PSI - Issue 72

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Procedia Structural Integrity 72 (2025) 1–4

12th Annual Conference of Society for Structural Integrity and Life (DIVK12) Editorial of the 12th Annual Conference of Society for Structural Integrity and Life (DIVK12) conference

Simon Sedmak a, * , Branislav Đorđević a , Aleksandar Sedmak a,b a Innovation Center of the Faculty of Mechanical Engineering, Kraljice Marije 16, Belgrade 11120, Serbia b University of Belgrade, Faculty of Mechanical Engineering, Kraljice Marije 16, Belgrade 11120, Serbia

Abstract The 12th Annual Conference of Society for Structural Integrity and Life (DIVK12), organized between 17th and 19th of November 2024, at the Faculty of Mechanical Engineering of the University of Belgrade, Serbia, gathered more than 160 participants (both in person and on-line) from all over the world, with more than 25 nationalities demonstrating the vitality and importance of this new event. This Special Issue gathers the 71 papers presented at the conference, including some keynote lectures and regular presentations. Awards for special contribution in certain topics were delivered attributed during the conference. The Organizing Committee of the DIVK12 conference sincerely thanks all contributing authors for playing a significant role in the overall success of this event, with their exciting presentations. The members of the International Scientific Committee are also fully acknowledged for their support of the DIVK12 event. Special thanks to the Keynote Speakers for their dedication and knowledge and energy brought to this event. The Organizing Committee would also like to express their gratitude to the sponsors for their support without which the conference would be impossible to organize. Finally, chairmen sincerely thank the tireless efforts of Organizing Committee members, as well as Faculty of Mechanical Engineering, IMS institute and Innovation Center of Faculty of Mechanical Engineering staff. © 2026 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Aleksandar Sedmak, Branislav Djordjevic, Simon Sedmak Dr. Simon Sedmak, ssedmak@mas.bg.ac.rs, Innovation Center of Faculty of Mechanical Engineering, Belgrade, Serbia

* Corresponding author. Tel.: /. E-mail address: ssedmak@mas.bg.ac.rs

2452-3216 © 2026 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Aleksandar Sedmak, Branislav Djordjevic, Simon Sedmak Dr. Simon Sedmak, ssedmak@mas.bg.ac.rs, Innovation Center of Faculty of Mechanical Engineering, Belgrade, Serbia 10.1016/j.prostr.2025.08.066

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1. Introduction This chapter opens with a brief overview of the Society for Structural Integrity and Life (DIVK), or "D ruštvo za integritet i vek konstrukcija 'Prof. Dr. Stojan Sedmak'" in Serbian. Since its establishment in 2001, this non governmental, non-profit society has grown to include over 240 registered experts. DIVK's primary focus is the practical application of fracture mechanics, through a range of activities including specialized seminars, publications, and strategic partnerships with other professional bodies. The 12th Annual Conference of Society for Structural Integrity and Life (DIVK12) is intended as a forum for discussion about recent advances in the fields of structural integrity: development and recent trends, classic approaches to structural integrity assessment, methods for reliability and probabilistic safety assessment, investigation on structural integrity of engineering structures under specific loading conditions, environmental effect concerning structural integrity and material properties, mechanical characterisation of engineering materials, structural integrity of newly developed materials in engineering application, finite element method and analytical modelling of failure under various loading conditions, fracture mechanics approach in structural integrity assessment, welding and welded structures as a specific problem, damage analysis, environmental effects and specificity and their applications in various fields, such as civil, mechanical, aerospace, traffic and chemical engineering, as well as to a wide variety of structures and equipment, including but not limited to bridges, buildings, dams, railways, pipelines, wind towers, offshore platforms, naval vessels, nuclear and hydropower plant. Members of organizing committee of DIVK12 conference were:  Professor Emeritus, Aleksandar Sedmak, Faculty of Mechanical Engineering, University of Belgrade, Serbia, DIVK president; ESIS president, conference chairman  Dr. Branislav Đorđević , Innovation center of Faculty of Mechanical Engineering in Belgrade, Serbia, conference secretary  Professor Dr. Ana Petrović , Faculty of Mechanical Engineering, University of Belgrade, Serbia, conference secretary  Professor Dr. Nenad Zrnić , Innovation center of Faculty of Mechanical Engineering in Belgrade, Serbia, director of Innovation center of Faculty of Mechanical Engineering in Belgrade  Dr. Dragan Bojović , IMS institute, Belgrade, Serbia, general manager of IMS institute  Dr. Mhajlo Aranđelović , Innovation center of Faculty of Mechanical Engineering in Belgrade, Serbia  Dr. (scientific associate) Simon Sedmak, Innovation center of Faculty of Mechanical Engineering in Belgrade, Serbia  Professor Dr. Zoran Radaković , Faculty of Mechanical Engineering, University of Belgrade, Serbia  Ivana Cvetković , Faculty of Mechanical Engineering, University of Belgrade, Serbia  Dr. Ž eljko Flajs, IMS institute, Belgrade, Serbia  Dr. Ksenija Đoković , IMS institute, Belgrade, Serbia  Dr. Isaak Trajković , Innovation center of Faculty of Mechanical Engineering in Belgrade, Serbia The 12th Annual Conference of Society for Structural Integrity and Life (DIVK12) was organized DIVK (Society for Structural Integrity and Life), with extensive support from local institutions, such as the Faculty of Mechanical Engineering and its Innovation Center. Conference was held at the Faculty of Mechanical Engineering of the University of Belgrade, Serbia, from 17-19 November 2024. Eight keynote lecture were presented:  Bojan Me đ o, University of Belgrade, Faculty of Technology and Metallurgy, Serbia “ Non-standard tensile and bending ring specimens for fracture examination of pipeline materials ”  Filippo Berto, Sapienza University of Rome, Department of Chemical Engineering, Materials and Environment, Italy “ Fatigue assessment of large structures: open issues and possible solutions ”  Dorin Radu, Faculty of Civil Engineering, Brașov, Romania “ Structural integrity assessment – part of a sustainable development ”  Francesco Iacoviello, Università di Cassino e del Lazio Meridionale, Cassino (FR), Italy “ Ductile cast irons: Porous steels or natural composites ?”

