Ardgermeli sürekli köprü tabliyelerinin yapısal davranışının incelenmesi
Investigation of the structural behavior of horizontally curved posttensioned continous bridges
Yazar: ESRA NAMLI
Danışman: PROF. DR. TURGUT ÖZTÜRK
İstanbul Teknik Üniversitesi / Lisansüstü Eğitim Enstitüsü / İnşaat Mühendisliği Ana Bilim Dalı / Yapı Mühendisliği Bilim Dalı
Derece: Doktora, 2024
Konu: İnşaat Mühendisliği = Civil Engineering

Özet:
Ulaşım sistemleri ve bunun bir parçası olan köprüler, ülkelerdeki ulaşım ağını sağlamalarının yanı sıra ülkenin medeniyet seviyesini de belirleyen en önemli unsurlardan biridir. Günümüzde, artan nüfusla birlikte şehir içi ve şehir dışı yolların birbirleriyle çakışması farklı kavşak çözümlerinin oluşturulması ihtiyacını doğurmuştur. Bu anlamda, yapım kolaylığı ve imalat hızı bakımından prefabrike öngermeli önçekim kirişli köprüler şehir içi kavşak projelerinde en fazla uygulanan köprü tipi haline gelmiştir.
Fakat bu tip köprülerde açıklıkların 30m-40m arasında kısıtlı olması, yol geometrisinin yatayda yüksek kurp yarıçapına ya da verevliğe sahip olması durumunda yetersiz kalmaktadır. Son zamanlarda, ardgerme sisteminde, beton kalitesinde ve mesnet tiplerinde teknolojinin ileri seviyelere taşınması sonucu prefabrike köprülerin yerini daha estetik, geometri olarak uyumluluk gösteren, daha uzun açıklıkların geçilebildiği yerinde dökme ardgermeli sürekli köprüler almıştır. Bu yöntemle ortalama 50m civarında açıklıklar dolu ya da boşluklu tabliyelerle rahatlıkla geçilebilmektedir. Ardgermeli sürekli kiriş sistemi kullanılarak tasarlanan hiperstatik tabliyelerde, oluşan eğilme momentleri, taşıyıcı sistemin mesnet ve açıklık bölgeleri tarafından paylaşılır. Köprü kesiti değişken boyutlu, mesnet kısmında daha derin (yüksek), açıklık ortasında ise daha az derinliğe sahip olarak oluşturulabilmektedir.
Bu tez çalışması kapsamında, yatay kurbalarda tasarlanan yerinde dökme ardgermeli sürekli ve özel mesnetli köprülerin depremli durum yükleri altında yapısal davranışı incelenmiş ve sonuçları özellikle tasarım optimizasyonu açısından değerlendirilmiştir.
Ayrıca, ilgili tez çalışması kapsamında, planda yatay kurba sahip köprülerin deprem etkileri altında davranışlarını dikkate alan, hesap esasları ve analiz yöntemleri hakkında kıstaslar getiren AASHTO LRFD şartnameleri irdelenmiştir. AASHTO LRFD 2020 ve AASHTO LRFD 2011 şartnamelerinde kurpta köprülerin doğru eksenli köprü şeklinde idealize edilebilmesi için birtakım koşullar belirlenmiştir. Köprü açıklık sayısı, açıklık oranları, ayak rijitlikleri ve kurp yay merkez açısı değerleri söz konusu çözüm yönteminde belirleyicidir. AASHTO LRFD 2020 şartnamesinde kurpta köprülerin doğru eksenli köprü şeklinde idealize edilebilme koşulu için kurp yayı merkez açısının 900 olması belirlenmiştir.   koşulları  kurp yayı merkez açısının 900 olması belirlenmiştir. Yapılan çalışmalar ışığında bu sınır AASHTO Guide Specifications (LRFD 2011) şartnamesinde 300 olarak belirlenmiştir. Bu çalışma kapsamında söz konusu sınırların gereklilik ve yeterliliği araştırılmıştır.
Bu kapsamda, yatay kurbada ardgermeli köprülerin yapısal davranışı ile ilgili olarak daha önce yapılan çalışmaların ışığında, konunun daha net bir şekilde anlaşılması için köprülerin 3-boyutlu gerçek geometrileriyle uyumlu modelleri gelişmiş paket programlar kullanılarak oluşturulup çözümler yapılmıştır. 
