# Issue 60

Issue 60 (April 2022) of Frattura ed Integrità Strutturale (Fracture and Structural Integrity; ISSN 1971-8993).

Vol XVI, Issue 60, April 2022

ISSN 1971 - 8993

Frattura ed Integrità Strutturale, 60 (2022); International Journal of the Italian Group of Fracture

Table of Contents

O. Shallan, T. Sakr, M. Khater, A. Ismail https://youtu.be/jKyxXpDIFpQ

Interaction diagram for RC column strengthened by steel angles and strips …………………... 1-12 M. Vyhlídal, I. Rozsypalová, H. Šimonová, B. Kucharczyková, P. Rovnaníková, Z. Keršner, L. Vavro, M. Vavro, J. N ě me č ek https://youtu.be/wXVefEIy5IE Effect of petrographic composition and chemistry of aggregate on the local and general fracture response of cementitious composites …………………………………………………...… 13-29 A. Deliou, B, Bouchouicha https://youtu.be/C6kcjP7H-5U Mechanical behavior of unidirectional composites according different failure criteria …………… 30-42 H. Guedaoura, Y. Hadidane https://youtu.be/Sy0y8xNhizY Web post-buckling strength of thin-webbed cellular beams using carbon PFRP profiles ………... 43-61 M. A. Bouchelarm, A. Boulenouar, M. Chafi https://youtu.be/PQ5ezmGkuuQ Numerical analysis of bonded composite patch efficiency in the case of lateral U and V-notched aluminium panels … …………………………………………………………….…... 62-72 A.A. Elakhras, M.H. Seleem, H.E.M. Sallam https://youtu.be/3soWj7V16eM Fracture toughness of matrix cracked FRC and FGC beams using equivalent TPFM ……….. 73-88 A. Boukhelkhal, S. Kenai https://youtu.be/WRLrKV6P1l4 Assessment of fluidity retention, mechanical strength and cost production of blended cement self- compacting concrete using the concept of a performance index ……...………………………... 89-101 T. Messas, D. Achoura, A. Boutrid, B. Mamen, https://youtu.be/Dx1sjLYGdDc Experimental investigation on the mechanical behavior of concrete reinforced with Alfa fibers …... 102-113 C. O. Bulut, S- P- Jena, S. Kurt https://youtu.be/JUMw2MR-EXM Experimental and computational study on dynamic analysis of cracked simply supported structures under moving mass …………………………………………………………. 114-133

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Fracture and Structural Integrity, 60 (2022); ISSN 1971-9883

G. C. Coêlho, A. A. Silva, M .A. Santos https://youtu.be/0YDJEIxUPcE Elastic surface crack interaction and its engineering critical assessment within the framework of fitness-for-service standards …………………………………………………………… 134-145 D. S. Lobanov, A. S. Yankin, N. I. Berdnikova https://youtu.be/5BYOp8tP848 Statistical evaluation of the effect of hygrothermal aging on the interlaminar shear of GFRP …... 146-157 A. Joshi, P. S. S. Gouda, I. Sridhgar, U. Farooq, V. Uppin, J. Vastrad, N. Gogoi, A. Edacherian https://youtu.be/6mM-RiyQ8gE Crack suppression by natural fiber integration for improved interlaminar fracture toughness in fiber hybrid composites …………………………………………………………….…. 158-173 M. B. Yasmine, B. Zeineddine https://youtu.be/x_022uItmJ4 Mechanical behaviour of sandy soils embankments treated with cement and reinforced with discrete elements (fibres) …………………....……………………………………………….... 174-186 R. Karimihaghighi, M. Naghizadeh, S. Javadpour https://youtu.be/JUkMYbIX50E FFS Master Software for Fitness-For-Service assessment of hydrogen induced cracking equipment based on API 579-1/ASME FFS-1 ………………………………………………… 187-212 B. Szabó, L. Pásthy, Á. Orosz, K. Tamás https://youtu.be/EUKN8mmcLck The investigation of additive manufacturing and moldable materials to produce railway ballast grain analogs ………………………………………………………………………... 213-228 G. R. Chate, R. M. Kulkarni, P. G. C. Manjunath, A. Lakshmikanthan, H. M. Harsha, S. Tophakhane, N. Shaikh, S. Kongi, P. Iranavar https://youtu.be/L5lNm2WCOBY Synthesis and characterization of Fe 2 O 3 nanoparticles reinforced to recycled industrial aluminium scrap & waste aluminium beverage cans for preparing metal matrix nanocomposites .................... 229-242 S. Ahmed, H. Atef, M. Husain https://youtu.be/WYIMBgKCI5w Improvement of mechanical properties of railway track concrete sleepers using ultra high performance concrete (UHPC) ………………………………………………………… 243-264 D. D’Angela, M. Ercolino https://youtu.be/4VtFdxBPWi4 Fatigue crack growth analysis of welded bridge details …………...………………………... 265-272 R. Gerosa, B. Rivolta, M. Boniardi, A. Casaroli https://youtu.be/N2KDLFdj2-I On the peak strength of 7050 aluminum alloy: mechanical and corrosion resistance ……...….... 273-282

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Frattura ed Integrità Strutturale, 60 (2022); International Journal of the Italian Group of Fracture

