##
Mevcut betonarme yapıların deprem güvenliklerinin belirlenmesi yapı sistemlerinin hesap yöntemlerinin karşılaştırılması

Mevcut betonarme yapıların deprem güvenliklerinin belirlenmesi yapı sistemlerinin hesap yöntemlerinin karşılaştırılması

##### Dosyalar

##### Tarih

1996

##### Yazarlar

Alemdar, A. Sinan

##### Süreli Yayın başlığı

##### Süreli Yayın ISSN

##### Cilt Başlığı

##### Yayınevi

Fen Bilimleri Enstitüsü

##### Özet

Yüksek lisans tezi olarak sunulan bu çalışma iki ana bölümden oluşmaktadır: "Mevcut Betonarme Yapıların Deprem Güvenliklerinin Belirlenmesi" ve "Yapı Sistemlerinin Hesap Yöntemlerinin Karşılaştırılması". Çalışmanın birinci bölümünde, deprem bölgelerindeki konut türü betonarme yapı sistemlerini temsil etmek üzere seçilen ve ülkemizde yürürlükte olan yönetmeliklere uygun olarak boyutlandırılan taşıyıcı sistem modeUerinin artan deprem etkileri altındaki lineer olmayan davranışları, göçme güvenlikleri, çeşitli boyutiandmna kriterlerinin sistem davranışına etkileri sayısal ve parametrik olarak araştırılmıştır Böylece, deprem bölgelerindeki mevcut betonarme yapıların deprem güvenlMerinin belirlenmesine ve depreme dayanıklı yapı tasarımına katkı sağlanması amaçlanmıştır. Araştırmada, malzeme ve geometri değişimleri bakımından lineer olmayan sistemlerin hesabı için geliştirilen bir yük artımı yönteminden ve bu yöntemin pratik uygulamaları için hazırlanan bilgisayar programlarından yararlanılmıştır. ikinci bölümde yapı sistemlerinin hesap yöntemleri, bir endüstri yapısını temsil etmek üzere seçilen üç açıkhkh bir düzlem çerçeve üzerinde çeşitli yükleme durumları için farklı hesap yöntemleri kullanılarak karşılaştmlmışür. Önce Açı Yöntemine göre yapının ön boyutlandmlması yapılmıştır. Daha sonra sırasıyla, yapı yükleri için Matris Kuvvet Yöntemi, Pı, P2 ilave yükleri için Cross Yöntemi, W (Deprem) yükü için Rölaksasyon Yöntemi, düzgün sıcaklık değişmesi için Matris Deplasman Yöntemi ve mesnet çökmeleri için Açı Yöntemi kullanılarak kesit zorlan hesaplanmıştır. En elverişsiz kesit zorlan, düzenlenen bir süperpozisyon tablosu yardımı ile bulunmuş, kritik kesitlerde botonarme kesit hesaplan yapılarak enkesit donatı krokileri çizilmiştir. Daha sonra sistemin iki kritik kesiti için kesit zorlan tesir çizgileri, İndirekt Deplasman Yöntemi yardımı ile elde edilmiştir.

