BULETIUL ISTITUTULUI POLITEHIC DI IAŞI Publicat de Universitatea Tehnică Gheorghe Asachi din Iaşi Toul LX (LXIV), Fasc. 3, 2014 Secţia COSTRUCŢII. ARHITECTURĂ IDUCED STRESSES DUE TO THERMAL EFFECTS I COMPOSITE STEEL COCRETE GIRDERS BY CLAUDIA PODICHI ALB * and CĂTĂLI MOGA Received: June 19, 2014 Accepted for publication: July 14, 2014 Technical University of Cluj-apoca Faculty of Civil Engineering Abstract. The teperature variations of the air in shadow, of the solar radiations and theral radiations produce variations in the teperature distribution in the individual ebers of a structure. This paper presents the influence of the difference of teperature between the opposite faces of a steel concrete coposite cross section upon the internal stresses state. In the steel concrete coposite structures, the concrete fro the coposite structure slab cannot have a free deforation arising fro the teperature variation along the height of the cross section because the slab is joined to the etal structure through joining ebers (connectors). Consequently, as the tendency to shorten or lengthen the concrete slab is prevented, internal stresses are induced to the coposite structure, and these stresses overlap those produced by shortening or lengthening in the slab area. The echanis through which stress develop fro teperature variation are exeplified for the case of a siply supported steel concrete coposite girder. Key words: coposite girders; theral effects; state of stresses; working exaple. 1. Introduction The daily and seasonal shadow air teperature variations, the variations of solar radiations and theral radiation produce variations of the teperature * Corresponding author: e-ail: Claudia.Alb@infra.utcluj.ro
80 Claudia Pondichi Alb and Cătălin Moga distribution in the individual ebers of a structure. The aplitude of theral effects depends upon local cliate conditions as well as upon the orientation, total weight and structure finishing. The teperature distribution inside an individual structural eber is ade up of the following ain coponents (Fig. 1): a) the coponent of unifor teperature, ΔT U ; b) the coponent of difference of teperature between the faces of the sae eber, ΔT M ; c) the nonlinear coponent of the difference of teperature, ΔT E. This coponent establishes a field of stresses in equilibriu that does not involve an actual effect of loading in the eber. The ational Annex recoends in the bridge design in Roania not to take into considerations the vertical nonlinear coponent in heat actions. Fig. 1 The deforations of the structural ebers and the resulting stresses depend upon the geoetry and boundary conditions of construction ebers (supports, joints, etc.) and the physical properties of the aterials used. When coposite aterials are used, special attention should be given to the fact that these aterials are ade up of coponents with differing coefficients of linear dilatation. In order to deterine theral effects, it is recoended to use the theral linear dilatation coefficient in aterials, as presented in Annex C fro SR E 1991-1-5. The paper presents the influence of the difference of teperature between the opposite faces of a steel concrete coposite cross section (the coponent of the difference of teperature) upon the internal stresses state. 2. The Difference of Teperature For a specified tie interval, the heating and cooling of the upper face of the bridge deck produces a variation of teperature that can lead to a axiu heating (when the upper face is warer) and a axiu cooling (when the lower face is warer). The vertical difference of teperature can produce effects in a structure, due to:
Bul. Inst. Polit. Iaşi, t. LX (LXIV), f. 3, 2014 81 a) the prevention of structure free deforation due to its shape (for exaple, bearing fraes, continuous beas, etc.); b) friction aong hinged supports; c) non-linear geoetrical effects (2 nd order effects). The effect of the difference of teperature along the vertical line can be treated by a linear or non-linear distribution. 2.1. The Vertical Coponent of the Difference of Teperature The effect of the difference of teperature along the vertical is taken into account by using several linear coponents for the difference of teperature equivalent to ΔT M.heating and ΔT M.cooling. The values of these coponents are applied to the area between the upper face and the lower face of the bridge deck. In the case of bridge decks with a coposite structure, for protection layers of 50, the following values are taken: ΔT M.heating = 15ºC; ΔT M.cooling = 18ºC. For protection layers different fro 50 the values for ΔT M.heating and ΔT M.cooling are ultiplied by the factor k surface given in SR E 1991-1-5. 2.2. The Horizontal Coponent of the Difference of Teperature In general, the coponent of difference of teperature requires consideration only in vertical direction. In several particular cases. (for instance, the configuration or orientation of the bridge ay require the stronger sun exposure of a part than another of the bridge) a horizontal coponent of the difference of teperature is taken into account. When no data are available and no higher values are indicated, it is recoended to use the value of 5ºC for the difference of teperature, as the linear difference of teperature between the external argins of the bridge, irrespective of the bridge width. 2.3. Stresses Produced fro the Vertical Coponent of the Difference of Teperature The concrete in the slab of the coposite structure cannot have a free deforation arising fro the teperature variation along the height of the cross section as the slab is joined to the etal structure by connectors. Consequently, the concrete slab tendency of shortening or lengthening is prevented and, within the coposite structure, internal stresses are induced; these stresses overlap the stresses produced during shortening or lengthening, in the slab area.
