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

Mevcut betonarme binaların deprem güvenliklerinin belirlenmesi yapı sistemlerinin hesap yöntemlerinin karşılaştırılması

##### Dosyalar

##### Tarih

1993

##### Yazarlar

Karadaş, Mustafa

##### Süreli Yayın başlığı

##### Süreli Yayın ISSN

##### Cilt Başlığı

##### Yayınevi

Fen Bilimleri Enstitüsü

##### Özet

Bu çalışma iki ana bölümden olusmaktadır. "Mevcut Betonarme Binaların Deprem Güvenliklerinin Belirlenmesi" ve "Yapı Sistemlerinin Hesap Yöntemlerinin Karşılaştırılması". Birinci kısımda mevcut betonarme binaların deprem güvenliklerinin belirlenmesi amacıyla yürütülen ve sistemlerin dış yükler altındaki elastoplastik davranışını esas alan bir çalışmanın esasları açıklanmış ve gerçek bir yapı sistemi üzerindeki sayısal uygulamaları verilmiştir. İncelenen yapının, ilk olarak, güçlendirilmemiş mevcut durumu ele alınarak her iki doğrultu için deprem güvenlikleri be lirlenmiştir. Depreme karşı güvenliği yetersiz bulunan bu yapı daha sonra her iki doğrultuda yatay yük taşıma kapa sitesi büyük olan perdelerle güçlendirilmiş ve yapının bu durumuna ait deprem güvenlikleri yeniden hesaplanarak sonuçlar karşılaştırılmıştır. İkinci kısımda, Yapı Sistemlerinin Hesap Yöntemleri, seçilen üç açıklıklı bir düzlem çerçeve üzerinde çeşitli yükleme durumları için farklı hesap yöntemleri kullanılarak karşılaştırılmıştır. önce Açı Yöntemine göre yapının ön boyutlandırılması yapılmıştır. Daha sonra sırasıyla, sabit yükler için Matris Deplasman Yöntemi, P,, P" ve P~ ilave yükler için Cross Yöntemi, W (Deprem) yükü için Rölaksasyon Yöntemi, düzgün sıcaklık değişmesi için Matris Kuvvet Yöntemi ve mesnet çökmeleri için de Açı Yöntemi kullanılarak kesit tesirleri hesaplanmıştır. Ayrıca, Endirekt Deplasman Yöntemi ile iki kesitteki M, N, T tesir çizgileri çizilmiştir.

