the other hand, Tables 4 (columns S2-0 withfy ¼ 250 MPa), 6 (columns L2-0 with fy ¼ 250 MPa) and 8(columns VL-0 with fy ¼ 250 MPa and imperfection amplitudee0 ¼ L/250) provide the variation of Pc and Pu with the number of

3 CFRPS

Pu (kN) Gain (%) PL (kN) Gain (%) Pu (kN) Gain (%)

35.7 – 23.3 – 35.7 –

39.8 11.3 27.3 17.3 41.9 17.3

37.9 6.1 26.8 14.9 40.7 2.8

41.9 17.2 30.7 31.7 44.3 24.1

43.9 22.9 31.5 35.0 47.4 32.7

5n L2 buckling and ultimate loads, for fy ¼ 250 and 550 MPa (2 CFRPS).

PD (kN) Gain (%) fy ¼ 250 MPa fy ¼ 550 MPa

Pu (kN) Gain (%) Pu (kN) Gain (%)

IL 102.7 - 107.5 - 169.9 -0 102.9 0.2 112.2 4.4 172.5 1.6-0 106.6 3.8 111.5 3.7 171.6 1.0F-0 106.8 4.0 118.9 10.6 178.0 4.8FL-0 109.0 6.1 123.2 14.6 182.2 7.390 106.0 3.2 107.9 0.4 170.3 0.3-90 112.0 9.1 108.1 0.6 170.7 0.5F-90 116.6 13.5 109.1 1.5 174.0 2.4FL-90 116.8 13.7 109.4 1.8 174.4 2.7

ARTICLE IN PRESS

Table 6Column L2-0 buckling and ultimate loads, for 2, 4 and 6 CFRPS (fy ¼ 250 MPa).

2 CFRPS 4 CFRPS 6 CFRPS

PD (kN) Gain (%) Pu (kN) Gain (%) PD (kN) Gain (%) Pu (kN) Gain (%) PD (kN) Gain (%) Pu (kN) Gain (%)

L2-NIL 102.7 – 107.5 – 102.7 – 107.5 – 102.7 – 107.5 –

L2-F-0 102.9 0.2 112.2 4.4 103.3 0.6 119.4 11.1 104.0 1.3 127.1 18.2

L2-W-0 106.6 3.8 111.5 3.7 110.7 7.8 117.7 9.5 114.8 11.8 119.8 11.5

L2-WF-0 106.8 4.0 118.9 10.6 111.1 8.2 126.7 17.9 115.3 12.3 134.4 25.0

L2-WFL-0 109.0 6.1 123.2 14.6 115.4 12.4 133.1 23.8 122.1 18.9 143.0 33.0

Table 7Column VL buckling and ultimate loads, for fy ¼ 250, 550 MPa and e0 ¼ L/250, L/1000 (3 CFRPS).

PFT (kN) Gain (%) e0 ¼ L/250 e0 ¼ L/1000

fy ¼ 250 MPa fy ¼ 550 MPa fy ¼ 250 MPa

Pu (kN) Gain (%) Pu (kN) Gain (%) Pu (kN) Gain (%)

VL-NIL 153.4 – 94.7 – 142.6 – 119.9 –VL-F-0 159.1 3.7 100.3 5.9 150.9 5.8 126.0 5.0VL-W-0 166.9 8.8 102.5 8.1 156.3 9.6 129.1 7.6VL-WF-0 172.2 12.3 108.2 14.3 165.7 16.2 135.0 12.6VL-WFL-0 174.3 13.7 109.0 15.1 167.0 17.1 137.3 14.5VL-F-90 154.3 0.6 95.6 1.0 143.8 0.8 120.9 0.9VL-W-90 155.9 1.6 95.9 1.2 144.2 1.1 121.4 1.3VL-WF-90 156.9 2.3 96.9 2.2 145.5 2.0 122.7 2.3VL-WFL-90 157.1 2.5 97.0 2.4 145.7 2.1 123.1 2.7

Table 8Column VL-0 buckling and ultimate loads, for 3, 6 and 9 CFRPS (fy ¼ 250 MPa, e0 ¼ L/250).

3 CFRPS 6 CFRPS 9 CFRPS

PFT (kN) Gain (%) Pu (kN) Gain (%) PFT (kN) Gain (%) Pu (kN) Gain (%) PFT (kN) Gain (%) PFT (kN) Gain (%)

VL-NIL 153.4 – 94.7 – 153.4 – 94.7 – 153.4 – 94.7 –

VL-F-0 159.1 3.7 100.3 5.9 165.0 7.6 105.9 11.8 171.2 11.6 111.6 17.8

VL-W-0 166.9 8.8 102.5 8.1 180.7 17.8 110.2 16.3 195.0 27.2 118.2 24.8

VL-WF-0 172.2 12.3 108.2 14.3 191.0 24.5 123.3 30.1 209.8 36.8 145.1 53.2

VL-WFL-0 174.3 13.7 109.0 15.1 195.4 27.4 124.9 31.9 216.6 41.2 148.1 56.3


CFRPS — 1-2-3 (columns S2-0), 2-4-6 (columns L2-0) or 3-6-9(columns VL-0).