This study which is submitted as Master Thesis, consists of two parts: 1. Determination of Seismic Safety for the Existing Reinforced Concrete Structures 2. Comparison of Methods of Structural Analysis In the first part of the thesis, through the use of a load increments method developed for the analysis of materially and geometrically non - linear reinforced concrete space frames and the computer programs prepared for the application of this method, the seismic safety of reinforced concrete structures built in earthquake zones is investigated in detail. The first part consists of four chapters. In the first chapter, after introducing the subject, the scope and the objectives of the study are given. The earthquakes that are encountered in our country cause more severe damages, losses of lives and properties, unexpectedly, when we consider their respective magnitudes. Moreover, such serious damages and losses due to earthquakes have been suffered in the rural areas, as well as in the more condensely settled urban areas. This situation shows the fact that, an important portion of buildings built in earthquake zones which are generally reinforced concrete structures, have not been properly designed and constructed. The objective of this study is to investigate the non - linear behavior and seismic safety of selected reinforced concrete space structures which represent the apartment type buildings built in earthquake zones. The second chapter is devoted to the investigation of non - linear behavior of reinforced concrete members subjected to bending moments combined with axial force. The investigation covers the actual internal force - deformation relationships, the yield ( failure ) conditions and the idealization of non - linear behavior. The internal force - deformation relationship for reinforced concrete members is idealized as elastic - plastic. This idealization corresponds to the plastic section hypothesis. XI When the state of internal forces at a critical section reach the ultimate value defined by the yield condition, plastic deformation occurs. The plastic deformations are limited to the rotational capacity. The rotational capacity may be expressed in terms of the length of plastic region and the ultimate plastic curvature. In the third chapter, the assumptions, the basic principles and mathematical formulation of the load increments method used in this study is outlined. In the load increments method used in this study, the structure is analyzed under factored constant gravity loads and proportionally increasing lateral loads. Thus, at the end of this analysis, the factor of safety against lateral earthquake loads is determined under the anticipated safety factor for gravity loads. When the gravity loads are known, the member axial forces can be easily estimated through equihbrium equations. Thus, the second - order effects are linearized by calculating the elements of stiffness and loading matrices for the estimated axial forces. In this method the structure is analyzed for successive lateral load increments. At the and of each load increment, the state of internal forces at a certain critical section reaches the limit state defined by yield condition, that is, a plastic section forms. Since the yield vector is assumed to be normal to the yield curve, the plastic deformation components may be represented by a single plastic deformation parameter which is introduced as a new unknown for the next load increment. Besides, an equation is added to the system of equations to express the incremental yield condition. This equation is linear, because the yield surface is approximated to be composed of linear regions. Since the system of equations corresponding to the previous load increment has already been solved, the solution for the current load increment is obtained by the elimination of the new unknown. In the second - order elastic - plastic theory, the structure generally collapses at the second - order limit load due to the lack of stability. This situation is checked by testing the determinant value of the extended system of equations. If the magnitude of determinant is less than or equal to zero, the second - order limit load is reached. Hence, the computational procedure is terminated. In some cases, the structure may be considered as being collapsed due to large deflections, excessive plastic rotations, large cracks or failure of critical sections. At each step of the load increments method, a structural system with several plastic sections is analyzed for a lateral load increment. In the mathematical formulation of the method, two groups of unknowns are considered, such as a- nodal displacement components, Xll b- plastic deformation parameters at plastic sections. The equations are also considered in two groups. a- The equilibrium equations of nodes in the directions of nodal displacement components. b- The incremental yield conditions of plastic sections, which express that the state of internal forces at a plastic sections remains on the yield surface during a load increment. In the fourth chapter of the first part, a numerical and parametric study has been carried out in order to investigate the non - linear behavior and seismic safety of reinforced concrete building structures built in earthquake zones. Three structural system models which represent the apartment type buildings are selected for numerical investigation. These are, System 1 : A four story reinforced concrete space frame which is designed according to the standards and earthquake regulations currently adopted in our country. In this design, the additional support reinforcement extends to L/3 where L is the span length System 1A : Same as System 1, with only difference that the additional support reinforcement extends to L/4. System 2 : Similar to System 1, but the strong column-weak beam design is adopted. The structural system models are analyzed according to the first - and second - order, elastic - plastic theories. The analyses have been performed through the load increments method