This study which is submitted as Master Thesis, consists of two major parts: 1- Evaluation of Seismic Capacity of Existing Reinforced Concrete Buildings 2- Comparison of Methods of Structural Analysis In the first part, the principles of a method for evaluation of seismic capacity of existing reinforced concrete buildings is given. The method which is based on the elastic-plastic analysis of lateral load resisting system, has been applied to the seismic evaluation of an existing building suffered from 1992 Erzincan earthquake. Experience from earthquakes occured in our country has demonstrated that most of the buildings in earthquake zones have not been properly designed and constructed. Therefore an earthquake with a magnitude of 6 -7 in Richter scale can cause large amount of life loss and buildings collapse. Based on this experience it is proposed that, starting from the high-risk earthquake zones, the seismic capacity of existing buildings be evaluated and the buildings without sufficient capacity be strengthened. The analytical methods for seismic capacity evaluation can be classified into two groups: a- Methods based on collapse with story panel mechanism, b- Methods based on overall structural behavior. In this study, under the factored gravity loads, the lateral load carrying capacity of the building (limit load) is determined through elastic-plastic analysis of the complete structure. By neglecting the torsion of the building under seismic loads and assuming that the floor slabs are infinitely rigid in their planes, the structural system can be modelled by plane frames connected to each other with bars of infinite axial rigidity. The plastic moments of beams and columns are determined by the ultimate vi strength theory. The reduction of plastic moments due to gravity loading is also considered. The elastic-plastic analysis of structural system has been carried by the use of a computer program developed for plane frames. The shear failure of columns are included in the analysis. The proposed method for the seismic capacity evaluation of an existing reinforced concrete building consist of the following phases: a- Study of the original project of building The structural system, cross-sectional dimensions of beams and columns, reinforcement are determined. Besides, the eccentiricity between centers of mass and rigidity, the effect of in-fill walls on the structural system are studied. b- Investigation on the existing building In this phase the correlation between the original design and the existing structure is determined. c- Gravity load analysis of the structural system The structural system is analyzed under factored gravity loads and beam and column internal forces are calculated. d- The bending moment capacities of beams and columns and shear capacity of columns are calculated according to the ultimate strength theory. e- Reserve capacities of beams and columns for seismic loads are determined by considering the reduction due to gravity loads f- Elastic-plastic analysis of the structural system is carried out as explained in the previous paragraphs. The application of the proposed method has been illustrated on an existing reinforced concrete building suffered from the Erzincan 1992 earthquake. The building is reinforced concrete frame structure with one basement story and four stories above ground level. The planar dimensions are 20 m by 10 m. The concrete class adopted in the original design has not been indicated on the project. However, the material test results have shown that the compressive strength of concrete is approximately f_k= 10 N/mm2. The existing reinforcement in beams and columns is 80-94% of the design reinforcement. vxi The elastic-plastic analysis of the existing structural system has been carried out in both longitudinal and transveral directions. The numerical results have shown that the seismic safety indexes (i.e. the ratio between the lateral load capacity and design seismic load) in longitudinal and transversal directions are 0.469 and 0.657 respectively. These results indicate that the safety of existing building against earthquake is insufficient. Therefore, the building has been strengthened by four shear walls arranged in both directions. Then the structural system with additional shear walls has been analyzed by the plastic hinge theory. The shear walls are taken as elastically supported on the ground. The bending moment capacities of shear walls are determined by the ultimate strength theory. The results of analyses have shown that the seismic safety indexes in longitudinal and transversal directions are 2.119 and 1.879 respectively. An increase of 450% an 285% in seismic safety is accomplished by strengthening. The drift index corresponding to limit load is reduced to 6/H= 0.0 06 from 6/H= 0.010 by strengthening. Based on the results of analyses, it is concluded that the strengthened structural system can resist to earthquake loads which correspond to earthquake coefficient of C= 0.15. In the second part, 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. At the end of this chapter, a sufficient result can be obtained in the preliminary design of the structural system by decreasing the characteristic strengths of material in some proportion since only the dead loads and live loads are considered. In the second chapter of the second part, the structure is analyzed by the Matrix Displacement Method for dead loads acting on the structure. In the Matrix Displacement Method the unknowns are the joint translations and rotations. This method is more useful for the systems having high degrees of statical indeterminacy. In other words, for systems having more members meeting at joints, this method enables the engineer to work with lesser unknowns. Although, the band width of simultaneous equations is limited and there is limited elasticity in choosing the unknowns. Generation of the stiffness matrix is usually not difficult because of localized effect, so a displacement of a joint effects only the members meeting viii at the given joint. Thus, it is easy to formulate the Matrix Displacement Method and this method is more suitable for computer programming. In the third chapter of this part, the structure is analyzed by the Moment distribution (Cross) Method for live loads P,, P_ and P_. As it is known, the analysis of statically indeterminate structures, generally, requires the solution of lineer simultaneous equations. In the Moment Distribution (Crdss) Method, the unknowns are rotations and translations of the joints. In this method, a part of ite simultaneous equations which correspond to the joint rotations are solved by using successive iterations. In the fourth part, the structure subjected to lateral loads is analyzed by the Relaxation Method. The unknowns and the equations, in this method, are the same as the Slope-Deflection Method. The unknowns, in this method are rotations of joints and independent relative displacements of the members ends. The linear simultaneous equations are obtained automatically and solved by Relaxation Method. The difference of the Relaxation Method from the Slope-Deflection Method is the solution of the simultaneous equations by various iteration techniques. In the fifth part, the uniform temperature changes have been taken into account as an external effect on the structure. Uniform temperature change is the temperature change at centerline of the members. Because of this effect, some internal forces acting on the cross-sections of statically indeterminate structure occur. To determine these forces the structure is analyzed by the Matrix Force Method. In the Matrix Force Method, the unknowns are the forces acting at the ends of the members which have formed the structure. In this method, first, a number of forces relased which are equal to number of unknowns (the degree of indeterminacy). Each release can be made by the removal of either support reactions or internal forces. Due to this property, analysis can be made with lesser unknowns for the systems having more numbers in a frame. In addition, it is possible to obtain equations in which the band width is kept small and system of equations is stable, by means of the freedom in choosing unknowns. These equations, are written systematically even they cannot be derived automatically. In the sixth chapter, the structure is solved for different support settlements. The structure is analyzed again by Slope Deflection Method. The unknowns, in this method, are the rotations of joints and independent end displacements of the member, as it is mentioned above. The linear simultaneous equations are obtained automatically and solved by means of a computer program. ix ~ At the end of these calculations, the dimensions of the critical cross-sections obtained from the preliminary analysis are checked under the most unsuitable loading conditions. These loading conditions are some combinations which consider different external effects acting in certain proportions according to Turkish Design Code. In this study, it is observed that the most unsuitable loading condition is obtained from the following combination: 1.4xG+-1.6xP where G : Dead Weight P : Live Load In the sixth part of the first part, finally, the influence lines for bending moment, axial force and shear force of two given sections are obtained by means of Indirect Displacement Method which is an efficient and reliable method.

