Fatigue strength assessment of riveted shear splices

Abstract

Old‐steel riveted bridges are part of the heritage asset in many countries. Assessing the remaining life and fatigue strength of their structural riveted details is crucial in managing these structures. According to JRC‐ECCS document Assessment of Existing Steel Structures: Recommendations for Estimation of Remaining Fatigue Life , fatigue class 71 is recommended to estimate the fatigue strength of riveted details. However, the predicted fatigue behaviour can lead to excessively conservative estimates. Hence the research community is still focusing on the suitability of current recommendations. This work performs a numerical study to evaluate the fatigue strength of riveted double‐shear splices. Experimental fatigue test results are collected from the literature, and some are used to develop a finite element model in ABAQUS and Fe‐Safe. The adopted modelling fatigue approach is applied to investigate the fatigue behaviour of double‐shear riveted connections with different geometrical properties. The numerical results are compared with all collected data, showing the procedure's effectiveness in predicting the fatigue strength of double‐shear riveted splices. Finally, the numerical and experimental results are compared with the recommended S‐N curves.

Full text

Fatigue strength assessment of riveted shear splices
Annarosa Lettieri1 | Massimo Latour1 | Gianvittorio Rizzano1 | Aldo Milone2 | Mario
D’Aniello2 | Raffaele Landolfo2
1 Introduction
Rivets are the oldest type of fasteners used to assemble
metal pieces and, since the 19th century, contributed to
manufacturing steel civil constructions, mainly railway and
highway bridges. Although welding and bolting have pro-
gressively replaced the riveting process, many old steel
riveted bridges still exist and are in operation. Due to the
high number of cyclic stresses such structures have sus-
tained over the years, they are prone to fatigue damages
[1]-[2] and, if not controlled, can reduce the structural
members’ bearing capacity. Therefore, to determine pos-
sible repairs able to guarantee their safety, the evaluation
of the fatigue behaviour of riveted details is required. Cur-
rent codes [3]-[4] use the fatigue curves (i.e., S-N
curves), formerly conceptualised by Wöhler, for fatigue
verification and design of steel structural details. S-N
curves are expressed both in terms of normal and tangen-
tial stresses. Besides, specific structural details are identi-
fied based on the potential fatigue crack location (e.g., the
gross or net section in a double-covered symmetrical joint)
and associated with S-N curves to be used for their fatigue
assessment. However, construction standards do not in-
clude riveted details, and some recommendations have
been proposed over time to compensate for the absence
of specific requirements. In particular, detail category 71
is recommended to verify the fatigue behaviour of any riv-
eted structural details according to the JRC-ECCS technical
report [5], as the 95% lower bound of experimental data
of full-scale fatigue tests. Moreover, conforming to
AASHTO guidelines [4], detail D, characterised by a slope
of 3 until a stress threshold value of 48.3 MPa (similarly to
detail category 71 of Eurocode), can be used. Although
using the coded structural details allows for the safe-sided
fatigue assessment of riveted assemblies, several studies
highlighted the excessive conservative estimation ob-
tained mainly in the long-life fatigue regime [6]-[7]. Be-
sides, more recent studies relying on the assessment of
the remaining capacity and life of existing steel bridges
demonstrated the importance of using suitable fatigue de-
tails to properly design maintenance or retrofit operations
(e.g., [8]-[11]). Recently, Taras and Greiner [12] dis-
cussed the inappropriate assumption that all riveted struc-
tural details behave similarly and developed a fatigue class
catalogue distinguishing five riveted constructional details.
The catalogue has been created as a result of the catego-
risation and statistical evaluation of prior fatigue test re-
sults [13]. However, correctly assessing the detail cate-
gory to predict the fatigue behaviour of riveted
connections is still an open issue in the research commu-
nity. This work presents a numerical study concerning the
ORIGINAL ARTICLE
Abstract
Old-steel riveted bridges are part of the heritage asset in many countries. Assessing
the remaining life and fatigue strength of their structural riveted details is crucial in
managing these structures. According to JRC-ECCS document Assessment of Exist-
ing Steel Structures: Recommendations for Estimation of Remaining Fatigue Life,
fatigue class 71 is recommended to estimate the fatigue strength of riveted details.