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 Grzegorz Lesiuk, Faculty of Mechanical Engineering, Wroclaw University of Science and Technology, Poland “ Strain energy density parameters as a crack driving force in fatigue crack growth rate analysis ”  Miloš Đukić, University of Belgrade, Faculty of Mechanical Engineering, Serbia “ Hydrogen embrittlement mechanisms synergy in metallic materials: HELP + HEDE model ”  R. Al-Sabur, Mechanical Department, Engineering College, University of Basrah, Basrah, Iraq “ Mechanical integrity and friction stir spot welding performance of aluminum and magnesium sheets for next-generation aerospace and automotive applications ”  Nenad Vidanovi ć , University of Belgrade, Faculty of Transport and Traffic Engineering, Serbia “ Study on optimisation-based approach conducted to estimate the life to failure of the damaged aircraft structure exposed to complex thermo-mechanical loading ” Within 2 keynote and 9 thematic sessions, 89 talks and 21 posters were presented by more than 160 participants (110 in person, 50 online). Across 9 thematic sessions, all important aspects of fracture mechanics and structural integrity were discussed. The conference placed a special emphasis on innovations and the latest trends, artificial intelligence, a multidisciplinary approach, and case studies. These case studies included structural integrity assessment, risk analysis, and the safety of engineering structures, taking into account environmental impacts, material behavior, their characterization, and the specificity of the structures themselves. This conference is firstly followed by Book of abstracts (https://machinery.mas.bg.ac.rs/handle/123456789/8113), while this Volume of Procedia Structural Integrity contains 71 manuscripts. The DIVK12 Organizing Committee extends its sincere gratitude to all contributing authors for their engaging presentations, which were vital to the event's success. We also deeply appreciate the support from the International Scientific Committee and the dedication, knowledge, as well as to all Keynote Speakers. Our heartfelt thanks go to our sponsors; without their time and support, this conference wouldn't have been possible. Finally, the chairmen commend the tireless efforts of the Organizing Committee members, as well as the students and staff from the Faculty of Mechanical Engineering (University of Belgrade), IMS Institute and Innovation Center of Faculty of Mechanical Engineering in Belgrade. 2. Thematic sessions and topics of the 12th Annual Conference of Society for Structural Integrity and Life (DIVK12) Aims of this international conference is to include researches concerning innovation and recent trends, multidisciplinary approach, as well as case studies, involving structural integrity assessment, risk analysis and safety of engineering structures taking into account environmental effects, materials behaviour, their characterisation, and the specificity of the structure itself. Following thematic sessions are covered by DIVK12 conference:  Computational fracture mechanics (dedicated to Prof. Dr. Mladen Berkovi ć )  Fatigue of engineering materials and structures  Failure analysis and forensic engineering  Numerical methods  Risk analysis and safety of large structures and components  Structural integrity of additive manufactured components  Structural integrity of welded joints  Data-driven methods and machine learning applied to structural integrity  Hydrogen embrittlement and transport

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3. DIVK12 awards It is our pleasure to present the Honorary Awards of our Society for Structural Integrity and Life (DIVK), which will hold the titles of our meritorious members. Following awards were attributed at DIVK12:  for contribution in computational fracture mechanics "Prof. Dr. Mladen Berković" - delivered to Professor Emeritus Aleksandar Sedmak  for contribution in weldment fracture mechanics "Prof. Dr. Stojan Sedmak" - delivered to Dr. Blagoj Petrovski  for contribution in numerical modelling of material behaviour "Prof. Dr. Marko Rakin" -delivered to Prof. Dr. Bojan Me đ o  for contribution in civil engineering struct ures "Mr. Tihoslav Tošić" - delivered to Dr. Dragan Bojo vić  for contribution in metallurgical aspects of fracture "Prof. Dr. Aleksandar Radović" -delivered to Dr. Vencislav Grabulov Awards Committee of Society for Structural Integrity and Life (DIVK) also announced Special Awards for:  extraordinary contribution in fatigue and fracture mechanics -delivered to Prof. Dr. Filippo Berto  extraordinary contribution in nanostructured materials and nanotechnology - delivered to Prof. Dr. Jianying He  Best Young Scientist Award - dedicated to the best contributions at DIVK12 conference selected by the Awards Committee - delivered to Prof. Dr. Shengwen Tu  Best poster award - presented by one of the author - delivered to Prof. Dr. Kwang-Bok Shin  Guest of honor award -delivered to Prof. Dr. Jovo Jarić Acknowledgements The Guest Editors of this Special Issue wish to express their profound gratitude to Prof. Dr. Francesco Iacoviello, Editor-in-Chief of Procedia Structural Integrity journal , and the dedicated Elsevier staff for their invaluable support throughout the preparation of this issue. Representing the Organizing Committee, the guest editors also extend their sincere appreciation to the Faculty of Mechanical Engineering (University of Belgrade), IMS Institute and Innovation Center of Faculty of Mechanical Engineering in Belgrade and all the esteemed sponsors of the event: Mont-R d.o.o., Refit Inženjering, Veritas, DGNDT d.o.o, Goša FOM , Sanacija i ispitivanje metala d.o.o., MIP Procesna oprema, Bureau Veritas (all based in Serbia). Particular recognition is extended to the Ministry of Science, Technological Development and Innovation of the Republic of Serbia and European Structural Integrity Society (ESIS).