Concerning the results obtained and displayed in these 6tables, the following remarks are appropriate:

(i)
The results presented in Table 3 show that the benefit (withrespect to the bare steel column) of placing the fibres at 01 orat 901 is similar for the local buckling load PL of the shortcolumn S2 (around 11%). However, as far as the ultimate loadPu is concerned, it is preferable to place the fibres at 01 than at901 (10.4% vs. 6.1% gains for the S2-WFL columns withfy ¼ 250 MPa). It is interesting to notice that the gain for theS2-WFL-0 columns with one single ply and fy ¼ 550 MPa(more than twice 250 MPa) is not much higher than 8.5% —
indeed, it is just 10.4%. On the other hand, Table 4 shows thatusing one, two or three CFRP plies in the column S2-WFL-0,with fy ¼ 250 MPa leads to Pu increases of 10.4%, 22.9% and32.7%, respectively. It is interesting to notice that the increasein Pu is almost proportional to the number of CFRPSemployed (i.e., the thickness of CFRP layers).

(ii)
The results shown in Table 5 reveal that placing the fibres at901 is beneficial for the column L2 distortional buckling loads
(PD) — it leads to gains that reach 13.7% (column L2-WFL-90).On the other hand, in order to increase ultimate loads (Pu), itis preferable to place the fibres at 01, which leads to gains upto 14.6% (column L2-WFL-0, with fy ¼ 250 MPa). Unlike in theshort columns, the gain associated with the column L2-WFL-0, with fy ¼ 550 MPa (7.3%) is precisely half of its fy ¼ 250MPa counterpart (14.6%). Moreover, the observation of Table6 makes it possible to conclude that attaching two, four or sixCFRPS to the column L2-WFL-0, with fy ¼ 250 MPa causes Pu

increases of 14.6%, 23.8% and 33.0%, respectively — onceagain, the Pu increase is nearly proportional to the number ofCFRPS.

(iii)
The values presented in Table 7 show that the carbon fibresoriented at 01 are most effective to increase both theflexural–torsional buckling load (PFT) and the correspondingultimate load (Pu). While the PFT gain may reach 13.7%(column VL-WFL-0), it is possible that the ultimate loadincrease is even more pronounced (15.1%). Interestinglyenough, increasing fy from 250 to 550 MPa leads to only aslightly higher ultimate load gain (17.1% vs. 15.1%) — notethat the same three-ply CFRP-strengthening is used. It isworth mentioning that this behaviour was not observed in

ARTICLE IN PRESS


columns S2 and L2. On the other hand, the gain is virtuallyindependent on the initial imperfection amplitude, due to thefact that the consideration of a much smaller amplitude (L/1000) leads to a marginal gain decrease (14.5% vs. 15.1%).Finally, the values given in Table 8 show that attaching three,six or nine CFRPS to the column VL-WFL-0 with fy ¼ 250 MPaleads to Pu increases of 15.1%, 31.9% and 56.3%, i.e., again fairlyproportional to the number of CFRPS employed — however,the gain associated with the nine-ply configuration (56.3%) ishigher than the expected (proportional) value (E46%).

4. The modified design provisions

4.1. Modified EC3

The Eurocode 3 [24,26] provisions for the design of cold-formed steel columns are based on the well-known ‘‘effectivewidth method’’ (EWM). If it is desired to retain these EC3provisions to evaluate the load-carrying capacity of CFRP-strengthened cold-formed steel columns, some changes must beincorporated — the main one resides in the fact that theslenderness l expressions must now depend on mechanical (bothgeometric and material) properties, rather than on materialproperties alone. In order to account for the local buckling effects,the EWM requires the determination of an effective (reduced) areaof the cross-section, a goal which is attained by calculating theeffective widths beff of all compressed walls, by using theexpressions (recall that lp is modified)

beff ¼ rb ¼

b if lppd

lp � c

l2p

b if lp4d

8>><>>:

lp ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffif yts þ f ctc

sLðts þ tcÞ

s(1)

where (i) r is the effective width reduction factor associated witheach wall, (ii) lp is the local (plate) slenderness of each cross-section wall, (iii) b and t are the wall width and overall thickness,(iv) ts and tc are the thickness values of the steel and CFRPS, (v) fy

is the steel yield stress, (vi) fc is the CFRPS ultimate stress, (vii) sL

is the local buckling stress of the wall, and (viii) c and d areauxiliary parameters that depend on the wall edge supportconditions (c ¼ 0.22, d ¼ 0.673 and c ¼ 0.188, d ¼ 0.748 forinternal and outstand walls, respectively). It should be noted thatthe plate slenderness lp must be calculated independently foreach wall, considering the web and flanges simply supported attheir longitudinal edges (ks ¼ 4) and the lips simply supported attheir non-free edge (ks ¼ 0.43). Note also that the plate slender-ness expression (Eq. (1)) recovers its usual form if tc ¼ 0 (i.e., abare steel wall — no CFRPS).