U. B. Gopal Krishna, B. Vasudeva, V. Auradi, M. Nagaral https://youtu.be/7jmptVl_i_M Mechanical characterization and tensile fractography of Al7075-WC P -Co P composite ………... 283-290 F. Awad, M. Husain, K. Fawzy https://youtu.be/-THMftRnlws Flexural behaviour of reinforced concrete beams strengthened by NSM technique using ECC ….. 291-309 A.-A. A. A. Graf, M. Bneni, A. M. I. El-Kholy, A. M. E. Elkilani, S. S. E. Ahmad https://youtu.be/oCLqaRMgXNc Experimental and numerical evaluation of compression confinement techniques for HSC beams reinforced with different ratios of high strength steel reinforcement ………………………….... 310-330 H. Benzineb, M. Berrahou, M. Serier https://youtu.be/edEe7_qvsqo Analysis of the adhesive damage for different shapes and types patch’s in corroded plates with an inclined crack ……………………………………………………………………….. 331-345 H. Djeloud, M. Moussaoui, A. Kellai, D. Hachi, F. Berto, B. Bouchouicha, B. E. Hachi https://youtu.be/Ecus9L7GERs Investigation fatigue crack initiation and propagation cruciform welded joints by extended finite element method (XFEM) and implementation SED approach ……………………………. 346-362 N. Hassani, H. Dehmous https://youtu.be/JpiNINFe2Uo Experimental analysis of short concrete column under hygrothermo-mechanical accelerated aging ... 363-379 L. Wang https://youtu.be/Mbza1XV_0rc Microstructure and anisotropic tensile performance of 316L stainless steel manufactured by selective laser melting .....……………….……………………….……………………... 380-391 N. Djellal, D. E. Mekki, E. Navarro, P. Marin https://youtu.be/RC9LHugGjW8 Influence of Pr 6 O 11 addition on structural and magnetic properties of mechanically alloyed Fe 65 Co 35 nanoparticles…………………………………………………………..……. 392-406 D.-E. Semsoum, S. Habibi, S. Benaissa, H. Merzouk https://youtu.be/-GBwidlzZW0 The proposition of analytical expression HM–( √ P/S) in microindentation pile-up deformation mode ………………………………………………………………………………. 407-415 A. Taibi, T.T Chimoto, F.K Maradzika, M. Matallah https://youtu.be/Be0ir8ZSaA0 Mesoscale investigation of mass concrete temperature control systems and their consequences on concrete mechanical behaviour …………………………………………………………. 416-437

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Fracture and Structural Integrity, 60 (2022); ISSN 1971-9883

A. Bekhedda, M. Merbouh https://youtu.be/ZfNI1jL-Pqw Recycling of plastic waste polyethylene terephthalate (PET) as a modifier in asphalt mixture: study of Creep-Recovery at Low, Medium, and Hot Temperatures …………………………. 438-450 R.R. Yarullin, M.M. Yakovlev https://youtu.be/M5b2195HXYI Fatigue growth rate of inclined surface cracks in aluminum and titanium alloys ……………… 451-463 F. Greco, D. Gaetano, L. Leonetti, P. Lonetti, A. Pascuzzo, A. Skrame https://youtu.be/aPAZQnX-S9U Structural and seismic vulnerability assessment of the Santa Maria Assunta Cathedral in Catanzaro (Italy): classical and advanced approaches for the analysis of local and global failure mechanisms ………………………………………………………………………… 464-487 N. Zekriti, F. Majid, R. Rajaa, I. Mrani, H. Rhanim https://youtu.be/lqGT6hNmB3U PVC failure modelling through experimental and digital image correlation measurements ……... 488-503 C. Morales, M. Merlin, A. Fortini, G. L. Garagnani, A. Miranda https://youtu.be/0TPNegK_TZo Impact behaviour of dissimilar AA2024-T351/7075-T651 FSWed butt-joints: effects of Al 2 O 3 -SiC particles addition ……………………………………………………….... 504-515

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Frattura ed Integrità Strutturale, 60 (2022); International Journal of the Italian Group of Fracture

Editorial Team

Editor-in-Chief Francesco Iacoviello

(Università di Cassino e del Lazio Meridionale, Italy)

Co-Editor in Chief Filippo Berto

(Norwegian University of Science and Technology (NTNU), Trondheim, Norway)

Section Editors Sara Bagherifard

(Politecnico di Milano, Italy) (Politecnico di Milano, Italy) (University of Porto, Portugal) (University of Belgrade, Serbia)

Marco Boniardi

José A.F.O. Correia

Milos Djukic

Stavros Kourkoulis

(National Technical University of Athens, Greece) (University Politehnica Timisoara, Romania)

Liviu Marsavina Pedro Moreira

(INEGI, University of Porto, Portugal) (Chinese Academy of Sciences, China)

Guian Qian

Aleksandar Sedmak Sabrina Vantadori

(University of Belgrade, Serbia) (Università di Parma, Italy)

Advisory Editorial Board Harm Askes

(University of Sheffield, Italy) (Tel Aviv University, Israel) (Politecnico di Torino, Italy) (Università di Parma, Italy) (Politecnico di Torino, Italy) (Politecnico di Torino, Italy)

Leslie Banks-Sills Alberto Carpinteri Andrea Carpinteri Giuseppe Ferro

Donato Firrao

Emmanuel Gdoutos

(Democritus University of Thrace, Greece) (Chinese Academy of Sciences, China)

Youshi Hong M. Neil James Gary Marquis

(University of Plymouth, UK)

(Helsinki University of Technology, Finland)

(Ecole Nationale Supérieure d'Arts et Métiers | ENSAM · Institute of Mechanics and Mechanical Engineering (I2M) – Bordeaux, France)

Thierry Palin-Luc Robert O. Ritchie Ashok Saxena Darrell F. Socie Shouwen Yu Cetin Morris Sonsino

(University of California, USA)

(Galgotias University, Greater Noida, UP, India; University of Arkansas, USA)

(University of Illinois at Urbana-Champaign, USA)