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Procedia Structural Integrity 72 (2025) 286–293

12th Annual Conference of Society for Structural Integrity and Life (DIVK12) Accidental load on Žeželj bridge and analysis of soil caisson bridge interaction Boris Folić a, * , Miloš Čokić b , Željko Žugić a, * a Innovation Center of Faculty of mechanical engineering, Kraljice Marije 16, Belgrade, Serbia. b Termoenergo inženjering , Bulevar Kralja Aleksandra 298, Belgrade, Serbia. Abstract This paper shows the influence of exceeded loads on foundation of caisson Žeželj bridge (ŽB) in Nov i Sad. The exceeded load occurred at the beginning of the 60s of the 20th century, that is, only a few years after the facility was put into operation. A long span arch AB bridge (or PC) is not designed in a plain, unless there is solid rock on the shore t o support it. Of course, Žeželj knew about the foundation problems on the banks of the Danube in the vicinity of Novi Sad, where the soil is usually loess, clay, alluvial sand and gravel, so he envisioned immovable supports on caissons on the banks and in the center of the river. It is known (at least to the older generations) that Žeželj first performed the so -called prestressing of the soil, namely behind the caisson towards the coastal part, the soil was replaced, and thanks to the AB diaphragms that were located between the caisson and the soil, passive resistance was activated with the help of hydraulic presses. Therefore, with that prestressing, the soil consolidation correction was executed, i.e. all horizontal movements of the supports (caissons) that would naturally occur and thus endanger the building, were carried out during construction, before commissioning (this means the sum of horizontal movements including the flow of concrete). This made the bridge stable with immovable supports, or so it wa s thought. A few years after being comissioned, ŽB was subjected to a flood wave and considering that the banks were not adequately supported, the integrity of the bridge was threatened. During the flood, there was an urgent intervention with ballasts, probably piles of rocks, in order to protect the bank from erosion and ensure the immobility of the supports. In this paper, the interaction of the structure and the caisson with the ground was analyzed through possible stages of loading. Different levels of influence and possible adequate combinations were treated: passive resistance of the soil and sliding in the coupling as well as the thrust force on the caissons. The modern project in the Radimpex Tower will not be treated here, but exclusively the calculation methods that were current in the late 1950s and early 1960s.

* Corresponding author. Tel.: /. E-mail address: zzugic@gmail.com * Corresponding author. Tel.: /. E-mail address: boris.r.folic@gmail.com

2452-3216 © 2026 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Aleksandar Sedmak, Branislav Djordjevic, Simon Sedmak Dr. Simon Sedmak, ssedmak@mas.bg.ac.rs, Innovation Center of Faculty of Mechanical Engineering, Belgrade, Serbia 10.1016/j.prostr.2025.08.105

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Keywords: Soil structure interaction; Žeželj’s bridge in Novi Sad; Prestress soil, caisson, passive earth pressure; integritiet construction 1. Introduction Žeželj bridge in Novi Sad is a concrete bridge fixed at both sides, with RC and prestress concrete. Longitudinal appearance of arch is sickle-shaped, Fig. 1, therefore it has variable hollow cross section, where the maximal moment of inertia is realized at the top of arch and it decreases towards supports. With this type of arch, there is often a problem of support, but this is solved here by expanding the cross-section of arch below the plate, which is visible in Fig. 2b. Let's not forget, the whole project (at the former conceptual level) was done by B. Žeželj on 1 sheet (so two pages) of A3 fo rmat, where all the necessary dimensions of the bridge were drawn with a single formula (for the moment of a simple beam). After that, the entire team of engineers worked for several months on the contractor's project in order to state that there were no significant differences in dimensions between Žeželj's conceptual project and the contractor's project. © 2026 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Aleksandar Sedmak, Branislav Djordjevic, Simon Sedmak Dr. Simon Sedmak, ssedmak@mas.bg.ac.rs, Innovation Center of Faculty of Mechanical Engineering, Belgrade, Serbia

Nomenclature α

angle of tangent to the arch at the contact with the caisson

BS Base Shear in the plane bellow the cassion D f

distance from ground surface to base of footing (cassion)

δ φ

the angle of rotation of the resultant of the ground pressure relative to the wall normal

internal angle friction

tg φ

coefficient of friction, without FOS (factor of safty)

γ

unit weight of soil

Fig. 1. View of the Žeželj bridge, by Pržulj (2014)

The bridge was founded on poor soil, but the problem was largely solved by the presses at the top of the arches, and presses between the reinforced concrete (RC) diaphragms and the caissons on the bank (Fig. 3). All consolidation horizontal settlement and concrete creep were completed within a few months of operation of these hydraulic presses. After that, the bridge structure was monolithic. Even though a whole team of top engineers

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worked on the project, the bridge still had to be repaired, primarily due to the displacement of the right caisson during the flood of 1965. This paper deals with the impacts that occurred during that flood.

Fig. 2. (a) Longitudinal section and plan of the bridge, by Žeželj (1969). (b) Cross section of the bridge, by Trojanović (1961).

2. Foundation on caisson

Fig. 3. (a) Cross section of the caisson, left bank of Danube, by Žeželj (1969); (b) Cross section of the caisson, right bank of Danube, Šram (1970).

Table 1. Left and Right bank Caisson. Soil layer. Left bank Caisson “E”

Right bank Caisson “B”

Middle Caisson

Df =62 mv I layer: 10-12m sandy clay

D f =64 mv I layer: thin surface layer of muddy sand

D f =55 mv

II layer: 12-15m fine-grained gravel III layer: blue highly compacted clay B=25m; L=20m;

II layer: fine compacted gravel

B=24m; L=16m; H=9.68m

B=39.5m; L=24.5 m;

It is interesting to note that the horizontal force on the left side of the Danube, i.e. on the caisson of the larger arch, from its own weight is 8700t, or 87 MN, and on the smaller arch it is 5600t, or 56 MN.

