In this paper, an analytical investigation is made of the frictional damping properties of axiall... more In this paper, an analytical investigation is made of the frictional damping properties of axially loaded metallic cables made from one layer of wires helically wrapped around a central wire. Our efforts are focused on the quantity of energy dissipated through friction due to the motions between wires when a cable is loaded. Although the local interwire pivoting drives the response of the cables studied, a first linear model is built where pivoting is allowed, but friction is not taken into account. Then, a law of friction is established and linearized to extend the linear model into a tractable piecewise linear hysteretic one. Through a variety of examples, it appears that the energy dissipated in friction over a load cycle is very small compared to other sources of dissipation, because axially loaded simple straight strands do not experience fretting-induced failures, except close to terminations. It is also shown that modifying the design of such cables is not expected to signifi...
Le comportement en fatigue des cables etant etroitement lie aux conditions de contact et de frott... more Le comportement en fatigue des cables etant etroitement lie aux conditions de contact et de frottement entre les fils constitutifs, il est indispensable d'avoir une description precise des mouvements et efforts interfilaires. Plusieurs modeles theoriques ont ete concus dans le but de mieux prevoir le comportement des cables. Cependant, meme si le comportement axial des cables est en general bien traite, les modeles de cables en flexion sont bases sur de nombreuses hypotheses simplificatrices. Dans ce contexte, nous avons developpe un modele elements finis specifique pour cables monotorons. Cette etude est restreinte au comportement statique des cables et les mouvements interfilaires sont supposes sans frottement. Les fils constitutifs sont modelises par des elements poutres de type deplacement bases sur une formulation cartesienne isoparametrique. Une premiere etude est faite sous l'hypothese des petites perturbations. Le modele permet d'envisager tous les cas de contact interfilaire possibles (roulement, glissement, pivotement) et offre la possibilite d'etudier l'effet de ces contacts sur le comportement global du cable. Les conditions de contact sont introduites au moyen de multiplicateurs de lagrange. Nous interessant principalement aux cables de genie civil qui supportent essentiellement des charges axiales mais aussi des actions de flexion secondaire, nous avons etudie le cas d'un chargement axial pur puis le cas de la flexion de faible amplitude d'un cable tendu. Le modele a permis de montrer que le pivotement interfilaire pilote le comportement axial du toron alors que le glissement joue un role predominant en flexion. De plus, des comparaisons avec des donnees experimentales prouvent que le pivotement peut etre considere comme libre dans un toron reel. Des tests de validation sont proposes pour differents cas de chargement. Enfin, une derniere partie est consacree a l'etude de l'importance des non-linearites geometriques pour le type de cable etudie.
The frictional damping properties of axially loaded simple straight wire rope strands are studied... more The frictional damping properties of axially loaded simple straight wire rope strands are studied using an analytical model for cables of current design. Since the cable axial response is driven by the interwire local pivoting, a first linear model is built in which pivoting occurs without friction. A hysteretic model is then built after a specific law of friction is established. Using comparisons with experimental results described in the literature, the frictional energy dissipated over a load cycle is shown to be very small compared to the elastic strain energy and other dissipations. This result is in agreement with the experimental fact that axially loaded simple straight strands do not experience fretting-induced failures, except when they are close to the terminations.
In this paper, which is the first part of our study, the theoretical bases of a new specific fini... more In this paper, which is the first part of our study, the theoretical bases of a new specific finite element model for cables are presented. A curved beam finite element based on a Cartesian isoparametric formulation is developed in order to model the constitutive wires of the cable, and the contact problem between the wires is addressed. The present model is especially designed to allow for the study of all the possible interwire motions in the cable, which is a major concern in fatigue design. The geometry and the assumptions made for this study are first presented and the description of the theoretical background follows. Then, the successive steps leading to the global finite element formulation are detailed. In a second paper (Part II), numerical and experimental validation tests are described and commented, together with application examples.
A finite element model of a simple straight wire rope strand is presented, which allows for the s... more A finite element model of a simple straight wire rope strand is presented, which allows for the study of all the possible interwire motions. The role of the contact conditions in pure axial loading and in axial loading combined with bending is investigated. The model proves to be reliable compared with experimental and theoretical data when available. It appears that the interwire pivoting and the interwire sliding govern the cable response, respectively, for axial and bending loads. Moreover, pivoting can be considered as free. Finally, the influence of bending on wire tension is studied.