(Tsinghua University, China) (Fraunhofer LBF, Germany) (Texas A&M University, USA) (University of Dublin, Ireland)

Ramesh Talreja David Taylor John Yates Shouwen Yu

(The Engineering Integrity Society; Sheffield Fracture Mechanics, UK)

(Tsinghua University, China)

Regional Editorial Board Nicola Bonora

(Università di Cassino e del Lazio Meridionale, Italy)

Raj Das

(RMIT University, Aerospace and Aviation department, Australia)

Dorota Koca ń da Stavros Kourkoulis

(Military University of Technology, Poland) (National Technical University of Athens, Greece)

Carlo Mapelli

(Politecnico di Milano, Italy)

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Fracture and Structural Integrity, 60 (2022); ISSN 1971-9883

Liviu Marsavina

(University of Timisoara, Romania) (Tecnun Universidad de Navarra, Spain)

Antonio Martin-Meizoso Mohammed Hadj Meliani

(LPTPM , Hassiba Benbouali University of Chlef. Algeria) (Indian Institute of Technology/Madras in Chennai, India)

Raghu Prakash

Luis Reis Elio Sacco

(Instituto Superior Técnico, Portugal) (Università di Napoli "Federico II", Italy) (University of Belgrade, Serbia) (Tel-Aviv University, Tel-Aviv, Israel)

Aleksandar Sedmak

Dov Sherman Karel Sláme č ka

(Brno University of Technology, Brno, Czech Republic) (Middle East Technical University (METU), Turkey)

Tuncay Yalcinkaya

Editorial Board Jafar Albinmousa Mohammad Azadi Nagamani Jaya Balila

(King Fahd University of Petroleum & Minerals, Saudi Arabia) ( Faculty of Mechanical Engineering, Semnan University, Iran)

(Indian Institute of Technology Bombay, India) (Indian Institute of Technology Kanpur, India)

Sumit Basu

Stefano Beretta Filippo Berto K. N. Bharath

(Politecnico di Milano, Italy)

(Norwegian University of Science and Technology, Norway) (GM Institute of Technology, Dept. Of Mechanical Engg., India)

Elisabeth Bowman

(University of Sheffield)

Alfonso Fernández-Canteli

(University of Oviedo, Spain) (Università di Parma, Italy)

Luca Collini

Antonio Corbo Esposito

(Università di Cassino e del Lazio Meridionale, Italy)

Mauro Corrado

(Politecnico di Torino, Italy)

Dan Mihai Constantinescu

(University Politehnica of Bucharest, Romania)

Manuel de Freitas Abílio de Jesus Vittorio Di Cocco Andrei Dumitrescu Riccardo Fincato Milos Djukic

(EDAM MIT, Portugal)

(University of Porto, Portugal)

(Università di Cassino e del Lazio Meridionale, Italy)

(University of Belgrade, Serbia)

(Petroleum-Gas University of Ploiesti, Romania)

(Osaka University, Japan)

Eugenio Giner

(Universitat Politecnica de Valencia, Spain) (Université-MCM- Souk Ahras, Algeria) (Middle East Technical University, Turkey) (Hassiba Benbouali University of Chlef, Algeria)

Abdelmoumene Guedri

Ercan Gürses

Abdelkader Hocine

Ali Javili

(Bilkent University, Turkey) (University of Piraeus, Greece)

Dimitris Karalekas Sergiy Kotrechko Grzegorz Lesiuk

(G.V. Kurdyumov Institute for Metal Physics, N.A.S. of Ukraine, Ukraine)

(Wroclaw University of Science and Technology, Poland)

Paolo Lonetti

(Università della Calabria, Italy)

Tomasz Machniewicz

(AGH University of Science and Technology)

Carmine Maletta

(Università della Calabria, Italy)

Fatima Majid Sonia Marfia

(University Chouaib Doukkali, El jadida, Morocco) (Università di Cassino e del Lazio Meridionale, Italy)

Lucas Filipe Martins da Silva

(University of Porto, Portugal) (Kyushu University, Japan) (University of Porto, Portugal) (University of Bristol, UK)

Hisao Matsunaga Milos Milosevic Pedro Moreira

(Innovation centre of Faculty of Mechanical Engineering in Belgrade, Serbia)

Mahmoud Mostafavi Vasile Nastasescu

(Military Technical Academy, Bucharest; Technical Science Academy of Romania)

Stefano Natali Andrzej Neimitz

(Università di Roma “La Sapienza”, Italy) (Kielce University of Technology, Poland)

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Frattura ed Integrità Strutturale, 60 (2022); International Journal of the Italian Group of Fracture

(Karpenko Physico-Mechanical Institute of the National Academy of Sciences of Ukraine, Ukraine)

Hryhoriy Nykyforchyn

Pavlos Nomikos

(National Technical University of Athens) (IMT Institute for Advanced Studies Lucca, Italy)

Marco Paggi Hiralal Patil Oleg Plekhov

(GIDC Degree Engineering College, Abrama-Navsari, Gujarat, India) (Russian Academy of Sciences, Ural Section, Moscow Russian Federation)

Alessandro Pirondi Maria Cristina Porcu Zoran Radakovi ć D. Mallikarjuna Reddy

(Università di Parma, Italy) (Università di Cagliari, Italy)

(University of Belgrade, Faculty of Mechanical Engineering, Serbia) (School of Mechanical Engineering, Vellore Institute of Technology, India)

Luciana Restuccia Giacomo Risitano Mauro Ricotta Roberto Roberti

(Politecnico di Torino, Italy) (Università di Messina, Italy) (Università di Padova, Italy) (Università di Brescia, Italy)

Elio Sacco

(Università di Napoli "Federico II")