However, the predicted fatigue behaviour can lead to excessively conservative es-
timates. Hence the research community is still focusing on the suitability of current
recommendations. This work performs a numerical study to evaluate the fatigue
strength of riveted double-shear splices. Experimental fatigue test results are col-
lected from the literature, and some are used to develop a finite element model in
ABAQUS and Fe-Safe. The adopted modelling fatigue approach is applied to inves-
tigate the fatigue behaviour of double-shear riveted connections with different geo-
metrical properties. The numerical results are compared with all collected data,
showing the procedure’s effectiveness in predicting the fatigue strength of double-
shear riveted splices. Finally, the numerical and experimental results are compared
with the recommended S-N curves.
Keywords
Steel Bridges, Riveted Connections, Fatigue Strength, S-N Curve, Finite Element
Model.
Correspondence
Annarosa Lettieri
Department of Civil Engineering
University of Salerno
Email: alettieri@unisa.it
1 University of Salerno, Salerno,
italy
2 University of Naples “Federico
II”, Naples, Italy
Proceedings
in civil engineering
Proceedings
in civil engineering
https://doi.org/10.1002/cepa.2464 wileyonlinelibrary.com/journal/cepa
ce/papers 6 (2023), No. 3-4
© 2023 The Authors. Published by Ernst & Sohn GmbH.
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and
reproduction in any medium, provided the original work is properly cited
2504

fatigue behaviour of riveted double-shear splices. Fatigue
literature data on riveted shear splices have been collected
and used to calibrate a numerical procedure to predict
their fatigue strength. Numerical models have been built
in ABAQUS [14] and used in conjunction with Fe-Safe [15]
to perform fatigue calculations. The fatigue strength of the
modelled connections is computed by determining the
number of cycles to crack initiation as the lower bound of
the number of cycles to fatigue failure and relevant phase
in the case of riveted and bolted connections [16]. The
numerical approach is successively used to implement a
numerical study on the fatigue behaviour of double-shear
splices with different geometrical properties (e.g., riveted
and hole diameters, pitch, width and thickness of the
plates). Numerical and experimental data are compared,
showing the reliability of the adopted procedure.
2 Prior literature fatigue data
Experimental results of fatigue tests on riveted shear
splices have been collected from [16]-[23] and depicted in
Figure 1. All collected fatigue test results refer to riveted
shear splices subjected to shear at constant stress ampli-
tude, characterised by different geometrical properties,
number of rivets and shear planes, steel type, bearing ra-
tio, test frequency and stress ratio (R = min/max, in which
min and max represent the maximum and minimum nor-
mal stresses applied to the specimen, respectively). In
particular, R values equal to -1, 0, 0.5 (corresponding to
complete reversal, zero-to-tension and half tension-to-
tension, respectively) and 0.1 are applied. It is noteworthy
that a negative R value means the application of both ten-
sion and compressive stresses. Current codes account for
the beneficial effect of compressive stresses on fatigue be-
haviour [3], reducing the stress range used to compute
the fatigue strength of detail, which will be increased ac-
cordingly.
Figure 1 Row prior literature data.
In this study, unsymmetrical connections (one shear
plane) and tests with no failure conditions are excluded to
reduce the scatter of the data and provide more reliable
comparisons. Besides, according to Eurocode [3], the ben-
eficial effect of compressive stresses on fatigue behaviour
is considered by correcting data with negative R values
[3]. Figure 2(b) depicts the filtered data.
Figure 2 Filtered and normalised collected data.
Among others, the results of the experimental tests car-
ried out by Da Silva et al. [16] are used to calibrate the
fatigue calculation presented in the following section. In
particular, the experimental campaign includes fatigue
tests on two series of double-shear riveted splices: with a
single row and two rows of rivets (four and eight rivets,
respectively). All specimens in each series have the same
geometrical properties and are subjected to cyclic stresses
with R equal to 0.01. In this work, only the experimental
results related to double-shear riveted splices with four
rivets arranged in a single row are considered (Section 3).