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3. Passive soil resistance and load phase changes on caissons Some phases of loading during installation and flooding of the right caisson should be considered. As for construction, the coastal caissons-pillars were cast in place and later pneumatically lowered to the foundation depth. The middle caisson was made on the shore, upstream, excavated until it started to float, and brought to the designed place. However, at the middle caisson, the vessels that were intended for delivery still did not have enough power, so the waterway was closed and help was sought in the form of additional vessels. After that, it was brought to the intended scaffolding and lowered to the designed height. A counterweight was used for lowering, and the upper part of the column was concreted. The central, river pillar in the longitudinal section has the shape of a boot, i.e. due to the significant difference in load, the foot of the pillar is eccentrically extended to the side towards a smaller arc. So we have the oblique force from the small arc, if we know the angle of the tangent at the support of the arc, we can decompose it into horizontal and vertical components. We will ignore the arc fixed moment at this stage.

Fig. 4. Picture of the Žeželj’s bridge with coastline after building.

Fig. 5. Plane view of the banks, new Žeželj bridge and left Varadin rainbow bridge. Google earth.

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Fig. 6. Embankment around the caisson on the right bank during 1965 flood. by Bojovi ć (2019)

Fig. 7. Lateral forces of soil resistance Left caisson is similar to the right one.

Designer for caissons, along with Žeželj, was Živorad Ćertić, from Department of Geomechanics IMS. Responsibility for designing the construction belonged to Dimitrije Ćertić, from Prestressing Department of IMS, and Ilija Stojadinović from Mostogradnja, by Petrović (2005).

Fig. 8. Approximate calculation of incident load, Right Saturated soil conditions. “Prestress” soil.

Presented here is the back calculation, the vertical components of the major and minor arch, as well as the base shear at the left and right caisson locations. Assumed parameters for the replaced soil, i.e. the compacted gravel of the great arch is 40º. For the smaller arch, Fig. 8 right, the angle of internal friction is reduced to 30º, due to erosion due to flooding.

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Fig.9. (a) Approximate calculation of soil-cassion resistance. Without self weight of cassion. Coff.of sefty on tg a is onli 1.

In the previous approximate calculation, the dimensions of the RC diaphragm of the caisson and the soil conditions that satisfy and do not satisfy the requirements of the caisson’s stability are presented. Changes in influence in the arch for moving supports can be calculated tabularly. 4. Passive resistance of the soil due to the friction force between the wall and the soil Due to the appearance of friction between the wall and the soil, the Rankine wedge of passive soil resistance has an addition, an area next to the wall that is assumed to be in the form of a logarithmic spiral. Also due to friction in the case of passive soil resistance, there is a (deflection) rotation of the resultant, in relation to the normal to the wall, by an angle δ, Fig. 8. That angle δ expressed in relation to φ is usually about 1/3 to ½.

Fig. 10. Passive earth pressure , model with friction between wall and soil; (a) vertically immovable wall (b) vertically movable wall. By Milović (1987), or Maksimović (2005) .

The pneumatic caisson is by definition watertight, in order to enable dry work inside the caisson. The movement of the wall (RC diaphragm) is possible only if the watertightness of the caisson is preserved, several years after construction, and if the thrust force is greater than the vertical force of its own weight. To the extent that the thrust force occurs, in this case, it affects the reduction of the intensity of the vertical component. Measurements after the rehabilitation showed that the right caisson moved downwards by about 10 cm and rotated. So there is no upward movement of the wall, unless the center of rotation is in the center of the caisson, then one end moves down and the other moves up. A small digression, with deep foundations it is assumed that the point of rotation is in the axis of the foundation, but the point of rotation can be located, under, in or above the foundation. As we can see in Fig. 10b, the Rankine wedge can be extended to the junction with the wall, and the resistance calculated with a smaller wall height. The passive resistance of the soil due to upward movement of the wall is shown in Fig. 10b, but in this case movement of the rear part of the caisson can occur only if the center of rotation is near the center of the caisson. The force acting on the RC diaphragm due to passive resistance, with the influence of friction between the wall and the ground (Fig. 10a) for the data from Fig. 8 left, (φ=40 ֩̊ ) where δ/φ=0.50, is 11724.9 kN/m. If we compare with the value from Fig. 8 left, 5564.08 kN/m, we can conclude before the flood if the model with and without the

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effect of friction is calculated, the force due to the effect of friction increases by 2.107 times. Activated force of passive resistance for RC diaphragm width 8m, see in Tab 2.

Table 2. Passive earth pressure on RC diaphragm Caisson. Soil condition; k p [1] γ [kN/m 3 ] H [m]

F p =k p ·γ·H

2 /2

B·F p [MN] 44.52 93.80 16.60

BS* [MN] 18.27 18.27 18.27

Σ H i [MN]

[kN/m]

Dry or moist Dry or moist

4.60 9.69 4.60

20 20 10

11 11

5564.08 11724.90 2075.26

62.79 112,07

34,87

Submerged, Saturated

9.5

*BS for right caisson

According to Fig. 7, the passive resistance of the soil is activated only behind the diaphragm of height H, while the shear force in base acts just below the depth D f . If there is an exclusively horizontal movement of the caisson at the base, due to shearing at the base, passive pressure is activated at the depth Df, but due to the movement of the supports, the integrity of the arches is threatened. As we are dealing with shallow fixed arches, this problem is further accentuated. The integrity of the bridge and immovability, i.e. controlled movement within the desired limits, is ensured exclusively through RC diaphragms at the depth H. The places of repair of the cracks on the small arch and the middle caisson can be seen in Fig. 11.

Fig. 11. (a) Below the deck view of the repaired middle caisson. (b) On the deck view of the repair on smaller arch.

Trojanović (1961) talks about the necessity of calculating rheology, and the influence of flow, on deflections. Four years before the flood, he states that external prestressing often does not give satisfactory behavior of the structure. But the Vallet II arch, in the hands of a skillful and dexterous designer, can be rational. Petrović (1994, 2004), states that "for months we calculated that bridge, the mobility, the rheology of the concrete, and as if to spite it, it has a stomach (think of a deck), you can see it in winter". The authors of the paper do not know whether this refers exclusively to the period after flood or before the accidental event, and it was not specified in the lectures. If it was not visible before the flood, then the flood caused the supports to move and rotate, in such a way that the road plate gets excessive deflection. The bridge has a small flaw, namely the road plate of the large arch does not have a longitudinal slope. It is usual to create an overhang in the middle (span), or to have a continuous slope towards one end. Here, it was logical to create an overhang in the middle by 20 cm (which is a slope of 2 ‰). It is possible that the "belly" would not appear then. The smaller arch has a constant longitudinal slope of the road towards the coast of 2 ‰.

