beaulieu-compression strength of corroded stel angle members (1)

Journal of Constructional Steel Research 66 (2010) 1366–1373

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Journal of Constructional Steel Research

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

Compression strength of corroded steel angle membersL.-V. Beaulieu, F. Legeron ∗, S. LangloisDepartment of Civil Eng., University of Sherbrooke, 2500 boul. de l’Université, Sherbrooke, Quebec, Canada J1K 2R1

a r t i c l e i n f o

Article history:Received 6 November 2009Accepted 17 May 2010

Keywords:CorrosionSteel structuresCompressive strengthCompression testingStructural integrityResidual capacity

a b s t r a c t

Steel structures corrode when exposed to the environment, and their capacity is reduced accordingly. Inpractice, when a member is found corroded during inspection, it is necessary to estimate the residualcapacity of corroded members in order to decide whether to change the member, repair it or just removecorrosion and re-protect the member.The objective of this article is to provide data to engineers on the structural behavior of corroded

steel angle members under compressive load. Sixteen angle members were corroded with an acceleratedprocedure and then tested in compression. Eight uncorroded members were also tested in compression.The influence of corrosion on compressive capacity was measured and compared to analytical methodsaccounting for weight loss. Recommendations are drawn from this research to provide guidance toengineers on how to evaluate compressive capacity of corroded members. Needs for future work are alsohighlighted.

© 2010 Elsevier Ltd. All rights reserved.

1. Introduction

Steel structures exposed to the environment are subject tocorrosion. Even galvanized steel can experience corrosion aftergalvanic protection is consumed. Corrosion can be particularlyimportant in transmission line foundations where steel anglemembers are often placed in direct contact with the soil andexposed to variable level of water table. It is also the case of manyindustrial facilities, antenna towers, bridges, and other exposedstructures.For utilities which manage very large structure networks, it is

very difficult to assess the residual capacity of an existing structureand determinewhen it is no longer safe after corrosion has started.One method based on qualitative parameters was developed byHathout [1] to evaluate the reliability of transmission lines. Toexamine the problem in detail, it would be useful to develop amodel predicting the residual capacity of corroded members.The traditional approach to evaluate residual capacity is to

perform visual inspection of the corroded members and classifythe members according to their level of damage. This method ishowever highly subjective. For members loaded in compression,the precision obtained by this method can be inadequate becausethe capacity is very sensitive to geometrical imperfections.Kayser and Nowak [2] developed a corrosion model for steel

girder bridges, which takes into account the location and rate

∗ Corresponding author. Tel.: +1 819 821 7395; fax: +1 819 821 7974.E-mail addresses: [email protected] (L.-V. Beaulieu),

[email protected] (F. Legeron),[email protected] (S. Langlois).

0143-974X/$ – see front matter© 2010 Elsevier Ltd. All rights reserved.doi:10.1016/j.jcsr.2010.05.006

of corrosion. Sarveswaran et al. [3] evaluated structural safetyof corroded steel structures by applying the theory of structuralreliability. The model predicts an interval of residual capacitybased on an estimate of the remaining thickness of the member.In [4], minimum capacity curves which vary with the percentageloss of flange thickness are presented. These curves account forthe principal modes of failure. However, variation in thicknessdue to corrosion and local concentration of corrosion are notconsidered in this approach. Corrosion might also modify steelfrom ametallurgical point of view and characteristics of remainingsteel, such as yield strength, can be altered. The phenomenon ofcorrosion is well studied but, very little research has been done onhow the compressive capacity of steel members is affected oncecorrosion has developed. There is a lack of experimental data onthe relation between weight loss due to corrosion and residualstrength.The objective of this study is to provide experimental data on

compressive capacity of corroded steel angle members that couldbe used by practical engineers. The simplified method to calculatethe residual capacity ofmembers according to the average residualthickness is evaluated.