In order to account for the influence of distortional buckling,EC3 (Part 1.3) [25] stipulates that the thickness of the cross-section ‘‘stiffeners’’ (lips plus the adjacent effective portion of theflanges) should be reduced by means of (recall that ld is modified)

tred ¼ wdt ¼

1 if ldp0:65

1:47� 0:723ld if 0:65oldo1:38

0:66=ld if ldX1:38

8><>:

ld ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffif yts þ f ctc

sDðts þ tcÞ

s(2)

where (i) wd is the reduction factor for distortional buckling, (ii) ld

is the cross-section distortional slenderness and (iii) sD is the

distortional buckling stress. Finally, note that EC3 allows thedesigner to determine the sD values either (i) exactly (by means ofnumerical methods, such as the shell finite element method, thefinite strip method or generalised beam theory) or (ii) approxi-mately (using the simplified methodologies included in the EC3-Part 1.3). Therefore, the design value of the CFRP-strengthenedcolumn load-carrying capacity reads

Pu ¼ wðAeff�sf y þ Aeff�cf cÞ (3)

where w is the strength reduction factor associated with global(flexural or flexural–torsional) buckling and based on bucklingcurve b (imperfection factor a ¼ 0.34), as prescribed in EC3-Part1.3 for singly symmetric sections. Note also that (i) all the lippedchannel cross-sections analysed in this work belong to Class 3(occasionally) or 4 (mostly) and that (ii) the web and flanges areclassified as ‘‘internal walls’’, while the lips are looked upon as‘‘outstand walls’’.

4.2. Modified AISI-DSM

Although the current North American Specification for thedesign of cold-formed steel columns [27] is also based on theeffective width concept, the DSM, originally proposed andcontinuously improved by Schafer [29], was recently allowed for— indeed, it was included in an appendix of the above code [28].The DSM provides an elegant, efficient and consistent approach toestimate the ultimate strength of cold-formed steel columns andbeams (i) experiencing global (flexural, torsional or flexural–tor-sional), local or distortional collapses or (ii) failing in mechanismsthat involve interaction between local and global buckling — itadopts ‘‘Winter-type’’ design curves, which are calibrated againsta large number of experimental and/or numerical results. It hasbeen shown that, for columns failing in global, local/global ordistortional collapse modes, accurate and safe ultimate strengthestimates can be obtained exclusively on the basis of the elasticbuckling and yield stress values — indeed, the DSM prescribesthat the column nominal strengths against global, local/global anddistortional failure (PnE, PnL and PnD) should be determinedthrough the expressions

PnE ¼

0:658l2c Py if lcp1:5

Py0:877

l2c

!if lc41:5

8>>><>>>:

lc ¼

ffiffiffiffiffiPy

PE

s(4)

PnL ¼

PnE if lLp0:776

PnEPL

PnE

� �0:4

1� 0:15PL

PnE

� �0:4" #

if lL40:776

8>><>>:

lL ¼

ffiffiffiffiffiffiffiPnE

PL

s(5)

PnD ¼

Py if lDp0:561

PyPD

Py

� �0:6

1� 0:25PD

Py

� �0:6" #

if lD40:561

8>><>>:

lD ¼

ffiffiffiffiffiffiPy

PD

s(6)

where Py is the column squash load (Py ¼ Asfy+Acfc, where As andAc are the gross section areas of steel and CFRPS) and PE is the

ARTICLE IN PRESS

Table 10Ultimate load estimates, for the columns L1.

Column Pu (kN) Pu.ap (kN) Pu.ap/Pu

FEA EC3 AISI EC3 AISI

L1-NIL 89.0 81.6 111.3 0.92 1.25L1-F-0 91.8 90.0 121.7 0.98 1.33L1-W-0 94.3 91.1 119.2 0.97 1.26L1-WF-0 98.4 99.2 129.0 1.01 1.31L1-WFL-0 102.5 101.0 131.5 0.99 1.28L1-F-90 93.7 84.5 114.2 0.90 1.22L1-W-90 93.5 85.1 116.7 0.91 1.25L1-WF-90 99.8 97.2 122.1 0.97 1.22L1-WFL-90 107.0 102.0 122.8 0.95 1.15


critical global buckling load. Moreover, the column ultimate loadreads

Pu ¼MinfPnE; PnL; PnDg (7)

It is worth mentioning that all the cross-sections dealt withhere satisfy the limits prescribed for pre-qualified columns —

however, it should be stressed that the short column ratio E/fy isquite close to one of these limits. Moreover, the critical globalbuckling load adopted to calculate (i) the AISI nominal strengthPnE or (ii) the EC3 strength reduction factor w, is obtained bymeans of GBT-based analyses that include only the first four(global) deformation modes — this procedure circumvents thedifficulties related to the evaluation of PE for the short columnsthrough shell FEAs, due to the fact that it corresponds to abuckling mode of a very high order.