explained in chapter three. Computer programs have been used in the analyses. The results of numerical investigation are discussed in detail. The main results are summarized below. a- The minimum factor of safety against earthquake is obtained as ey= 1.307 for System 1 which is designed according to the current standard and specifications. Considering the load and resistance factors adopted in TS 500 Turkish Standard for Reinforced Concrete Structures, this value is approximately equal to the minimum required safety. b- The limit load of four story frame is decreased 6.8 - 8.7 % Xlll due to second - order effects. c-As expected for reinforced concrete structures, the structure collapses due to eccessive plastic rotations. The ratio of collapse load to limit load varies between 0.869 - 0.984 for different analyses. d- Most of the plastic sections ( 72 - 92 % ) develop in columns, because the strong column - weak beam design is not adopted for System 1. e- First plastic section develops in columns for the lateral load parameter of Py=0.984-1.102. f- For System 1A, most of the beam plastic sections develop at locations where the amount of reinforcement is changed abruptly. The first plastic sections always develop in beams before the service loads. g- For System 2, which is designed according to current standard and specifications by taking into account the strong column - weak beam principle, the increase in seismic safety is remarkable (26.4 - 28.6 %) although the cost of structural system is almost same as that of System 1. Therefore, it can be concluded that the strong column - weak beam design provides higher seismic safety and ductility whitout increasing the building cost. In the second part of the thesis, the analysis of a three-span reinforced concrete plane frame subjected to various external effects is presented. Different analysis methods have been used for each external loading. Thus, the application and comparison of these methods have been illustrated. The preliminary cross-sectional dimensions of the frame have been determined through the utilization of the Slope-Deflection method. In the preliminary design of the structural system, realistic member sizes can be obtained by decreasing the characteristic strengths of material in some proportion since only the dead loads and live loads are considered. In Chapter numbered 2.4.1 of this part, the structure is analyzed by the Matrix Force Method for dead weight acting on the structure. The unknowns are the end forces of members which forms the structure. In this method, first, a number of forces which are equal to the number of unknowns (the degree of indeterminacy) are released. Each release can be made by the removal of either support reactions or internal forces. In this method, analysis can be made with lesser unknowns for the systems having more members in a frame. Further, it is possible to obtain equations with sufficient stability and with narrower band width by means of the freedom in choosing unknowns. The analysis of the structure under the live loads is performed through Moment Distribution (Cross) Method. xiv As it is known, the analysis of statically indeterminate structures generally requires the solution of linear simultaneous equations. In this method however, a part of the simultaneous equations which correspond to the joint rotations are solved by using successive iterations. In Chapter 2.4.3, the structure subjected to lateral earthquake loads is analyzed by the Relaxation Method. The unknowns and the equations in this method are same as those of the Slope-Deflection Method. The linear simultaneous equations are obtained automatically and solved by Relaxation Method. The only difference between the Relaxation Method and the Slope-Deflection Method is the solution technique of the linear simultaneous equations. In the next chapter, the uniform temperature changes have been taken into account as an external effect on the structure. Uniform temperature change is the temperature change at the centerline of members. Due to this effect, internal forces occur in statically indeterminate structures. In order to determine these forces the structure is analyzed by the Matrix Displacement Method. In the Matrix Displacement Method, the unknowns are the joint translations and rotations. This method is more convenient for those systems having high degree of statical indeterminacy. In other words, for systems having more members meeting at joints this method enables designer to deal with less unknowns. Although the eleasticity in choosing the unknowns is limited, the generation of the stiffness matrix is usually practical because of localized effect, i.e., a displacement of a joint effects only the members meeting at the same joint. Thus, the formulation of the Matrix Displacement Method is easier and this method is more suitable for computer programming. In Chapter 2.4.5 of this part, the structure is analyzed by the Slope-Deflection Method for different support settlements. The unknowns, in this method, are rotations of joints and independent relative displacements of members. The linear simulbtaneous equations can be obtained automatically. At the end of these analysis, the dimensions of critical cross - sections obtained from the preliminary analysis are checked under the most unsuitable loading conditions. These loading conditions are several combinations which consider different external effects acting in certain proportions in accordance with the Turkish Reinforced Concrete Design Code. In this study, it is observed that the most unsuitable loading condition is generally obtained from the factored dead and live loads. In the last chapter of this part, the influence lines for bending moment, axial force shear force of two given sections are obtained by means of Indirect Displacement Method which is an efficient and relaible method. The third part of the thesis covers the conclusions. The basic results obtained in the study and the evaluation numerical investigations are presented in this part.

