Finite element analysis of corroded steel angles under compression

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Conference of Junior Researchers in Civil Engineering 163
Oszvald, K.: Finite element analysis of corroded steel angles under compression
Finite element analysis of corroded steel angles under compression
Katalin Oszvald
BME Department of Structural Engineering, e-mail: oszvaldkata@gmail.com

Abstract
Steel structures corrode almost in every environment. The measure of the corrosion can be especially significant if the
maintenance is insufficient. In practice it is necessary to determine the ultimate failure mode and estimate the resistance of the
corroded members to decide it should be replaced or it is enough to remove the corrosion and re-paint the structure. The subject of
this paper is a finite element study of corroded angle section members under centric compression. The joint influence of three
main corrosion parameters is analyzed on the buckling behaviour. The investigated basic elements have different cross-section
sizes and lengths. The behaviour is determined in the function of the parameters of the corrosion and the cross-section
characteristics.
Introduction
Single steel angles section members are used in many various structures as bridges, trusses and latticed
transmission towers. Every structure is exposed to the effects of different environmental influence. The
circumstances, which include the inadequate maintenance lead to corrosi on on the structures. The rate of the
corrosion can be very significant and can cause failures in the st ructures. There are many various corrosion
types with different appearance forms like average, pitting, and crevice c orrosion. Because of the diversity of
corrosion, it is difficult to describe it by only one parameter. C orrosion can occur anywhere along the
member length and has various size extensions and rarely extends t o the whole member. The place of the
corrosion also can be various within the cross-section. The standards, a s e.g. Eurocode [1], do not give any
suggestion [2] how to analyse the corroded members. In the practice the engineers apply an average cross-
section decrease, what is supposed along the whole element. In some ca ses this assumption can be good
approach, but for example in case of localized corrosion it is not accurate enough to de termine the behaviour.
In the current research a numerical model is developed and verified by experimental results. Geometrically
and material nonlinear analysis is used to follow the stability phe nomena of the compressed angle section.
The resistance of the corroded members are determined, considering the cross-section classification of the
Eurocode. Three different corrosion parameters are studied: (i) cr oss-section reduction; (ii) extension of
corrosion and (iii) location of corrosion. The structural behaviour is de termined in the function of the
corrosion parameters and the cross-section characteristics. In t his paper the main focus is on the behaviour of
the corroded members, based on the finite element parametric study.
Previous research
The corrosion is a significant problem in the world, therefore many researcher analyze the effect of it on the
various members of the structures. All of the studies deal with the remaining capacity of the members and
give recommendation how can be assessed the influence of the corrosion. Numerical study was completed
on sheared plates with pitting corrosion by Paik at el. [3]. In the function of the corroded surface and the
plate thickness the ratio of the stress of the corroded and the non-corr oded plates was determined. In other
study Rahgozar [4] developed residual capacity curves of corroded I -section on the basis of thickness
reduction. Corrosion on the lower flange and on the web was assumed. Effect of localized corrosion on
buckling plate was investigated by Sadovsy and Drdacky [5]. The influe nce of pitting corrosion on the hold
frames of bulk carrier was extensively analyzed by Nakai e t al. [6, 7]. The research of Heinemeyer and
Feldman [8] focused on the influence of the corrosion on riveted connections. Angle sect ion members, which
are investigated in this study too, were previously analyzed by B eaulieu et al. [2]. The specimens were
