Final Report Summary - DERESTAR (Development of structural DEsign REcommendations for STeel ARches)
The aim of the DERESTAR project was the proposal of design recommendations for steel arches, taking into account their specific characteristics, which means considering them as what they are: curved and not straight, contrary to what one actually does when applying current recommendations in structural engineering. What first excited our curiosity for this problem were two sections of the specialist design guide edited by the Steel Construction Institute entitled 'Design of curved steel' (2001), which pointed out two phenomena that may have a noticeable influence on the behaviour and stability of steel arches.
The first one is the influence of the fabrication process and more precisely the cold curving process, which is the least expensive and most common way to produce curved members by bending or curving of straight members. It is a repetitive process during which the straight member passes several times through a machine with bending rolls imposing progressively the desired curvature. The non-reversible deformations introduced by this process are associated with additional self-equilibrated stresses locked in the section which have an influence on the amount of stresses that the curved member can resist during service. Analytical and numerical studies were thus conducted to quantify this influence. They have shown that it can be characterised by two dimensionless parameters, which depend on the geometrical characteristics of the section, on the curving radius and on the type of loading (opening or closing bending moment, compression or tension). Based on those parameters, interaction diagrams between normal forces and bending moments, which are of significant practical use for structural engineers, have been developed for I-section beams, to determine easily the limits of the elastic and of the plastic region. Qualitatively, the results confirmed the intuition: the smaller the curving radius and the stockier the section, the more significant the influence of the curving residual stresses.
The second interesting phenomenon encountered in curved members is the influence of the trans-verse bending stresses on their inelastic behaviour. These stresses do not appear in straight members because they result from the curvature: bending moment induces normal compression stresses and normal tension stresses which are not self-equilibrated in curved members. They induce thus radial pressures which are resisted first by transverse bending of the flanges (causing section distortion) and then by normal stresses in the webs. Analytical models based on advanced mechanics of materials and three dimensional computational models have outlined the influence of transverse stresses on the member's strength and the influence of the section distortion on the member's stiffness. Beyond some parameters linked with the shape of the cross-section, it has been shown that the influence of transverse stresses and distortion were characterised, respectively, by a reduced width and reduced height depending on the curvature and on thickness of the section walls. It was, hence, possible to propose some thresholds for these reduced dimensions, above which the effects of transverse bending stresses and distortion have to be taken into account, and above which the straight beam model is no more valid and a curved beam model has to be considered.
An experimental program was also included, from the very beginning, in the project. It had a double objective: first, to validate on the field the models developed previously and second, to study the relative influence of the investigated phenomena on the overall behaviour of arches. The technical and financial constraints of the program led to a set of twelve experiments on hinged circular arches loaded by a concentrated force at the crown. This set comprised six compression tests inducing opening bending moments at the crown and six tension tests inducing closing bending moments at the crown, for two different radii of curvature. A common cross-section was chosen for all specimens: a rectangular hollow section RHS 100 x 50 x 5, made of S355 quality steel. The members were curved along their weak axis to give them higher out-of-plane stiffness and to allow working with lower loads.
The experimental program was overall successful. The collaboration with the company which supplied the specimens and with the team operating the laboratory facility was really fruitful on both sides. The experimental tests have verified some important general features of the behaviour of arches: the influence of geometrical imperfections, that of geometrical non-linearities and that of the stiffness of the supports and of the necessary clearances. They have also helped point out that working with cold formed members such as rectangular hollow sections, means working with steel members with complex hardening elasto-plastic behaviour. Concerning the two specific phenomena investigated in the project, the measurements of transverse strains clearly validated the model for the transverse bending stresses and the section distortion. The influence of the curving process and the asymmetry of the behaviour induced by the residual stresses could not be quantified as planned, mainly because of the non-linear behaviour of the arch under compression. The influence of the curving process on the material law was however evidenced.
Most of the scientific objectives of the program were fulfilled and the understanding of the characteristics of steel arches made several steps forward. Some structural design recommendations or design tools were proposed to improve or complete existing standards for steel structures. These recommendations do not, however, cover the whole range of structural members used for steel constructions, so that additional research (like the extension of the study to a wider variety of cross-sections and to the out-of-plane behaviour) are actually under progress to reach the expected level of European standards like EC3. Moreover, the investigations of the influence of the cold curving process on residual stresses have shown that there was a lack of experimental data in this field, so that it seems necessary to plan complementary campaigns of measurements using preferably non-destructive methods.
