Iš anksto įtemptųjų gelžbetoninių elementų įtempių ir deformacijų apskaičiavimo sluoksnių modelis ; Layer Model for Stress and Strain Analysis of Prestressed Concrete Members

Darius Bamuene Solo

Description

Renata Zamblauskait ė LAYER MODEL FOR STRESS AND STRAIN ANALYSIS OF PRESTRESSED CONCRETE MEMBERS Summary of Doctoral Dissertation Technological Sciences, Civil Engineering (02T) 1182 Vilnius „Technika“ 2005 VILNIUS GEDIMINAS TECHNICAL UNIVERSITY Renata Zamblauskait ė LAYER MODEL FOR STRESS AND STRAIN ANALYSIS OF PRESTRESSED CONCRETE MEMBERS Summary of Doctoral Dissertation Technological Sciences, Civil Engineering (02T) Vilnius „Technika“ 2005 Doctoral dissertation was prepared at Vilnius Gediminas Technical University in 2001-2005 Scientific Supervisor Prof Dr Habil Gintaris KAKLAUSKAS (Vilnius Gediminas Technical University, Technological Sciences, Civil Engineering – 02T) The Dissertation is being defended at the Council of Scientific Field of Civil Engineering at Vilnius Gediminas Technical University: Chairman Prof Dr Habil Juozas ATKO ČI ŪNAS (Vilnius Gediminas Technical University, Technological Sciences, Civil Engineering – 02T) Members: Prof Dr Habil Audronis Kazimieras KVEDARAS (Vilnius Gediminas Technical University, Technological Sciences, Civil Engineering – 02T) Prof Dr Habil Romualdas MA ČIULAITIS (Vilnius Gediminas Technical University, Technological Sciences, Civil Engineering – 02T) Dr Habil Leonidas SAKALAUSKAS (Institute of Mathematics and Informatics, Physical Sciences, Informatics – 09P) Prof Dr Habil Vytautas

Sujets

• Creep
• Curvature
• Deflection
• Shrinkage

Informations

• Publié par: vilnius_gediminas_technical_university
• Publié le: 01 janvier 2005
• Nombre de lectures: 36

Extrait

 

              Renata Zamblauskaitė         LAYER MODEL FOR STRESS AND STRAIN ANALYSIS OF PRESTRESSED CONCRETE MEMBERS         Summary of Doctoral Dissertation Technological Sciences, Civil Engineering (02T)                   Vilnius Technika 2005

 

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VILNIUS GEDIMINAS TECHNICAL UNIVERSITY                       Renata Zamblauskaitė         LAYER MODEL FOR STRESS AND STRAIN ANALYSIS OF PRESTRESSED CONCRETE MEMBERS           Summary of Doctoral Dissertation Technological Sciences, Civil Engineering (02T)                   Vilnius Technika 2005

 

Doctoral dissertation was prepared at Vilnius Gediminas Technical University in 2001-2005   Scientific Supervisor Prof Dr HabilGintaris KAKLAUSKAS Gediminas Technical (Vilnius University, Technological Sciences, Civil Engineering  02T)   The Dissertation is being defended at the Council of Scientific Field of Civil Engineering at Vilnius Gediminas Technical University:   Chairman Prof Dr HabilJuozas ATKOČIŪNAS Gediminas Technical (Vilnius University, Technological Sciences, Civil Engineering  02T) Members: Prof Dr HabilAudronis Kazimieras KVEDARAS (Vilnius Gediminas Technical University, Technological Sciences, Civil Engineering 02T)  Prof Dr HabilRomualdas MAČIULAITIS(Vilnius Gediminas Technical University, Technological Sciences, Civil Engineering  02T) Dr HabilLeonidas SAKALAUSKAS (Institute of Mathematics and Informatics, Physical Sciences, Informatics  09P) Prof Dr HabilVytautas STANKEVIČIUS of Architecture and (Institute Construction of Kaunas University of Technology, Technological Sciences, Civil Engineering  02T) Opponents: Prof Dr HabilJonas BAREIIS (Kaunas University of Technology, Technological Sciences, Mechanical Engineering  09T)   Prof Dr HabilGediminas MARČIUKAITIS (Vilnius Gediminas Technical University, Technological Sciences, Civil Engineering 02T)    The dissertation will be defended at the public meeting of the Council of Scientific Field of Civil Engineering in the Senate Hall of Vilnius Gediminas Technical University at 10 a.m. on 28 October 2005. Address: Saulėtekio al. 11, LT-10223 Vilnius-40, Lithuania Tel.: [phone]; fax [phone], e-mail [e-mail]   The summary of the doctoral dissertation was   distributed on 28 September 2005. A copy of the doctoral dissertation is available for review at the Library of Vilnius Gediminas Technical University (Saulėtekio al. 14, Vilnius, Lithuania)   © Renata Zamblauskaite, 2005