Bu çalışmada incelenen köprülerin tabliyesi çubuk elemanlarla ve shell elemanlarla temsil edilerek SAP2000 ve CSiBridge programı yardımıyla modellenmiştir. Köprü tasarımına etki eden parametreler (köprü tabliyesi enkesiti, köprü açıklığı, kurp yarıçapı (kurp yay merkez açısı), ayak yükseklikleri, mesnetlenme koşulları ve sismik yükler (ve geliş doğrultuları değiştirilerek) ile zemin sınıfları farklı köprü modelleri oluşturulmuştur. Oluşturulan köprü taşıyıcı sistemlerine ait sayısal modeller düşey yükler ve deprem yükleri etkisinde doğrusal ve doğrusal olmayan hesap yöntemleriyle çözümlenmiştir. Doğrusal elastik olmayan analiz yöntemleri 01.01.2019 tarihinde yürürlüğe giren Türkiye Bina Deprem Yönetmeliği (TBDY 2018) ile uluslararası yönetmeliklerde (AASHTO LRFD Bridge Design Specifications 2017, AASHTO Guide Specifications for LRFD Seismic Bridge Design, Caltrans 2013, New Zealand Bridge Manual 2013) tanımlanan hesap esaslarına uygun olarak farklı deprem düzeyleri için öngörülen  performans seviyelerine göre gerçekleştirilecektir. Ayrıca 6 ekim 2020'de resmi gazetede yayımlanan "Deprem Etkisi Altında Karayolu Ve Demiryolu Köprü ve Viyadükleri Tasarımı İçin Esaslar" yönetmeliği de dikkate alınmıştır.
Elde edilen çok sayıda yapısal analiz sunucundan hareketle belirlenen farklı köprü konfigürasyonları için dinamik modal büyüklükler (doğal periyot-frekans, kütle katılım oranı), ayak üst ucu en büyük yerdeğiştirmeleri ile yapısal elemanların iç kuvvetleri (normal kuvvet, kesme kuvveti, eğilme momenti ve burulma momenti) elde edilmiştir. Belirlenen çok sayıda köprü konfigürasyonu farklı değişken parametlerle incelenmiş olup, sonuçların değerlendirilmesi ile yatay kurpta köprülerin yapısal çözüm yöntemlerine dair önerile getirilmiştir. Ayrıca, ulusal ve uluslararası şartnamelerin konuyla ilgili esaslarının ve limitlerinin yeniden değerlendirilmesi gerektiği sonucuna varılmıştır.

Abstract:
Transportation systems and bridges, which are an integral part of these systems, are not only crucial for establishing the transportation network in countries but also serve as important indicators of the country's level of civilization. Bridge damage resulting from significant seismic ground movements not only disrupts transportation but also has a indirect effect on the socio-economic conditions of nations, depending on the extent of the damage. Thus, understanding the seismic performance of bridges and designing them accordingly is a crucial work. Numerous studies have been conducted to analyze the types of damage observed in past earthquakes, aiming to enhance bridge design in this regard. As urban and suburban populations continue to grow, the need for innovative intersection solutions has become apparent. Consequently, horizontally curved bridges have gained popularity due to their aesthetic appeal and cost-effectiveness, which align well with geometric requirements. The geometric irregularities of these type of bridges cause more complex and more destructive behavior compared to straight bridges. The seismic performance of bridges with curved alignments possesses additional risks due to their intricate geometries, even though similar types of damage have been recorded in both curved and straight bridges during past earthquakes. Notably, the severe damage to bridges following the 1971 San Fernando earthquake highlighted the vulnerability of these structures to significant ground movements. Subsequent events, such as the 1989 Loma Prieta earthquake, the 1992 Petrolia earthquake, the 1994 Northridge earthquake, and the 2008 Wenchuan earthquake, further underscored the critical nature of bridge damage in horizontal curve alignments. Common types of damage in these bridges included the unseating of superstructures, shear failure of columns, foundation failures, bearing collapses, and inadequate bending capacity in columns. Consequently, numerous studies have been conducted to better understand the seismic behavior of horizontally curved bridges and to implement necessary design measures for creating more resilient structures.  Moreover, seismic design standards have established limits on the maximum curvature of bridges, allowing engineers to utilize an equivalent straight bridge for their analysis and design. As the population continues to rise, the convergence of urban and interurban roads has generated a demand for various intersection solutions. In this context, prefabricated pre-tensioned girder bridges have become the most commonly applied bridge type in urban intersection projects due to their ease of construction and manufacturing speed.