This study which is submitted as Master Thesis, consists of two major parts: 1- Evaluation of Seismic Capacity of Existing Reinforced Concrete Buildings 2- Comparison of Methods of Structural Analysis In the first part, the principles of a method for evaluation of seismic capacity of existing reinforced concrete buildings is given. The method which is based on the elastic-plastic analysis of lateral load resisting system, has been applied to the seismic evaluation of an existing building suffered from 1992 Erzincan earthquake. Experience from earthquakes occured in our country has demonstrated that most of the buildings in earthquake zones have not been properly designed and constructed. Therefore an earthquake with a magnitude of 6 -7 in Richter scale can cause large amount of life loss and buildings collapse. Based on this experience it is proposed that, starting from the high-risk earthquake zones, the seismic capacity of existing buildings be evaluated and the buildings without sufficient capacity be strengthened. The analytical methods for seismic capacity evaluation can be classified into two groups: a- Methods based on collapse with story panel mechanism, b- Methods based on overall structural behavior. In this study, under the factored gravity loads, the lateral load carrying capacity of the building (limit load) is determined through elastic-plastic analysis of the complete structure. By neglecting the torsion of the building under seismic loads and assuming that the floor slabs are infinitely rigid in their planes, the structural system can be modelled by plane frames connected to each other with bars of infinite axial rigidity. The plastic moments of beams and columns are determined by the ultimate vi strength theory. The reduction of plastic moments due to gravity loading is also considered. The elastic-plastic analysis of structural system has been carried by the use of a computer program developed for plane frames. The shear failure of columns are included in the analysis. The proposed method for the seismic capacity evaluation of an existing reinforced concrete building consist of the following phases: a- Study of the original project of building The structural system, cross-sectional dimensions of beams and columns, reinforcement are determined. Besides, the eccentiricity between centers of mass and rigidity, the effect of in-fill walls on the structural system are studied. b- Investigation on the existing building In this phase the correlation between the original design and the existing structure is determined. c- Gravity load analysis of the structural system The structural system is analyzed under factored gravity loads and beam and column internal forces are calculated. d- The bending moment capacities of beams and columns and shear capacity of columns are calculated according to the ultimate strength theory. e- Reserve capacities of beams and columns for seismic loads are determined by considering the reduction due to gravity loads f- Elastic-plastic analysis of the structural system is carried out as explained in the previous paragraphs. The application of the proposed method has been illustrated on an existing reinforced concrete building suffered from the Erzincan 1992 earthquake. The building is reinforced concrete frame structure with one basement story and four stories above ground level. The planar dimensions are 20 m by 10 m. The concrete class adopted in the original design has not been indicated on the project. However, the material test results have shown that the compressive strength of concrete is approximately f_k= 10 N/mm2. The existing reinforcement in beams and columns is 80-94% of the design reinforcement. vxi The elastic-plastic analysis of the existing structural system has been carried out in both longitudinal and transveral directions. The numerical results have shown that the seismic safety indexes (i.e. the ratio between the lateral load capacity and design seismic load) in longitudinal and transversal directions are 0.469 and 0.657 respectively. These results indicate that the safety of existing building against earthquake is insufficient. Therefore, the building has been strengthened by four shear walls arranged in both directions. Then the structural system with additional shear walls has been analyzed by the plastic hinge theory. The shear walls are taken as elastically supported on the ground. The bending moment capacities of shear walls are determined by the ultimate strength theory. The results of analyses have shown that the seismic safety indexes in longitudinal and transversal directions are 2.119 and 1.879 respectively. An increase of 450% an 285% in seismic safety is accomplished by strengthening. The drift index corresponding to limit load is reduced to 6/H= 0.0 06 from 6/H= 0.010 by strengthening. Based on the