Remaining Capacity Assessment of Corrosion Damaged Beams Using Minimum Curves

Journal of Constructional Steel Research 65 (2009) 299–307www.elsevier.com/locate/jcsr

Remaining capacity assessment of corrosion damaged beamsusing minimum curves

R. Rahgozar∗

Department of Civil Engineering, University of Kerman, Kerman, P.O. Box: 76169-133, Iran

Received 29 September 2007; accepted 10 February 2008

Abstract

The number of exposed steelwork structures used in various industries is steadily increasing as a result of building new structures and extendingthe life of older structures. Most of these structures are subjected to corrosion due to environmental exposure which can reduce their carryingcapacity. Corrosion damage is a serious problem for these structures. Current assessment methods of corrosion damaged steelwork involve visualinspection which tends to be used very conservatively. There is a need for more accurate assessment method which can be used to make reliabledecisions affecting the cost and safety. In this paper, various forms of corrosion are reviewed along with how uniform corrosion affects steelstructures. Corrosion decay models are developed based on the information on the locations where corrosion occurs. The effects of corrosion onsteel beams are analyzed by evaluating the remaining capacity with regard to bending stresses, shear failure, lateral torsional buckling, and bearingfailure. Four samples of corrosion damaged beams, which were removed from a chemical works, were measured for their thickness loss and thensubjected to load test for their ultimate capacities. The failure loads of the beams are compared with the calculated capacities of various corrosiondamage models. In order to estimate the percentage remaining capacity of corrosion damaged I-beams, minimum curves for different types ofuniversal beams which are developed can be used in conjunction with the information on the thickness loss.c© 2008 Published by Elsevier Ltd

Keywords: Corrosion; Damaged beam; Minimum curves; Remaining capacity

1. Introduction

Corrosion of steel structures is a serious problemthroughout the world. Many of these structures are undergoingdeterioration due to corrosion. The deterioration of steelstructures has become a very important issue. In the USA,40% of the bridges are built of steel. Many of these bridgesare deteriorating due to corrosion caused by aggressiveenvironments and inadequate maintenance Kayser [1]. Inthe UK the petrol-chemical industry has been using steelextensively as the primary structural material for structuressuch as pipe bridges, frame support for vessels and processequipment. Many of these structures have reached nearly50 years of service life are in a severely deteriorated conditiondue to aggressive environments combined with their age [2].

As a consequence, inspection, maintenance and repair arebecoming increasingly complex and costly because of the

∗ Fax: +98 341 3220054.E-mail address: [email protected].

0143-974X/$ - see front matter c© 2008 Published by Elsevier Ltddoi:10.1016/j.jcsr.2008.02.004

need to keep important manufacturing processes in continuousoperation. The cost of closing down plants and consequent lossof production of a continuous process may be very high. Thiscost should, if possible, be compared with costs arising fromstructural failure. The latter may also be very high dependingon the nature of the materials being processed, whether they aretoxic, explosive, inflammable, or alternatively, relatively lesshazardous.

Currently deteriorated structures are visually inspected andcategorized into four condition categories according to thelevel of deterioration [3]. The categories with most severecondition are then subjected to design checks using sectionproperties based on the measured section sizes. Although thesepractices appear to be reasonably safe, on the one hand theymay be conservative while on the other hand there may becritical details which receive insufficient attention. Therefore,a more precise method of evaluation of remaining capacity ofdeteriorated structures will be an advantage in terms of cost andsafety.

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300 R. Rahgozar / Journal of Constructional Steel Research 65 (2009) 299–307

(a) Uniform thickness loss (Model 1).

(b) Varying thickness loss (Model 2).

Fig. 1. Corrosion decay models simulated by reducing the thickness of element (uniform and varying thickness loss).

2. Corrosion of steel structures

2.1. Forms of corrosion

Steel has been used extensively throughout the world forthe construction of buildings, bridges, factories, etc. In order toproduce steel, iron ores must be processed. During the processof metal extraction, it consumes a large amount of energy toseparate the metal from ore. In the natural environment, it hasa tendency to oxidize to a form similar to its natural stateunder the influence of air and water. This deterioration processis known as corrosion. Corrosion may appear in many forms.These forms are classified according to how the corrosionattacks the metal. The types of metal corrosion which occurin different types of steel structures are uniform corrosion,pitting corrosion, crevice corrosion, stress corrosion, galvaniccorrosion and corrosion fatigue.