2. Experimental program

In order to evaluate the residual capacity of corroded anglemembers, an experimental program was performed. The mainparameters of this study are: (i) the overall slenderness ratio (L/r),(ii) the width-to-thickness ratio (b/t), and (iii) the corrosion level.The slenderness ratio (L/r) is one of the main factors affecting

the capacity of steel members under compression load. This isthe ratio of the unsupported length L to the radius of gyration,r . The length of the test specimens was selected such that two

L.-V. Beaulieu et al. / Journal of Constructional Steel Research 66 (2010) 1366–1373 1367

Nomenclature

A Section areaAeff Effective areab Leg widthbeff Effective leg widthb/t Width-to-thickness ratioE Modulus of elasticityFa Allowable compression stressFe Elastic critical buckling stressFcr Effective yield stressFy Specified minimum or measured yield stressKL Effective lengthKL/r Effective slenderness ratioL Length of membert Leg thicknessr Radius of gyrationw Flat width (b− t)

levels of this variable are investigated: (i) slenderness ratio ofapproximately 40, and (ii) slenderness ratio of approximately 110.The width-to-thickness ratio (b/t) is defined as the ratio of

the leg width to the leg thickness. This ratio affects the classof the member based on the definitions of the CAN/CSA S16-09 standard [5], and therefore the method for calculating thecompression capacity of the member. The two levels of width-to-thickness ratio are 6.66 and 13.3. With b/t = 6.66, the member issupposed to yield before local buckling in compression happens.These members are classified as Class 1, 2 or 3 in CAN/CSA S16-09. On the contrary with b/t = 13.3, the member is supposedto be subjected to local buckling before yielding in compression.The latter type of member is classified as Class 4 in CAN/CSA S16-09. In AISC standard 2005 [6], the angles in compression only withb/t = 6.66 is classified as non compact and angles with b/t =13.3 is classified as slender elements. Even if the classificationfollows different wording, both standards recognize that memberwith b/t = 6.66 should buckled globally before local bucklingis reached whereas member with b/t = 13.3 may reach localbuckling first.The corrosion level is measured as a mass loss percentage.

Three levels of this variable were investigated: 0% (not corroded),25% (moderate corrosion), and 40% (severe corrosion). Galvanizedmembers were used in this project because most angle membersexposed to the environment are galvanized and it could have aneffect on the development of corrosion.Table 1 shows all specimens and the level for each variable

mentioned above, as well as the section, length, S16-09 class,and gross area. Each specimen is named after its leg thickness(first two digits), length (L for long and S for short), approximatecorrosion level (0%, 25% or 40%), and specimen number (1 or 2).Two replicate specimens of each combination of leg thickness,length, and corrosion level were tested.

2.1. Accelerated corrosion procedure

The steel members were corroded by the galvanic corrosionprocess [7]. The members were immersed in a conductive solutionsaturatedwith copper sulphate, and connected to the positive nodeof an electric circuit. The galvanized steel piece then plays the roleof the anode. A copper plate cathode was also immersed in thesolution and connected to the negative node of the circuit. Currentwas applied with a constant intensity generator to oxidize thesteel member (from the anode to the cathode). Current intensityand voltage were monitored. Standard assembly for the corrosionprocess is shown in Fig. 1.

Fig. 1. Standard assembly for corrosion.

The steel members were submitted to the process for durationsbetween 250 and 1820 h. The level of corrosionwas determined bythe ratio of the mass of the steel member altered during corrosionto the mass of the intact steel member. Measurements of the legwidth (b) and leg thickness (t) were taken during and after thecorrosion process at three or four locations along the member,depending on the member length. The development of corrosionwas verified regularly on the members.

2.2. Experimental set-up

The experimental set-up developed at the University ofSherbrooke to study the compression capacity of single and Xdiagonal bracing members was used here to assess the strength incompression of the corroded members. The set-up was developedto represent the type of connection used in practice with gussetplates. Computation of end flexibility have shown that for a widerange of members, the boundary conditions of the experimentalset-up replicate adequately the type of flexibility found in practicein bracings. A sketch of the test set-up is shown in Fig. 2. Furtherdetails can be found in [8].Compressive tests were performed under displacement control

using a 500 kN hydraulic actuator in order to develop a stablepost-buckling behavior. The anglememberswere connected to theframe with bolted connections on one leg only (three bolts perconnection). Holes in the angle members were drilled after thecorrosion process.As shown in Fig. 3, the displacement in the axial (z-axis),

in-plane buckling (x-axis) and out-of-plane buckling (y-axis)directions were measured during the tests to observe the non-linear behavior of the steel members. The axial displacementwas evaluated using a potentiometer fixed at the centre bolt ofboth connections. The displacement in the y-axis at the centre ofthe angle member was measured by a linear variable differentialtransformer (LVDT) and adjusted relative to the displacementat the connections, which were evaluated with potentiometersaligned with the centre bolt of each connection. Similarly, thedisplacement in the x-axis was measured by a LVDT at the centreof the member and adjusted relative to the displacement at theconnections measured by a LVDT.