results of analyses, it is concluded that the strengthened structural system can resist to earthquake loads which correspond to earthquake coefficient of C= 0.15. In the second part, 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. At the end of this chapter, a sufficient result can be obtained in the preliminary design of the structural system by decreasing the characteristic strengths of material in some proportion since only the dead loads and live loads are considered. In the second chapter of the second part, the structure is analyzed by the Matrix Displacement Method for dead loads acting on the structure. In the Matrix Displacement Method the unknowns are the joint translations and rotations. This method is more useful for the systems having high degrees of statical indeterminacy. In other words, for systems having more members meeting at joints, this method enables the engineer to work with lesser unknowns. Although, the band width of simultaneous equations is limited and there is limited elasticity in choosing the unknowns. Generation of the stiffness matrix is usually not difficult because of localized effect, so a displacement of a joint effects only the members meeting viii at the given joint. Thus, it is easy to formulate the Matrix Displacement Method and this method is more suitable for computer programming. In the third chapter of this part, the structure is analyzed by the Moment distribution (Cross) Method for live loads P,, P_ and P_. As it is known, the analysis of statically indeterminate structures, generally, requires the solution of lineer simultaneous equations. In the Moment Distribution (Crdss) Method, the unknowns are rotations and translations of the joints. In this method, a part of ite simultaneous equations which correspond to the joint rotations are solved by using successive iterations. In the fourth part, the structure subjected to lateral loads is analyzed by the Relaxation Method. The unknowns and the equations, in this method, are the same as the Slope-Deflection Method. The unknowns, in this method are rotations of joints and independent relative displacements of the members ends. The linear simultaneous equations are obtained automatically and solved by Relaxation Method. The difference of the Relaxation Method from the Slope-Deflection Method is the solution of the simultaneous equations by various iteration techniques. In the fifth part, the uniform temperature changes have been taken into account as an external effect on the structure. Uniform temperature change is the temperature change at centerline of the members. Because of this effect, some internal forces acting on the cross-sections of statically indeterminate structure occur. To determine these forces the structure is analyzed by the Matrix Force Method. In the Matrix Force Method, the unknowns are the forces acting at the ends of the members which have formed the structure. In this method, first, a number of forces relased which are equal to number of unknowns (the degree of indeterminacy). Each release can be made by the removal of either support reactions or internal forces. Due to this property, analysis can be made with lesser unknowns for the systems having more numbers in a frame. In addition, it is possible to obtain equations in which the band width is kept small and system of equations is stable, by means of the freedom in choosing unknowns. These equations, are written systematically even they cannot be derived automatically. In the sixth chapter, the structure is solved for different support settlements. The structure is analyzed again by Slope Deflection Method. The unknowns, in this method, are the rotations of joints and independent end displacements of the member, as it is mentioned above. The linear simultaneous equations are obtained automatically and solved by means of a computer program. ix ~ At the end of these calculations, the dimensions of the critical cross-sections obtained from the preliminary analysis are checked under the most unsuitable loading conditions. These loading conditions are some combinations which consider different external effects acting in certain proportions according to Turkish Design Code. In this study, it is observed that the most unsuitable loading condition is obtained from the following combination: 1.4xG+-1.6xP where G : Dead Weight P : Live Load In the sixth part of the first part, finally, the influence lines for bending moment, axial force and shear force of two given sections are obtained by means of Indirect Displacement Method which is an efficient and reliable method.

##### Açıklama

Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 1993

##### Anahtar kelimeler

Betonarme binalar,
Bina bilgisi,
Deprem,
Yapı sistemleri,
Reinforced concrete buildings,
Building information,
Earthquake,
Structure systems