This study which is submitted as Master Thesis, consists of two parts: 1. Determination of Seismic Safety for the Existing Reinforced Concrete Structures 2. Comparison of Methods of Structural Analysis In the first part of the thesis, through the use of a load increments method developed for the analysis of materially and geometrically non - linear reinforced concrete space frames and the computer programs prepared for the application of this method, the seismic safety of reinforced concrete structures built in earthquake zones is investigated in detail. The first part consists of four chapters. In the first chapter, after introducing the subject, the scope and the objectives of the study are given. The earthquakes that are encountered in our country cause more severe damages, losses of lives and properties, unexpectedly, when we consider their respective magnitudes. Moreover, such serious damages and losses due to earthquakes have been suffered in the rural areas, as well as in the more condensely settled urban areas. This situation shows the fact that, an important portion of buildings built in earthquake zones which are generally reinforced concrete structures, have not been properly designed and constructed. The objective of this study is to investigate the non - linear behavior and seismic safety of selected reinforced concrete space structures which represent the apartment type buildings built in earthquake zones. The second chapter is devoted to the investigation of non - linear behavior of reinforced concrete members subjected to bending moments combined with axial force. The investigation covers the actual internal force - deformation relationships, the yield ( failure ) conditions and the idealization of non - linear behavior. The internal force - deformation relationship for reinforced concrete members is idealized as elastic - plastic. This idealization corresponds to the plastic section hypothesis. XI When the state of internal forces at a critical section reach the ultimate value defined by the yield condition, plastic deformation occurs. The plastic deformations are limited to the rotational capacity. The rotational capacity may be expressed in terms of the length of plastic region and the ultimate plastic curvature. In the third chapter, the assumptions, the basic principles and mathematical formulation of the load increments method used in this study is outlined. In the load increments method used in this study, the structure is analyzed under factored constant gravity loads and proportionally increasing lateral loads. Thus, at the end of this analysis, the factor of safety against lateral earthquake loads is determined under the anticipated safety factor for gravity loads. When the gravity loads are known, the member axial forces can be easily estimated through equihbrium equations. Thus, the second - order effects are linearized by calculating the elements of stiffness and loading matrices for the estimated axial forces. In this method the structure is analyzed for successive lateral load increments. At the and of each load increment, the state of internal forces at a certain critical section reaches the limit state defined by yield condition, that is, a plastic section forms. Since the yield vector is assumed to be normal to the yield curve, the plastic deformation components may be represented by a single plastic deformation parameter which is introduced as a new unknown for the next load increment. Besides, an equation is added to the system of equations to express the incremental yield condition. This equation is linear, because the yield surface is approximated to be composed of linear regions. Since the system of equations corresponding to the previous load increment has already been solved, the solution for the current load increment is obtained by the elimination of the new unknown. In the second - order elastic - plastic theory, the structure generally collapses at the second - order limit load due to the lack of stability. This situation is checked by testing the determinant value of the extended system of equations. If the magnitude of determinant is less than or equal to zero, the second - order limit load is reached. Hence, the computational procedure is terminated. In some cases, the structure may be considered as being collapsed due to large deflections, excessive plastic rotations, large cracks or failure of critical sections. At each step of the load increments method, a structural system with several plastic sections is analyzed for a lateral load increment. In the mathematical formulation of the method, two groups of unknowns are considered, such as a- nodal displacement components, Xll b- plastic deformation parameters at plastic sections. The equations are also considered in two groups. a- The equilibrium equations of nodes in the directions of nodal displacement components. b- The incremental yield conditions of plastic sections, which express that the state of internal forces at a plastic sections remains on the yield surface during a load increment. In the fourth chapter of the first part, a numerical and parametric study has been carried out in order to investigate the non - linear behavior and seismic safety of reinforced concrete building structures built in earthquake zones. Three structural system models which represent the apartment type buildings are selected for numerical investigation. These are, System 1 : A four story reinforced concrete space frame which is designed according to the standards and earthquake regulations currently adopted in our country. In this design, the additional support reinforcement extends to L/3 where L is the span length System 1A : Same as System 1, with only difference that the additional support reinforcement extends to L/4. System 2 : Similar to System 1, but the strong column-weak beam design is adopted. The structural system models are analyzed according to the first - and second - order, elastic - plastic theories. The analyses have been performed through the load increments method explained in chapter three. Computer programs have been used in the analyses. The results of numerical investigation are discussed in detail. The