1368 L.-V. Beaulieu et al. / Journal of Constructional Steel Research 66 (2010) 1366–1373

Table 1Test specimens.

Specimen Section L (mm) Nominal % of corrosion b/t Class L/r A (mm2)

48S-00-1 L64× 64× 4.8 500 0 13.3 4 39.7 58248S-00-2 L64× 64× 4.8 500 0 13.3 4 39.7 58248L-00-1 L64× 64× 4.8 1358 0 13.3 4 108 58248L-00-2 L64× 64× 4.8 1358 0 13.3 4 108 58295S-00-1 L64× 64× 9.5 500 0 6.66 1 40.3 112095S-00-2 L64× 64× 9.5 500 0 6.66 1 40.3 112095L-00-1 L64× 64× 9.5 1358 0 6.66 1 110 112095L-00-2 L64× 64× 9.5 1358 0 6.66 1 110 112048S-25-1 L64× 64× 4.8 500 25 13.3 4 39.7 58248S-25-2 L64× 64× 4.8 500 25 13.3 4 39.7 58295S-25-1 L64× 64× 9.5 500 25 6.66 1 40.3 112095S-25-2 L64× 64× 9.5 500 25 6.66 1 40.3 112048L-25-1 L64× 64× 4.8 1358 25 13.3 4 108 58248L-25-2 L64× 64× 4.8 1358 25 13.3 4 108 58248S-40-1 L64× 64× 4.8 500 40 13.3 4 39.7 58248S-40-2 L64× 64× 4.8 500 40 13.3 4 39.7 58295S-40-1 L64× 64× 9.5 500 40 6.66 1 40.3 112095S-40-2 L64× 64× 9.5 500 40 6.66 1 40.3 112095L-25-1 L64× 64× 9.5 1358 25 6.66 1 110 112095L-25-2 L64× 64× 9.5 1358 25 6.66 1 110 112095L-40-1 L64× 64× 9.5 1358 40 6.66 1 110 112095L-40-2 L64× 64× 9.5 1358 40 6.66 1 110 112048L-40-1 L64× 64× 4.8 1358 40 13.3 4 108 58248L-40-2 L64× 64× 4.8 1358 40 13.3 4 108 582

Table 2Results of the corrosion process and compression tests.

Specimen Actual % ofcorrosion

t (average) (mm) t (standarddeviation)

b/t (mm) Class KL/r (S16 andAISC)

KL/r(ASCE)

A (mm2) Exp.capacity (kN)

Failuremodea

48S-00-1 0.00 4.76 – 13.3 4 90.9 79.9 582 n/a 348S-00-2 0.00 4.76 – 13.3 4 90.9 79.9 582 114 248L-00-1 0.00 4.76 – 13.3 4 123.4 114 582 91 148L-00-2 0.00 4.76 – 13.3 4 123.4 114 582 88 495S-00-1 0.00 9.53 – 6.66 1 91.6 80.2 1120 323 195S-00-2 0.00 9.53 – 6.66 1 91.6 80.2 1120 335 195L-00-1 0.00 9.53 – 6.66 1 125.3 115 1120 168 195L-00-2 0.00 9.53 – 6.66 1 125.3 115 1120 167 448S-25-1 26.4 4.32 0.45 14.6 4 91.1 80.0 526 57 348S-25-2 26.6 4.18 0.41 15.1 4 91.0 80.0 509 n/a 295S-25-1 26.9 7.28 0.50 8.65 2 91.5 80.3 864 253 195S-25-2 25.3 7.18 0.47 8.77 2 91.5 80.2 853 251 148L-25-1 27.4 3.86 0.19 16.3 4 123.6 114 471 80 148L-25-2 27.3 3.84 0.27 16.4 4 123.6 114 469 79 148S-40-1 37.2 3.51 0.24 17.9 4 90.9 79.9 430 66 248S-40-2 37.3 3.37 0.39 18.7 4 90.9 79.9 413 63 295S-40-1 37.1 6.43 0.51 9.80 3 91.4 80.2 769 216 195S-40-2 36.1 6.25 0.54 10.1 3 91.3 80.2 748 202 295L-25-1 22.4 7.80 0.33 8.08 2 125.1 115 922 151 195L-25-2 21.5 7.98 0.37 7.89 2 125.1 115 942 150 195L-40-1 30.7 6.79 0.49 9.28 3 124.7 115 809 99 395L-40-2 27.2 7.08 0.88 8.90 2 124.8 115 842 99 1b48L-40-1 40.7 3.28 0.24 19.2 4 123.4 114 403 65 148L-40-2 47.1 2.63 0.39 24.0 4 123.1 114 324 25 1b