Hossam El-Din M. Sallam

(Jazan University, Kingdom of Saudi Arabia) (Università di Roma "Tor Vergata", Italy)

Pietro Salvini Mauro Sassu

(University of Cagliari, Italy) (Università di Parma, Italy)

Andrea Spagnoli Ilias Stavrakas Marta S ł owik Cihan Teko ğ lu Dimos Triantis

(University of West Attica, Greece) (Lublin University of Technology)

(TOBB University of Economics and Technology, Ankara, Turkey

(University of West Attica, Greece)

Paolo Sebastiano Valvo Natalya D. Vaysfel'd

(Università di Pisa, Italy)

(Odessa National Mechnikov University, Ukraine)

Charles V. White Shun-Peng Zhu

(Kettering University, Michigan,USA)

(University of Electronic Science and Technology of China, China)

Special Issue Salvinder Singh Shahrum Abdullah Roberto Capozuzza

Failure Analysis of Materials and Structures

(Universiti Kebangsaan, Malaysia) (Universiti Kebangsaan, Malaysia)

(Polytechnic University of Marche, Italy)

IGF26 - 26th International Conference on Fracture and Structural Integrity

Special Issue Sara Bagherifard Chiara Bertolin Luciana Restuccia Sabrina Vantadori

(Politecnico di Milano, Italy)

(Norwegian University of Science and Technology, Norway)

(Politecnico di Torino, Italy) (Università di Parma, Italy)

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Fracture and Structural Integrity, 60 (2022); ISSN 1971-9883

Frattura ed Integrità Strutturale is an Open Access journal affiliated with ESIS

Sister Associations help the journal managing Algeria: Algerian Association on Fracture Mechanics and Energy -AGFME Australia: Australian Fracture Group – AFG Czech Rep.: Asociace Strojních Inženýr ů (Association of Mechanical Engineers) Greece: Greek Society of Experimental Mechanics of Materials - GSEMM India: Indian Structural Integrity Society - InSIS Israel: Israel Structural Integrity Group - ISIG Italy: Associazione Italiana di Metallurgia - AIM Italy: Associazione Italiana di Meccanica Teorica ed Applicata - AIMETA Italy:

Società Scientifica Italiana di Progettazione Meccanica e Costruzione di Macchine - AIAS Group of Fatigue and Fracture Mechanics of Materials and Structures

Poland:

Portugal: Portuguese Structural Integrity Society - APFIE Romania: Asociatia Romana de Mecanica Ruperii - ARMR Serbia:

Structural Integrity and Life Society "Prof. Stojan Sedmak" - DIVK Grupo Espanol de Fractura - Sociedad Espanola de Integridad Estructural – GEF

Spain: Turkey: Ukraine:

Turkish Solid Mechanics Group

Ukrainian Society on Fracture Mechanics of Materials (USFMM)

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Frattura ed Integrità Strutturale, 60 (2022); International Journal of the Italian Group of Fracture

Journal description and aims Frattura ed Integrità Strutturale (Fracture and Structural Integrity) is the official Journal of the Italian Group of Fracture. It is an open-access Journal published on-line every three months (January, April, July, October). Frattura ed Integrità Strutturale encompasses the broad topic of structural integrity, which is based on the mechanics of fatigue and fracture and is concerned with the reliability and effectiveness of structural components. The aim of the Journal is to promote works and researches on fracture phenomena, as well as the development of new materials and new standards for structural integrity assessment. The Journal is interdisciplinary and accepts contributions from engineers, metallurgists, materials scientists, physicists, chemists, and mathematicians. Contributions Frattura ed Integrità Strutturale is a medium for rapid dissemination of original analytical, numerical and experimental contributions on fracture mechanics and structural integrity. Research works which provide improved understanding of the fracture behaviour of conventional and innovative engineering material systems are welcome. Technical notes, letters and review papers may also be accepted depending on their quality. Special issues containing full-length papers presented during selected conferences or symposia are also solicited by the Editorial Board. Manuscript submission Manuscripts have to be written using a standard word file without any specific format and submitted via e-mail to gruppofrattura@gmail.com. Papers should be written in English. A confirmation of reception will be sent within 48 hours. The review and the on-line publication process will be concluded within three months from the date of submission. Peer review process Frattura ed Integrità Strutturale adopts a single blind reviewing procedure. The Editor in Chief receives the manuscript and, considering the paper’s main topics, the paper is remitted to a panel of referees involved in those research areas. They can be either external or members of the Editorial Board. Each paper is reviewed by two referees. After evaluation, the referees produce reports about the paper, by which the paper can be: a) accepted without modifications; the Editor in Chief forwards to the corresponding author the result of the reviewing process and the paper is directly submitted to the publishing procedure; b) accepted with minor modifications or corrections (a second review process of the modified paper is not mandatory); the Editor in Chief returns the manuscript to the corresponding author, together with the referees’ reports and all the suggestions, recommendations and comments therein. c) accepted with major modifications or corrections (a second review process of the modified paper is mandatory); the Editor in Chief returns the manuscript to the corresponding author, together with the referees’ reports and all the suggestions, recommendations and comments therein. d) rejected. The final decision concerning the papers publication belongs to the Editor in Chief and to the Associate Editors. The reviewing process is usually completed within three months. The paper is published in the first issue that is available after the end of the reviewing process.