Mean 0.96 1.25Standard Deviation 0.04 0.05

Table 11Column S2 ultimate load estimates, for fy ¼ 250 and 550 MPa (1 CFRPS).


5. Assessment of the modified EC3 and AISI ultimate loadestimates

Finally, the ‘‘quality’’ (safety and accuracy) of the ultimate loadestimates yielded by the application of the following two designmethodologies is assessed:

(i)
TablUltim

Colu

S1-N

S1-F

S1-W

S1-W

S1-W

S1-F

S1-W

S1-W

S1-W

fy ¼ 250 Mpa

Modified EC3 provisions incorporating approximate sD valuesdetermined by means of the EC3 simplified methodology.

S2-NIL 35.7 32.4 34.3 0.91 0.96
(ii) S2-F-0 37.6 42.7 43.8 1.14 1.16
S2-W-0 36.5 43.4 43.4 1.19 1.19

S2-WF-0 38.9 53.4 51.9 1.37 1.33

Modified AISI-DSM provisions incorporating exact PL and PD

values determined by means of shell FEAs that model the true(fixed) end support conditions.

S2-WFL-0 39.4 56.3 53.6 1.43 1.36

S2-F-90 36.2 33.2 35.2 0.92 0.97

S2-W-90 36.4 33.7 36.3 0.93 1.00

S2-WF-90 37.5 38.1 39.2 1.02 1.05

S2-WFL-90 37.9 39.2 40.1 1.03 1.06

fy ¼ 550 Mpa

S2-NIL 58.4 46.4 55.9 0.79 0.96

S2-F-0 60.0 53.0 63.2 0.88 1.05

S2-W-0 60.6 53.9 63.0 0.89 1.04

The ultimate load values yielded by the above design meth-odologies are presented in Tables 9–16 — also given are theultimate loads Pu obtained numerically from shell FEA. Inaddition, the ratios between the ultimate load estimates (Pu.ap)and numerical values (Pu) are also supplied. Initially, a discussionof results concerning the short and long columns testedexperimentally is presented — they are shown in Tables 9 (S1)and 10 (L1) and lead to the following conclusions:

S2-WF-0 62.6 60.4 70.1 0.96 1.12

S2-WFL-0 63.4 62.1 71.5 0.98 1.13

S2-F-90 61.1 49.2 58.2 0.81 0.95
(i)
e

m

-

-

S2-W-90 59.9 52.0 59.2 0.87 0.99

S2-WF-90 60.6 59.2 61.0 0.98 1.01

S2-WFL-90 60.6 60.2 62.3 0.99 1.03

Mean 1.00 1.08Standard Deviation 0.18 0.12

The short and long column ultimate loads yielded by the EC3method are quite accurate (6% and 4% mean errors). More-over, their values also exhibit a rather low scatter. Note that,in both cases, the bare steel column estimates (S1-NIL andL1-NIL) are the most conservative ones and that, in general,the accuracy of the estimates increases with the amount ofCFRP-strengthening — e.g., the ratios concerning columnsS1-WFL-0, S1-WFL-90 and L1-WFL-0 equal to either 0.99 or1.00.

9ate load estimates, for the columns S1.

n Pu (kN) Pu.ap (kN) Pu.ap/Pu


IL 55.9 45.4 81.1 0.81 1.45

0 57.4 51.9 94.7 0.90 1.65

-0 57.3 53.5 89.2 0.93 1.56

F-0 62.8 60.0 102.3 0.96 1.63

FL-0 63.4 62.5 104.2 0.99 1.64

90 56.8 52.3 90.1 0.92 1.59

-90 56.3 54.2 92.3 0.96 1.64

F-90 61.4 60.8 96.3 0.99 1.57

FL-90 62.3 62.1 98.4 1.00 1.58

Mean 0.94 1.59

Standard Deviation 0.06 0.06

(ii)
For the particular columns dealt with here, all AISI predic-tions concerning the bare steel columns (S1-NIL and L1-NIL)already overestimate the ‘‘exact’’ values by a considerableamount (45% and 25%, respectively). Moreover, their CFRP-strengthened column counterparts still overestimate the‘‘exact’’ ultimate loads by larger amounts — the errors reach65% and 33% in the two column sets. Therefore, it seems fairto say that the inadequacy of the AISI provisions to predictthe ultimate strength of the CFRP-strengthened columnsstems, to a considerable extent, from a similar shortfall forthe bare steel column — i.e., if the performance of the DSMfor bare steel columns is improved, its application to CFRP-strengthened columns will also provide ‘‘better’’ ultimateload estimates.
(iii)
The large inaccuracy (on the unsafe side) of the AISIshort column ultimate load estimates is due to the preva-lence of the local failure provisions (Pu ¼ PnL), which donot adequately model the column collapse mechanisms

ARTICLE IN PRESS

Table 13Column L2 ultimate load estimates, for fy ¼ 250 and 550 MPa (2 CFRPS).