a Legend for failure modes: 1-global buckling, 2-local buckling near connections, 3-local buckling near centre, 4-mode not clearly identified in the test.b Perforated members.

3. Experimental results

3.1. Geometry of corroded members

The steel members reached corrosion levels between 21% and47% when submitted to the accelerated corrosion process. Thecorrosion level is measured in terms of weight loss. Each memberwas weighed before being corroded. During accelerated corrosionand at the end, the member was cleaned from corrosion with abrush and weighed. Half of the specimens are displayed in Fig. 4,showing the samples after the compression test. Two memberswere perforated and are displayed in Fig. 5. One of the legs ofmember 95L-40-2 was very lightly perforated near the centre.Member 48L-40-2 nearly lost an entire leg over a short length near

the centre. The circular hole in this member was drilled before thecorrosion process.Themain properties and the S16-09 class of the specimens after

corrosion are shown in Table 2. The leg width (b) for corrodedmembers was approximately constant at 63 mm for all specimens.The thickness of the member was also measured on each leg atthree locations for short members and four locations for longmembers to provide an average thickness to be used to predictthe residual strength. In practice, weight measurements are notan option, but it is common to measure the residual thickness andvarious measuring tools are available for this purpose. Hence, toinsure that the predicted strength is obtained in a realistic manner,the parameters b/t , KL/r and A from Table 2 were calculated basedon the average measured thickness of the corroded members.In this table r is the radius of gyration around the minor axis.


Fig. 2. Elevation of the compression test assembly.

Fig. 3. Position of the instruments.

Fig. 4. Selection of corroded members after the compression.

The ratio of average thickness over nominal thickness is graphedwith respect to the level of corrosion in Fig. 6. Error bars arealso present in this figure to show the minimum and maximumthicknessesmeasured on themembers and illustrate the variabilityof corrosion. Fig. 6 shows that the average leg thickness iscorrelated to the level of corrosion (measured by weight loss) andtherefore it can be used as a practical measure of corrosion.

Fig. 5. Perforated members 95L-40-2 and 48L-40-2.

To providemore information on the uniformity of the corrosion,the thickness of corroded members was measured at each point ofthe grid shown in Fig. 7. The standard deviation on thickness forall corroded members is shown on Table 2. It is interesting to notethat the standard deviation on thickness is not clearly related tothe initial member thickness and to the corrosion level, althoughthere is a lot of variability.

3.2. Compression tests

Fig. 8 shows the results of the tests in terms of ratio betweenresidual strength and uncorroded strength. The value of theuncorroded strength is taken as the average of the experimentalstrength of the two members of the same series that are notcorroded. Table 2 presents the capacity obtained during the testsand the observed failure modes. It is observed in Fig. 8 thatthe rate of capacity loss tends to increase with the level ofcorrosion. Indeed, most points at low corrosion levels are abovethe reference line whereas most points at high corrosion levelare below the reference line. The reference line supposes a linearrelation between level of corrosion and capacity loss. The tworeplicate specimens generally gave very similar results. The type offailure was observed to be either local or global and the bucklingoccurred at various locations along the members. It should benoted that the classification of failuremodes is not straightforwardand therefore these observations should be analyzed with care.Nevertheless, the following comments can be made:• 48S members generally showed local buckling.• The three other types of members generally displayed globalbuckling, except for some severely corroded members.


Fig. 6. Ratio of average thickness to nominal thickness versus level of corrosion.