 

VILNIAUS GEDIMINO TECHNIKOS UNIVERSITETAS                     Renata Zamblauskaitė       I ANKSTOĮTEMPTŲJŲEBOTININ EGLŲELEMENTŲ   ĮTEMPIŲIR DEFORMACIJŲAPSKAIČIAVIMO SLUOKSNIŲMODELIS           Daktaro disertacijos santrauka Technologijos mokslai, statybos ininerija (02T)                   Vilnius Technika 2005  

 

Disertacija   rengta   2001-2005   metais   Vilniaus   Gedimino   technikos universitete.   Mokslinis vadovas prof. habil. dr.Gintaris KAKLAUSKAS (Vilniaus Gedimino technikos universitetas, technologijos mokslai, statybos ininerija  02T).   Disertacija ginama Vilniaus Gedimino technikos universiteto Statybos ininerijos mokslo krypties taryboje:   Pirmininkas prof. habil. dr. ATKO JuozasČIŪNAS (Vilniaus Gedimino technikos universitetas, technologijos mokslai, statybos ininerija  02T). Nariai: prof. habil. dr.Audronis Kazimieras KVEDARAS Gedimino (Vilniaus technikos universitetas, technologijos mokslai, statybos ininerija  02T), prof. habil. dr.Romualdas MAČIULAITIS Gedimino (Vilniaus technikos universitetas, technologijos mokslai, statybos ininerija  02T), habil. dr.Leonidas SAKALAUSKAS ir informatikos (Matematikos institutas, fiziniai mokslai, Informatika  09P), prof. habil. dr.Vytautas STANKEVIČIUS technologijos (Kauno universiteto Architektūros ir statybos institutas, technologijos mokslai, statybos ininerija  02T).   Oponentai: prof. habil. dr. Jonas BAREIIS technologijos universitetas, (Kauno technologijos mokslai, mechanikos ininerija  09T), prof. habil. dr. MAR GediminasČIUKAITIS(Vilniaus Gedimino technikos universitetas, technologijos mokslai, statybos ininerija  02T).   Disertacija bus ginama vieame Statybos ininerijos mokslo krypties tarybos posėdyje 2005 m. spalio 28 d. 10 val. Vilniaus Gedimino technikos universiteto senato posėdiųsalėje. Adresas: Saulėtekio al. 11, LT-10223 Vilnius-40, Lietuva. Tel.: [phone]; faksas [phone], el. patas [e-mail]   Disertacijos santrauka isiuntinėta 2005 m. rugsėjo 28 d. Disertaciją galima periūrėti Vilniaus Gedimino technikos universiteto bibliotekoje (Saulėtekio al. 14, Vilnius, Lietuva) VGTU leidyklos Technika 1182 mokslo literatūros knyga   © Renata Zamblauskaitė, 2005

 