fy ¼ 250 Mpa

L2-NIL 107.5 92.8 99.1 0.86 0.92

L2-F-0 112.2 118.7 125.9 1.06 1.12

L2-W-0 111.5 120.2 115.5 1.08 1.04

L2-WF-0 118.9 143.2 139.6 1.20 1.17

L2-WFL-0 123.2 145.7 143.2 1.18 1.16

L2-F-90 107.9 97.2 102.1 0.90 0.95

L2-W-90 108.1 102.7 103.7 0.95 0.96

L2-WF-90 109.1 104.2 110.2 0.96 1.01

L2-WFL-90 109.4 106.1 111.7 0.97 1.02

fy ¼ 550 MPa

L2-NIL 169.9 133.4 148.0 0.79 0.87

L2-F-0 172.5 149.4 165.7 0.87 0.96

L2-W-0 171.6 150.6 160.2 0.88 0.93

L2-WF-0 178.0 165.0 177.0 0.93 0.99

L2-WFL-0 182.2 166.6 180.5 0.91 0.99

L2-F-90 170.3 140.0 155.1 0.82 0.91

L2-W-90 170.7 142.9 157.9 0.84 0.93

L2-WF-90 174.0 150.1 168.1 0.86 0.97

L2-WFL-90 174.4 151.9 168.9 0.87 0.97

Mean 0.94 0.99


Table 14Column L2 ultimate load estimates, for 2, 4 and 6 CFRPS (fy ¼ 250 MPa).



2 ply

L2-NIL 107.5 92.8 99.1 0.86 0.92

L2-F-0 112.2 118.7 125.9 1.06 1.12

L2-W-0 111.5 120.2 115.5 1.08 1.04

L2-WF-0 118.9 143.2 139.6 1.20 1.17

L2-WFL-0 123.2 145.7 143.2 1.18 1.16

4 plies

L2-F-0 119.4 138.9 147.2 1.16 1.23

L2-W-0 117.7 144.6 130.6 1.23 1.11

L2-WF-0 126.7 180.1 171.4 1.42 1.35

L2-WFL-0 133.1 184.2 178.4 1.38 1.34

6 plies

L2-F-0 127.1 156.6 165.5 1.23 1.30

L2-W-0 119.8 165.9 144.8 1.38 1.21

L2-WF-0 134.4 208.0 198.9 1.55 1.48

L2-WFL-0 143.0 212.8 209.7 1.49 1.47

Mean 1.25 1.22


Table 12Column S2 ultimate load estimates, for 1, 2 and 3 CFRPS (fy ¼ 250 MPa).



1 ply

S2-NIL 35.7 32.4 34.3 0.91 0.96

S2-F-0 37.6 42.7 43.6 1.14 1.16

S2-W-0 36.5 43.4 43.4 1.19 1.19

S2-WF-0 38.9 53.4 51.9 1.37 1.33

S2-WFL-0 39.4 56.3 53.6 1.43 1.36

2 plies

S2-F-0 39.8 51.4 52.2 1.29 1.31

S2-W-0 37.9 54.2 51.8 1.43 1.37

S2-WF-0 41.9 72.4 67.4 1.73 1.61

S2-WFL-0 43.9 78.2 70.3 1.78 1.60

3 plies

S2-F-0 41.9 59.3 60.3 1.42 1.44

S2-W-0 40.7 64.7 59.9 1.59 1.47

S2-WF-0 44.3 90.3 81.8 2.04 1.85

S2-WFL-0 47.4 99 85.9 2.09 1.81

Mean 1.49 1.42



(experimentally observed to be predominantly distortional[22]) — note that PD ¼ 130 kN is much higher than PL

(26.8oPLo29.5 kN). Conversely, the AISI distortional failureprovisions (Pu ¼ PnD) prevail for the long columns. However,the close proximity of PL and PD indicates the occurrence oflocal/distortional mode interaction (also observed experi-mentally [22]), a phenomenon known to erode the ultimateload of bare steel columns [35] — the authors believe that

this fact also provides a (partial) explanation for theoverestimation of the column ultimate loads.

Tables 11–16 concern columns S2, L2 and VL and provide (i)‘‘exact’’ ultimate loads Pu, obtained by means of shell FEAs and (ii)estimates provided by the proposed EC3 and AISI designmethodologies. The observation of these results prompts thefollowing comments:

(i)
Unlike their column S1 and L1 counterparts, the AISIestimates concerning columns S2 (1 CFRPS — Table 11) andL2 (2 CFRPS — Table 13) are quite accurate, regardless of thesteel yield stress value. On the other hand, the EC3 predictionsretain the same level of accuracy that was exhibited for thecolumns S1 and L1. Concerning the columns VL (3 CFRPS —
Table 15) with fy ¼ 250 MPa, the ‘‘quality’’ of the EC3 and AISIestimates is higher for the larger (e0 ¼ L/250) and smaller(e0 ¼ L/1000) imperfection amplitudes, respectively — whilethe EC3 estimates are too safe for e0 ¼ L/1000, the AISI valuesare too unsafe for e0 ¼ L/250. For the larger yield stress(fy ¼ 550 MPa) and imperfection amplitude (e0 ¼ L/250), theAISI results provide fairly accurate safe predictions of the VLcolumn ultimate loads — the EC3 estimates, on the otherhand, are excessively conservative.