Publisher Gruppo Italiano Frattura (IGF) http://www.gruppofrattura.it ISSN 1971-8993 Reg. Trib. di Cassino n. 729/07, 30/07/2007

Frattura ed Integrità Strutturale (Fracture and Structural Integrity) is licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0)

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Fracture and Structural Integrity, 60 (2022); ISSN 1971-9883

FIS news

D

ear friends, after 16 years, now we are publishing our 60 th issue. Considering that the journal was founded in 2007 as a small and local journal and that now it is a full international publishing media with authors of about 20 nationalities (only in this last issue), this is an amazing result. Behind this result, there is the continuous support of the Italian Group of Fracture – IGF … somebody has to pay the bills! It is only thanks to the IGF support that it is possible to publish a “Diamond open access journal” that is increasing day by day its own visibility and prestige.

(https://en.wikipedia.org/wiki/Diamond_open_access). We are all grateful to the continuous support of the community around Frattura ed Integrità Strutturale – Fracture and Structural Integrity that is many times larger than the IGF community. All the authors, reviewers, editorial boards members and readers allow to this journal to live and to improve its own quality… thank you!

Francesco Iacoviello Frattura ed Integrità Strutturale Editor in Chief

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O. Shallan et al., Frattura ed Integrità Strutturale, 60 (2022) 1-12; DOI: 10.3221/IGF-ESIS.60.01

Interaction diagram for RC column strengthened by steel angles and strips

Osman Shallan, Thrwat Sakr, Mahmoud Khater, Ahmed Ismail Department of Structural Engineering, University of Zagazig, Zagazig, Egypt Osmanshalan@yahoo.com, thsakr@gmail.com, khater_civil@yahoo.com a.es.gabr@gmail.com, https://orcid.org/0000-0002-5942-5340 A BSTRACT . This paper presents an analytical model to construct the interaction diagrams (normal force and moment) for the RC column strengthened using the steel jacket technique. The proposed model is defined using the strain distribution block by determining the location of the neutral axis in the concrete section. The proposed analytical formulation is verified by experimental results performed by previous researches and numerical models using the nonlinear program ANSYS. The factors affecting the capacity of the strengthened column are taken into consideration, such as the amount of loads resisted by the steel cage, steel strips spacing, and the effect of concrete confinement. The results of the proposed model are in good agreement with the results from the experimental and numerical work used in verification. A practical design formula has been presented for strengthened columns. K EYWORDS . Reinforced concrete; Strengthening; Steel angles; Strips; Eccentricity; Interaction diagrams.

Citation: Shallan, O., Sakr, T., Khater, M., Ismail, A., Proposed Design Criteria for column strengthened using steel angles and strips , Frattura ed Integrità Strutturale, 60 (2022) 1-12.

Received: 18.07.2021 Accepted: 05.01.2022 Online first: 22.01.2022 Published: 01.04.2022

Copyright: © 2022 This is an open access article under the terms of the CC-BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

I NTRODUCTION

R

C columns usually require strengthening to increase their capacities to sustain loads. For RC columns strengthened by steel angles and strips, four steel angles are fixed at the RC column corner and steel strips spaced at a suitable spacing and welded to the angles to form the steel jacket in this technique. Grouting is used to fill the small gaps between the steel cage and the concrete column. This strengthening system requires a limited area around the column section when compared with concrete jackets. Many researchers studied the behavior and efficiency of the strengthened column using the steel jacket under purely axial loads [1–5]. They studied the strengthening parameters as the size of the angles and strips, concrete strength, steel strips spacing, and direct or indirect loading on steel angles. Analytical models for determining the capacity of the strengthened column using the steel jacket under axial load were also carried out [4, 6–9]. They discussed the factors affecting the capacity of the strengthening columns as the amount of load resisted by the steel angles, the effect of steel strips spacing, the effect of direct and indirect loading on the steel cage, and the effect of concrete confinement. For studying the strengthened column using steel jacketing under the eccentric load and slender column, some researchers conducted experimental and numerical studies to determine the capacity and mode failure of these columns [10,11]. Others

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Osman S et al., Frattura ed Integrità Strutturale, 60 (2022) 1-12; DOI: 10.3221/IGF-ESIS.60.01

construct the interaction diagram N-M using the experimental and numerical investigation to predict the capacity of the strengthened column for different eccentricities [12–15]. In this study, a practical analytical formulation is presented to construct the interaction diagram for columns strengthened using steel jackets. The proposed formulation is practical for determining the capacity of the strengthened columns under different eccentricities. The proposed model is verified using previous experimental work results done by [10, 12, 14, 16]. Finite element models using the ANSYS program were also used to validate the proposed design formula .

S TUDYING THE BEHAVIOR OF STRENGTHENED COLUMNS USING STEEL JACKETING

I

n order to study the behavior of concrete columns strengthened using steel jacketing (steel angles and strips), two main factors would be discussed. The first factor is the amount of load that the steel jacket can resist. The second factor is the improvement in concrete strength due to the confinement caused by the steel jacket. The majority of the researches conducted is carried out in their formulation of the ultimate load capacity of the strengthened column based on two basic modes of failure, failure caused by yielding of steel angles and failure caused by yielding in steel strips as follows. Failure in the strengthened column due to yield in angles. In case of failure due to yielding in angles, local buckling occurs in angles. Subsequently, the steel jacket is no longer able to confine the column. This behavior is based on the assumption that there are three points between every two strips, The two points at each strip are assumed to be hinged, while the point in the middle of the distance between strips is considered as a weak point in the angles as shown in Fig. (1).

Figure 1 : (a) The equilibrium model for the local buckling of the steel angles failure prediction. (b) Failure of the strengthened column due to local buckling in steel angles experimental work of Tarabia and Albakry [8].