Uniform corrosion is the formation of oxide, distributeduniformly over an exposed surface. This is the most commonform of the corrosion, which will lead to the gradual thinning ofmembers, accordingly for the greatest destruction of metal [4].Also it has been pointed out by Kayser [1] that this typeof corrosion is the most serious form of corrosion observedon steel bridge. The rate of uniform corrosion loss is highlyvariable, depending on conditions such as temperature, time ofwetness, and chemistry.

If the corrosion is concentrated in small area it may form apit at the metal surface. This form of corrosion can be seriousin high-stress region because it can penetrate into the metal

showing little evidence of its existence [5]. Pits will formimperfections on the metal surface and these imperfections willact as stress concentrations, reducing the fatigue capacity ofthe metal and increasing the metal’s sensitivity to cracking [6].Pitting is random in nature and occurs quickly. Pitting may beinitiated by external factors, e.g. where external deposits suchas debris and de-icing salts have settled on the metal surface.Pitting corrosion is prone to occur in certain environments,particularly in the presence of salt. For more details about alltypes of corrosion refer to Fontana [4].

2.2. Corrosion pattern

The main critical factor corrosion of steel is the localenvironment. Another important aspect is the occurrence ofvarious forms of corrosion. The most common form is thegeneral surface corrosion which causes the gradual thinning ofmembers. Corrosion of steel occurs on the surface where waterand contaminants can accumulate. Detailed measurementsof corrosion penetration lead to the following conclusionsconcerning the corrosion pattern of an I-beam [1]; as shownin Fig. 1:

1. The top surface of the bottom flange and the bottom part ofthe web (0.25hw) are the places where the severest corrosiontakes place.

2. Corrosion takes place on the surface of the top flange but notto the extent of bottom flange.

3. Corrosion also takes place in the top part of the web (0.75hw)but the loss is very much less compared to that bottom partof the web.

R. Rahgozar / Journal of Constructional Steel Research 65 (2009) 299–307 301

Table 1Average measured thickness of samples of corrosion damaged beams

Element As-new Beam 1 Beam 2 Beam 3 Beam 4

Top flange (TT ) 10.20 7.45 7.81 7.23 7.83Bottom flange (TB ) 10.20 5.62 5.85 4.84 7.61Average flange thickness (T ) 10.20 6.54 6.83 6.04 7.72Average thickness loss of (T ) 0.00 3.66 3.37 4.16 2.48%Average thickness loss of (T ) 0.00 35.9 33.0 40.8 24.3

Upper part of web, 0.75hw , (tU ) 6.10 5.63 5.74 5.45 5.84Lower part of web, 0.25hw , (tL ) 6.10 3.16 4.32 3.18 4.74Average web thickness (t) 6.10 5.01 5.39 4.88 5.57Average thickness loss of (t) 0.00 1.09 0.71 1.22 0.53%Average thickness loss of (t) 0.00 17.8 11.7 20.0 8.77

Average stiffener thickness (tS) 9.53 8.55 8.66 8.63 8.71Average thickness loss of (tS) 0.00 0.98 0.87 0.90 0.82%Average thickness loss of (tS) 0.00 10.3 9.13 9.44 8.60All measurements are in millimeters

4. In the initial stages of corrosion, corrosion penetration maybe taken uniform everywhere.

The top surface of the top flange can also accumulatecontaminants due to spillage from tanks especially in chemicalindustries. This would cause the corrosion of the top surfaceof the top flange as well, but may not be to the extent of thebottom flange. Loss of material in the web near the supportsmay also occur because of the leakage from the top. Visualexamination and measurement of the thickness of four corrodedI-beam obtained from a chemical industry also indicated thatthe corrosion pattern is similar to what is described above.