In two cases, as shown in Fig. 5, complete perforation of themember was observed. In the case of member 48L-40-2, theperforation was major and observations of the failed membershow that the perforation affected the overall compressioncapacity. Specimens 48S-00-1 and 48S-25-2 did not produce anycompressive capacity results due to difficulties in the experimentalprocedure.The radius of gyration varied moderately due to the moderate

change of the leg width which affects the inertia of the member.The slenderness ratio is directly dependent on the variationof the radius of gyration and therefore was subject to minormodifications only. However, the section area of the membersvaried significantly, causing major changes to the compressivecapacity of the steel angle members.

4. Analysis of results

4.1. Strength prediction

The CAN/CSA S16-09 standard [5], AISC 2005 [6] and the ASCE10-97 standard [9] were used to calculate the theoretical capacityin compression of the corroded steel members based on theaverage leg thickness measured in the laboratory.The modulus of elasticity E assumed in the calculations is

200,000 MPa. The yield stress Fy is 365 MPa for L64 × 64 × 4.8members, and 345MPa for L64×64×9.5members asmeasured oncoupons cut from the members before the corrosion process. Theyield stress was measured as per the ASTM E8-61T standard [10].The three codes use a column strength curve where maximumstress is related to effective slenderness KL/r . In order to accountfor the way the loads are applied in a real single angle bracing(loads not applied at centroid and retraints different from simplesupport at end) the three codes propose equations to estimate

parameterK .Wewill first present the column strength curves usedby the three codes, and after the estimation of K .ASCE 10-97 proposes a strength equation accounting for both

local and global buckling. The allowable compression stress Fa isgiven by Eqs. (1)–(3).

Fa =[1−

12

(KL/rCc

)]Fy for

KLr≤ Cc (1)

Fa =π2E( KLr

)2 forKLr> Cc (2)

Cc = π

√2EFy. (3)

To account for local buckling of angle sections, Fy is replacedin Eqs. (1)–(3) by Fcr for large width-to-thickness ratios w/t . Forsimplicity, the flat width w is defined in the present study as theleg width bminus the thickness t . Eqs. (4)–(6) present the variousexpressions for Fcr and their corresponding width-to-thicknessratios.(wt

)lim=80ψ√Fy

(4)

Fcr =[1.677− 0.677

w/t(w/t)lim

]Fy

for(wt

)lim≤w

t≤144ψ√Fy

(5)

Fcr =0.0332π2E(w/t)2

forw

t≥144ψ√Fy

(6)

with ψ = 2.62 for SI units. Similarly to ASCE10-97, AISC 2005 hasincluded in the column curve the leg slenderness effect through theuse of parameter Q :

(a)KLr≤ 4.71

√EQFy

or Fe ≥ 0.44QFy (7a)

Fcr = Q[0.658

QFyFe

]Fy

(b)KLr> 4.71

√EQFy

or Fe < 0.44QFy (7b)

Fcr = 0.877Fewhere Q is calculated from the ratio b/t:

(i)Whenbt≤ 0.45

√EFy

Q = 1. (8a)

(ii)When 0.45

√EFy<bt≤ 0.91

√EFy

Fig. 7. Sketch of thickness measurements.


Fig. 8. Experimental percentage of residual capacity in compression versus level ofcorrosion.

Q = 1.34− 0.76(bt

)√FyE

(8b)

(iii)Whenbt> 0.91

√EFy

Q =0.53E

Fy( bt

)2 . (8c)

The CAN/CSA S16-09 provides only a strength curve accountingfor global buckling. The local buckling is accounted for througha reduction of the member cross-section named ‘‘effective area’’.To calculate the capacity of the members as per CAN/CSA S16-09standard (2005), the effective area Aeff has to be calculated for allclass 4 angle members. Please note that the area shown in Table 2is the area evaluated from the measured leg thickness and notthe effective area. Eq. (9) below represents the limit of width-to-thickness ratio that must be respected in the S16-09 standard forclass 3 members. If it is not respected, the member is class 4, anda value of beff is determined such that beff/t respects the criteria ofEq. (9).

bt≤200√Fy. (9)

An effective area is then calculated using Eq. (10).