82 Claudia Pondichi Alb and Cătălin Moga The echanis through which stress develop fro teperature variation are exeplified for the case of a siply supported steel concrete coposite girder. When the slab is colder than the lower part of the cross section, the slab has a shortening tendency and the stresses developed are siilar to those produced by concrete shrinkage, respectively stresses with an opposite sign when the slab has a higher teperature. Loading arising fro teperature is regarded as a short ter load, the calculus section being defined with the help of the coefficient of equivalence for short ter loadings (that is the equivalence coefficient, n 0 ). The specific deforation fro the teperature variation is c. T T TM, (1) 5 0 where: T 1 10 / C is the theral dilation coefficient of the concrete and steel in the steel-concrete coposite structures (SR E 1991-1-5, Annex C, Table C.1). The axial stress produced in the concrete slab will be E A. (2) c. T. T c. T c c Fig. 2 presents the stresses occurring in the coposite cross section when the slab has a lower teperature than the part opposite to the cross section (the teperature difference being ΔT M.cooling = 18ºC). Fig. 2 Developent of stresses due to concrete slab contraction. When the concrete slab teperature is higher than that of the opposite end (with a teperature difference of ΔT M.heating = 15ºC), the stresses produced have an opposite sign, than previously.
Bul. Inst. Polit. Iaşi, t. LX (LXIV), f. 3, 2014 83 The stresses in the concrete slab and etal girder are as follows: a) in concrete: b) in steel: 1 M A n A I c. T. T. T c c 0 z ; (3). T M. T a z. (4) A I A and I represent the area and the inertia oent of the coposite concrete-steel section where the equivalence coefficient taken is n 0. 3. uerical Application The state of stresses is assessed in the cross section of a steel concrete coposite girder following the variation of teperature along the height of the girder). The following data are known: a) coposite girder cross section (Fig. 3); b) concrete grade: C40/50; c) S420 steel. The web of the etal girder is provided with longitudinal stiffening eleents so that the grade for the section is 3 (stresses are considered). Fig. 3 Cross section of coposite girder. 3.1. Stress Calculus when the Slab is Colder (ΔT M.cooling = 18ºC) The specific deforation arising fro the difference of teperature: 5 4 c. T T TM 1 10 18 1.8 10.
84 Claudia Pondichi Alb and Cătălin Moga The equivalence coefficient for short ter loadings is: Ea 210,000 210, 000 210, 000 n 0 5.96; 0.3 0.3 E c f 48 35, 220 c 22,000 22, 000 10 10 E c 0.3 48 22,000 = 35, 220 / 10 The axial stress developed in the concrete slab will be: E A c. T. T c. T c c The bending oent:. T. T c 4 6 1.8 10 0.3522 10 12,000 = 3 = 760 10 da. M z 760 10 55.6=422.56 10 da c. 1. The equivalent steel section The equivalent steel width of the concrete slab: b 6,000 = 1,007. 5.96 * beff eff n0 The coposite section equivalent in steel is given in Fig. 4. 2. A I 3,934 c 2.5 10 c 2 7 4 Fig. 4 Characteristics of equivalent in steel cross section. The unit stresses found fro teperature are: a) in concrete: a 1 ) in the upper fibre:
Bul. Inst. Polit. Iaşi, t. LX (LXIV), f. 3, 2014 85 1 M c. T. T. T c. sup z cs Ac n0 A I 12, 000 5. 96 3, 934 2. 5 10 3 760 10 1 760 10 422.56 10 2 7 65.6 12.3 da/c ; a 2 ) in the lower fibre: 1 c. T. T M. T c. inf z ci Ac n0 A I 12, 000 5. 96 3, 934 2. 5 10 3 760 10 1 760 10 422.56 10 2 7 45.6 18 da/c ; b) in steel: b 1 ) in the upper fibre: M. T. T 760 10 422.56 10 2 a. sup z as 7 45.6 270.3 da/c ; A I 3, 934 2. 5 10 b 2 ) in the lower fibre: M. T. T 760 10 422.56 10 2 a. inf ai 7 132.4 30.6 da/c A I 3,934 2. 5 10 z. The stresses diagra arising fro shrinkage is given in Fig. 5. Fig. 5 Stress distribution due to effect of cooling. 3.2. Stress Calculus when the Slab is Warer (ΔT M.heating = 15ºC) The specific deforation arising fro the difference of teperature: 5 4 c. T T TM 1 10 15 1.5 10.