(ii)
Concerning the influence of the number of CFRPS attachedto the column outer surfaces, it seems fair to say that,regardless of the column being short (S2 — Table 12), long (L2— Table 14) or very long (VL — Table 16), increasing thecomposite layer thickness always leads to a ‘‘quality’’ decreaseof the EC3 and AISI ultimate load estimates — they over-estimate the ‘‘exact’’ values by progressively larger amounts(i.e., become more unsafe). In the columns with moreCFRPS (thicker composite layer), the ultimate load over-estimation can be partially explained by the fact that themodified EC3 and AISI provisions dependent excessively onthe characteristic value of column squash load (a function ofthe steel yield stress fy and CFRPS ultimate stress fc, the later

ARTICLE IN PRESS

Table 15Column VL ultimate load estimates, for fy ¼ 250 and 550 MPa (3 CFRPS).

Column Pu (kN)-FEA Pu.ap (kN) e0 ¼ L/250 e0 ¼ L/1000

e0 ¼ L/250 e0 ¼ L/1000 EC3 AISI EC3 AISI EC3 AISI

fy ¼ 250 Mpa

VL-NIL 94.7 119.9 91.2 108.5 0.96 1.15 0.76 0.90

VL-F-0 100.3 126.0 109.8 134.9 1.09 1.34 0.87 1.07

VL-W-0 102.5 129.1 111.3 132.5 1.09 1.29 0.86 1.03

VL-WF-0 108.2 135.0 125.0 149.9 1.16 1.39 0.93 1.11

VL-WFL-0 109.0 137.3 127.2 152.2 1.17 1.40 0.93 1.11

VL-F-90 95.6 120.9 92.1 121.1 0.96 1.27 0.76 1.00

VL-W-90 95.9 121.4 93.2 122.9 0.97 1.28 0.77 1.01

VL-WF-90 96.9 122.7 94.9 125.3 0.98 1.29 0.77 1.02

VL-WFL-90 97.0 123.1 95.3 125.9 0.98 1.30 0.77 1.02

fy ¼ 550 Mpa

VL-NIL 142.6 – 109.3 134.5 0.77 0.94 – –

VL-F-0 150.9 – 117.8 139.5 0.78 0.92 – –

VL-W-0 156.3 – 122.2 146.4 0.78 0.94 – –

VL-WF-0 165.7 – 129.8 151.0 0.78 0.91 – –

VL-WFL-0 167.0 – 131.5 152.9 0.79 0.92 – –

VL-F-90 143.8 – 112.9 138.1 0.79 0.96 – –

VL-W-90 144.2 – 114.1 142.1 0.79 0.99 – –

VL-WF-90 145.5 – 118.9 146.3 0.82 1.01 – –

VL-WFL-90 145.7 – 120.1 146.9 0.82 1.01 – –

Mean 0.92 1.13 0.82 1.03

Standard Deviation 0.14 0.19 0.07 0.06

Table 16Column VL ultimate load estimates, for 3, 6 and 9 CFRPS (fy ¼ 250 MPa).



3 ply

VL-NIL 94.7 91.2 108.5 0.96 1.15

VL-F-0 100.3 109.8 134.9 1.09 1.34

VL-W-0 102.5 111.3 132.5 1.09 1.29

VL-WF-0 108.2 125 149.9 1.16 1.39

VL-WFL-0 109 127.2 152.2 1.17 1.40

6 plies

VL-F-0 105.9 120.7 144.7 1.14 1.37

VL-W-0 110.2 128 151.8 1.16 1.38

VL-WF-0 123.3 147 167.5 1.19 1.36

VL-WFL-0 124.9 150.8 171.4 1.21 1.37

9 plies

VL-F-0 111.6 129.6 150.1 1.16 1.34

VL-W-0 118.2 143.2 168.4 1.21 1.42

VL-WF-0 145.1 166.3 183.9 1.15 1.27

VL-WFL-0 148.1 172.2 189.9 1.16 1.28

Mean 1.14 1.34


1 In the EC3 case, a ‘‘modified first yield stress’’ equal to (fyts+f1tc)/(ts+tc)

should be employed in the slenderness definitions.


being very high). Nevertheless, it is also clear that both theproposed EC3 and AISI-based approaches provide fairly goodultimate load predictions for the columns with less CFRPS(thinner composite layer): S2 with 1 CFRPS, L2 with 2CFRPS and VL with 3 CFRPS. Therefore, for composite layerthickness values (tc) not exceeding 10–15% of the steelcolumn wall thickness (ts), both approaches provide ‘‘goodquality’’ estimates of the CFRP-strengthened column ultimateloads.