3 Finite element modelling
3D finite element models (FEM) are built in ABAQUS [14],
aiming to numerically investigate the fatigue behaviour of
riveted shear splices. Using two symmetry planes (i.e., XY
and XZ planes), only ¼ of the geometry is modelled, and
the displacement/rotation of the nodes at such planes is
constrained according to the symmetry conditions. Figure
3(a) and (b) depict an overview of the adopted boundaries
and meshing approach, respectively. Null clearance be-
tween the rivet shanks and the holes is adopted, as char-
acteristic property resulting from the riveting process
([24],[25]), whereas a ‘Bolt load’ is used to introduce the
rivet clamping. The material of both rivets and plates is
modelled as linear elastic and isotropic, considering a
young modulus equal to 210 GPa and a Poisson ratio of
0.27. The ‘surface-to-surface’ interaction property defines
the contact behaviour among steel surfaces. In particular,
the ‘Hard contact’ option describes the interaction in the
normal direction. In contrast, the tangential one is mod-
elled with a ‘Penalty’ friction formulation with friction co-
efficients equal to 0.30.
The adopted fatigue analysis procedure comprises two
main steps (Figure 4(a)): 1) the linear-elastic FEM analysis
to compute the initial stress distribution within the con-
nection; 2) the fatigue evaluation of the number of cycles
to crack initiation (assumed in this work as the lower
bound of the fatigue strength). The elastic analysis is per-
formed in ABAQUS[14]. In particular, a single stress range
is applied at the left gross section end as ‘pressure’, and
the corresponding elastic stress distribution is obtained us-
ing the static solver. Fe-Safe software [15] reads the ob-
tained datasets as an ODB file. Successively, the fatigue
calculation is performed by scaling the stress distribution
according to a sinusoidal signal and applying the strain-life
approach with the Coffin-Manson cyclic constitutive rela-
2505
25097075, 2023, 3-4, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/cepa.2464 by Nagoya Institute Of Technology, Wiley Online Library on [01/10/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

tion [26]-[27]. Specifically, the material constants are ob-
tained from experimental fatigue tests published in [16]
and statistically evaluated considering a 95% tolerance in-
terval, as shown in Figure 4(b).
Figure 5 illustrates the numerical results obtained by ap-
plying the adopted procedure. In particular, Figure 5(a)
and (b) depict the contour stresses at the end of the static
analysis in ABAQUS and Fe-Safe fatigue results for a single
riveted shear splice investigated, respectively. A maxi-
mum stress value in the net section of the central plate
characterises the elastic stress field obtained by applying
uniform tensile stress (Figure 5(a)), and the corresponding
predicted fatigue life reports the same critical position. It
is noteworthy that the distribution of the fatigue life is ob-
tained in a logarithmic scale (i.e., log(N)), and the most
critical value for the crack initiation is the lowest log(N),
depicted in red in Figure 5(b). For the sake of brevity, the
results related to the other connections investigated are
not reported. However, all the riveted shear splices stud-
ied exhibit net-area tensile failure of the plates, in agree-
ment with the experimental results [16].
Figure 3 Overview of the (a) boundaries and (b) meshing approach used in the ABAQUS models.
Figure 4 (a) Fatigue calculation procedure adopted in this study; (b) cyclic constitutive law of the constituent material [16].
Figure 5 (a) Linear-elastic static analysis output obtained from ABAQUS; (b) fatigue calculation in Fe-Safe.
For the sake of clarity, the dimensions of the selected riv-
eted shear splices [16] are depicted in Figure 6(a). The
comparison between the numerical and experimental data
is reported in Figure 6(b). In particular, the experimental
fatigue results are depicted with black markers and de-
scribed through the mean linear regression (black line)
and the 99% tolerance interval (filled grey area). The nu-
merical results are obtained by adopting the mean, the
lower and the upper properties of the confidence interval
of the material’s cyclic constitutive law, previously re-
ported in Figure 3(b). It can be observed that the curves
have the same slope but different intercepts, and the fa-
tigue strength is generally underestimated. It is important
to highlight that the adopted modelling approach com-
putes only the fatigue crack initiation. Additionally, the
preload provided by the riveting process and its influence
on fatigue behaviour is challenging to quantify rigorously
[16]. The best prediction is obtained when the upper fa-
tigue material constants are used. Nevertheless, for the
numerical study presented in Section 4, the lower fatigue
material constants are used for safe-sided predictions.