Aeff = A− 2(b− beff)t. (10)

The capacity of the angle is therefore calculated with

Cr = ϕAFy(1+ λ2n

)−1/n(11)

where

n = 1.34

λ =

√FyFe

Fe =π2E( KLr

)2 .Calculation of strength is based on the determination of variableKL/r . The length of the member L is taken in the calculation asthe distance from centroid of connection to centroid of connection.Experimental evidence has however shown that the effectivelength KL may be different from theoretical length and thatbuckling may not occur around the minor axis. For example, itcan be seen in Figs. 9 and 10 that at the time initial bucklingoccurs, i.e. when the force is a maximum, the displacement inthe in-plane and out-of-plane directions are different, indicatingthat the failure did not initiate in the minor axis as it would

Fig. 9. In-plane and out-of-plane displacements at centre of angle member 95S-25-1.

be predicted assuming simple connections and no eccentricity.This phenomenon is due to the effect of the connections and iscurrently studied at the University of Sherbrooke. Nevertheless,because the gusset plates in the tests had flexibility very close tothe flexibility of gusset plates or angle leg of cord members usedin practice, it was considered that the codes should take this effectinto account, at least in a limited way. Indeed, ASCE 10-97 allowsmodifying KL/r with Eq. (12) for members with normal framingeccentricities at both ends of the unsupported panel and Eq. (13)for members partially restrained against rotation at both ends ofthe unsupported panel (ASCE 10-97).

KLr= 60+ 0.5

Lrfor 0 ≤

Lr≤ 120 (12)

KLr= 46.2+ 0.615

Lrfor 120 ≤

Lr≤ 250. (13)

Both effects are found in the present study, but in agreement withASCE 10-97, it is assumed that for L/r below 120, the eccentricityof connections governs and Eq. (12) is used to calculate KL/r . AISC2005 and S16-09 have introduced such a method to calculate theeffective length. Both codes have the same equations:

0 ≤Lrx≤ 80 :

KLr= 72+ 0.75

Lrx

(14a)

Lrx> 80 :

KLr= 32+ 1.25

Lrx≤ 200. (14b)

Even if ASCE10-97 uses radius of gyration around the principal axisand AISC 2005 as well as S16-09 use radius of gyration around thegeometrical axis, both approach provide values close to each otheras it is seen in Table 2, S16-09 and AISC 2005 providing slightlylarger KL/r than ASCE10-97.

4.2. Comparison of experimental and theoretical results

Table 3 shows the predicted capacity. The calculation of thetheoretical strength was based on an average thickness measuredin laboratory. The theoretical calculations therefore assume aconstant corroded thickness. Predictions with ASCE 10-97 areusually better than S16-09 and AISC 2005. It is seen from Table 3that if codes S16-09 AISC 2005 and ASCE 10-97 can capture wellthe strength loss of some members, capacities are sometimes notwell predicted. This can be attributed to the lack of uniformityof the corrosion. In fact, complete perforation was found on twomembers (see Fig. 5). In particular, the capacity of member 48L-40-2 was greatly reduced due to perforation because most of oneleg was lost near the centre. Another example is member 48S-25-1 which is particularly weaker than its predicted capacity.


Table 3Experimental and theoretical results for the compression capacity.

Specimen Actual % of corrosion Exp.capacity (kN)

CapacityS16-09 (kN)

CapacityASCE (kN)

CapacityAISC (kN)