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5. Conclusion The Lack of sufficient riprap on the bank and extremely large floods in 1965 threatened the integrity of this unique bridge. Due to the extreme loads it was exposed to at the time, causing erosion and caisson to move, bridge had to be repaired in the following decades. Also, the maintenance of the bridge was not at the appropriate level, but the genius of the designers, and the skill of the contractors, as well as the robustness of the building, saved this bridge. Unfortunately, as if all that was not enough... „The destructive drive of NATO destroyed this unique bridge in 1999“. Prof. dr. Pržulj Milenko. Acknowledgements This work was supported by the Ministry of Science, Technological Development and Innovation of the Republic of Serbia (Contract No. 451-03-66/2024-03/ 200213 from 05.02.2024). References Петровић, Б., 1998. „...о објектима Бранка Жежеља„. Предавање у Новом Саду на ФТН. Serija predavanja 1994, 1996 and 2004 Petrović, B., 2005. Branko Žeželj (1910 -1995). Reprinted from publication Lives and work of the Serbian scientist, 10. Serbian Academy of Sciences and Arts, Biographies and bibliographies vol.X, II section, book 10. Belgrade Prakash, S., 1995. Fundamental of soil mechanics. University of Missouri-Rolla. Shamsher Prakash Foundation Rolla, MO, USA Pržulj, M., 2014. Mostovi: koncipiranje, projektovanje, konstruisanje, pouzdanost, građenje, gospodarenje, obnova. Bridges: conception, design, construction, reliability, building, management, restoration. Udruženje „Izgradnja“. Beograd Šram, S., 2002. Gradnja mostova. Betonski mostovi. Golden marketing Zagreb. Sveučilište J.J.S. Osijek Šram, S., 1970. Fundiranje mostova pomoću kesona. Specijalno izdanje časopisa „Izgradnja“. Geomehanika i fundiranje.. Beograd Stojadinović, I., 1969. Paški most. Specijalno izdanje časopisa „Izgradnja“. Betonske predapre gnute konstrukcije. Beograd Trojanović, M. 1961. Betonski mostovi I. Teorija i analiza osnovnih sistema i konstrukcija betonskih mostova. Naučna knjiga. Beograd. 246b Žeželj, B., 1969. Razvoj građenja u prednapregnutom betonu u svetu i kod nas. Specijalno izdanje časopisa „Izgradnja“. Betonske predapregnute konstrukcije. Beograd. 1-45 Veljković, N., Fundiranje pomoću kesona. Specijalno izdanje časopisa „Izgradnja“. Geomehanika i fundiranje. Beograd , 30-48 Bojović, A., 2019. Željezničko -drumski most preko D unava u Novom Sadu: istorijat, projekat, izgradnja. Udruženje „Izgradnja“ Beograd.58 -60, 132-135 Milović, D., 1987. Mehanika tla. FTN, OOUR IIG. Novi Sad , 148,160-174 Maksimović, M., 2005. Mehanika tla. Građevinska knjiga. Beograd , 324-328

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Procedia Structural Integrity 72 (2025) 34–42

Keywords: Tubular adhesive joints; Structural adhesive; Finite Element Method; Cohesive Zone Models; Strength prediction 1. Introduction There are different geometries of adhesive joints, namely single and double-lap joints, stepped joints, scarf joints, and tubular joints. Tubular joints may have different geometrical configurations. In overlap tubular joints, a tube with a lower diameter is introduced into a tube with a larger diameter, and both are joined along the overlap length (Faria and Campilho 2024). Tubular adhesive joints are widely used in industries that make use of tubular constructions, such as civil construction (to join tubular trusses), pressure vessels, and medium-sized metalworking Abstract There are different geometries of adhesive joints, including tubular joints, where a tube with a lower diameter is introduced into a tube with a larger diameter. This joint geometry promotes high strength/weight ratio, improved stresses distribution and good corrosion resistance. The present work numerically compares the performance of three adherend materials in overlap tubular joints, considering the variation of the adherend material and overlap length ( L O ). The numerical analysis, using Cohesive Zone Models (CZM), was initially validated with experimental data. The developed numerical work enabled to obtain the peel ( σ y ) and the shear stresses ( τ xy ) in the adhesive layer using purely elastic models. Then, by CZM, strength prediction was carried out. The joint composed of DIN 55Si7 steel adherends and the adhesive Araldite ® AV138 showed the highest tensile strength. © 2026 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Aleksandar Sedmak, Branislav Djordjevic, Simon Sedmak Dr. Simon Sedmak, ssedmak@mas.bg.ac.rs, Innovation Center of Faculty of Mechanical Engineering, Belgrade, Serbia 12th Annual Conference of Society for Structural Integrity and Life (DIVK12) Adherend effect on the tensile behavior of tubular adhesive joints C.F.F. Gomes a , R.D.S.G. Campilho a,b, *, R.D.F. Moreira a , K. Madani c , S.C. Djebbar c a CIDEM, ISEP – School of Engineering, Polytechnic of Porto, R. Dr. António Bernardino de Almeida, 431, 4200-072 Porto, Portugal. b INEGI – Pólo FEUP, Rua Dr. Roberto Frias, 400, 4200-465 Porto, Portugal c Department of Mechanical Engineering, University of Sidi Bel Abbes, BP 89, Ci té Ben M’hidi, 22000, Sidi Bel Abbes, Algeria.

