Asma köprülerde ana açıklık ile kablo sarkma boyu arasındaki ilişki ve bunun kablo üzerinde oluşan eksenel kuvvete olan etkisinin incelenmesi
Effect of change in the ratio of the main cable sag depth to main span distance on the normal force generated on the suspended main cable
Yazar: MUSTAFA YETİM
Danışman: PROF. DR. ELİŞAN FİLİZ PİROĞLU
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / İnşaat Mühendisliği Ana Bilim Dalı / Yapı Mühendisliği Bilim Dalı
Derece: Yüksek Lisans, 2018
Konu: Mühendislik Bilimleri = Engineering Sciences ; Ulaşım = Transportation ; İnşaat Mühendisliği = Civil Engineering
Dizin: Asma köprüler = Suspension bridges ; Eksenel yük = Axial load ; Hareketli yük = Moving load ; Statik yükler = Static loads ; Çelik halat = Steel rope

Özet:
Bu tezin amacı günümüzde uzun açıklıkların geçilmesinde en çok tercih edilen yapı olan asma köprülerde ana taşıyıcı kablo sarkma derinliği ile orta açıklık arasındaki bağıntının anlaşılmasını sağlamak ve oluşacak geometrik değişimler sebebiyle ana taşıyıcı kabloya etkiyen eksenel yüklerin değişimini incelemektir. 
Konunun gerçek bir örnek üzerinden modellenerek incelenmesi uygun görülmüştür. Bu sayede hem analiz sürecinde bulunan değerlerin doğruluğunun kontrolü yapılabilecek hem de amaçlanan inceleme ve karşılaştırma değerlerinin daha somut bir şekilde anlaşılması sağlanacaktır. Bu sebeple analizlerde kullanılmak üzere 1550 m orta açıklığı ile dünyanın dördüncü en uzun asma köprüsü olan Osmangazi Köprüsü referans alınmıştır.
Öncelikle MIDAS programı kullanılarak Osmangazi Köprüsü'nün bir modeli oluşturulacaktır. Burada amaç ana taşıyıcı kablonun incelenmesi olduğu için kablo üzerinde kritik etkileri olan yükler dikkate alınacaktır. Bu yükler; zati yükler, süperpoze zati yükler ve trafik yükleri olarak ilgili standartlara uygun şekilde ilgili programda tanımlanmıştır. Akabinde gerekli analizler yapılarak hizmete elverişli limit yükleme durumu altında ana taşıyıcı kablo üzerinde oluşan maksimum eksenel kuvvet değerleri bulunacaktır. MIDAS programı kullanılarak modellenen referans köprü için orta açıklık ve yan açıklıkta elde edilen eksenel kuvvet değerleri, Osmangazi Köprüsü'nün tasarımcı firmasının bulmuş olduğu değerler ile karşılaştırılacak ve modelin doğruluğu teyit edilecektir. 
Bu aşamadan sonra yaklaşım viyadüğü izdüşümündeki tabliye ve ana taşıyıcı kablo kotu, orta açıklık merkezindeki tabliye ve ana taşıyıcı kablo kotu, ana taşıyıcı kablo dışındaki malzeme kesit özellikleri, sabit ve hareketli yükleme tipleri, tabliye eğimi ve eğrilik yarıçapı özellikleri sabit tutulmak koşuluyla kule yüksekliği ve dolayısıyla kule üzerindeki ana taşıyıcı kablo kotu değiştirilerek farklı köprü modelleri tasarlanacaktır. Kablo sarkma derinliğinin orta açıklığa oranı farklı olarak tasarlanan bu köprü modellerinin aynı düşey yükler altında çözümü yapılacak ve bulunan sonuçlar referans köprü modeli ile kıyaslanacaktır.
Bu kıyaslar sonucunda, kule yüksekliğindeki azalma ve artmalar sebebiyle aynı yükler altında ana taşıyıcı kabloya etkiyen eksenel kuvvetlerin hangi mertebelerde değiştiği gözlenmiş ve kuvvet değişimleri sonucu kullanılması gereken kablo kesiti ve malzemesindeki artış ve azalışlar hesaplanmıştır.

Abstract:
This thesis intends to investigate and evaluate the effect of a change in the ratio of the main cable sag depth and main span distance on the axial force generated on the main cable of suspension bridge under constant load cases and the change on the main cable section property caused by the mentioned axial force variation. 
For this purpose the Osmangazi Suspension Bridge which is located 60km south-east of downtown Istanbul and carries the Gebze-Orhangazi-Bursa-Izmir motorway across the Sea of Marmara at the Bay of Izmit in northern Turkey, is chosen as the reference model. The Osmangazi Suspension Bridge consists of a three span continuous suspended box girder having a 1550m main span length where span at both sides 566m long so that being the 4th longest bridge span in the world. The bridge further consists of two H shaped steel towers and an orthotropic deck with 30.1m width excluding inspection walkways. The two 3025m long main cables carrying the three lanes of highway traffic in each direction that comprises 110 (main span) and 112 (side span) parallel wire strands (PPWS) in which one strand is constituted by 127 galvanized wires with a nominal diameter of 5.91mm. Osmangazi Suspension Bridge's main cables have a sag to span ratio of 1:9. The main cables are supported at the level 252m by saddles on top of the steel tower, and the cable sag point in the main span is located at the level 80.330m. 