2.3. The effects of corrosion damage

The main effects of corrosion on steel structures can be lossof material from the surface which leads to thinner sections, lossof material strength and accumulation of corrosion products(rust) on the surface. The section properties of a member, suchas second moment of area, area, radius of gyration, etc., wouldbe reduced due to loss of material, thus causing a reductionin the carrying capacity of the structure. There is a danger ofcrevice corrosion in bolted joints which will lead to loss of areaof the bolts.

The class of a section (plastic, compact, semi-compact, orslender) may be changed from one to another due to the lossof thickness of compression flange and web due to corrosion.For example, a section that is plastic or compact at its as newcondition may become semi-compact due to loss of thicknessand local buckling may prevent the development of full plasticmoment [7] in such cases.

3. Development of minimum curves

3.1. Analysis of corrosion damaged beams

A steel member subjected to bending can fail in differentways depending on the governing factor. The main mode offailures can be:

(1) The webs, which carry shear forces, can fail in shear.

(2) Excessive yielding of steel under direct stresses.(3) Lateral torsional buckling.(4) Bearing failure can occur in the web near the support or at

the loads.

In order to estimate the percentage remaining capacity ofcorroded I-beams with regard to all the above mentioned failuremodes, an analysis was carried out on a corrosion damagedmodel which is simulated by reducing the thickness of flangesand webs. Four identical universal beams (305×165 UB 40 kg)were recovered from the site of a chemical plant undergoingdemolition. The beams formed corner supports for a steeltank, all in severely corroded condition (nearly 30 years old).The thicknesses of these beams were measured. The measuredthicknesses of the elements are given in Table 1. As manyreadings as possible (up to 200 readings for each element) weretaken in order to increase the accuracy of the measurements. Itwill be noted in Table 1 that the loss of thickness on averagewas more significant in the flange than the web. The loss ofthickness of flange and web in this model were in similarproportion to the thickness loss of the corrode beams obtainedfrom ICI Ltd as shown in the Fig. 1.

The beams obtained from ICI Ltd have a cut-out at one endof the top flange. These beams are called “coped beams” and thelateral end restraint is considerably reduced because rotationof the flange in plan is not resisted at the coped end. Lateraltorsional buckling is the most important failure mechanism forthese coped beams. The method of assessment proposed byCheng et al. [8] was used in this case. BS 5950 was used for theassessment of the moment capacity, which is mainly dependenton the yield strength of the steel and the flange area [7].

Failure of the web due to shear was the next most significantfailure mechanism. The effect of varying web thickness andthe effect of uniform thickness loss were calculated based onBS 5950 [4]. The buckling capacity of web was estimated byusing the method proposed for the local buckling of plates byJohnston [9] and Timoshenko et al. [10]. The edge conditionsfor the web were considered as simply supported. The webbearing capacity and stiffener buckling capacity were estimatedusing BS 5950 [7]. The results obtained from the theoretical


(a) Geometry of a web panel. (b) Buckled shape.

Fig. 2. Web buckling due to pure shear.

Table 2Results obtained from the theoretical analysis of samples of corrosion damagedbeams

Beam no. Thicknessloss/mm

Ultimate load/kN

Moment Shear Bearing Lateraltorsionalbuckling

As-new 0.00 672.2 667.1 857.1 523.9Beam1 3.94 404.7 233.4 667.7 212.1Beam2 3.65 424.7 348.9 716.7 240.5Beam3 4.51 377.9 212.7 655.7 170.5Beam4 2.63 471.7 462.6 742.8 340.4

analysis of samples of corrosion damaged beams are given inTable 2.

3.2. Shear capacity

The shear capacity of corroded beams can be evaluated usingBS 5950: Part 1: 1985 [7]. The shear capacity of a section isdependent on the slenderness of the web which in turn dependson the depth to thickness ratio, d/t . The code recommends thatwhen d/t exceeds 63ε it should be checked for shear bucklingin accordance with BS 5950. This shows that ‘ε’ can be animportant factor on the shear capacity. The equation for ‘ε’

which is given by ε =

√(275/Py

), shows that the design

strength, py , can be an important factor on the shear capacity.The code recommendations for the shear capacity without usingtension field action were based on the theory of buckling ofplates [9,10].