Figure 2 : Failure of the strengthened column due to failure in strips experimental work Tarabia and Albakry [8]

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O. Shallan et al., Frattura ed Integrità Strutturale, 60 (2022) 1-12; DOI: 10.3221/IGF-ESIS.60.01

Failure in the strengthened column due to yield in strips. In this case, failure caused by yielding in strips due to the compression load on the column which leads to lateral strain in the concrete column and the steel jacket and causes an elongation in the strips subsequently the steel jacket isn't able to confine the column and the failure of the strengthened column occurred as shown in Fig. (2).

A NALYTICAL MODELS FOR L OAD -C ARRYING C APACITY :

B

elow are some of the analytical expressions for determining the ultimate load for the strengthened column using steel angles and strips, which would be used to produce the proposed formula. Fig. (3) shows the dimensions of the strengthened column using steel angles and strips used in the equations.

b

steel strips

S

s 2 xt 2

L1

t 2

h

A

A

L1

L1

t 1

S2

steel angles L1xL1xt1 4L

Sec A-A

Figure 3: Main dimensions of the strengthened column using steel angles and strips.

Eurocode (2008) [ 17 ]: Some researchers consider the column strengthened by steel angle and strips as a composite column. According to Eurocode, the ultimate load of composite columns can be expressed by the following equation:

0.85

c

/ 2.5

p

b d f

A f

b d f

/

/

(1)

EC

c

s

ys

s

L a

where c , s , and a are the reduction factors for concrete, reinforcement, and structural steel strength at the ultimate limit states in practical design. However , for real comparison with the experimental work, these factors can be dispensed with. There are two main differences between the composite column behavior and the column strengthened by steel angle and strips, the first difference is the behavior of the composite action between the steel jacket and the concrete column. The second difference is the improvement of the concrete properties and strength due to the confinement of steel jacketing on the column, which would be addressed in the following researches. Calderon et al. [ 6 ] Calderon et al. [6] proposed a design formulation for determining the ultimate load carried by the strengthened column using steel angles and strips. The formula is based on the failure mode analysis observed in a numerical and experimental study presented in his research. The proposed design equation is expressed by the following equation: (2) The factors N L (axial load carried by steel angles) and f L (confinement pressure) are calculated by two possible failure modes: failure due to material yielding of strips or yielding in angles as formed in the following equation. 0.85 b d f A f 2.5 ca c s ys L L p b d f N

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Osman S et al., Frattura ed Integrità Strutturale, 60 (2022) 1-12; DOI: 10.3221/IGF-ESIS.60.01

1 1.5 s b

2 2 . . . . t s s b

f

f

e

(3)

L ystrip

where: ( f L ) when failure due to yield in strips

M

16.

2 1 .

p

f

(4)

L

b s s

f

2

c

where: ( f L ) when failure due to yield in angles. Badalamenti et al. [7]

Badalamenti et al. [7] proposed a design equation for determining the ultimate load that is carried by the RC column strengthened with steel angles and strips based on the effect of concrete confinement and load carried by the steel angles. The formula is expressed as the following equation : campione 1 1 8 cc s ys a yL p b d f A f n L t f (5)

where, f cc = compressive strength of confined concrete; n a = Maximum axial force in angles; n a and fcc are calculated by using the following formula.

0.87

f

1 4.74 l

f

f

(6)

cc

co

f

co

2

max q s

2

t f 1

t f 1

L

yl

yl

1

3

n

(7)

1

a

L t f 1 1

2

yl

Campione [1 8 ] Campione [18] proposed an equation for calculating the capacity of the strengthened column using steel jacketing. To determine the confinement pressure, it is assumed that the confinement pressure is reduced in steel strips suddenly while it remains constant along the steel angle. The effect of concrete confinement and composite action between the concrete column and steel jacketing is taken into consideration, as the following equation :

p n b d f . . .

1 1 . 8. . . n L t f a

. A f

(8)

ult

c

ys

L yL

where, n is the dimensionless load capacity of confined concrete core and n a is the maximum axial force available indirectly loaded angles in the dimensionless as the following equation :

0.87

1.5 s

f

1 1.42 cc s

b

f

e

(9)

cc

f

cd

s b

1.5

s

1

1

1 0.63

n

e

(10)

a

b L

0.5

t

b

L

1

1

1

s t

s

t

2 2

4

O. Shallan et al., Frattura ed Integrità Strutturale, 60 (2022) 1-12; DOI: 10.3221/IGF-ESIS.60.01

Tarabia A. M. and Albakry H. F. [8] Tarabia A. M. and Albakry H. F. [8] proposed an equation for determining the carried load by a column strengthened by steel angles and strips, compared to that proposed equation in Calderon et al. [6] only with different in determining confinement effect on concrete core and load carried by steel jacketing, as the following equation.

c

2 F N b L

(11)

b s E s t E 2 2. c

1

2

s

The load carried by the steel jacketing when axial compression of the column happens called direct loading, in this case, the steel jacket resists load with the concrete column from the beginning the load carried by the strengthened column, as the following equation.

1 1 2

p

L t f

(12)

ult

yL

Campione et al. [14] Campione et al. [14] proposed a design formula to define a plane fiber-section model of the column cross-section and take into consideration the frictional action along the column-angle face. The proposed formula is calibrated and validated by experimental results. The simple analytical stress-block procedure to derive continuous and simplified axial force bending moment domains is illustrated as a method for the hand-verification of reinforced cross-sections. The stress-strain laws assumed for the materials, the equilibrium equations of a reinforced cross-section written in the following form.