* Corresponding author. Tel.: +351939526892; fax: +351228321159. E-mail address: raulcampilho@gmail.com

2452-3216 © 2026 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Aleksandar Sedmak, Branislav Djordjevic, Simon Sedmak Dr. Simon Sedmak, ssedmak@mas.bg.ac.rs, Innovation Center of Faculty of Mechanical Engineering, Belgrade, Serbia 10.1016/j.prostr.2025.08.071

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industry applications (Parashar and Mertiny 2012). Adhesive joining is also applied to join tubular components in the pipe manufacturing industry, such as in oil and energy production or wastewater treatment, in automotive chassis (aircraft, cars and buses), and even in space structures (Barbosa et al. 2018). The development of Finite Element Method (FEM) makes it possible to numerically predict the behavior of adhesive joints by simulating the geometry of the joint, the stresses involved and the plasticity of the adhesive and adherends. Cohesive Zone Models (CZM) combine the strength and toughness parameters of adhesives to accurately predict the joint performance (Khoramishad and Khakzad 2018). Strength prediction of tubular joints can be carried out using modelling software such as Abaqus ® or Ansys ® , which allows stresses and strains to be analyzed in the different loading phases, and application of advanced fracture criteria. The tubular joint can be modelled numerically in axisymmetric 2D models to analyze peel and shear stresses and predict failure under tensile or bending loads, or in 3D models if the joint is subjected to a torsional moment. The adhesive can be modelled with identical elements to obtain stress distributions or strength predictions using techniques such as continuum mechanics, fracture mechanics or Extended Finite Element Method (XFEM), or with cohesive elements in the case of CZM modelling. The topic of numerical prediction of tubular adhesive joints is addressed in the literature. Aimmanee et al. (2018) proposed a simplified analytical model to evaluate the tensile behavior of adhesive-bonded tubular strap joints. The tubes can have isotropic, orthotropic, or multilayer composite properties. Linear elastic adherends and adhesives, and axisymmetric conditions were enforced in the models. The obtained results provided design principles for these joints with different tube materials. The numerical work carried out by Rosas et al. (2021) using CZM studied the tensile performance of tubular overlap adhesive joints with aluminum adherends bonded with Araldite ® 2015. Different geometric parameters were studied (chamfers and fillets in the adhesive layer). The results of the joints with the addition of adhesive fillets at the overlap ends showed a significant reduction in shear stresses (60%), but this did not translate into an increase in joint strength due to plasticization of the adherends. The impact resistance of a tubular overlap joint with AW6082-T651 aluminum adherends bonded with the Araldite ® AV138 was studied by Silva et al. (2021) using a triangular CZM. Increasing the overlap length ( L O ) from 10 to 20 mm was shown to positively influence the joint’s strength by 43.7%. This trend also reflected on the joint’s energy dissipation at failure ( U ). Eusebio and Campilho (2019) evaluated the XFEM predictive capabilities for the strength of tubular overlap adhesive joints subjected to tensile loads, with different L O . The results showed an increase in stress concentrations with increasing L O . Smaller strength improvements with L O were observed for brittle adhesives compared to more ductile adhesives. The XFEM method showed worse predictions for highly ductile adhesives. The present work numerically compares the performance of three adherend materials in overlap tubular joints, considering the variation of the adherend material and L O . The developed numerical work enabled to obtain σ y and τ xy stresses in the adhesive layer using purely elastic models. Then, by CZM, strength prediction was carried out. 2. Materials and methods 2.1. Joint geometry The proposed technique, CZM, is initially validated by experimental test results. Thus, the overlap tubular joint geometry is initially introduced for both the validation study and numerical analysis that follows (Fig. 1). In this study, a single geometric parameter is varied, namely L O . This parameter has values of 20 and 40 mm for the validation study, and between 10 mm and 40 mm for the subsequent numerical analysis. Since the length of the adhesive joint remained the same, the adherends’ length ( L S ) varied depending on L O . The other parameters remained unchanged, and their designations and dimensions can be found in Table 1.

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Fig. 1 . Schematic representation of the tubular joints’ geometry.

Table 1. Dimensions of the overlap tubular adhesive joints.

Description

Dimensions [mm]

Overlap length, L O Adherends’ length, L S

10 45

20 50 80 20

40 60

Total length, L T

Outer diameter of inner adherend, d SI Outer diameter of outer adherend, d SE Thickness of inner adherend, t SI Thickness of outer adherend, t SE

24.4

2 2

Adhesive thickness, t A

0.2

2.2. Materials

The adherends for the validation study were made from the aluminum alloy AW 6082-T651, characterized by Campilho et al. (2011) (Fig. 2 ). The results showed a tensile strength of 324.00±0.16 MPa, a Young’s modulus of 70.07±0.83 GPa, a tensile yield strength of 261.67±7.65 MPa, and a tensile fracture strain of 21.70±4.24%.

100 150 200 250 300 350

 [MPa]

Experimental Numerical approximation

0 50

0

0.05

0.1

0.15

0.2

0.25



Fig. 2. Stress-strain ( σ - ε ) curves of the aluminum alloy AW6082-T651. The CZM study that followed used this aluminum alloy and two additional materials. The first one is a Carbon Fiber Reinforced Polymer (CFRP), obtained by hand lay-up of 16 individual plies of SEAL ® Texipreg HS 160 RM prepreg. The CFRP elastic properties were obtained in previous studies (Campilho et al. 2005) (Table 2).

Table 2. Elastic properties of the CFRP (Campilho et al. 2005).

E 1 [MPa] 109000

E 2 [MPa]

E 3 [MPa]

G 12 [MPa]

G 13 [MPa]

G 23 [MPa]

 12

 13

 23

8819

8819

0.342

0.342

0.38

4315

4315

3200

The second additional adherend material is the DIN 55Si7 steel. This high-strength steel aims to prevent plastic deformation of the adherends during testing due to its high elastic limit. This aspect is significant because it enables comparing different adhesives without the interference of adherend plasticization or failure. The properties of this material have been previously estimated (Valente et al. 2019) and are presented in Table 3.

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Table 3. Properties of DIN 55Si7 steel adherend (Valente et al. 2019).