corroded by galvanic process and the tests results were compar ed to the analytical results which were
calculated according to Canadian and American standards. In the te st set-up eccentric compression was
applied by gusset plate. Comprehensive study on corroded angle secti on members is not found in the
literature, where the effect of the main corrosion parameters on the buckling behaviour is analyzed.
Therefore, to determine the behaviour and the resistance decrease of the corroded members a numerical
study program is carried out.
Conference of Junior Researchers in Civil Engineering 164
Oszvald, K.: Finite element analysis of corroded steel angles under compression
Experimental and numerical background
In the first phase of the research compressive buckling tests wer e carried out on 24 specimens. The corrosion
was artificially created in the members; part of the le g thickness was eliminated by mechanical process.
During the test centric compression was applied and the obtained max imal load and the vertical and
horizontal displacements were measured. Details of the test ca n be found in [9]. In parallel with the tests, a
numerical model was developed using Ansys program [10]. The corroded angle section members and the
corrosion appearance in the model can be various by changing the di fferent corrosion parameters. In the
linear and non-linear analyses the applied finite element is a brick element (SOLID 45 of [10]). The size of
the finite elements is half of the original thickness of the leg s. The support is hinge connection in the center
of the gravity of the non-corroded elements. The model contains about 100000 e lements. By the model the
experimental tests are simulated on the accuracy was verifi ed. Based on the test results the equivalent
geometric imperfection was determined on every specimens of the t est. The developed finite element model
is proved to be accurate and efficient to complete a parametric study on centric c ompression angle members.
Numerical study program
Design buckling resistance in the research is determined by num erical simulation; this process is a general
proposal in the Eurocode standard. In the finite element simulation t he nominal yield stress and the
equivalent geometric imperfection are used. In the case of the corrode d members the aim is to give a
recommendation based on the results of the numerical study, how can take into account the effect of the
corrosion in the design method. In the first step the behaviour must be det ermined. Therefore bifurcation
stability analysis is carried out on perfect corroded elements in order to find the critical compressive force
(geometric non-linear buckling analysis  GNB). In the GNB anal ysis the first buckling mode (eigenvector)
is determined. The applied equivalent geometrical imperfection in the geometrically and material non-linear
analyses (GMNI) follows the shape of the determined first mode. I n the simulations linear elastic  plastic
material model is applied (steel grade of S235 with the nominal y ield strength of f
y
= 235 N/mm
2
). In the
following parametric study three different cross-section sizes and three element lengths are applied, it means
nine different basic non-corroded elements are analyzed. Table 1 contains the cross-section sizes, the lengths
of the elements, the relative slendernesses and the legs initi al b/t (width/thickness) ratios of the non-
corroded elements.
ID
Cross-section
[mm×mm×mm]
Length
[mm]
Slenderness b/t
RF-1 40×40×4 510 0.7 10
RF-2 40×40×4 840 1.15 10
RF-3 40×40×4 1100 1.5 10
RF-4 60×60×8 750 0.7 7.5
RF-5 60×60×8 1250 1.15 7.5
RF-6 60×60×8 1640 1.5 7.5
RF-7 100×100×12 1280 0.7 8.3
RF-8 100×100×12 2100 1.15 8.3
RF-9 100×100×12 2760 1.5 8.3
Table 1. Basic non-corroded elements
The thickness reduction ( T
red
), the extension of corrosion ( Ext) and the position of the corrosion ( p
c
) along
the whole element are the three main parameters which are consi dered in the analyses, as corrosion
parameters, defined in Eqs. (1) and (2). Two different basic corrosion pa tterns ( A and B) are applied in the
analyses, as it is shown in Figs. 1 and 2. The crosshatched area marks the corrosion i n the member.
Conference of Junior Researchers in Civil Engineering 165
Oszvald, K.: Finite element analysis of corroded steel angles under compression
0 1
0 1
L/2
x
y