A A A A \ \ \ \

N b x f

s

a

s

a

(13)

u

c

cc

s

a

s

a

x

l

s A d \ \ s

a A d t \ \ a

c

M b x f

d

u

c

cc

2

4

(14)

2

l

d

A

1

N

a

a

u

4

where x c = concrete block neutral axis from compression zone; σ ' s and σ s = steel stress for top and bottom reinforcement; A ' s and A s = steel bars areas respectively; σ ' a and σ a = steel stresses for top and bottom angles. Salman and Sherrawi [15]

Salman and Sherrawi [15] performed a nonlinear numerical analysis in order to determine the carried load of the high- strength column with steel angles in the corner of the column. Their numerical model takes into consideration the confinement effect of the concrete column due to existing steel angles and local buckling of it. They proposed a numerical method to predict the load capacity of the composite column at failure and study the efficiency of the steel angles in confining the concrete core. According to the numerical models, the column carried a large load after concrete cover spalling as discussed in their research. P ROPOSED ANALYTICAL MODEL numerical method will be discussed to construct the interaction diagram (M-N) for the strengthened column using steel angles and strips as shown in Fig. (4). The axial load is plotted versus the bending moment M till failure. This method is based on the stress-strain compatibility procedure [ 17 ] . The effect of confinement on the concrete core, A

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Osman S et al., Frattura ed Integrità Strutturale, 60 (2022) 1-12; DOI: 10.3221/IGF-ESIS.60.01

the carried load by the steel jacket, the reduction in compression load in the steel jacket, and the steel jacket parameters are taken into consideration. The formulation is produced using the main four points from A to D as following .

Figure 4 : Main points used to plot the interaction diagrams for the strengthened column using steel angles and strips. Point A (pure compression load : Point A will be plotted as a point referring to pure compression failure. The maximum load-carrying capacity of the strengthened column takes into consideration the main parameters such as the concrete strength, the amount of steel reinforcement in the column, the steel yield stress, the effect of confinement on the concrete core, the carried load by steel jacket, the dimension of the steel angles and strips, and the composite action between the concrete column and steel jacket. The design model of Campione, [18] will be used to calculate the ultimate carried load capacity of the strengthened column with the equation’s parameters shown in the previous section as following :

f b h n A f s angles cc a

P

A f

(15)

u

y angles

s

ys

Point B (compression failure assumed) : Point B will be plotted as a point referring to compression failure with a minimum eccentricity of the strengthened column. The compression failure is assumed to occur when the depth of the neutral axis is greater than its depth at the balanced position, Fig. (5).

Figure 5 : Stress-strain distributions of Point B which are used to plot the interaction diagrams for the strengthened columns.

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O. Shallan et al., Frattura ed Integrità Strutturale, 60 (2022) 1-12; DOI: 10.3221/IGF-ESIS.60.01

In this case, the tension steel stress in the steel angles and reinforcement is below the yield stress, and for simplicity, the neutral axis position is chosen at the tension steel location (c=d). Thus, the developed force in the tension steel is equal to zero. The ultimate load and moment will be illustrated as follows:

\ A f sc

\

\

\

a

P

cc f b

A f

(16)

u

sc

s

ys

2 2 h a

h

2 h

\

M C

C d S

x

(17)

u

c

s

c

2

Point C (balanced failure assumed) Point C refers to the balanced failure of the column section. The failure of the balanced section occurs when the concrete reaches its maximum strain simultaneous with the yield strain in steel Fig. (6). By definition, the point at the balanced section, the strain in the tension steel equals ( s). Thus, the stress in the tension steel equals (fy). The ultimate load and moment will be illustrated as follows:

T s cc b P C S C S T f b a u c c s

(18)

a

h

h

h

\

b

x

M C

C d S

2

(19)

u

c

s

c

2 2

2

2

Figure 6 : Stress-strain distributions of Point C which are used to plot the interaction diagrams for the strengthened column. Point D (Pure bending) In the case of a column subjected to pure bending or infinity eccentricity, the axial load is considered to be zero Fig. (7). The locating of the neutral axis must be performed by applying the equilibrium equation as following: c c s T s C S C S T (20)

\

c d

c x

a f b

c

E

E

A f

st A f

0.8

(21)

cc

c

s

c

s

s

ys

yst

c

c

V ERIFICATION OF THE ANALYTICAL PROPOSED FORMULA n order to verify the results of the proposed model in this study, some experimental researches work and numerical models have been concerned with stresses, strains, and deflections for the strengthened column to verify the proposed I

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Osman S et al., Frattura ed Integrità Strutturale, 60 (2022) 1-12; DOI: 10.3221/IGF-ESIS.60.01

formula. In this study, strengthened columns are modeled and studied using the commercial finite element software (ANSYS -Version 19.2) .

Figure 7 : Stress-strain distributions of Point C which are used to plot the interaction diagrams for the strengthened column. Verification using finite element models. In order to verify the proposed model finite element models established in this paper using ANSYS software, the experimental researches work used in Verification has been concerned with stresses, strains, and deflections for the strengthened column. The methods for implementing the test, and the quality of the materials, and the configuration of the specimens. Solid element 65 is used to define concrete in 3D, link element 180 is used for steel reinforcement, solid 185 is defined for steel angles and strips, and steel plates for load distribution are defined as solid element 45. The components of the model, elements used, and boundary conditions are shown in Fig. 8 .

Figure 8: The numerical model’s component used in the verification.

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O. Shallan et al., Frattura ed Integrità Strutturale, 60 (2022) 1-12; DOI: 10.3221/IGF-ESIS.60.01

Verification using previous experimental work. Experimental work results of previous researches will be used to validate the proposed analytical model. The first experimental work was taken from Montuori et al.[16], their specimens were (E-R1, D-R1, A-R1, and B-R1a) the second experimental work was taken from Elsamny et al.[12] their specimens were (Cl T3, C2 T5, C3 T7, C4 T3, C5 T5 , C6 T7, C7 T3, C8 T5, and C9 T7) . The third experimental work was taken from Ezz-Eldeen . [10] their specimens were (CS22e1 ,CS22e2, CS22e3 and CS22e4) . The fourth experimental work was taken from compaine et al. [14] their specimens were (RCAEX1 ,RCAEY1 ,RCBEX1 and RCBEY1). Tab. 1 shows the specimen's details and experimental work results. The results of the finite element models will be discussed in the next section.

