Çelik Yapılarda Stabilite Analizi Yaklaşımlarının Değerlendirilmesi

Abstract

Yüksek lisans tezi olarak sunulan bu çalışmada son yıllarda hızla gelişen bilgisayar teknolojilerine paralel olarak özellikle dayanım esaslı tasarım felsefelerinin de gelişmesiyle standartlarda yer almaya başlayan stabilite analizi yöntemleri incelenmiştir. Birinci bölümde stabilite analizinin AISC standartlarına ilk olarak nasıl dahil edildiği ve günümüze kadar olan süreçte nasıl bir yol izlendiği açıklanmıştır. Etkileşim ifadelerinin gelişimi detaylı bir şekilde irdelenmiştir. İkinci bölümde EC3 Standardında stabilite analizine olan yaklaşım kısaca ele alınmıştır. Üçüncü bölümde AISC 360-10 Standardında yer alan stabilite analizi yöntemleri, Doğrudan Analiz Yöntemi ve Etkili Uzunluk Yöntemi ayrıntılı bir şekilde ele alınmıştır. Birinci mertebe analiz yöntemi ise sadece bölümün sonunda, yöntemler arasında karşılaştırmanın yapıldığı çizelgede ele alınmıştır. Ayrıca yaklaşık ikinci mertebe analizinin nasıl yapıldığı da bu bölümde anlatılmıştır. Basit örneklerle tez kapsamında açıklanan yöntemlerin nasıl kullanıldığı açıklanmıştır. Örneklerde kullanılan tasarım yaklaşımları ile ilgili bilgiler Ek B'de bulunmaktadır. Yöntemler ile ilgili yapılan karşılaştırmaya ait bir çizelge de bölümün sonunda yer almaktadır. Dördüncü bölümde beş katlı çelik bir binanın dört farklı yönteme göre stabilite analizi ve kolon tasarımı yapılmıştır. Öncelikle TS 648 (AISC-ASD89) Standardına göre analizi yapılarak en elverişsiz tesirlere sahip kolon için tahkik yapılmıştır. Daha sonra AISC 360-10 Standardına uygun bir şekilde yaklaşık ikinci mertebe analizi kullanılması sonucu elde edilen değerlere göre, Doğrudan Analiz Yöntemi ve Etkili Uzunluk Yöntemine göre kolon tasarımı yenilenmiştir. Yük kombinasyonları ASCE 7-10 Standardına uygun bir şekilde kullanılmıştır. Deprem yüklü kombinasyonlarda DBYBHY-2007'ye uygun bir şekilde her iki doğrultunun da ortak etkisi dikkate alınmıştır. Son olarak da SAP 2000 ile yapılan doğrusal olmayan (nonlineer) analiz sonucu elde edilen ikinci mertebe değerlerine göre kolon tasarımı yapılmıştır. Farklı yöntemler kullanılarak bulunan sonuçlar arasında karşılaştırmaların yapıldığı çizelgeler de bölümün sonunda bulunmaktadır. Son bölümde ise bulunan sonuçların değerlendirilmesi yapılmıştır. Standartlar ve yöntemler arasındaki benzerlik ve farklılıklar ortaya konmuştur. İkinci mertebe etkilerinin sonuçlara dahil edilmesi durumunda ortaya çıkan farklardan bahsedilmiştir. Seçilen çelik yapının ikinci mertebe etkilerini incelemek adına yeterli olup olmadığı ve çalışmanın amacı vurgulanmıştır.