Exp./S16-09

Exp./ASCE Exp./AISC

48S-00-1 0.00 n/a 77.2 142 108 n/a n/a n/a48S-00-2 0.00 114 77.2 142 108 1.48 0.80 1.0648L-00-1 0.00 91 49.6 88.6 66.1 1.84 1.03 1.3848L-00-2 0.00 88 49.6 88.6 66.1 1.77 0.99 1.3295S-00-1 0.00 323 186 278 209 1.74 1.16 1.5595S-00-2 0.00 335 186 278 209 1.81 1.21 1.6095L-00-1 0.00 168 119 168 123 1.42 1.00 1.3695L-00-2 0.00 167 119 168 123 1.41 0.99 1.3548S-25-1 26.4 57 63.4 121 95.3 0.89 0.47 0.5948S-25-2 26.6 n/a 59.4 114 91.6 n/a n/a n/a95S-25-1 26.9 253 144 214 162 1.77 1.18 1.5795S-25-2 25.3 251 142 212 160 1.77 1.19 1.5748L-25-1 27.4 80 32.5 70.4 53.4 2.44 1.13 1.4948L-25-2 27.3 79 32.2 69.9 53.2 2.46 1.13 1.4948S-40-1 37.2 66 41.9 80.6 73.1 1.57 0.82 0.9048S-40-2 37.3 63 38.7 73.0 69.1 1.62 0.86 0.9195S-40-1 37.1 216 128 191 144 1.69 1.13 1.5095S-40-2 36.1 202 125 186 140 1.62 1.09 1.4495L-25-1 22.4 151 97.9 137 102 1.54 1.10 1.4895L-25-2 21.5 150 99.9 140 104 1.50 1.07 1.4495L-40-1 30.7 99 86.4 121 90.1 1.15 0.82 1.1095L-40-2 27.2 99 89.7 126 93.6 1.10 0.79 1.0648L-40-1 40.7 65 23.5 54.3 45.2 2.76 1.20 1.4448L-40-2 47.1 25 15.2 32.1 33.2 1.65 0.78 0.76

Fig. 10. In-plane and out-of-plane displacements at centre of angle member 95S-40-2.

The failure mode of this member was very localized on one legnear the centre. The failure in this case was due to the largeb/t and is not influenced by its KL/r value. The thickness nearits failure point is approximately 3.3 mm, nearly 1 mm smallerthan its average measured thickness. The experimental capacityof 57 kN would be obtained for a thickness of approximately3.1 mm with ASCE 10-97. As seen in these two examples, thecompression capacity is largely dependent on the extent and thelocation of the corrosion. Concentration of corrosion reduces inan acute way the capacity of the member, specifically when suchconcentration occurs near the middle of the member. Corrosionis critical at the middle of the member because this is where themoment due to the eccentricities of the connections is amaximum.This non-uniformity of the phenomenon explains in large part thedifferences between the experimental and theoretical results.Study of the failure modes and comparison of the experimental

and predicted strength is best observed with the help of Fig. 11.In this figure, the compressive stress, equals to the compressivestrength divided by the average section area, is plotted againstthe width-to-thickness ratio. The 48S and 95S members should becompared to the S16 and AISC, KL/r = 91 and ASCE, KL/r = 80curves. On the other hand, 48L and 95L members are compared to

Fig. 11. Stress versus width-to-thickness ratio.

the S16, KL/r = 125 and ASCE, KL/r = 115 curves. The slender-ness ratios used in the ASCE 10-97 are larger due to themodifications of Eqs. (12)–(14). Members 95S are found in anarea of the strength curve, which is not affected by the width-to-thickness ratio. Consequently, as observed in the tests, thesemembers generally display global buckling. Similar observationscan be made for 95L members. Members 48S, however, mostlydisplayed local buckling, which is in accordancewith their locationin the strength curve: the capacity in this area is influenced bythe width-to-thickness ratio. Except for member 48L-40-2, whichhas a very large width-to-thickness ratio, 48L members are notinfluenced by b/t . For this reason, the predictions of the ASCE 10-97 are much more accurate than those of the S16-09 for this typeof member. AISC 2005 provides better results than S16-09 becausethe b/t is better accounted for even if the larger KL/r reduces thecapacity predicted for those members as compared to ASCE10-97.Table 4 presents various averages and standard deviations

for the ratio of experimental to theoretical capacity. ASCE 10-97generally provides averages closer to one and smaller standarddeviations than S16-09. AISC is generally between ASCE and S16in terms of prediction and standard deviation. As expected, thevariability in the prediction of capacity is larger for corrodedmembers than for uncorroded members.


Table 4Average ratio of experimental to theoretical capacity.