However, the limitation of spans to 30m-40m in these types of bridges becomes insufficient when the road geometry has high radius of curvature angle or skew. 
Recently, advancements in post-tensioning systems, concrete quality, and bearing types have led to the replacement of prefabricated bridges with more aesthetically pleasing, geometrically compatible, and longer-span cast-in-place post-tensioned continuous bridges. With this method, spans of approximately 50m can be comfortably achieved with solid or hollow slabs. In hyperstatic slabs designed using the post-tensioned continuous girder system, the bending moments are shared by the bearing and span regions of the load-bearing system. 
The bridge section can be formed with varying dimensions, being deeper (higher) at the support regions and shallower at the mid-span.
Within the scope of this thesis, the structural behavior of cast-in-place post-tensioned continous and specially supported bridges designed on horizontal curves under seismic loads has been investigated, and the results have been evaluated, particularly in terms of design optimization.
Additionally, within the scope of the thesis, the AASHTO LRFD specifications, which provide criteria regarding the principles and analysis methods for considering the seismic behavior of bridges with horizontal curves, have been examined. Certain conditions have been determined in the AASHTO LRFD 2020 and AASHTO LRFD 2011 specifications for idealizing curved bridges as straight bridges. The number of spans, span ratios, pier stiffnesses, and subtended angle values of the curved span are determinative in this solution method. In the AASHTO LRFD 2020 specification, the condition for idealizing curved bridges as straight bridges is specified as having a subtended angle of 90°. In light of conducted studies, this limit was set at 30° in the AASHTO Guide Specifications (LRFD 2011) specification. This study investigates the necessity and adequacy of these limits.
In this context, in light of previous studies on the structural behavior of post-tensioned bridges on horizontal curves, to better understand the subject, models compatible with the 3-dimensional real geometries of bridges were generated and analyzed using advanced software packages. In this study, the deck of the examined bridges was modeled using bar elements and shell elements with the help of SAP2000 and CSiBridge programs. Different bridge models were created considering the parameters affecting bridge design (bridge deck cross-section, bridge span, curvature radius (central angle of the curved span), pier heights, bearing conditions, seismic loads (and their changing directions), and soil classes). The numerical models of the created bridge load-bearing systems were analyzed using linear and nonlinear analysis methods under vertical loads and seismic loads. Nonlinear elastic analysis methods were performed according to the performance levels anticipated for different earthquake levels, in accordance with the calculation principles defined in the Turkish Building Earthquake Code (TBDY 2018), which came into effect on 01.01.2019, as well as international regulations (AASHTO LRFD Bridge Design Specifications 2017, AASHTO Guide Specifications for LRFD Seismic Bridge Design, Caltrans 2013, New Zealand Bridge Manual 2013). Additionally, the "Design Principles for Highway and Railway Bridges and Viaducts under Seismic Effect" regulation, published in the Official Gazette on October 6, 2020, was also considered.
Bridges with significant horizontal curvature do not exhibit the idealized behavior of a typical single degree of freedom (SDOF) system. Therefore, the effect of curvature must also be included in the analyses. 
On the other hand, the behavior of bridges with relatively less horizontal curvature can be idealized as a single degree of freedom system (SDOF). A curved bridge that can be idealized as an SDOF system can be analyzed as if it were a straight bridge. While the force-based seismic analysis design philosophy is adopted in the AASHTO LRFD 2010 specifications, the deformation-based design philosophy is emphasized in the AASHTO Guide Specifications (LRFD 2011). The AASHTO 2010 specification stipulates that the condition for idealizing curved bridges as straight bridges is having a central angle of 90° for the curved span. In light of studies, this limit has been set at 30° in the AASHTO Guide Specifications (LRFD 2011). The design philosophy of this specification favors the deformation-based method over the traditional force-based design.