In this study presented as a master science thesis, methods of stability analysis are addressed because of the development in the design, which is based on resistance, together with the computer technology. In the first chapter, how to include the stability analysis in AISC and the process of the subject are expressed. Second-order effects, P-delta effects, are explained briefly. The development of interaction expressions is examined. Interection expressions, which are used for beams-columns, are addressed according to AISC 360-10. In the second chapter, the approach of stability analysis in EC3 is explained briefly. How to include the second-order effects is expressed for structural elements, which are considered to contribute to the stability of the structure, moment frames and braced frames. In the third chapter, the Direct Analysis Method and Effective Length Method according to AISC 360-10 are detailed. In the Direct Analysis Method, how to calculate of required strengths is explained. General analysis requirements are mentioned. While using the Direct Analysis Method to determine required strengths, it is very important to include P-delta effects for second-order analysis. How to include both P-Δ and P-δ effects is described. When some conditions are satisfied, it is permissible to neglect the effect of P-δ. If P-Δ only analysis is used providing these conditons, some errors can occur because of the negligence. Some error rates for different conditions are mentioned in this method. Consideration of initial imperfections on the stability of the structure is examined. Direct modeling of imperfections or aplication of notional loads are explained. When the Direct Analysis Method is prefered, reduced stiffnesses are used in the analysis. The reason of using reduced stiffness and how to apply the reduced stiffnesses for different conditions is addressed. For calculation of available strengths, what to take the effective length factor, K, is explained. The most important advantage of using the Direct Analysis Method, it doesn’t need to calculate the effective length factor, K. How to calculate of required strengths for the Effective Length Method is explained. In the analysis for calculation required strengths, the information about initial imperfections and stiffnesses is addressed. It is the most important subject to determine the effective length factor, K, in the Effective Length Method. For calculation of available strengths, what to take the effective length factor, K, is explained in the Effective Length Method. The table abaout the effective length factor, K, for specific frames and loading conditions is addressed. Using aligment charts is the the most common method for determining the effective length factor, K. These are addressed for frames with sidesway inhibited (braced frame) and frames with sidesway unhibited (moment frame). There are some assumptions to use these aligment charts. Adjusments for column and girders with differing end conditions are explained for frames with sidesway inhibited and frames with sidesway unhibited. The effective length for story stability is addressed. Two approaches, which are the story stiffness approach and the story buckling approach, for evaluting story stability are addressed. Additionally an approach produced by Le Messuier is explained in the Effective Length Method. First-order analysis method is mentioned only in the table, in which is at the end of this chapter. Because of being the kind of the Direct Analysis Method, first-order analysis method isn’t presented detailly. In addition, approximate second-order analysis, as an alternative to a rigorous second-order analysis, is addressed in this chapter. Approximate second-order analysis means that account for second-order effects by amplifying the required strengths indicated by a first-order analysis. How to calculate the multiplier B1, account for P-δ effects in the analysis, is explained. There are some graphics and table about Cm, which is very important to determine multiplier B1. How to calculate the multiplier B2, account for P-Δ effects in the analysis, is explained. Rm, which is the coefficient to account for influence of P-δ on P-∆, is mentioned for calculation multiplier B2. By solving easy examples, the methods are described how to use. There are some comprehensive information in Appendix B about the philosophy of design methods and examples. At the end of this chapter, there is a comparison about methods of stability analysis. In the forth chapter, steel building is choosen to analyze statically and design. It has been five storeys. 3-D view, axis view and floor plans are addressed for steel building. SAP 2000 is used to analyze the steel building. TS 498 is used for load types. Seismic loads are determined according to DBYBHY-2007. Four methods are used for stability analysis and design of columns. It is statically analyzed statically and results of the structural analysis are used to design according to the TS-648 (AISC-ASD89). Load combinations are chosen from ASD89. DBYBHY-2007 is took into account for combinations, which are about seismic, to include effects of both directions of the earthquake. Using the same model, the analysis of the steel building is repeated according to the Direct Analysis Method. Initial imperfections and reduced stiffnesses are used for the same model in the analysis. The same column is designed according to the Direct Analysis Method (AISC 360-10). Load combinations are chosen from ASCE 7-10. DBYBHY-2007 is took into account for combinations, which are about seismic, to include effects of both directions of the earthquake. Using the same model, analysis of the steel building is repeated according to the Effective Length Method (AISC 360-10). However, nominal stiffnesses are used for the same model in the analysis. The same column is designed according to the Effective Length Method (AISC 360-10). The effective length factor, K, is calculated for required strengths. Load combinations are chosen as the Direct Analysis Method. The same model, which is used in the Direct Analysis Method, for SAP 2000 nonlineer analysis is realized. Second-order axial forces and bending moments are took from SAP 2000 analysis. Design of the same column is done for second-order effects. At the end of this chapter, results about design of the column are discussed. There are a table about second-order axial forces and bending moments and a table about capacity ratios for whole stability analysis methods. In the last chapter, there is an assesment about results. Between codes and methods of design similarly and differences are revealed. While using the second-order effects, change of results that about internal forces and moments are specified. Finally it is emphasized the aim of study.