The shear stress at which the web buckles can be predictedfrom plate buckling theory [10]. It is assumed that all four edgesof the web are simply supported. As shown in Fig. 2, the elasticcritical web buckling stress, τcr , is given by:

τcr = k

{π2 E

12(1− ν2

)(d/t)2

}(1)

where k is given by [9]:

k = 4.00+5.34

α2 for α ≤ 1 (2a)

k = 5.34+4

α2 for α > 1 (2b)

where α = a/d as shown in Fig. 2. If the numerical values forν = 0.3, E = 205 KN/mm2 and each of the Eqs. (2a) and (2b)substituted into Eq. (1) separately, then:

τcr =

{0.75+

1

(a/d)2

}{1000

(d/t)

}2

for α ≤ 1 (3a)

τcr =

{1+

0.75

(a/d)2

}{1000

(d/t)

}2

for α > 1. (3b)

The code uses the notation, qe, instead of τcr for the elasticcritical shear stress. The code identifies three modes of behaviorof webs. The first is where the web strength is governed byits ultimate web capacity, i.e. 0.6pyw, the third is where thecapacity is solely governed by the elastic critical shear stress,qe, and the intermediate stage is where an interaction occursbetween the first and third behaviors. The divisions betweenthe three modes are quantified by equivalent web slendernessfactor. λw, which is given by:

λw =

(0.6Pyw

qe

)1/2

. (4)

The code gives the critical shear strength, qcr , of a web panelas follows:

qcr = 0.6pyw for λw ≤ 0.8 (5a)

qcr = 0.6pyw [1− 0.8 (λw − 0.8)] for 0.8 < λw < 1.25 (5b)

qcr = qe for λw ≥ 1.25. (5c)

3.3. Effect of corrosion on shear capacity

The corrosion in the web and flanges results in the reductionin shear capacity. In addition, the class of a section may bechanged from one to another due to the loss of thickness of web.For example, an element that is plastic or compact at its as newcondition may become semi-compact due to loss of thickness.The code recommends that when d/t exceeds 63ε it should bechecked for shear buckling. The web thickness of a corrodedbeam can be uniform at the initial stages of corrosion. If websof corrosion damaged beams vary in thickness significantly,the shear capacity should be calculated from first principlesassuming elastic behavior. In sections where the variation in theweb thickness due to corrosion is small, average web thicknessmay be used for evaluating the shear capacity.

The aim of this study is to obtain minimum curves forthe percentage remaining shear capacity that can be caused topredict the shear capacity of corroded beams. This minimumcurve can be obtained by identifying the worst possible case.The Eq. (3b) shows that a minimum qe can be obtained whenα = a/d is large or infinitive, i.e. when no stiffener is provided.


Using Eqs. (3b) and (4) and a/d = ∞, it can be shown that,

d

t= 62.3ε for λw = 0.8 (6a)

d

t= 97.3ε for λw = 1.25. (6b)

Therefore, using the above information and taking into accountthe fact that corrosion may change the class of an element, twomain categories of sections in terms of d/t are considered forthe development of minimum curves for the shear capacity. Thetwo categories are given below:

Category 1— sections with d/t ≤ 63ε

Category 2— sections with d/t > 63ε.

3.4. Minimum curves for shear capacity

The category 1 (C1) sections are considered first to analyzeand possibly identify minimum curves that can be used toestimate the remaining shear capacity of corroded beams.Although the corrosion reduces the thickness of a web, somesections which have lowest value of d/t at their as newcondition may remain as C1 throughout or part of their servicelife. For C1 beams, the shear capacity, PνN, is given by:

PνN = 0.6py D t for as new section. (7)

Shear capacity of a rolled I-beam,

PνC = 0.6py AνC for corroded section (8)

where Aν , is the shear area taken as tD for rolled I-sections,and td for welded I-sections. For corroded I-beams of the samesection size, the depth, D and d can be taken as constantthroughout its service life. The percentage remaining shearcapacity (%RSC) of a corroded beam is the ratio of the capacityof the corroded beam (PνC ) to the capacity of the beam at its asnew condition (PνN ).