E [GPa]

σ y [MPa]

σ f [MPa]

ε f [%]

ρ [g/cm

3 ]



210

1078

1600

6

0.3

7.8

Three different adhesives were selected, including both ductile and brittle types, enabling a broader exploration of joint behavior. The chosen adhesives were Araldite ® AV138 (epoxy-based and brittle), Araldite ® 2015 (epoxy based with moderate ductility), and Sikaforce ® 7752 (polyurethane-based, ductile but less strong). These adhesives underwent various experimental tests, resulting in the data presented in Table 4. Table 4. Mechanical and fracture properties of the selected adhesives (Neto et al. 2012, Campilho et al. 2013, Faneco et al. 2017). Property Araldite ® AV138 Araldite ® 2015 Sikaforce ® 7752 Young’s modulus, E [GPa] 4.89 ± 0.81 1.85 ± 0.21 493.81 ± 89.6 Poisson’s ratio, ν b 0.35 a 0.33 a 0.33 a Tensile yield stress, σ y [MPa] 36.49 ± 2.47 12.63 ± 0.61 3.24 ± 0.5 Tensile strength, σ f [MPa] 39.45 ± 3.18 21.63 ± 1.61 11.49 ± 0.3 Tensile failure strain, ε f [%] 1.21 ± 0.10 4.77 ± 0.15 19.18 ± 1.4 Shear modulus, G [GPa] 1.56 ± 0.01 0.56 ± 0.21 187.75 ± 16.4 Shear yield stress, τ y [MPa] 25.1 ± 0.33 14.60 ± 1.30 5.16 ± 1.1 Shear strength, τ f [MPa] 30.2 ± 0.40 17.90 ± 1.80 10.17 ± 0.6 Shear failure strain, γ f [%] 7.8 ± 0.7 43.90 ± 3.40 54.82 ± 6.4 Toughness in tension, G IC [N/mm] 0.20 b 0.43 ± 0.02 2.36 ± 0.2 Toughness in shear, G IIC [N/mm] 0.38 b 4.70 ± 0.34 5.41 ± 0.5 a Manufacturer’s data. b Estimated in reference (Neto et al. 2012). The chosen software for the static numerical simulations was Abaqus ® 6.21 (Dassault Systèmes) considering a quadratic stress criterion for damage initiation and a linear energetic criterion to assess crack growth in CZM modeling. The triangular cohesive law is widely used due to its simplicity and accuracy, involving parameters such as the tensile and shear stiffness ( K n and K s ), cohesive tractions in tension and shear ( t n 0 and t s 0 ), and fracture toughness in tension and shear ( G n c and G s c ) (Rocha and Campilho 2018). The numerical analysis uses deformable four-node axisymmetric elements (CAX4 in Abaqus ® ) and axisymmetric cohesive elements (COHAX4R in Abaqus ® ) for the adhesive layer. The model geometry was discretized into finite elements, with refined meshing in high-stress areas. The CZM meshes involved a minimum element size of 0.2×0.2 mm 2 , applied at the overlap edges of the adhesive, with size grading effects applied to reduce the computational load. 2.3. Model pre-processing

Fig. 3. Mesh details for the CZM model for L O =10 mm. Figure 3 shows the mesh details for L O =10 mm and boundary conditions. The models for stress analysis were more refined, to accurately capture peak stresses, considering a ratio 0.1× ratio in the edge size of the elements. Results were visualized, with P - δ curves being created by summing fixed-end reactions and plotting against displacement values at the opposite edge of the joint, providing comprehensive data on the adhesive joint’s behavior to be collected and analyzed in the Results section.

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3. Results 3.1. Validation with experiments

The CZM approach is initially validated by comparing it with experimental data. The chosen tubular joint configuration includes an L O ranging from 20 to 40 mm, an outer diameter of 20 mm, and an adhesive thickness of 0.2 mm. The specimens were tested using a Shimadzu-Autograph AG-X tester (Shimadzu, Kyoto, Japan) equipped with a 100 kN load cell. The experimental maximum load ( P m ) was plotted against L O in Fig. 4, alongside numerical predictions. Both experimental and numerical analyses indicated cohesive failures of the adhesive.

50

40

30

P m [kN]

20

10

0

0

10

20

30

40

50

L O [mm]

Exp AV138 Num AV138

Exp 2015 Num 2015

Exp 7752 Num 7752

Fig. 4. Experimental and numerical P m results for validation. The AV138 showed minimal differences between experimental and numerical results, with deviations of 2.4% for L O =20 mm and 4.7% for L O =40 mm. Similarly, for the 2015, the deviation was 6.1% for L O =20 mm, decreasing to 2.9% for L O =40 mm. Conversely, the tubular joints using the 7752 exhibited moderately lower numerical P m . Despite the differences, of 18.4% for L O =20 mm and 14.3% for L O =40 mm, with experimental values consistently higher, the numerical values are considered acceptable for comparative study of parameters and geometries. 3.2. Stress analysis Stresses are normalized by the average  xy stress along L O ( τ avg ). The adhesive layer length is normalized, such that the x -axis is represented between 0 and 1, which makes it easier to compare all the joints analyzed. 3.2.1. Peel stress The results of adhesive joints with L O =20 mm and the 2015 on all adherends were compared (Fig. 5 a). The maximum value of σ y / τ avg =2.00 was observed at the overlap edges for the CFRP joints. Since the longitudinal modulus ( E 1 ) of CFRP is greater than the Young´s modulus ( E ) of aluminum it gives rise to higher σ y peak stresses. The second highest peak stress was recorded by aluminum, with a maximum of σ y / τ avg =1.98. Given that steel is the adherend with the highest E value, the expected strain gradient will be lower than that of the others ( σ y / τ avg =1.09).