Fig. 1.  A pattern Fig. 2.  B pattern

2
/
L
y
p
c
= (1)

100×=
L
x
Ext (2)
L [mm]: member length; x,y see Fig. 1.
Table 2 shows the applied parameters, in the table the corrosion is marked by black. The corrosion position
is calculated by the ratio of the centre of the corroded area and the half of the member length, Eq. (1). The
length of the corroded area is calculated by extension parameter Eq. (2).
The number of the studied members is about 2000; 238 different corroded cases are analyzed for each non-
corroded members.
Pattern

Cross - section

T
red
[%]
Ext
[%] Corrosion position (p
c
)

20 0.20, 0.47, 0.73, 1.00
30 0.30, 0.53, 0.77, 1.00
A

40 0.40, 0.70, 1.00
50 0.50, 0.75, 1.00
70 0.70, 1.00
B

20
30
40
50
60
70
80
100 1.00
Table 2. Corrosion parameters
GNB analyses  equivalent geometric imperfections
The observed bucking around the weak axis is shown in Fig. 3. The width-to -thickness ratio of the legs is
changed due to thickness reduction by corrosion and it leads to change the buckling shape and failure mode.
For the relative slenderness of 1.15 and 1.5 the buckling modes follow the first buckling mode. This is also
valid if the thickness reduction is greater than 50%. If the rela tive slenderness is 0.7 the first mode is not the
same in every case as in the previous elements. Beside the global buckling shape a local buckling is
observed, as shown in Figs. 4 and 5. The length of the local buckling wave is approximately two times the
free width of the outstanding plates if the corrosion is on one leg (pa ttern A). In case of pattern B the length
of the buckling wave is the length of the corroded area, represent ing flexural-torsional buckling in the
corroded area, as it is shown in Fig. 6.
The buckling mode is very much dependent on the corrosion parameters. The reduced area can lead to
different modes of buckling due to the different b/t ratios. The reduced cross-section is in class 4 in all cases
if the thickness reduction is greater than 50%, but the b/t ratio is not the same on the studied elements. Table
3 presents the first mode of buckling of part of the studied elements. In RF-1 members with pattern A and
where the T
red
is 80% the first buckling mode is local independently of the other two parameters. It is not
valid in case RF-4 and RF-7 members, because the p/t ratio is lowe r in these cases than in case of RF-1
elements. The position of corrosion also important parameter; if it is closer to the support (ID  171) local
buckling mode is observed by members with lower b/t ratio. But if the corrosion is in the middle (ID  174)
in the cases of RF-4 and RF-7 global bucking mode is observed. The ext ension of corrosion ( Ext) is also an
Conference of Junior Researchers in Civil Engineering 166
Oszvald, K.: Finite element analysis of corroded steel angles under compression
important parameter. Having the same thickness reduction ( T
red
) and corrosion position ( p
c
), but different
extension (Ext) causes different buckling mode, e.g. on RF-7 element in case of ID  175 and ID  182. This
is almost valid in cases of elements with corrosion pattern B. Local mode is observed already by 70%
thickness reduction, but the number of this type of mode is lower as in t he cases of pattern A, beside the
same corrosion parameters.
The shape of the first mode of stability analysis is applied as equivalent geometrical imperfection in the
numerical simulation. The amplitude of the imperfection is L/200 in t he analyses, following the
recommendation of the standard and the results of the model verification.


Fig. 3. Ext=20%, p
c
=0.47, T
red
=80 Fig. 4. Ext=70%, p
c
=1.0, T
red
=80


Fig. 5. Ext=70%, p
c
=1.0, T
red
=80 Fig. 6. Ext=70%, p
c
=1.0, T
red
=80



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Oszvald, K.: Finite element analysis of corroded steel angles under compression
ID
Corrosion
pattern
T
red
[%] Ext [%] p
c
RF-1 RF-4 RF-7
171 A 80 20 0,20 Local Local Local
172 A 80 20 0,47 Local Global Local
173 A 80 20 0,73 Local Global Local
174 A 80 20 1,00 Local Global Global
175 A 80 30 0,30 Local Global Local
176 A 80 30 0,53 Local Global Local
177 A 80 30 0,77 Local Global Global
178 A 80 30 1,00 Local Global Global
179 A 80 40 0,40 Local Global Local
180 A 80 40 0,70 Local Global Global
181 A 80 40 1,00 Local Global Global
182 A 80 50 0,50 Local Global Global
183 A 80 50 0,75 Local Global Global
184 A 80 50 1,00 Local Global Global
185 A 80 70 0,70 Local Global Global
186 A 80 70 1,00 Local Global Global
187 A 80 100 1,00 Local Global Global
205 B 70 20 0,20 Local Global Global
209 B 70 30 0,30 Local Global Global
222 B 80 20 0,20 Local Local Local
223 B 80 20 0,47 Local Global Global
225 B 80 20 1,00 Local Global Global
226 B 80 30 0,30 Local Global Local
227 B 80 30 0,53 Local Global Global
228 B 80 30 0,77 Local Global Global
230 B 80 40 0,40 Local Global Global
233 B 80 50 0,50 Local Global Global
Table 3. Bucking modes in the function of corrosion parameters
GMNI analysis  behaviour modes
The results of GMNI analyses are evaluated by the behaviour mode s function of the different parameters.
Generally the observed failure mode is global flexural buckling about the weak axis on elements with 1.15
and 1.5 relative slenderness. The yield mechanism is developed at the half-length of the member according
to the expectation on the non-corroded members, but on corroded members it is shifted. In these cases the
buckling mode and the failure mode are same. In some cases, when the buckling mode is global, the
behaviour mode in the simulation is different. The observed behaviour is an elastic-plastic failure mode.
After an initial global behaviour the failure mode is local. A third type of behaviour mode is also observed,
in this case the first buckling mode and the failure mode are the s ame. This is valid if the corrosion is on one
or both of the legs. Figure 7 presents the deformed shape of three dif ferent behaviour modes. The first is the
global-global (RF-1-1), the second is global-local (RF-1-52) and the third is local-local (RF-1-222).The
second and the third type of failure modes are observed just on the ele ment with 0.7 relative slenderness. In
two cases the behaviour is clearly global buckling around the y-y axis (the y-y axis is parallel with the leg).
Conference of Junior Researchers in Civil Engineering 168
Oszvald, K.: Finite element analysis of corroded steel angles under compression
The corrosion is on one leg and it is on the whole elements and the T
red
is 60% and in the other case T
red
is
70%.