%RSC = 100(

PvC

PvN

). (9)

Using Eq. (8),

PνN = 0.6pywDtN (10)

PνC = 0.6pywDtC , (11)

where tN and tC are web thicknesses at its as new condition andcorroded state respectively. By substituting Eqs. (10) and (11)into Eq. (9), the percentage remaining shear capacity (%RSC)is given by:

%RSC = 100(

tCtN

). (12)

Eq. (12) can be given in another form in terms of the percentageloss of web thickness (%LWT) as follows:

%RSC ≈ 100(

1−tN − tC

tN

)(13)

%RSC ≈ 100−%LW T . (14)

Therefore, the percentage remaining shear capacity curve ofsections that are C1 at their as new condition and remain thesame throughout their service life will be a straight line witha slope of approximately −1. In this case, the Eq. (14) can beused as the minimum curve for the remaining shear capacity ofsections that are C1 ate their as new condition and remain thesame throughout or part of their service life, as the percentageremaining shear capacity is a function of percentage loss of webthickness alone.

Minimum curves may also be obtained using anotherapproach. If the percentage remaining capacity of a beam withregard to a particular failure mode against the loss of thicknessis plotted, we will get a curve which gives the relationshipbetween them. If this is repeated for all of the availableI-section, we will get a number of curves from which we shouldbe able to identify the curve that gives the lowest value ofremaining capacity. This curve can be taken as the “minimumcurve” for that particular failure mode and can be used toestimate the percentage remaining capacity with regard to thatparticular failure mode. The estimates will be conservativesfor some sections since we considered the worst case as theminimum curve.

Based on the above approach a family of sections wasanalyzed to study the behavior of the percentage remainingshear capacity of corroded beams. The design strength waschosen such that all the sections remain as C1. The results areshown in Fig. 3.

It can be seen from Fig. 3 that the percentage remainingshear capacity curves of beams that are C1 at their as newcondition and remain the same throughout their service lifeare straight lines with slopes of approximately −1 as predictedearlier. The section with the lowest value of ‘d/t’ gives theminimum curve for the family when they remain as C1 beams.

Based on the above observation, sections with the least valueof ‘d/t’ from each of the families were analyzed to obtain aminimum curve for the sections that are C1 at their as newcondition and remain the same throughout or part of theirservice life. The results for five sections are shown in Fig. 4.

The Fig. 4 shows that the section with the lowest value of‘d/t’ gives the minimum curves for the whole range of beamsthat are C1 at their as new condition and remain the samethroughout or part of their service life. As predicted earlier, theminimum curve is a straight line with a slope of approximately−1. The variation in the percentage remaining shear capacityof beams with the maximum and minimum of d/t is verynegligible (<1%).

In order to verify the effect of design strength on thepercentage remaining shear capacity of corroded beams, auniversal beam, UB 16, was analyses. Four cases wereconsidered by varying the design strength from 245 to450 N/mm2 and using the same section size. The results fromthe analysis are shown in Fig. 5. It can be seen from Fig. 5that the effect of design strength on the percentage remainingshear capacity is quite considerable. When the design strengthincreases the percentage remaining shear capacity of the sectionis decreases. The highest value of the design strength gives theminimum curve for the section.


Fig. 3. Behavior of a family that remains as C1.

Fig. 4. Sections with the least value of ‘d/t’ from five families.

Fig. 5. Effect of design strength on percentage remaining shear capacity.

These analyses show that it is possible to obtain minimumcurves that can be used to estimate the percentage remainingshear capacity of corrosion damaged beams with considerable

accuracy. By repeating the above analysis, taking into accountthe effect of design strength on the percentage remaining shearcapacity and the effect of corrosion on the class of section,


Fig. 6. Minimum curves to estimate the remaining shear capacity of corrodedbeams with uniform loss of web thickness.