General Characteristic of the Dissertation   Need for research in the field.Application of refined ultimate state theories and use of high strength materials have resulted in longer spans and smaller depths of reinforced and prestressed concrete structures. Consequently, the condition of the limiting deflection rather than the strength requirement often is the governing design criterion. Long-term deflections might be up to 3 to 4 times larger than the short-term deflections. Such increments are caused by complex physical effects such as concrete creep, shrinkage and cracking, bond defects, etc. Long-term concrete creep and shrinkage deformations govern prestress losses. Structural analysis can be carried out either by traditional design code methods   or numerical techniques. Although design code methods ensure safe design, they have significant limitations. Different techniques are used for strength, deflection, crack width and prestress loss analyses. Besides, most of the simplified approaches do not assess such factors as concrete shrinkage, cracking or tension stiffening. Based on a large number of empirical expressions and factors, they lack physical interpretation and do not reveal the actual stress-strain state of cracked structures. On the other hand, numerical techniques are universal and can take into account each physical effect. However, inadequacies made in the prediction of each effect might lead to significant inaccuracies when integral magnitudes such as deflection are to be assessed. Consequently, the predictions by the numerical techniques might be even less accurate than those obtained by the code methods. A new statistically verified constitutive model, called the Flexural, has been developed at Vilnius Gediminas technical university for deformational analysis of flexural reinforced concrete members subjected to short-term and long-term loading. In the present research, the Flexural deformational model has been extended for case of prestressed members. The analysis includes concrete creep, shrinkage, cracking and tension stiffening effects. It is based on the classical techniques of strength of materials, extended to application of layered approach and the use of the material diagrams of the Flexural constitutive model. Methodology of research. thesis deals with short- and long-term The deformational analysis of cracked flexural RC/PC members. A simple analytical technique based on layered approach and the Effective Modulus (EM) method has been proposed. Modified stress and strain relationships for compressive and tensile concrete are a significant part of the deformational model. The object considered has been dealt at macro level using analytical, theoretical and statistical methods. Main objective.The main objective of this work was to extend the Flexural Constitutive Model for case of short- and long-term deformational  

analysis of flexural PC members with consideration of concrete creep, shrinkage and cracking and tension stiffening effects. Main tasks.to achieve the main objective, the following problemsIn order have to be solved: 1. to review critically methods and constitutive relationships used for deformational analysis of flexural PC members; 2. to propose a model for deformational analysis of PC members in case of short- and long-term loading; 3. to investigate accuracy of the EM method performing parametric analysis of deflections/cambers and prestress losses of non-cracked RC/PC members and comparison with the predictions made by the Step-by-Step (SBS) method; 4. using the proposed method, to investigate increase of prestress losses due to concrete cracking; 5. to investigate accuracy of the proposed deformational model by calculating deflections/cambers and prestress losses for a large number of experimental RC/PC beams reported by various investigators and performing comparison with the predictions made by design code methods. Scientific novelty 1. A short- and long-term deformational analysis method for flexural PC members has been proposed. It is based on the classical techniques of strength of materials extended to application of the layered approach and the use of the materials diagrams of the Flexural Constitutive Model. 2. Comparative parametric analyses of long-term strain and prestress loss predictions made by EM and SBS methods have been carried out for different geometrical and physical parameters of non-cracked RC/PC members. 3. Increase in prestress losses due to concrete cracking has been investigated by the method proposed. 4. For a large number of experimental RC/PC members reported by various investigators, statistical comparative analysis has been carried out for short- and long-term deflection/camber and prestress loss predictions made by the proposed and design code methods.   Approbation and publications.The main results of this work were reported at four scientific technical conferences. Seven papers were published on the topic of the dissertation and two of them were published in the magazines from the list approved by the Department of Science and Higher Education (see 16-17 p.). The scope of the thesis.The thesis consists of general characteristics, list of notations, 47 pictures, 53 tables, four main chapters, general conclusions,  

appendices and a list of references. The total scope of the dissertation is 154 pages.   Content of the Work   1. Review of Reference Literature   This chapter critically reviews methods and constitutive relationships for deformational analysis of flexural PC members. In the state-of-art summary, basic factors influencing stress and strain behaviour of PC members subjected to short- and long-term loading have been discussed. As a conclusion, the main objective of developing a simple analytical model for short- and long-term deformational analysis of flexural PC members was set for the present research.   2. Layer Model for Deformational Analysis of PC members   This chapter presents short- and long-term deformational analysis model for flexural PC members. Present analysis method is based on the classical techniques of strength of materials extended to application of the layered approach and the use of the materials diagrams of the Flexural Constitutive Model. Stress and strain relationships for concrete and reinforcement.For both short- and long-term analysis, the stress and strain relationships of the compressive concrete are shown in Fig 1.   c ( t,t 0 ) f c,max ( t 0 ) 0,15f c,max t 0 ) f c, ax ( t,t ) 0,15f c,max t,t 0 ) m 0