"MIDAS CIVIL – Bridge Engineering" software is used to create the model and make analysis of subject reference suspension bridge model. Actual geometrical and material properties that derived from the design reports and drawings prepared by the designer company (COWI) of the Osmangazi Suspension Bridge will be used during creating reference bridge model. Once the modelling of reference suspension bridge completed in the software relevant load cases that is considered in this thesis will be defined accordingly. 
Before continue with the analysis results of reference model, it is better to mention the assumptions made for both the reference and comparison models (which will be defined later). First assumption is that the suspended deck will be kept same for all bridge models having different sag to span ratios and will be defined as a beam element having with 30.1m width and 4.75m height. Second assumption is the same tower cross sections will be used for all bridge models; however once the tower height of the comparison bridge model is changed, the cross sections will be arranged in a certain ratio by keeping upper and lower sections constant. Third assumption is related to the main cable area, which has the diameter given by the designer (COWI), and will be used in the reference model. Then the main cable section area will be adjusted linearly in accordance with the variation on the axial force created by the same load cases. 
Fourth and fifth assumptions are that the hanger cables' section properties will be defined similar in all models, and the material used for the cables shows linear elastic behavior, respectively. The load cases considered for the bridge analysis will be dead load, superimposed dead load and the traffic load. Effect of temperature and wind on the main cable will not be considered since the normal forces generated by the temperature and wind effects are approximately 3% of the total force. 
In the light of above-mentioned assumptions, reference suspension bridge model is analyzed by using MIDAS and the results are compared with those given in the design reports of Osmangazi Suspension Bridge. It is seen that there is only 2.43% difference between the MIDAS and IBDAS (is the software used by the designer of Osman Gazi Bridge) software results for the service limit state (SLS) load combination (excluding temperature and wind load cases) which is the most critical load combination for the main cable according to designer (COWI).   
Afterwards four suspension bridge models that have different sag to span ratios, are created by changing tower height and accordingly main cable sag depth to compare normal force variance with the reference model. The chosen cable sag to span ratio values for the comparison bridge models are as 8.49%, 9.78%, 12.36%, and 13.66% for which top level of steel tower is defined as 212m, 232m, 272m, and 292m, respectively. All other geometrical parameters are constant for all models.
Analysis for all suspension bridges under same load cases is performed, and the results are compared with the reference model. The normal force under SLS combination on the main cable of the bridge which has 8.49% sag to span ratio, is increased 29.82% compared to reference bridge model. On the contrary, for the bridge that has 13.66% sag to span ratio, the normal force generated on main cable under SLS is decreased 17.93% compared to reference bridge model. Moreover required main cable material quantity also changes, i.e. 23348 kN additional strand shall be used for one main cable for the bridge having 8.49% sag to span ratio, on the other hand 133288,5 kN lesser strand shall be needed for the bridge having 13.66% sag to span ratio. That means the main cable material quantity that is required for the bridge having 212m tower top level will increase 26.45% compared to the reference model's main cable material quantity and for the bridge having 292m tower top level, required main cable material will decrease 15.39%.
In conclusion, it is observed that if the sag to span ratio decreases by means of decrease on tower height, normal force generated on the main cable and consequently required cable cross section will increase. Furthermore if the sag to span ratio increases (tower height increases), normal forces generated on main cable and required cable cross section will decrease. However the increase rate of normal force caused by tower top-level decrease is higher than the decrease rate of normal force caused by the tower top level increase. It is clearly seen that higher cable sag to main span ratio under the same load combinations and constant main span distance benefits for the main cable. However to find and decide optimum sag to span ratio and/or optimum tower height, detailed analysis including other structural elements as steel tower, hanger cables, suspended deck, structures beneath the bridge, is required since changing tower height of suspension bridge will affects all member and general geometry not only main cable. 
As an example; if the tower height is more, the dynamic behavior of the steel tower under the wind and earthquake load cases will change, construction period of steel tower will be longer and also after some specific height constructability may cause difficulties as well as be time-consuming and expensive comparing with the obtained gains in the main cable element. Hanger cable length will be more even it may be neglectable besides advantage on main cable. Moreover, there may also be some restrictions for the tower height because of some environmental circumstances based on the construction location of the bridge.
Due to all of these reasons, further and detailed analysis shall be done for determination of optimum cable sag to span ratio during design phase of each suspension bridges. It is hard to define a right justification that may be applied for all suspension bridges, since each project is unique and has a different circumstance considering all aspects.