Öngerilmeli inşaat elemanlarında gerilme analizi
Stress analysis in prestressed structural elements
Yazar: ABDULLAH DÖNMEZ
Danışman: PROF. DR. ZİYA ABDULALIYEV ; DOÇ. DR. ŞENOL ATAOĞLU
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / İnşaat Mühendisliği Ana Bilim Dalı / Yapı Mühendisliği Bilim Dalı
Derece: Doktora, 2015
Konu: İnşaat Mühendisliği = Civil Engineering

Özet:
İnşaat sanayinde yaygın olarak kullanılan öngerilmeli beton elemanlarda üretim aşamasında oluşturulan öngerilmelerin değerleri, onun bazı bölgelerinde ilgili betonun mukavemet karakteristiklerinin sınırları ile karşılaştırılabilecek seviyeye ulaşabilirler. Bu bakımdan söz konusu elemanların tasarımının başarılı olarak yapılabilmesi için oluşturulması öngörülen gerilmelerin yapıda dağılması ile ilgili detaylı bilgi gerekmektedir. Fotoelastik yöntem ile incelenen elemanın her noktasında gerilme durumunun kesin değerleri ölçülebilir. Bu bakımdan öngerilmeli beton elemanlarda üretim aşamasında oluşan gerilmelerin incelenmesi için ilgili öngerilmelerle ısıl gerilmeler arasındaki benzeşime dayanarak fotoelastik modelleme yönteminin uygulanması amaca uygundur. 
Bu çalışmada, inşaat elemanlarında öngerilmeler fototermoelastisitenin "gerilmelerin dondurulması" metodu kullanılarak incelenmiştir. Gerilmelerin incelenmesi 2-B veya 3-B fotoelastik modeller ve sayısal analizler kullanılarak gerçekleştirilmiştir.  Öngerilmeli beton elemanların fotoelastisite ile modellenmesinde kullanılabilecek malzemeler mekanik parametrelerin deneysel çalışmalar ile elde edilmesi sonucunda belirlenmiştir. Fotoelastik modellerin deneysel analizi sonucunda farklı malzemelerin birleşim bölgeleri olan aderans ve birleşim yüzeyinin serbest kenarı olan ankraj bölgeleri ile ilgili gerilme dağılımları bakımından önemli sonuçlar elde edilmiştir. Elde edilen sonuçlar bazı bölgelerde analitik ve sayısal yöntemlerle bulunan verilerle karşılaştırılmıştır. Sonuçların incelenmesi ile öngerilme uygulanan bir yapının ankraj bölgelerinde oluşan gerilme yığılmalarının ekstremum değerlerinin kullanılan malzemelerin elastik sabitlerine ve verilen ilk öngerilme değerine bağlı olarak değiştiği görülmüştür. Ayrıca transfer boyu olarak adlandırılan öngerilme değerinin etkili öngerilme değerine ulaşması için aderans üzerinde gerekli olan mesafe, verilen öngerilme değerine ve bahsedilen elastik sabitlerin oranına bağlı olarak değişmektedir. Öngerilmeli beton elemanların beton kısmında oluşan herhangi bir çatlak, boşluk veya kusurun modellenmesi ile elde edilen sonuçlar geometrik süreksizliğin, gerilme yığılmalarının değerleri bakımından, yapının güvenliğini tehdit edecek seviyelerde çıkabileceği sonucuna varılabilir. Termal gerilmelerle beton elemanlarda oluşturulan öngerilmeler arasındaki analojiye dayanarak bazı bölgeler için gerilme durumu hesap edilebilir. Analitik olarak hesaplanan gerilme değerleri deneysel verileri desteklemektedir. Bulgular dahilinde varılan souçlar öngerilmeli tabliye ve kiriş elemanların servis yükleri altında mukavemet sınırlarına ulaşabileceğini göstermektedir. Elde edilen bilgiler öngerilmeli beton elemanların tasarımının optimizasyonu için kullanılabilir.

Abstract:
Prestressed concrete is a reinforced concrete type in which the steel rebars have been tensioned against concrete member. This tensioning performance results in a self-equilibrating system of internal stresses which improves the response of the concrete member to external loads. Whilst concrete has a high strength in compression it is brittle and weak in tension, and thus it gains improvement against service loads.
Pre-stressed elements are commonly being used in constructions due to the engineering and architectural needs. 
The use of high strength steel wires in practice leads to production of pre-stressed concrete members. In practice, it is possible to create more uniform stress distributions in the structural members taking into account the generated elastic strains via pre-stressing during the fabrication process of the structural member. In this context, the stress values at the fabrication process should be taken into account at the design stage. 
As it is known, pre-stressed members can be fabricated in different ways, bonded and unbounded tendons, which are pre-tensioned and post-tensioned concrete members. A pre-tensioned concrete is a prestressed concrete in which the prestressing tendon is tensioned prior to casting the section, while a post-tensioned concrete member is one in which the prestressing tendon is tensioned in a longitudinal duct after the concrete has been cast and achieved a major portion of its strength. Therefore, pre-stressing was divided into two main categories, which are pre-tensioned and post-tensioned concrete members, in other words, pre-stressing with bonded and unbounded tendons with the concrete material.