E e t ) E c ( t 0 ) 0 0 t 0 ) u t 0 ) 0 t,t 0 ) u t,t 0 )     Fig 1.Stress and strain relationships for compressive concrete: ( ) -for the case of short-term loading ( ) -for the case of long-term loading   The ascending branches of the compressive concrete diagrams shown in Fig 1 have the following expressions:   σ c ( t 0 ) = f c,max ( t 0 ⎪ ⎪ ⎩ ⎧ ⎨ ) 2ε ε 0 c ( ( t t 0 0 ) − ) ⎜ ⎝ ⎛ ε ε 0 c ( (t t 0 0 ) ) ⎟ ⎠ ⎞ 2 ⎭ ⎪ ⎬ ⎪ ⎫ , (1)  

  σ c ( t,t 0 ) = f c,max ( t,t 0 ⎪ ⎨ ⎪ ⎩ ⎧ ) 2ε ε 0 c t (t, t t 0 0 − ) ⎜ ⎛ ε ε ⎝ c 0 ( t t, t t 0 0 ) ⎟ ⎠ ⎞ 2 ⎬ ⎫ ⎭ ⎪ , (2) ( , ) ( , ) ⎪ t 2f c t2f c t,t ,t,t=    ε 0 ( 0 ) = E , c m ( a t x 0 ( ) 0 ) ε 0 ( 0 ) E , e m ( a t x ,t ( 0 ) 0 ) , (3) heret 0  time at first loading (in days); is time under consideration (in is days); c t 0 ), c (t,t 0 )are the compressive stress;f c,max t 0 ),f c,max (t,t 0 )are the maximum compressive stress and 0 t 0 ), 0 t,t 0 ) the corresponding are strain for short- and long-term loading, respectively. Strength of compressive concrete varies with time. Structural defects initiated by hardening of concrete further develop with time and cause reduction of compressive strength. On the other hand, concrete strength increases with time due to hydration of cement. In the present study, these effects are accounted for by factors cc  and c,sus  in CEB-FIB Model given Code 1990. The maximum compressive stressf c,max (t) is any time at determined as follows:     f c,max t,t 0 ) = f c 28 ) cc t ) c,sus t,t 0 ) , (4)   heref c ( 28 ) is short-term compressive   strength (at timet 0 =28 days); cc ( t )   is the factor assessing influence of cement hydration process on compressive strength of concrete and c,sus t,t 0 )is the factor accounting for micro-cracking effects on concrete strength.   The effective modulus of elasticity of concreteE e t,t 0 ) for modelling the effects of creep in concrete is expressed as:     E e (t,t 0 ) = 1+ E c (φ t t, 0 t ) 0 ) , (5) hereE c ( t 0 ) is the modulus of elasticity of concrete at timet 0 ;t,t 0 ) is the creep coefficient at time for concrete loaded att 0 . Present analysis employs the Flexural constitutive relationship of cracked tensile concrete proposed by G. Kaklauskas and D. Bacinskas for modelling short- and long-term loading, respectively. The descending branches of the tensile concrete diagrams shown in Fig 2 have the following expressions:     f t (t 0 ) =0,625f cr (t 0 ⎪ ⎩ ⎪ ) ⎧ ⎨ 1 β ε − t ( t t 0 0 + ) ) 1 β +0, ε t 6 (t β 0 ) t 0 ⎫ ) ⎪ ⎭ ⎪ ⎬ , (6)  