RF-1-1 RF-1-52 RF-1-222
Fig. 7. Observed behaviour modes
The load and vertical displacement curve is similar in the cas e of the three modes. The curves are presented
on the right side of Fig. 8. On the left side of Fig. 8 the displacem ents of the middle point are shown (the
middle point is considered in the middle of the element length, in the c orner edge of the cross-section). The
coordinate axes are the displacements in direction of x and y. The c urve of RF-1-52 presents the behaviour;
in the initial phase the line goes together with RF-1-1 an in the moment of failure the direction changes,
because the reduced leg loses its stiffness.
0
10
20
30
40
50
60
0 0,5 1 1,5
Load [kN]
Vertical displacement [mm]
RF-1-52
RF-1-1
RF-1-222

-5
-4
-3
-2
-1
0
1
2
3
4
-2 0 2 4
dy [mm]
dx [mm]
RF-1-52
RF-1-1

Fig. 8. Behaviour curves
In GNB analyses the cases are determined when the first buckli ng is local, in GMNI analyses this statement
is also relevant. Table 4 contains some elements with the ID numbe rs and corrosion parameters, where the
first buckling mode and the failure mode are different in the GNB a nd GMNI analyses. The results show that
the b/t ratio is not negligible in the determination of the failure mode.
Changing the parameter b/t (modify T
red
) and set to parameter of RF-1 the same behaviour occurs on the
examined RF-4 and RF-7 parameters. By more than 40% thickness reducti on the second type of behaviour
mode appears if the b/t ratio is more or equal than 15. This is not a sufficient, but a necess ary condition. The
position of the corrosion must be close to the support. As the T
red
is getting greater the number of this type of
behaviour is increased; e.g. 70% thickness reduction just in one case t he result is not the second mode. By
this scale of T
red
the condition, corrosion close to the support, is not important. Necess ary condition to local
failure mode is more than 80% thickness reduction and more or equal than 50 b/t ratio. If the thickness
Conference of Junior Researchers in Civil Engineering 169
Oszvald, K.: Finite element analysis of corroded steel angles under compression
reduction is on both of the legs, almost the same conditions are necess ary to the various failure modes. In
these cases the second mode does not appear, because after the thickne ss reduction the symmetry of the
cross-section does not change. The local buckling failure mode is obse rved, however, by 70% thickness
reduction (more or equal than 35 b/t ratio). On the basis of the completed analyses the resistance of the
corroded members is determined, as a peak value of the applied compressive force.
ID Cross-section T
red
Ext p
c
b/t
RF-1-35 40×40×4 40 20 0,2 16,67
RF-1-52 40×40×4 50 20 0,2 20
RF-1-53 40×40×4 50 20 0,47 20
RF-1-56 40×40×4 50 30 0,3 20
RF-4-52 60×60×8 50 20 0,2 15
RF-7-52 100×100×12 50 20 0,2 16,67
Table 4. Element parameters  Global flexural buckling about strong axis
GMNI analysis  resistances
The corrosion causes resistance reduction, but the measure of the decr ease is different function of the
parameters. Results of RF-1 elements show the tendencies of the r esistance decrease function of the different
parameters, as illustrated in Fig. 9. In the left side the hori zontal axis is the whole cross-section reduction
(C
red
[%]), what can be calculated from T
red
. The tendency is almost linear, but there are some differences. In
the different cases the behaviour is the second and the third mode. If the results are plotted in the function of
the b/t ratio, the tendency is non-linear and there are no significant diffe rences when the failure mode is
different. In Fig. 10 part of results are presented in the function of the b/t ratio. The corrosion parameters
what belongs to the plotted results are: Ext = 100% and p
c
= 1. In the case of the same b/t value the ratio of
the corroded and non-corroded element resistance can be different. The tendencies similar but the measure of
the decrease is greater if the initial b/t is lower.
0,00
0,20
0,40
0,60
0,80
1,00
1,20
0 50 100
Nb
/N
b0
C
red
[%]