Failure load

Comparison

Ref.

specimen

column section

fc'

steel bars mm

steel angles

strips

fya

e

N

N

N

EXP

FEM design

mm

MPa 26.4

mm MPa mm kN kN kN

4 φ 16 mm 4 φ 16 mm 8 φ 10 mm 8 φ 10 mm 4 φ 8 mm 4 φ 8 mm 4 φ 8 mm 4 φ 8 mm 4 φ 8 mm 4 φ 8 mm 4 φ 8 mm 4 φ 8 mm 4 φ 8 mm 4 φ 8 mm 4 φ 8mm 4 φ 8 mm 4 φ 8mm 6 φ 12 mm 6 φ 12 mm 6 φ 12 mm 6 φ 12 mm

4 L 30×2 4 L 30×2 4 L 30×2 4 L 30×2 4 L 20×2 4 L 20×2 4 L 20×2 4 L 20×2 4 L 20×2 4 L 20×2 4 L 20×2 4 L 20×2 4 L 20×2 4 L 20×2 4 L 20×2 4 L 20×2 4 L 20×2 4 L 50×5 4 L 50×5 4 L 50×5 4 L 50×5

15x3@125 mm 15x3@125 mm 15x3@125 mm 15x3@125 mm 20x2@490 mm 20x2@245 mm 20x2@164 mm 20x2@490 mm 20x2@245 mm 20x2@164 mm 20x2@490 mm 20x2@245 mm 20x2@164 mm 20x2@250 mm 20x2@250 mm 20x2@250 mm 20x2@250 mm 40x4@136 mm 40x4@136 mm 40x4@136 mm 40x4@136 mm

E-R1

150×150x500

353

50

745

782.7

630

0.85

0.80

353

75

556

583.5

530

0.95

0.91

D-R1

150×150x500

26.4

Montuori et al.[16]

353

50

717

752.6

620

0.86

0.82

A-R1

150×150x500

26.4

353

75

524

550.1

520

0.99

0.95

B-R1a

150×150x500

26.4

Cl T3

120×120x1000

15

320

10

390

409.5

325

0.83

0.79

C2 T5

120×120x1000

15

320

10

360

378

310

0.86

0.82

320

10

340

357

305

0.90

0.85

C3 T7

120×120x1000

15

320

20

290

304.5

235

0.81

0.77

C4 T3

120×120x1000

15

Elsamny et al.[12]

320

20

250

262.5

225

0.90

0.86

C5 T5

120×120x1000

15

320

20

250

262.5

215

0.86

0.82

C6 T7

120×120x1000

15

320

30

255

267.8

185

0.73

0.69

C7 T3

120×120x1000

15

320

30

210

220.5

170

0.81

0.77

C8 T5

120×120x1000

15

320

30

210

220.5

160

0.76

0.73

C9 T7

120×120x1000

15

380

10

643

675.2

575

0.89

0.85

CS22e1

120×160x1000

28

Ezz‐ Eldeen . [10]

CS22e2

120×160x1000

28

380

20

552

579.6

510

0.92

0.88

380

30

474

497.7

455

0.96

0.91

CS22e3

120×160x1000

28

380

40

420

441

410

0.98

0.93

CS22e4

120×160x1000

28

RCAEX1

220x300x820

12.7

275

65

1048

1100

1150

1.10

1.05

RCAEY1

220x300x820

12.7

275

55

1205

1266

1175

0.97

0.93

compaine et al. [14]

275

65

1370

1439

1250

0.91

0.87

RCBEX1

220x300x820

24

275

55

1476

1550

1350

0.91

0.87

RCBEY1

220x300x820

24

Table 1: specimens details and experimental work results and numerical models results.

R ESULTS AND D ISCUSSION

he comparison between the result of the proposed interaction diagram, experimental and numerical models is shown in Tab. 1. It can be seen that the results obtained using the proposed interaction diagram give a difference from 2 % to 30 % with an average difference of 12 % as illustrated in Tab. 1. It can be seen that the value of the experimental and numerical is bigger than the value of the proposed model, which is considered as an advantage of the proposed method as a conservative design approach. It is also noticed that the results of the strengthened column with big eccentricity have a small difference with the proposed model results than the column with small eccentricity. Fig. from (9-12) shows the comparison between the proposed interaction diagram and the experimental work of the researches used in verification. T

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Osman S et al., Frattura ed Integrità Strutturale, 60 (2022) 1-12; DOI: 10.3221/IGF-ESIS.60.01

Figure 9: Comparison between the proposed I-D and the experimental work of Ezz-Eldeen, [10]).

Figure 10: Comparison between the proposed I-D and the experimental work of Elsamny et al.[12] )

Figure 11: Comparison between the proposed I-D and the experimental work of (Montuori, and Rizzano [16]).

Figure 12: Comparison between the proposed I-D and the experimental work of compaine et al. [14] .

As shown in Fig. (9-12), the interaction diagram constructed from the proposed model comparison with the experimental work results are in good agreement and gives a practical design method for determining the capacity of the strengthened column under the different cases of loading. It can be noticed that the first point (A) which refers to pure axial load is almost underestimation, while the other points have a good agreement with the experimental and numerical results. Fig. 13 shows the results of the numerical work using the finite element program.

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