86 Claudia Pondichi Alb and Cătălin Moga The equivalence coefficient for short ter loadings is n0 5.96 ; 2 Ec 35,220 /. The axial stress developed in the concrete slab will be E A c. T. T c. T c c The bending oent:. T. T c 4 6 3 1.5 10 0.3522 10 12, 000 634 10 da. M z 634 10 55. 6 352. 5 10 da c. The unit stresses found fro teperature are: a) in concrete: a 1 ) in the upper fibre: 1 c. T. T M. T c. sup zcs Ac n0 A I 12,000 5.96 3,934 2. 5 10 a 2 ) in the lower fibre: 1 c. T. T M. T c. inf zci Ac n0 A I 3 634 10 1 634 10 352.5 10 2 7 65.6 10.3 da/c ; 12,000 5. 96 3, 934 2.5 10 3 634 10 1 634 10 352.5 10 2 7 45.6 15 da/c ; b) in steel: b 1 ) in the upper fibre: M. T. T 634 10 352.5 10 2 a. sup z as 7 45.6 225.4 da/c ; A I 3, 934 2.5 10 b 2 ) in the lower fibre: M. T. T 634 10 352.5 10 2 a. in f ai 7 132.4 25.5 da/c A I 3, 934 2. 5 10 z. The unit stress diagra arising fro shrinkage is given in Fig. 6. In Fig. 7 are presented coparatively the stresses resulting in the two possible situations, that is when: a) the concrete slab has a lower teperature than the opposite part; b) the concrete slab has a higher teperature than the opposite part.
Bul. Inst. Polit. Iaşi, t. LX (LXIV), f. 3, 2014 87 Fig. 6 Stress distribution due to effect of heating. Fig. 7 Stress distribution due to theral effect of cooling and heating. 4. Final Rearks And Conclusions The variation of the teperature field along the height of the coposite girder cross section odifies the internal state of stresses both in the concrete slab and the etal part. The stresses overlap those produced fro peranent and net loads having an iportant effect upon the overall state of stresses.. According to SR E 1994-2, the theral stress effects can be neglected in the analyses that check the ultiate stress states other than fatigue, in the case
88 Claudia Pondichi Alb and Cătălin Moga of coposite ebers in all cross sections of Class 1 or Class 2, where no approxiations are required for the lateral buckling in the liit states of usual service. Fro the nuerical exaple given above, it yields that the stresses produced fro the difference of teperature between the two end faces of the section have high values, with axiu values of 8%...12% fro the strength of the aterials in use, steel and concrete. REFERECES Guţiu Şt., Moga C., Structuri copuse oţel beton. U.T. PRESS, 2014. Moga P., Pasarele pietonale etalice. U.T. PRESS, 2014. Vayas I., Iliopoulos A., Design of Steel-Concrete Coposite Bridges to Eurocodes. CRC Press. Taylor & Francis Group, 2014. * * * Design Concrete Structures. Part 1-1: General Rules and Rules for Buildings. SR E 1992-1-1: 2006, Eurocode 2. * * * Design of Coposite Steel and Concrete Structures. Part 1-1: General Rules and Rules for Buildings. SR E 1994-1-1: 2006, Eurocode 4. * * * Design of Coposite Steel and Concrete Structures. Part 2: General Rules and Rules for Bridges. SR E 1994-2: 2006, Eurocode 4. EFORTURI DI VARIAŢIA CÂMPULUI DE TEMPERATURĂ PE SECŢIUEA GRIZILOR COMPUSE OŢEL BETO (Rezuat) Variaţiile de teperatură ale aerului la ubră, radiaţiei solare şi radiaţiei terice, produc variaţii ale distribuţiei de teperatură în eleentele individuale ale unei structuri. Se studiază influenţa diferenţei de teperatură între feţele opuse ale unei secţiuni transversale copuse oţel beton asupra stării de eforturi unitare interioare. În structurile copuse oţel beton, betonul din dala structurii copuse nu poate avea deforaţia liberă din variaţia de teperatură pe înălţiea secţiunii deoarece dala este legată de structura etalică prin eleentele de legătură (conectori). Prin urare, tendinţa de scurtare sau de alungire a dalei de beton fiind îpiedicată, în structura copusă sunt induse eforturi interioare, eforturi care în zona dalei se suprapun peste cele produse din scurtare sau din alungire. Mecanisul de dezvoltare a eforturilor din variaţia de teperatură se exeplifică pe structura unei grinzi copuse oţel beton siplu rezeate, de tip cheson.