Moreover, in the "Design Principles for Highway and Railway Bridges and Viaducts under Seismic Effect" regulation, the definition of bridges with critical load-bearing system behavior considers a central angle of 20° or greater for the curved span. The design philosophy of this regulation takes into account a two-stage calculation. In the first stage, the calculation is based on strength, and in the second stage, a deformation-based evaluation is considered.
To determine the seismic demands of curved bridges, the AASHTO Guide Specifications (LRFD 2011) suggests that curved bridges can be analyzed as straight bridges if they meet the regular bridge conditions specified in Table 4.2-3. This hypothesis was evaluated through a comprehensive parametric study involving curved bridges with varying angles between 0 and 180 degrees and total arc lengths corresponding to the straight bridge length. Additionally, to examine the regular bridge conditions specified in the regulations, analytical models will be created considering the parameters listed in Table 4.2-3: bridge span, central angle of the curved span, pier rigidities, as well as abutment conditions and different earthquake directions.
Bridge configurations were determined by considering these parameters. In this context, a three-span bridge was initially selected. Bridge geometries were created, and calculation models were established in the SAP2000 program. In the relevant model, vertical dead loads and seismic loads were applied to the bridge. Modal analysis of the bridges under dead loads was conducted, yielding values such as period, frequency, and mass participation. The effects of changes in the central angle of the curved span on the modal behavior of the bridges were examined. Subsequently, linear elastic modal analyses of four-span and five-span bridges were carried out in sequence. 
Values such as period, frequency, and mass participation were obtained, and the effects of changes in the central angle of the curved span on the modal behavior of the bridges were analyzed.
In the design of bridges under seismic effects, earthquake data for different earthquake ground motion levels defined in Section 2.2 of the Turkish Building Earthquake Code (TBDY 2018) were obtained from the "Turkey Earthquake Hazard Maps" and the relevant website https://tdth.afad.gov.tr/.
Horizontal elastic design spectra specified for Earthquake Ground Motion Level-1 (DD-1) and Earthquake Ground Motion Level-2 (DD-2) were defined in the bridge models, and linear modal analyses of the bridges were performed. The sectional effects of the elements obtained under these loadings were compared. Additionally, the effect of changing the local soil classes defined in the bridge design (ZB/ZC) was also considered.
To determine the behavior of bridges under site-specific earthquake ground motion, site-specific ground motion spectra were defined, and nonlinear time history analyses were conducted. In this regard, 11 earthquake records were scaled to match the defined horizontal elastic earthquake spectrum, and 22 earthquake records were modeled for the X-Y directions. Sectional effect values, base shear force, and mid-pier displacement values in the structural elements of the bridges under the influence of these earthquake loads and vertical dead loads were obtained over time.
Based on the numerous structural analysis results obtained, dynamic modal quantities (natural period-frequency, mass participation ratio), the maximum displacements at the top of the piers, and the internal forces (axial force, shear force, bending moment, and torsional moment) of the structural elements were determined for different bridge configurations. Various bridge configurations were examined with different variable parameters, and the evaluation of the results provided recommendations for the structural analysis methods of bridges on horizontal curves. Additionally, it was concluded that the principles and limits of national and international specifications on the subject need to be reevaluated.
Numerical parametric structural models have been generated for the selected variables such as; bridge length, span number, span length and subtended angle. By using the structural analysis programme, multi-mode response spectral analysis have been performed for the maximum credible earthquake (MCE) excitation level.  The modal periods and frequencies, modal mass participating ratios, maximum displacement of the pier and the internal forces of the structural elements are obtained from the structural analysis of the bridges. The analysis results are compared with horizontally curved bridges and equivalent straight bridges to determine the effect of subtended angle to seismic behavior of the bridges. 
It was shown that, bridge length and span number had a significant effect on the seismic response of the horizontally curved bridges compared to straight bridges. Besides, the subtended angle limitations which AASHTO LRFD specifications put forward regarding to allow the curved bridges to use an equivalent straight bridge should be reviewed again.  It suggests that a bridge is considered regular if the subtended angle is smaller than 900. However, according to the analysis results, the dynamic modal quantities, the displacement and rotations of the pier and the internal forces of the pier columns and the deck of the bridges could reach their maximum values at lower angles of curvature than 900. 
Therefore, the limitations of the subtended angle should be reviewed and re-evaluated for several variable parameters by using linear and non-linear analysis methods.