Fig. 7. Minimum curves to estimate the remaining shear capacity of corrodedbeams with varying loss of web thickness.

minimum curves were obtained for the cases described belowand are given in Figs. 6 and 7. Alternatively these results can beformulated as below:

I. Uniform or average web thicknessA. Sections that are C1 at their as new condition and

remains the same throughout or part of their service life(C1),

B. Sections that are C1 at their as new condition andbecome C2 due to corrosion and Py = 245 (C1 and C2;Py = 245),

C. Sections that are C1 at their as new condition andbecome C2 due to corrosion and 245 ≤ Py ≤ 275 (C1and C2; Py = 275),

D. Sections that are C1 at their as new condition andbecome C2 due to corrosion and 275 ≤ Py ≤ 355 (C1and C2; Py = 355),

E. Sections that are C2 at their as new condition and 355 ≤Py ≤ 450 (C2; Py = 450).

II. Varying web thickness

Fig. 8. Minimum curves to estimate the remaining moment capacity ofcorrosion damaged beams.

A. Sections that are C1 at their as new condition and remainthe same throughout their service life or become C2due to corrosion and Py < 275 (C1 or C1 and C2;Py < 275),

B. Sections that are C1 at their as new condition andbecome C2 due to corrosion and Py > 275 or sectionthat are C2 at their as new condition (C1 and C2 or C2;Py > 275).

Using the similar approaches, minimum curves can bedeveloped to estimate the remaining capacity of corrodedbeams with regard to other failure modes.

3.5. Minimum curves for remaining moment capacity

The corrosion in the flanges and web results the reduction inthe moment capacity. In addition, the class of a section (plastic,compact, semi-compact, or slender) may be changed from oneto another due to the loss of thickness of compression flange.For example, a section that is plastic or compact at its as newcondition may become semi-compact due to loss of thicknessand local buckling may prevent the development of full plasticmoment [7] in such cases. In order to estimate the remainingmoment capacity, taking into account the above facts, fourminimum curves, shown in Fig. 8, were developed for the casesgiven below:

1. Plastic, Compact or Semi-Compact Sections with Low ShearLoad, LSL (C1, 2 or 3), Although the corrosion reduces thethickness of compression flange of a section, some sectionsthat are plastic, compact or semi-compact at their as newcondition may remain as the same during their part of orwhole service life.

2. Plastic or Compact to Semi-Compact with Low Shear Load,LSL (C1, 2 to 3),

Sections that are plastic or compact at their as newcondition may become semi-compact due to corrosionduring their service life.


Fig. 9. Minimum curves to estimate the remaining lateral torsional bucklingcapacity of corrosion damaged beams.

Fig. 10. Minimum curves to estimate the remaining web buckling and bearingcapacities of corrosion damaged sections.

3. Semi-Compact to Slender with Low Shear Load, LSL (C3 to4),

Sections that are semi-compact at their as new conditionmay become slender due to corrosion during their servicelife.

4. Any compact sections with High Shear Load, HSL (AC).

For sections that change from plastic or compact to semi-compact during their service life, the minimum curve ‘LSL (C1,2 or 3)’ when the section is plastic or compact and the minimumcurve ‘LSL (C1, 2 to 3)’ when the section is semi-compact canbe used. For sections that change from semi-compact to slender,the part of the minimum curve ‘LSL (C3 to 4)’ with increasedslope can be used when section is slender.

3.6. Minimum curves for lateral torsional buckling capacity

The lateral torsional buckling capacity of beams dependson several geometric parameters such as the beam length, endsupport condition, plastic modulus, lateral stiffness, torsional

properties and the warping resistance of the section. Afteranalyzing the importance of these factors on the lateraltorsional buckling capacity, four cases were identified for thedevelopment of minimum curves to assess the percentageremaining of lateral torsional buckling capacity of corrodedbeams. The restraint condition was taken as simply supportedat the ends which is the worst possible case.

For uncoupled beams, two groups namely short beams withL E(Crit) and long beams with L E/D = 30 or λ = 200 spanlength beams were used to obtain minimum curves. For copedbeams, two minimum curves were obtained for the case of shortbeams coped at one end and both ends. For long coped beamsit was found that the minimum curves for the uncoupled longspan beam can be used. The minimum curves for these casesare given in Fig. 9. The minimum curves for the short and longspan length beams may be used to estimate the remaining lateraltorsional buckling capacity of intermediate span length beamsby using interpolation.