It was observed that a CFRPS thickness increase always leads tomore unsafe EC3 and AISI-DSM ultimate load estimates. Thisprobably means that the squash load definition used in this study(Py ¼ Asfy+Acfc), which depends on the CFRPS ultimate strength fc,overestimates the cross-section strength for the thicker layers. Inview of this fact, it should be mentioned that another viableapproach consists of using the first yield load (P1 ¼ Asfy+Acf1)instead of the squash load (Py ¼ Asfy+Acfc), where f1 ¼ Ecey is theelastic stress at the CFRPS when the steel yields (ey is the cross-section strain for fs ¼ fy). This alternative approach is based on theassumption that the maximum strength of the cross-section isreached when the steel yields, with the CFRP remaining elastic atf1, and not when both materials are squashed (P1oPy, since f1ofc).This approach would probably lead to more accurate AISI-DSMand EC31 results for the thicker CFRPS strengthening — thisavenue will be explored in the near future.

6. Concluding remarks

This paper reported an investigation on the applicability ofmodifications of the EC3 (Part 1.3) and AISI Specificationprovisions to estimate the ultimate loads of CFRP-strengthenedcold-formed steel lipped channel columns — these provisions arebased on different approaches, namely the ‘‘effective width’’concept and the ‘‘Direct Strength Method’’, and were originallydeveloped for bare steel members. After a brief description of theexperimental and numerical analyses carried out earlier, the paperpresented and discussed a novel numerical investigation aimed atacquiring a more extensive ultimate load ‘‘data bank’’ and, inparticular, to study the influence of the number of CFRPS adoptedto strengthen the columns. Then, the ultimate load estimatesyielded by the slightly modified (to account for the CFRP-

ARTICLE IN PRESS


strengthening) EC3/AISI provisions were compared with the‘‘exact’’ numerical values obtained (part of them have alreadybeen shown to correlate quite well with the experimental results).This comparison showed that the design formulae provide unsafeestimates in several situations, which means that the coefficientsdefining the design curves must be adequately modified/cali-brated in order to take into consideration the specificities of CFRP-strengthening. Nevertheless, the correlation detected was ratherencouraging and provides ample evidence that it is worth furtherexploring this avenue, namely to modify existing design ap-proaches, developed for bare steel members, so that they can beapplied to design CFRP-strengthened cold-formed steel members.

It was possible to identify and discuss some sources of theultimate load overestimation associated with the proposed(modified) EC3 and AISI-based design approaches. However, it isalso fair to say that the ultimate loads of the CFRP-strengthenedcold-formed steel lipped channel columns are fairly well esti-mated by both approaches, provided that (i) their predictions areaccurate for the bare steel columns to be strengthened (this wasnot always the case) and (ii) the thickness of the composite layer(i.e., all carbon fibre sheets) does not exceed 10–15% of the column(steel) wall thickness. Further research work is currently underway to overcome some of the limitations detected, thus making itpossible to improve the design methodologies proposed here.

References

[1] Teng JG, Chen JF, Smith ST, Lam L. FRP-strengthened RC structures. London:Wiley; 2002.

[2] Sen R, Liby L, Mullins G. Strengthening steel bridge sections using CFRPlaminates. Compos: Part B 2001;32(4):309–22.

[3] Miller TC, Chajes MJ, Mertz DR, Hastings JN. Strengthening of a steel bridgegirder using CFRP plates. J Bridge Eng (ASCE) 2001;6(6):514–22.

[4] Tavakkolizadeh M, Saadatmanesh H. Strengthening of steel–concrete compo-site girders using carbon fiber reinforced polymer sheets. J Struct Eng (ASCE)2003;129(1):30–40.

[5] El Damatty AA, Abushagur M, Youssef MA. Experimental and analyticalinvestigation of steel beams rehabilitated using GFRP sheets. Steel ComposStruct 2003;3(6):421–38.

[6] El Damatty AA, Abushagur M. Testing and modeling of shear and peelbehaviour for bonded steel/FRP connections. Thin-Walled Struct 2003;41(11):987–1003.

[7] Lam D, Clark KA. Strengthening steel sections using carbon fibre reinforcedpolymers laminates. In: Hancock GJ, Bradford MA, Wilkinson T, Uy B,Rasmussen KJR, editors. Advances in structures, Asscca’03, Sydney. Lisse:Balkema; 2003. p. 1369–74.

[8] Al-Saidy AH, Klaiber FW, Wipf TJ. Repair of steel composite beams withcarbon fiber-reinforced polymer plates. J Compos Constr (ASCE) 2004;8(2):163–72.

[9] Buyukozturk O, Gunes O, Karaca E. Progress on understanding debondingproblems in reinforced concrete and steel members strengthened using FRPcomposites. Constr Build Mater 2004;18(1):9–19.

[10] Hollaway LC, Zhang L, Photiou NK, Teng JG, Zhang SS. Advances in adhesivejoining of carbon fibre/polymer composites to steel members for repair andrehabilitation of bridge structures. Adv Struct Eng 2006;9(6):791–803.