2506
25097075, 2023, 3-4, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/cepa.2464 by Nagoya Institute Of Technology, Wiley Online Library on [01/10/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

Figure 6 (a) Illustration (dimensions in mm) of the considered con-
nections [16]; (b) Comparison between the experimental and numeri-
cal results.
4 Numerical fatigue prediction
A numerical study has evaluated the fatigue behaviour of
double-shear splices with different geometrical properties
(Figure 7). The fatigue modelling follows the approach de-
scribed in the previous section and focuses on the fatigue
behaviour f double-shear riveted splices listed in Table 1.
The connections differ in rivet and hole diameters, width
and thickness of the plates, and pitch.
In the present study, each connection is subjected to ten
cyclic loadings to build its S-N curves. In particular, five
maximum stresses ranging from 100 MPa to 225 MPa are
selected, and two R values are adopted (i.e., 0 and 0.5),
keeping the maximum stress unchanged. Figure 8 shows
the comparison between the numerical results, their sta-
tistical evaluation carried out according to [28], and the
experimental filtered data (previously shown in Figure
2(b)). The numerical results are described by a mean
curve (blue line) with a slope equal to 6.64 and a fatigue
resistance of 124 MPa at 2 x 106 cycles. In addition, 95%
and 99% tolerance intervals are represented by filled ar-
eas. Sinoce the above intervals include almost all the ex-
perimental data, the modelling approach adopted in this
work can be considered a good tool for estimating the fa-
tigue strength of the investigated double-shear riveted
splices.
Figure 7 Indication of the parameters varied in the numerical study.
Table 1 Geometrical properties of the investigated double-shear riveted splices.
Identifier
Diameter
, (mm)
Width
w, (mm)
Thickness
t, (mm)
Edge distance
a, (mm)
Pitch
p, (mm)
p/
ratio
R2-13-8-2.95
13
34.22
8
17.11
38.30
2.95
R2-13-8-3.50
13
34.22
8
17.11
45.50
3.50
R2-13-8-4.50
13
34.22
8
17.11
58.50
4.50
R2-13-12-2.95
13
34.22
12
17.11
38.30
2.95
R2-13-12-3.50
13
34.22
12
17.11
45.50
3.50
R2-13-12-4.50
13
34.22
12
17.11
58.50
4.50
R2-19-8-3.50
19
50.00
8
30.00
66.50
3.50
R2-19-8-4.50
19
50.00
8
30.00
85.50
4.50
R2-19-12-2.95
19
50.00
12
30.00
56.00
2.95
R2-19-12-3.50
19
50.00
12
30.00
66.50
3.50
R2-19-12-4.50
19
50.00
12
30.00
85.50
4.50
R2-25-8-2.95
25
65.80
8
39.50
73.70
2.95
R2-25-8-3.50
25
65.80
8
39.50
87.50
3.50
R2-25-8-4.50
25
65.80
8
39.50
112.50
4.50
R2-25-12-2.95
25
65.80
12
39.48
73.70
2.95
R2-25-12-3.50
25
65.80
12
39.48
87.50
3.50
R2-25-12-4.50
25
65.80
12
39.48
112.50
4.50
a)
b)
2507
25097075, 2023, 3-4, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/cepa.2464 by Nagoya Institute Of Technology, Wiley Online Library on [01/10/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

Figure 9 and Figure 10 compare the numerical fatigue re-
sults to detail category 71 and Taras’ proposal, respec-
tively. In the first comparison (Figure 9), detail 71 overes-
timates the fatigue resistance for the riveted splices
investigated subjected to a stress range over 125 MPa.