3.7. Minimum curves for web buckling and bearing capacity

The buckling resistance of unstiffened webs can be evaluatedusing BS 5950: Part 1 [7]. The code suggests that if compressiveforces applied through a flange by loads or reactions exceed thebuckling resistance, Pw, of unstiffened webs, load carrying webstiffeners should be provided. The web bearing capacity can beevaluated using BS 5950: Part 1 [7]. The code suggests that ifthe forces applied through a flange by loads or reactions exceedthe local capacity of the web at its connection to the flange,then bearing stiffeners should be provided. It was found thatonly one minimum curve is adequate to assess the remainingweb buckling and bearing capacities of unstiffened web. Theminimum curves are given in Fig. 10.

4. Comparison of experimental failure loads

An attempt was made to compare the suggested minimumcurve for the short beams coped at one end with the failureloads of four corroded damaged I-beams under uniformcorrosion, obtained from ICI Ltd. These four beams were testedindividually for their ultimate failure loads in the laboratory.The comparison of the experimental results and the suggestedminimum curve is given in Fig. 11. This figure suggeststhat it may be possible to estimate the remaining capacity ofcorroded beams using the minimum curve. The estimates willbe conservative since the minimum curves were obtained forthe worst possible sections.

It should be noted that in order to calculate the percentageremaining capacities of these beams, the capacity of the newbeam is required. Since such a beam was not tested in thelaboratory, an estimate of its failure load had to be made basedon the theory of lateral torsional buckling capacity of a newbeam with the same size and the pattern in which the theoreticalcapacities of corroded beams differed from their experimentalcapacities.


Fig. 11. Comparison of experimental results with the minimum curve for shortbeams coped at one end.

5. Conclusions

The analysis of corrosion effects on the carrying capacity ofcorrosion damaged beams showed that while loss of thicknessof a section due to corrosion generally reduces the capacity ofa loaded beam, it can also change the mode of failure fromone mechanism to another depending on the relative thicknessloss in the various parts. In addition to these, loss of thickness,may also change the class of an element from one to another(e.g. plastic to semi-compact).

It is possible to obtain minimum curves for reliableestimation of the percentage remaining capacity of corrosiondamaged beams with regard to any failure mode. In relation

to corrosion pattern, it may be possible to find this solution totwo cases namely uniform thickness loss and varying thicknessloss due to uniform corrosion, where loss of thickness in thebottom flange is greater than that of top flange. For all practicalpurposes, the purposed minimum curves can be used alongwith the information on the material loss (percentage loss ofthickness) to estimate the percentage remaining capacities ofcorrosion damaged beams.

References

[1] Kayser JR. The effects of corrosion on the reliability of steel girderbridges. Ph.D thesis. Department of Civil Engineering, University ofMichigan; 1988.

[2] Gallon MJ. ICI Engineering. Managing structural corrosion in chemicalplants. New Steel Construction; Feb. 1993.

[3] ICI Engineering, Procedure for: Condition categories for inspection ofplant structures and pipe bridges. Standards & Technical InformationServices, ICI Engineering, Cheshire, England; June 1990.

[4] Fontana MG. Corrosion engineering. New York: McGraw Hill; 1987.[5] Rahgozar R, Smith JW. Fatigue endurance of steel structures subjected to

pitting corrosion. In: Fourth international conference on civil engineering,Sharif University of Technology. May 1997. p. 237–46.

[6] Rahgozar R, Khalaghi AR, Javanmardi R. Fatigue notch factor in steelbridges due to corrosion. In: Seventh international congress on civilengineering, Tarbiat Modares University. May 2006. p. 46–53.

[7] BS 5950, Structural use of steel work in building: Part 1. Code of practicefor design in simple and continuous construction, Hot rolled sections.British Standards Institution, London; 1985.

[8] Cheng JR, Yura JA, Johnson CP. Lateral buckling of coped steel beams.Journal of Structural Engineering, ASCE 1988;114(1):1–15.

[9] Johnston BG. Guide to stability design criteria for metal structures. 3rd ed.New York: John Wiley & Sons; 1976.

[10] Timoshenko SP, Gere JM. Theory of elastic stability. 2nd ed. New York:McGraw-Hill; 1961.

Remaining Capacity Assessment of Corrosion Damaged Beams Using Minimum Curves

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