main results are summarized below. a- The minimum factor of safety against earthquake is obtained as ey= 1.307 for System 1 which is designed according to the current standard and specifications. Considering the load and resistance factors adopted in TS 500 Turkish Standard for Reinforced Concrete Structures, this value is approximately equal to the minimum required safety. b- The limit load of four story frame is decreased 6.8 - 8.7 % Xlll due to second - order effects. c-As expected for reinforced concrete structures, the structure collapses due to eccessive plastic rotations. The ratio of collapse load to limit load varies between 0.869 - 0.984 for different analyses. d- Most of the plastic sections ( 72 - 92 % ) develop in columns, because the strong column - weak beam design is not adopted for System 1. e- First plastic section develops in columns for the lateral load parameter of Py=0.984-1.102. f- For System 1A, most of the beam plastic sections develop at locations where the amount of reinforcement is changed abruptly. The first plastic sections always develop in beams before the service loads. g- For System 2, which is designed according to current standard and specifications by taking into account the strong column - weak beam principle, the increase in seismic safety is remarkable (26.4 - 28.6 %) although the cost of structural system is almost same as that of System 1. Therefore, it can be concluded that the strong column - weak beam design provides higher seismic safety and ductility whitout increasing the building cost. In the second part of the thesis, the analysis of a three-span reinforced concrete plane frame subjected to various external effects is presented. Different analysis methods have been used for each external loading. Thus, the application and comparison of these methods have been illustrated. The preliminary cross-sectional dimensions of the frame have been determined through the utilization of the Slope-Deflection method. In the preliminary design of the structural system, realistic member sizes can be obtained by decreasing the characteristic strengths of material in some proportion since only the dead loads and live loads are considered. In Chapter numbered 2.4.1 of this part, the structure is analyzed by the Matrix Force Method for dead weight acting on the structure. The unknowns are the end forces of members which forms the structure. In this method, first, a number of forces which are equal to the number of unknowns (the degree of indeterminacy) are released. Each release can be made by the removal of either support reactions or internal forces. In this method, analysis can be made with lesser unknowns for the systems having more members in a frame. Further, it is possible to obtain equations with sufficient stability and with narrower band width by means of the freedom in choosing unknowns. The analysis of the structure under the live loads is performed through Moment Distribution (Cross) Method. xiv As it is known, the analysis of statically indeterminate structures generally requires the solution of linear simultaneous equations. In this method however, a part of the simultaneous equations which correspond to the joint rotations are solved by using successive iterations. In Chapter 2.4.3, the structure subjected to lateral earthquake loads is analyzed by the Relaxation Method. The unknowns and the equations in this method are same as those of the Slope-Deflection Method. The linear simultaneous equations are obtained automatically and solved by Relaxation Method. The only difference between the Relaxation Method and the Slope-Deflection Method is the solution technique of the linear simultaneous equations. In the next chapter, the uniform temperature changes have been taken into account as an external effect on the structure. Uniform temperature change is the temperature change at the centerline of members. Due to this effect, internal forces occur in statically indeterminate structures. In order to determine these forces the structure is analyzed by the Matrix Displacement Method. In the Matrix Displacement Method, the unknowns are the joint translations and rotations. This method is more convenient for those systems having high degree of statical indeterminacy. In other words, for systems having more members meeting at joints this method enables designer to deal with less unknowns. Although the eleasticity in choosing the unknowns is limited, the generation of the stiffness matrix is usually practical because of localized effect, i.e., a displacement of a joint effects only the members meeting at the same joint. Thus, the formulation of the Matrix Displacement Method is easier and this method is more suitable for computer programming. In Chapter 2.4.5 of this part, the structure is analyzed by the Slope-Deflection Method for different support settlements. The unknowns, in this method, are rotations of joints and independent relative displacements of members. The linear simulbtaneous equations can be obtained automatically. At the end of these analysis, the dimensions of critical cross - sections obtained from the preliminary analysis are checked under the most unsuitable loading conditions. These loading conditions are several combinations which consider different external effects acting in certain proportions in accordance with the Turkish Reinforced Concrete Design Code. In this study, it is observed that the most unsuitable loading condition is generally obtained from the factored dead and live loads. In the last chapter of this part, the influence lines for bending moment, axial force shear force of two given sections are obtained by means of Indirect Displacement Method which is an efficient and relaible method. The third part of the thesis covers the conclusions. The basic results obtained in the study and the evaluation numerical investigations are presented in this part.

##### Açıklama

Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 1996

##### Anahtar kelimeler

Betonarme hesapları,
Betonarme yapılar,
Deprem analizi,
Karşılaştırmalı analiz,
Reinforced concrete calculation,
Reinforced concrete structures,
Earthquake analysis,
Comparative analysis