0,00
0,20
0,40
0,60
0,80
1,00
1,20
0 20 40 60
Nb
/N
b0
b/t

Fig. 9. Resistances in the function of the C
red
and b/t parameters
The development of a design method  on the basis of the completed paramet ric study  to determine the
buckling resistance of corroded angle section members is in process. In the method the application rule of
the Eurocode 3 is used with a cross-section dependent reduction factor.
Summary and conclusions
In the current research corroded compressed angle section elements are analysed. A numerical parametric
study is carried out on different corroded elements. In the complete d numerical analyses, the effect of cross-
section reduction, position and extension of corrosion are analyzed on the stability be haviour. On the basis of
the simulation results the first buckling modes and the failure m odes are determined. On the basis of the
numerical study the following conclusions can be made:
Conference of Junior Researchers in Civil Engineering 170
Oszvald, K.: Finite element analysis of corroded steel angles under compression
0
0,2
0,4
0,6
0,8
1
1,2
5 10 15 20 25
Nb/N
bo
b/t ratio
RF-1
RF-4
RF-7

Fig. 10. Results of RF-1, RF-4 and RF-7 (Ext=100%, p
c
=1.0)
· Three different failure modes are determined, as follows: first is global flexural buckling about weak
axis; second is an elastic-plastic failure mode (initial globa l behaviour with local failure mode); third is local
buckling. In the case of pattern A all of the modes are appeared, but in the case of pattern B just the first and
the third.
· The knowledge of the corrosion parameters is not sufficient to deter mine the different buckling and
failure modes.
· The width to remaining thickness ratio is important characteristi c and it is a necessary but not
sufficient parameter to determine the first buckling and the ultimate failure modes.
· The observed failure mode is global flexural buckling around the weak a xis in the case of relative
slenderness greater than 1.15. Simulation results show that it is re levant in every corroded element,
irrespectively of the corrosion parameters.
· The second behaviour mode is observed on the elements where, the b/t ratio is greater than 15 and the
corrosion is located close to the support, and the extension is around 20-30%.
· Local failure mode can be observed on elements with greater than 3 5 b/t ratio. This is also a
necessary condition, but not sufficient.
Acknowledgement
This work is connected to the scientific program of the Development of quality-oriented and harmonized
R+D+I strategy and functional model at BME. This project is support ed by the New Széchenyi Plan (Project
ID: TÁMOP-4.2.1/B-09/1/KMR-2010-0002).
References
[1] EN 1993-1-1:2005 Eurocode 3: Design of steel structures. Part 1-1: General rules and rules for buildings.
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Steel Research, vol. 66, pp. 1366-1373, 2010.
[3] Paik JK, Lee JM, Ju Ko M, Ultimate shear strength of plate members with pit corrosion wastage, Thin-Walled Structures,
vol. 42, pp. 1161-1176, 2004.
[4] Rahgozar R, Remaining capacity assessment of corrosion damaged beams using minimum curves, Journal of
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[5] Sadovsky Z, Drdacky M, Buckling of plate strip subjected to localised cor rosion  a stochastic model, Thin-Walled
Structures, vol. 39, pp. 247-259, 2001.
[6] Nakai T, Matsushita H, Yamamoto N, Arai H, Effect of pitting corrosion on local strength of h old frames of bulk carrier
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st
report), Marine Structures, vol. 17, pp. 403-432, 2004.
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nd
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Oszvald, K.: Finite element analysis of corroded steel angles under compression
[8] Heinemeyer C, Feldman M, The influence of rivet corrosion on the durability of riveted connections, 6th European
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[10] ANSYS
®
v11.0, Canonsburg, Pennsylvania, USA.