  f t ( t,t 0 ) = 0,625f cr ( t,t 0 ) ⎧ ⎪ ⎨ ⎪ ⎩ 1− β ε t (t t, ,t t 0 0 + ) ) 1 β +0, ε t 6 (t β , t t 0 ,t ) 0 ⎪ ⎭ ⎫ ⎬ ) ⎪ , (7) heref cr ( t 0 ) ,f cr ( t,t 0 )  are the short- and long-term strength of tensile concrete, respectively;ε t ( t 0 ) ,ε t ( t,t 0 ) and cr t 0 ) , cr t,t 0 ) are the strain and the cracking strain of tensile concrete at timet 0  respectively.and , The factors ( t 0 )  andt,t 0 )  the length of the descending describing branch of the constitutive relationship for the case of short- and long- term loading (Fig 2), respectively, are expressed as:   β(t 0 ) =32,8−27,6p+7,12p 2 ,βt 0 ) =5,if p≥2%, (8) (t 0 t,t   (β 0 ) η = c 2 r [1( β φ+t ) ,t 0 )] , (9) wherepis the reinforcement percentage. The factor cr describing the reduction of the concrete tensile strength due to sustained loading is obtained from the following expression:   η cr = f c f c r t (t ,t 0 ) = ) 0,794−0,06 log(t−t 0 ). (10) r0 c (t,t 0 ) f cr (t 0 ) cr f cr (t 0 )

cr ( t,t 0 ) c (t,t 0 ) 0 cr (t 0 ) (t 0 ) cr (t 0 ) (t,t 0 ) cr (t,t 0 )     Fig 2.Stress and strain relationships for concrete in tension under: short - ( ) and long ( ) - term loading   For reinforcement material idealization, a bilinear, tri-linear or more complex stress and strain relationship can be adopted. The stress and strain curve for the long-term analysis is taken the same as for the short-term analysis, i.e. no creep is assumed in the steel. Short- and long-term deformation analysis of RC/PC concrete members.   A powerful approach for short- and time-dependent analysis of the cracked cross-  

section has been adopted. The section may contain multiple levels of both prestressed and non-prestressed reinforcement (Fig 3, a) and is subjected to bending moment and axial forces with the top fibre taken as the reference level (Fig 3, c). The members cross-section is divided into a number of horizontal layers (Fig 3, b) corresponding to either concrete or reinforcement. The non- linear material properties are assessed in iterative calculation by means of secant deformation modulus which is the ratio of stress and strain. The cross section analysis is performed on the so-called transformed section. The proposed calculation technique is based on the following approaches and assumptions: 1) smeared crack approach; 2) linear distribution of strain within the depth of the section; 3) perfect bond between concrete and reinforcement; 4) EM method based on effective modulus of elasticity of concrete, is used for modelling the effects of creep in concrete; 5) uniform concrete shrinkage within the depth of the section.   a) ' b)c) d) ε T , 0 ) b f 11 c t t ' d sp2 h f 3 2 y c d y n ε cT t 0 ) )( A sp2 y i h d  d s t i i b i ( t 0 ) t,t 0 sp1 b A s A sp1 h f n n −1 ε cB ( t 0 ) b f y ε cB t,t 0 )   Fig 3.Time-dependent strains of flexural PC section: short - ( ) and long ( ) - term loading   Longitudinal strain i (t,t 0 )at every layeri(Fig 3, c, d) is taken as:   ε i t,t 0 ) = ε cT t,t 0 ) +y i κt,t 0 ), (11) wherey i  the distance of the isi- th layer from the top edge;ε cT t,t 0 )  and ( t,t 0 ) strain and curvature, respectively, and are obtained are the top fibre from the following expressions:   T −S eT [M−Pd n +M shr (t,t 0 ) −I eT P+N shr t,t 0 ] c t,t 0 =   ε ( ) E e ( t,t 0 ⎛ ⎜ ⎝ ) A e I eT − ] S eT [ 2 )( ⎠ ⎞ ⎟ , (12) κt,t 0 = A e M−Pd n +M shr t,t 0 +S eT [P 2 +N shr t,t 0 )] , (13)   ( )  [ E e ( t,t 0 ) ⎜ ⎝ ( ⎛ A e I ) eT − ] S eT ⎟ ⎠ ⎞ (