[11] Schnerch D, Dawood M, Rizkalla S, Sumner E, Stanford K. Bond behavior ofCFRP strengthened steel structures. Adv Struct Eng 2006;9(6):805–17.

[12] Colombi P, Poggi C. An experimental, analytical and numerical study of thestatic behaviour of steel beams reinforced by pultruded CFRP strips. Compos:Part B 2006;37(1):64–73.

[13] Al-Emrani M, Kliger R. Experimental and numerical investigation on thebehaviour and strength of composite steel — CFRP members. Adv Struct Eng2006;9(6):819–31.

[14] Shaat A, Fam A. Axial loading tests on short and long hollow structural steelcolumns retrofitted using carbon fibre reinforced polymers. Can J Civil Eng2006;33(4):458–70.

[15] Jiao H, Zhao XL. CFRP-strengthened butt-welded very high strength (VHS)circular steel tubes. Thin-Walled Struct 2004;42(7):963–78.

[16] Zhao XL, Fernando D, Al-Mahaidi R. CFRP strengthened RHS subjected totransverse end bearing force. Eng Struct 2006;28(11):1555–65.

[17] Shaat A, Fam A. Fiber-element model for slender HSS columns retrofitted withbonded high-modulus composites. J Struct Eng (ASCE) 2007;133(1):85–95.

[18] Shaat A, Fam A. Finite element analysis of slender HSS columns strengthenedwith high modulus composites. Steel Compos Struct 2007;7(1):19–34.

[19] Zhao XL, Zhang L. State-of-the-art review on FRP strengthened steelstructures. Eng Struct 2007;29(8):1808–23.

[20] Young B, Silvestre N, Camotim D. Experimental and numerical analysisof the structural response of FRP-strengthened cold-formed steel columns. In:Mirmiran A, Nanni A, editors, Proc compos civil eng, CICE 2006, Miami.13–15 December 2006, International Institute for FRP in Construction,p. 725–728.

[21] Silvestre N, Camotim D, Young B. Numerical analysis of the non-linearbehaviour of CFRP-strengthened cold-formed steel columns. In: Wang YC,Choi CH, editors. Steel and composite structures (Proceedings of 3rdInternational Conference on steel and composite structures), ICSCS’07,Manchester. London: Taylor & Francis; 2007. p. 969–75.

[22] Silvestre N, Young B, Camotim D. Non-linear behaviour and load-carryingcapacity of CFRP-strengthened lipped channel steel columns. Eng Struct2008;30(10):2613–30.

[23] Hibbit, Karlsson and Sorensen Inc. Abaqus Standard, version 6.3-1, 2002.[24] Comite Europeen de Normalisation (CEN). Eurocode 3: Design of Steel

Structures, Part 1.1: General Rules and Rules for Buildings, EN 1993-1-1,2005.

[25] Comite Europeen de Normalisation (CEN). Eurocode 3: design of steelstructures, part 1.3: general rules — supplementary rules for cold formedmembers and sheeting, prEN 1993-1-3; 2005.

[26] Comite Europeen de Normalisation (CEN). Eurocode 3: design of steelstructures, part 1.5: plated structural elements, prEN 1993-1-5; 2004.

[27] American Iron and Steel Institute (AISI). North American specification for thedesign of cold-formed steel structural members, Washington DC; 2001.

[28] American Iron and Steel Institute (AISI). Appendix I of the North Americanspecification (NAS) for the design of cold-formed steel structural members:design of cold-formed steel structural members with the direct strengthmethod, Washington DC; 2004.

[29] Schafer BW. Review: the direct strength method of cold-formed steel memberdesign. J Constr Steel Res 2008;64(7–8):766–8.

[30] Australian Standards (AS). Steel sheet and strip-hot-dipped zinc-coated oraluminium zinc-coated. AS 1397, Standards Association of Australia, Sydney,Australia; 1993.

[31] Schafer BW, Pekoz T. Computational modeling of cold-formed steel:characterizing geometric imperfections and residual stresses. J Constr SteelRes 1998;47(3):193–210.

[32] Yan J, Young B. Column tests of cold-formed steel channels with complexstiffeners. J Struct Eng (ASCE) 2002;128(6):737–45.

[33] Young B, Yan J. Finite element analysis and design of fixed-ended plainchannel columns. Finite Elem Anal Des 2002;38(6):549–66.

[34] Dinis PB, Camotim D. Post-buckling analysis of cold-formed steel lippedchannel columns affected by distortional/global mode interaction. In: ProcSSRC (Structural Stability Research Council) Annu Stability Conf, Nashville,2–5 April 2008, p. 405–431.

[35] Dinis PB, Camotim D, Silvestre N. FEM-based analysis of the local-plate/distortional mode interaction in cold-formed steel lipped channel columns.Comput Struct 2007;85(19–20):1461–74.

on the use of the ec3 and aisi specifications to estimate the ultimate load of cfrp-strengthened...

Documents