Therefore, it does not represent the lower boundary of the
investigated connections. Conversely, Taras’ suggested
fatigue curves are close to the 95% lower tolerance limit
of the numerical results (Figure 10), better estimating
their fatigue behaviour.
Figure 8 Comparison between the experimental and numerical results.
Figure 9 Comparison with detail 71.
Figure 10 Comparison with Taras’ suggested fatigue curves.
Figure 11 finally shows the S-N curve that best fits all the
considered results. In particular, the curve is characterised
by a slope equal to 7 (higher than the aforementioned rec-
ommended details) and a fatigue strength of 90 MPa for
2x106 cycles.
Figure 11 S-N curve describing the fatigue strength of the investigated
case-studies.
5 Conclusions
This work performs a numerical study to investigate the
fatigue behaviour of double-shear riveted splices. Finite
Element Models are built in ABAQUS and Fe-Safe to per-
form fatigue calculations. The fatigue modelling approach
is calibrated against fatigue results collected from the lit-
erature and successively used to conduct a numerical
study to predict the fatigue strength of double-shear riv-
eted splices with different geometrical properties. The fol-
lowing outcomes can be made: i) the number of cycles to
crack initiation can be assumed as a reasonable lower
bound to fatigue estimation of riveted double-shear
splices; ii) the adopted numerical fatigue calculation ap-
proach can be adopted to estimate the fatigue strength of
riveted double-shear splices. It is noteworthy that the pro-
cedure requires the cyclic properties of the constituent
materials.
References
[1] Yen B.T., Huang T., Lai L-Y., Fisher J.W. (1990) Man-
ual for inspecting bridges for fatigue damage condi-
tions. January 1990, 174p. (Final report), Fritz Labor-
atory Reports, Paper 534.
[2] Haghani R., Al-Emrani M., Heshmati M. (2012) Fa-
tigue-Prone Details in Steel Bridges. Buildings, 2, 456-
476. DOI: 10.3390/buildings2040456.
[3] EN 1998-1, Eurocode 3: Design of Steel Structures –
Part 1-9: Fatigue. European Committee for Standard-
ization, Brussels.
[4] AASHTO LRFD (1994) Bridge Design Specifications, SI
units. 1st Edition, American Association of State High-
way and Transportation Officials, Washington, D.C.
[5] Kühn B., Lukic M., Nussbaumer A., Günther H.-P.,
Helmerich R., Herion S., Kolstein M.H., Walbridge S.,
Androic B., Dijkstra O., Bucak O. (2008) Assessment
of Existing Steel Structures: Recommendations for Es-
timation of Remaining Fatigue Life. JRC Scientific and
Technical Reports – ECCS European Commission.
[6] Bruhwiler E., Smith I.F.C., Hirt M.A. (1990) Fatigue
and Fracture of Riveted Bridge Members. Journal of
Structural Engineering, 116(1).
2508
25097075, 2023, 3-4, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/cepa.2464 by Nagoya Institute Of Technology, Wiley Online Library on [01/10/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

[7] Di Battista J.D., Adamson D.E.J., Kulak G.L. (1998)
Fatigue Strength of Riveted Connections. Journal of
Structural Engineering, 124(7).
[8] Bertolesi E., Buitrago M., Adam J.M., Calderón P.A.
(2021) Fatigue assessment of steel riveted railway
bridges: Full-scale tests and analytical approach. Jour-
nal of Constructional Steel Research, 182, 106664.
DOI: 10.1016/j.jcsr.2021.106664.
[9] Stamatopoulus G.N. (2013) Fatigue assessment and
strengthening measure to upgrade a steel railway
bridge. Journal of Constructional Steel Research, 80,
346-354. DOI: 10.1016/j.jcsr.2012.10.004.
[10] Pipinato A., Pellegrino C., Modena C. (2014) Re-
sidual life of historic riveted steel bridges: an analyti-
cal approach. Bridge Engineering, 1100014. DOI:
10.1680/bren.11.00014.
[11] Pipinato A., Pellegrino C., Bursi O.S., Modena C.