4

4

3

3

2

2

 y /  avg

 y /  avg

1

1

0

0

-1

-1

0

0.2

0.4

0.6

0.8

1

0

0.2

0.4

0.6

0.8

1

x / L O

x / L O CFRP AW 6082-T651 aluminum DIN 55Si7 steel

a)

b)

10 mm

20 mm

40 mm

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4

3

2

 y /  avg

1

0

-1

0

0.2

0.4

0.6

0.8

1

x / L O

c)

Araldite AV138

Araldite 2015

SikaForce 7752

Fig. 5. σ y / τ avg stress distributions depending on: a) adherend materials; b) L O , and c) type of adhesive. Fig. 5 (b) shows σ y stress distributions of CFRP adhesive joints, bonded with the 2015, as a function of L O (10, 20 and 40 mm). An upward trend is detected in peak stresses with increasing L O . As expected, peak σ y stresses appear at the overlap edges. The transverse deformation of the joint give rise to more significant tensile stresses in these regions. The maximum stresses were obtained for L O =40 mm ( σ y / τ avg =3.08) at x / L O =0 (proximity to the smallest deformed cross-section between the two adherends). Fig. 5 (c) reports the influence of the type of adhesive on σ y stress distributions. For this case, CFRP tubular joints with L O =20 mm bonded with different types of adhesives were analyzed. The results show higher peak σ y stresses in the AV138 compared to the 2015 and 7752. This difference arises from the higher elastic stiffness, which results in higher stress concentration at the overlap edges. The 7752 is the adhesive with the lowest σ y / τ avg stress gradient, since this adhesive has the lowest stiffness between the three adhesives studied. The AV138 showed σ y / τ avg =2.92 while the 7752 only revealed σ y / τ avg =1.07 (peak values along the overlap). 3.2.2. Shear stress Fig. 6 shows  xy stress distributions.  xy stresses have low magnitude at the inner overlap and peak at the overlap edges. These peak stresses arise due to the differential deformation of the tubes along the overlap.

4

4

3

3

2

2

 xy /  avg

 xy /  avg

1

1

0

0

0

0.2

0.4

0.6

0.8

1

0

0.2

0.4

0.6

0.8

1

x / L O CFRP AW 6082-T651 aluminum DIN 55Si7 steel

x / L O

10 mm

20 mm

40 mm

a)

b)

4

3

2

 xy /  avg

1

0

0

0.2

0.4

0.6

0.8

1

x / L O

Araldite AV138

Araldite 2015

SikaForce 7752

c)

Fig. 6. τ xy / τ avg stress distributions depending on: a) adherend materials; b) L O , and c) type of adhesive.

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The influence of the adherend materials on  xy stresses is shown in Fig. 6 (a). It is possible to observe an upward trend in the stresses at the overlap edges, i.e., x / L O =0 and x / L O =1, similar to the behavior of σ y stresses. The adherend with the highest peak stresses was the aluminum alloy, with  xy / τ avg =2.19 near to x / L O =0. The results for the other adherends were then coherent with the stiffness difference, and the steel adherend exhibited lower  xy stress values, of  xy / τ avg =1.54 near to x / L O =0 and  xy / τ avg =1.26 in the region of x / L O =1. Fig. 6 (b) shows  xy / τ avg stresses as a function of L O for CFRP joints bonded with the 2015, considering L O values of 10, 20, and 40 mm. There is an increasing trend in the peak stresses for higher L O , as it was observed with the σ y stresses. The large bonding areas and the applied loads result in an increase of the stress gradients  xy with greater L O . As a result, the inner overlap loses capability to transfer loads in the elastic regime. The comparison between the adhesives for joints with CFRP adherends and L O =20 mm is presented in Fig. 6 (c). The AV138 achieved the highest peak of  xy / τ avg =2.26 at the overlap edges due to its high stiffness. The 7752 showed a more uniform distribution of  xy stresses and reached a maximum value of only  xy / τ avg =1.33, since it has a lower elastic stiffness. 3.3. Joint strength Fig. 7 P m data was generated from the CZM analysis taking into account variations in L O (10, 20, and 40 mm), different adhesive materials and adherends. Each graph represents an adherend material and includes three curves representing the strength of the different adhesives studied. Fig. 7 (a) shows P m of the different adhesives as function of L O for the CFRP adherends. The P m evolution is linear up to L O =20 mm for three adhesives and the AV138 reveals the highest strength, around 15% higher than the 2015 and 43% higher than the 7752. By increasing the L O from 20 to 40 mm, the increase in P m for the 2015 continues to be linear, while for the AV138 and the 7752 it is possible to observe an inflection point, which means that, if L O increases further, there would be no significant improvement in P m for these two adhesives. In addition, the highest P m value recorded for L O =40 mm, was around 56489.2 N for joints bonded with the 2015. For this L O the P m value of the 2015 is 10% higher than AV138 and 40% higher than the 7752. In Fig. 7 (b), P m is presented for different L O and different adhesives for aluminum AW 6082-T651 bonded tubular joints. When increasing L O from 10 to 20 mm, the increase of P m is practically linear for the three analyzed adhesives, and the AV138 shows higher P m in comparison to the other ones, around 33% higher than the 2015 and 52% higher in relation to the 7752. For an L O of 40 mm and the 2015, which until then presented 14% less strength than the AV138, equals the P m of the AV138. The behavior of the 7752 is the most linear and it shows reduced P m values throughout the L O analyzed. For L O =20 mm, there is a percentile P m difference between the 7752 and 2015 of 33%. On the other hand, for L O =40 mm, the difference between the adhesives is around 23%. Fig. 7 (c) shows the P m results, of the DIN 55Si7 steel joints, as a function of L O for the three adhesives. The results showed no discrepancy in the trends, i.e. the increase of P m is linear for all cases. In the complete range of the L O variation, the AV138 always proved to be the most capable, followed by the 2015 and finally the 7752.

50

60

50

40

40

30

30

P m [kN]

P m [kN]

20

20

10

10

0

0

0

10

20

30

40

0

10

20

30

40

L O [mm]

L O [mm]

Araldite AV138

Araldite 2015

SikaForce 7752

Araldite AV138

Araldite 2015

SikaForce 7752

a)

b)