Scientific in charge: Associate Professor Charalampos Gantes
NTUA - School of Civil Engineering- Metal Structures Laboratory
Heroon Polytechniou 9, 15780, Athens, Greece
Tel: +30-210-772-3440,
Fax: +30-210-772-3442
e-mail: chgantes@central.ntua.gr
Fellow researcher: Dr Cyril Douthe
IFSTTAR - Departement Structures et Ouvrages d'Art (Pt 34)
58, Boulevard Lefebvre, 75732, Paris Cedex 15, France
Tel: +33-1-4043-5136, Fax: +33-1-4043-5343
e-mail: cyril.douthe@ifsttar.fr
The first one is the influence of the fabrication process and more precisely the cold curving process, which is the least expensive and most common way to produce curved members by bending or curving of straight members. It is a repetitive process during which the straight member passes several times through a machine with bending rolls imposing progressively the desired curvature. The non-reversible deformations introduced by this process are associated with additional self-equilibrated stresses locked in the section which have an influence on the amount of stresses that the curved member can resist during service. Analytical and numerical studies were thus conducted to quantify this influence. They have shown that it can be characterised by two dimensionless parameters, which depend on the geometrical characteristics of the section, on the curving radius and on the type of loading (opening or closing bending moment, compression or tension). Based on those parameters, interaction diagrams between normal forces and bending moments, which are of significant practical use for structural engineers, have been developed for I-section beams, to determine easily the limits of the elastic and of the plastic region. Qualitatively, the results confirmed the intuition: the smaller the curving radius and the stockier the section, the more significant the influence of the curving residual stresses.
The second interesting phenomenon encountered in curved members is the influence of the trans-verse bending stresses on their inelastic behaviour. These stresses do not appear in straight members because they result from the curvature: bending moment induces normal compression stresses and normal tension stresses which are not self-equilibrated in curved members. They induce thus radial pressures which are resisted first by transverse bending of the flanges (causing section distortion) and then by normal stresses in the webs. Analytical models based on advanced mechanics of materials and three dimensional computational models have outlined the influence of transverse stresses on the member's strength and the influence of the section distortion on the member's stiffness. Beyond some parameters linked with the shape of the cross-section, it has been shown that the influence of transverse stresses and distortion were characterised, respectively, by a reduced width and reduced height depending on the curvature and on thickness of the section walls. It was, hence, possible to propose some thresholds for these reduced dimensions, above which the effects of transverse bending stresses and distortion have to be taken into account, and above which the straight beam model is no more valid and a curved beam model has to be considered.
An experimental program was also included, from the very beginning, in the project. It had a double objective: first, to validate on the field the models developed previously and second, to study the relative influence of the investigated phenomena on the overall behaviour of arches. The technical and financial constraints of the program led to a set of twelve experiments on hinged circular arches loaded by a concentrated force at the crown. This set comprised six compression tests inducing opening bending moments at the crown and six tension tests inducing closing bending moments at the crown, for two different radii of curvature. A common cross-section was chosen for all specimens: a rectangular hollow section RHS 100 x 50 x 5, made of S355 quality steel. The members were curved along their weak axis to give them higher out-of-plane stiffness and to allow working with lower loads.
The experimental program was overall successful. The collaboration with the company which supplied the specimens and with the team operating the laboratory facility was really fruitful on both sides. The experimental tests have verified some important general features of the behaviour of arches: the influence of geometrical imperfections, that of geometrical non-linearities and that of the stiffness of the supports and of the necessary clearances. They have also helped point out that working with cold formed members such as rectangular hollow sections, means working with steel members with complex hardening elasto-plastic behaviour. Concerning the two specific phenomena investigated in the project, the measurements of transverse strains clearly validated the model for the transverse bending stresses and the section distortion. The influence of the curving process and the asymmetry of the behaviour induced by the residual stresses could not be quantified as planned, mainly because of the non-linear behaviour of the arch under compression. The influence of the curving process on the material law was however evidenced.
Most of the scientific objectives of the program were fulfilled and the understanding of the characteristics of steel arches made several steps forward. Some structural design recommendations or design tools were proposed to improve or complete existing standards for steel structures. These recommendations do not, however, cover the whole range of structural members used for steel constructions, so that additional research (like the extension of the study to a wider variety of cross-sections and to the out-of-plane behaviour) are actually under progress to reach the expected level of European standards like EC3. Moreover, the investigations of the influence of the cold curving process on residual stresses have shown that there was a lack of experimental data in this field, so that it seems necessary to plan complementary campaigns of measurements using preferably non-destructive methods.
Scientific in charge: Associate Professor Charalampos Gantes
NTUA - School of Civil Engineering- Metal Structures Laboratory
Heroon Polytechniou 9, 15780, Athens, Greece
Tel: +30-210-772-3440,
Fax: +30-210-772-3442
e-mail: chgantes@central.ntua.gr
Fellow researcher: Dr Cyril Douthe
IFSTTAR - Departement Structures et Ouvrages d'Art (Pt 34)
58, Boulevard Lefebvre, 75732, Paris Cedex 15, France
Tel: +33-1-4043-5136, Fax: +33-1-4043-5343
e-mail: cyril.douthe@ifsttar.fr