Characteristic ofspecimens

Average ratio S16-09 Standard deviationS16-09

Average ratio ASCE10-97

Standard deviationASCE 10-97

Average ratio AISC Standarddeviation AISC

All specimens 1.68 0.43 1.00 0.19 1.29 0.29Uncorroded 1.64 0.19 1.03 0.13 1.38 0.18Corroded 1.70 0.51 0.98 0.21 1.25 0.33Corroded 4.8 mm 1.92 0.66 0.91 0.26 1.08 0.38Corroded 9.5 mm 1.52 0.26 1.05 0.16 1.39 0.2025% nominalcorrosion

1.77 0.55 1.04 0.25 1.38 0.35

40% nominalcorrosion

1.65 0.51 0.94 0.17 1.14 0.29

It is interesting to note in Table 4 that predictions of the capacityof members with 9.5 mm legs are better than the predictionson 4.8 mm leg members. The average of the predictions is closeto experimental results for 9.5 mm leg members and variabilityis smaller than for 4.8 mm leg members. The scatter in theratio experimental/prediction observed on 4.8-mm leg thicknessmembers might be attributed to the irregularity of the corrosionprocess when corrosion level increases.Surprisingly, members with nominal level of corrosion 40% do

not have larger variability than 25% corroded members. This ispartly due to the large scatter obtained for some 25% corrodedmembers, in particular member 48S-25-1. More specimens with alarger range of level of corrosion would be needed to further studythe effect of corrosion on the difference between predicted andexperimental capacity.

5. Conclusions and recommendations

This article presents the compression test of 24 members, 16of them being corroded at a level corresponding to weight lossranging from 21% to 47%. The corrodedmembers lost between 10%and 70% of their uncorroded capacity.The reduction in capacity of many members was not predicted

accurately using the S16-09, ASCE 10-97, and AISC codes. Thevariation in the results can be explained by the non-uniformity ofcorrosion. ASCE 10-97 predicts the strength reduction of membersmore accurately because it offers a better way to predict localbuckling due to large width-to-thickness ratio.This experimental program showed that it may be possible to

estimate the capacity of a corroded angle steel member using apredictionmethod based on average residual thickness of memberand ASCE 10-97. For members with initial thickness of 9.5 mm, theratio of predicted/experimental capacity has an average of 1.05 anda standard deviation of 0.16. For members with thickness 4.8 mm,the ratio of predicted/experimental capacity has an average of 0.91and a standard deviation of 0.26.Themethod needs improvement to be able to predict accurately

residual strength. For example, it is required to take into accountthe unevenness of corrosion and concentration of corrosion aswellas location of those concentrations.

To develop empirical charts that can be used in practice toevaluate directly the residual strength, it is believed that additionalexperimental data would be required, in particular for memberswith level of corrosion between 0% and 20%. Additional data forother leg thickness and KL/r would also be interesting. For utilities,residual strength curves as a function of time are also necessary toplan asset repairs and replacements. For this purpose, additionalresearch is required to transform corrosion level into remaininglife time, depending on environment aggressiveness. Finally, it isalso necessary to verify that the actual corrosion pattern found onsteel structures is similar to the corrosion pattern obtained in thisexperiment through an accelerated corrosion method.

Acknowledgements

The research was performed within the Industrial ResearchChair NSERC/HQT on Mechanics and Structures of TransmissionLines. The financial support of NSERC and Hydro-Québec TransÉn-ergie (HQT) is therefore acknowledged. The valuable collaborationof Maryse Lavoie and André Vallée fromHQT for this project is alsoacknowledged. The help of Jonathan Dubuc, graduate student atthe University of Sherbrooke was greatly appreciated.

References

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[2] Kayser JR, Nowak AS. Capacity loss due to corrosion in steel-girder bridges.J Struct Eng 1989;115:1525–37.

[3] Sarveswaran V, Smith JW, Blockley DI. Reliability of corrosion-damaged steelstructures using interval probability theory. Struct Safety 1998;20:237–55.

[4] Sarveswaran V, Smith JW. Structural assessment of corrosion-damaged steelbeams using minimum capacity curves. Struct Eng 1999;77:17–23.

[5] CAN/CSA S16-09. Limit states design of steel structures. 2005.[6] ANSI/AISC 360-05. Specification for structural steel building. 2005.[7] Winston Revie R. Uhlig’s corrosion handbook. 2nd ed. New York: John Wiley& Sons; 2000.

[8] Morissette E. Évaluation des normes de calcul et du comportement descornières simples en compression utilisées comme contreventements dans lespylônes à treillis en acier. M.Sc.A. thesis; 2008.

[9] ASCE 10-97. Design of latticed steel transmission structures. 1997.[10] ASTM E 8-61T. Tentative methods of tension testing of metallic materials.

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beaulieu-compression strength of corroded stel angle members (1)

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