(2009) High-cycle fatigue behavior of riveted connec-
tions for railway metal bridges. Journal of Construc-
tional Steel Research, 65, 2167-2175. DOI:
10.1016/j.jcsr.2009.06.019
[12] Taras A., Greiner R. (2009) Development and Ap-
plication of a Fatigue Class Catalogue for Riveted
Bridge Components. Structural Engineering Interna-
tional, 1, 91-103.
[13] Greiner R., Taras A., Brunner H. (2007) Statistisch
begründete Festigkeitskennwerte genieteter Bauteile
– statische Festigkeit und Wöhlerlinienkatalog. Verlag
für Architectur und technische Wissenschaften GmbH
& Co. KG, Berlin Stahlbau, 76, 537-552. DOI:
10.1002/stab.200710056.
[14] ABAQUS – Analysis User’s Manual Version 6.17,
Abaqus Inc., 2017.
[15] Dassault, FE-SAFE 2021 User’s Manual, 2021.
[16] da Silva A.A.L. (2015) Advanced methodologies
for the fatigue analysis of representative details of
metallic bridges. PhD Thesis, Universidade do Porto,
Faculty of Engineering.
[17] da Silva A.A.L., Correia J.A.F.O., de Jesus A.M.P.,
Figueiredo M.A.V., Pedrosa B.A.S., Fernandes A.A.,
Rebelo C.A.S., Berto F. (2019) Fatigue characteriza-
tion of a beam-to-column riveted joint. Engineering
Failure Analysis, 103, 95-123.
[18] Correia J.A.F.O. (2014) An integral probabilistic
approach for fatigue lifetime prediction of mechanical
and structural components. PhD Thesis, Universidade
do Porto, Faculty of Engineering.
[19] Parola J.F., Chesson E., Munse W.H. (1965) Effect
of bearing pressure on fatigue strength of riveted con-
nections. Engineering Experiment Station, Bulletin
481.
[20] Sire S., Caiza P.D.T., Espion B., Ragueneau M.
(2020) Contribution to the study of the influence of
the stress ratio on the high cycle fatigue behaviour of
riveted joints. Fatigue & Fracture of Engineering Ma-
terials & Structures, 43, 3027-3026. DOI:
10.1111/ffe.13324.
[21] Graf O. (1935) Dauerversuche mit Nietverb-
indungen. Berichte des Ausschusses für Versuche im
Stahlbau. Heft 5. Berlin: Deutscher Stahlbau Ver-
band/SpringerVerlag.
[22] Klöppel K. (1936) Gemeinschaftsversuche zur
Bestimmung der Schwellzugfestigkeit voller, gelochter
und genieteter Stäbe aus St 37 und St 52. Stahlbau
Hefte 13714.
[23] Graf O. (1941) Versuche mit Nietverbindungen.
Berichte des Deutschen Ausschusses für Stahlbau.
Heft 12. Berlin. Deutscher Ausschuss für
Stahlbau/Springer Verlag 1941.
[24] D’Aniello M., Portioli F., Fiorino L., Landolfo R.
(2011) Experimental investigation on shear behaviour
of riveted connections in steel structures. Engineering
Structures, 33, 516-531. DOI: 10.1016/j.eng-
struct.2012.11.010.
[25] Milone A., D’Aniello M., Landolfo R. (2023) Influ-
ence of camming imperfections on the resistance of
lap shear riveted connections, Journal of Construc-
tional Steel Research, 203, 107833. DOI:
10.1015/j.jcsr.2023.107833.
[26] Coffin L.F. (1954) A study of the effect of the cyclic
thermal stresses on a ductile metal, Translations of
the ASME, 76, 931-950.
[27] Manson S.S. (1954) Behaviour of materials under
conditions of thermal stress, NACA TN-2933, National
Advisory Committee for Aeronautics.
[28] ASTM. E-739-91 (2005) Standard Practice for Sta-
tistical Analysis of Linear or Linearized Stress-Life (S-
N) and Strain-Life (

-N) Fatigue Data. DOI:
10.1520/E0739-10R15.
2509
25097075, 2023, 3-4, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/cepa.2464 by Nagoya Institute Of Technology, Wiley Online Library on [01/10/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License