In this paper, which is the first part of our study, the theoretical bases of a new specific fini... more In this paper, which is the first part of our study, the theoretical bases of a new specific finite element model for cables are presented. A curved beam finite element based on a Cartesian isoparametric formulation is developed in order to model the constitutive wires of the cable, and the contact problem between the wires is addressed. The present model is especially designed to allow for the study of all the possible interwire motions in the cable, which is a major concern in fatigue design. The geometry and the assumptions made for this study are first presented and the description of the theoretical background follows. Then, the successive steps leading to the global finite element formulation are detailed. In a second paper (Part II), numerical and experimental validation tests are described and commented, together with application examples. 1 Research Associate; author to whom correspondence should be addressed. 2 Research Associate 3 Associate Professor
In this paper, an analytical investigation is made of the frictional damping properties of axiall... more In this paper, an analytical investigation is made of the frictional damping properties of axially loaded metallic cables made from one layer of wires helically wrapped around a central wire. Our efforts are focused on the quantity of energy dissipated through friction due to the motions between wires when a cable is loaded. Although the local interwire pivoting drives the response of the cables studied, a first linear model is built where pivoting is allowed, but friction is not taken into account. Then, a law of friction is established and linearized to extend the linear model into a tractable piecewise linear hysteretic one. Through a variety of examples, it appears that the energy dissipated in friction over a load cycle is very small compared to other sources of dissipation, because axially loaded simple straight strands do not experience fretting-induced failures, except close to terminations. It is also shown that modifying the design of such cables is not expected to signifi...
Le comportement en fatigue des cables etant etroitement lie aux conditions de contact et de frott... more Le comportement en fatigue des cables etant etroitement lie aux conditions de contact et de frottement entre les fils constitutifs, il est indispensable d'avoir une description precise des mouvements et efforts interfilaires. Plusieurs modeles theoriques ont ete concus dans le but de mieux prevoir le comportement des cables. Cependant, meme si le comportement axial des cables est en general bien traite, les modeles de cables en flexion sont bases sur de nombreuses hypotheses simplificatrices. Dans ce contexte, nous avons developpe un modele elements finis specifique pour cables monotorons. Cette etude est restreinte au comportement statique des cables et les mouvements interfilaires sont supposes sans frottement. Les fils constitutifs sont modelises par des elements poutres de type deplacement bases sur une formulation cartesienne isoparametrique. Une premiere etude est faite sous l'hypothese des petites perturbations. Le modele permet d'envisager tous les cas de contact interfilaire possibles (roulement, glissement, pivotement) et offre la possibilite d'etudier l'effet de ces contacts sur le comportement global du cable. Les conditions de contact sont introduites au moyen de multiplicateurs de lagrange. Nous interessant principalement aux cables de genie civil qui supportent essentiellement des charges axiales mais aussi des actions de flexion secondaire, nous avons etudie le cas d'un chargement axial pur puis le cas de la flexion de faible amplitude d'un cable tendu. Le modele a permis de montrer que le pivotement interfilaire pilote le comportement axial du toron alors que le glissement joue un role predominant en flexion. De plus, des comparaisons avec des donnees experimentales prouvent que le pivotement peut etre considere comme libre dans un toron reel. Des tests de validation sont proposes pour differents cas de chargement. Enfin, une derniere partie est consacree a l'etude de l'importance des non-linearites geometriques pour le type de cable etudie.
The frictional damping properties of axially loaded simple straight wire rope strands are studied... more The frictional damping properties of axially loaded simple straight wire rope strands are studied using an analytical model for cables of current design. Since the cable axial response is driven by the interwire local pivoting, a first linear model is built in which pivoting occurs without friction. A hysteretic model is then built after a specific law of friction is established. Using comparisons with experimental results described in the literature, the frictional energy dissipated over a load cycle is shown to be very small compared to the elastic strain energy and other dissipations. This result is in agreement with the experimental fact that axially loaded simple straight strands do not experience fretting-induced failures, except when they are close to the terminations.
In this paper, which is the first part of our study, the theoretical bases of a new specific fini... more In this paper, which is the first part of our study, the theoretical bases of a new specific finite element model for cables are presented. A curved beam finite element based on a Cartesian isoparametric formulation is developed in order to model the constitutive wires of the cable, and the contact problem between the wires is addressed. The present model is especially designed to allow for the study of all the possible interwire motions in the cable, which is a major concern in fatigue design. The geometry and the assumptions made for this study are first presented and the description of the theoretical background follows. Then, the successive steps leading to the global finite element formulation are detailed. In a second paper (Part II), numerical and experimental validation tests are described and commented, together with application examples.
A finite element model of a simple straight wire rope strand is presented, which allows for the s... more A finite element model of a simple straight wire rope strand is presented, which allows for the study of all the possible interwire motions. The role of the contact conditions in pure axial loading and in axial loading combined with bending is investigated. The model proves to be reliable compared with experimental and theoretical data when available. It appears that the interwire pivoting and the interwire sliding govern the cable response, respectively, for axial and bending loads. Moreover, pivoting can be considered as free. Finally, the influence of bending on wire tension is studied.
In this paper, which is the first part of our study, the theoretical bases of a new specific fini... more In this paper, which is the first part of our study, the theoretical bases of a new specific finite element model for cables are presented. A curved beam finite element based on a Cartesian isoparametric formulation is developed in order to model the constitutive wires of the cable, and the contact problem between the wires is addressed. The present model is especially designed to allow for the study of all the possible interwire motions in the cable, which is a major concern in fatigue design. The geometry and the assumptions made for this study are first presented and the description of the theoretical background follows. Then, the successive steps leading to the global finite element formulation are detailed. In a second paper (Part II), numerical and experimental validation tests are described and commented, together with application examples. 1 Research Associate; author to whom correspondence should be addressed. 2 Research Associate 3 Associate Professor
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