This study deals with the investigation of the prestress distribution after the fabrication process of the pre-tensioned concrete members. With considering the technical literature, it is needed to investigate the stress distribution at the vicinity of the free edges and bonding area of the reinforcing material of the pre-stressed structural members. The pre-tensioning tendons for prestress distributions are being uniaxially tensioned according to the design values just before the casting. So, the bonding stresses have significant importance for redistribution of the self-equilibrated internal stresses after the release. Similarly, the difference of the free thermal expansions causes the thermal stresses in the joint of mechanically dissimilar materials during the uniform heat distribution.
Therefore, it is clear that there is an analogy between the generated stresses by the pre-stressing process of the structural members and thermal stresses via the temperature change in the dissimilar material joints. Hence, investigation of the stress distribution of the pre-tensioned concrete members can be conducted by the analytical and experimental methods used for the thermal stress analysis.
In modeling, materials should have similar ratio of elastic moduli in order to sustain the analogy between the stress distribution of prototype and model, made from dissimilar materials. In practice, ratio of the Young moduli of concrete and reinforcing steel varies between 5$\sim$10. This range must be taken into account when the prototypes are modeled. Stress "freezing" cycle, one of the most important stages of the used modeling technique, should be implemented at the freezing temperature.
In order to fulfill the necessary similarity relationship between the model and prototype, the ratio of the Young moduli of the materials at the freezing temperature, which are representing the concrete and steel bars, should be inside the range mentioned above. At present, it is necessity to use an opaque material for modeling the tensioning bars because of the absent information about the optically sensitive materials satisfying the required ratio. To determine the proper material which contains the required conditions for the model, some tests are conducted using Dynamical Mechanical Analysis (DMA Q800) for different opaque plastic materials. Therefore, an optically sensitive material, araldite for concrete and an opaque plastic material, nylon6 (Quadrant Engineering Plastic Products ERTALON6SA) for steel bars are selected as the model materials. 
Naturally, obtaining the stress-strain limits of the concrete part of reinforced concrete member has a major role for the safe design margins. In this context, modeling the concrete part of the reinforced concrete structure with optically sensitive material and steel part with selected opaque nylon 6, is determined for the photoelastic modeling. The models of investigated structures are prepared taking into account the geometrical similarity ratios of the prototype-model conversion.
Two and three-dimensional photoelastic models are prepared and analyzed for the regions of interest.  Using the "freezing" method of photothermoelasticity leads to analyze the "frozen" stresses in 2-D and 3-D photoelastic models. Analytical and numerical analysis are made in order to satisfy the obtained results from experimental work and make the predictions for real members. 2-D model has three bars as prestressing tendons. It contains defects in different shapes and sizes. It also contains a staged section which models a geometrical discontinuity often being encountered in practice.  3-D models have square prism and cylindrical geometries with containing a single inclusion at their centers. Neither of them contains any type of defects. Hence the only stress concentration is formed at the anchorage zones. The conversion of the obtained results are made with using the prototype-model analogy formula. Strength limits of the materials are considered with checking the measured and converted stress values of the prototype.
Analytical analysis are made with using thermal analogy. Some basics of theory of elasticity are used depending on the nature of the problems. Numerical simulations are made using one of the most common commercial finite element software, ABAQUS. All the symmetry conditions considering the loading and geometrical structures of the models are used when necessary. 2-D model is implemented with using 2-D shell elements. Cylindrical specimen of the 3-D photoelastic model is simulated by axisymmetric elements. The obtained results from linear elastic implementation of the aforementioned models are sufficiently consistent with the experimental data. 
As an initial inspection, all the geometrical discontinuities in a uniform stress field result in remarkable stress concentrations according to the geometry, level of the non-homogeneity and the loading conditions. All the voids and defects modeled in 2-D have stress concentrations in some extent. Geometrically and physically discontinuous locations of the models produce the stress concentrations at the anchorage zones of the model. Pre-stressing of these members in the fabrication process can produce very high stress values in some particular regions of the concrete. In this context, it is very important to know the details of the designed stress distribution in the structural element in order to keep the safety design margins. 
Results are compared with analytical solutions in some regions of the 2-D model. Maximum shear stresses appear where the interface intersects with the free edges, and reach the level which may be compared with the concrete strength. The existence of discontinuities on the interface region yields high values of shear stresses in which the Tresca stresses are multiple times of the initial prestress values. This is crucial for the unknown internal stress state in practice for prestressed members used in infrastructures. This phenomena may cause prestress loss with the prestressing tendon slips. Moreover, because of the complex micro structure of concrete material, hydration may yield in some voids and defects inside the bulk material. Generated stress concentration results in cracking inside the concrete. Thus propagation of the cracks caused by the stress concentrations cannot be avoided which leads to strength reduction of the structure. At the considered regions of the structural member, cracking might be occurred and growth of the cracks might cause destructive damage.
The values of maximum shear stresses at the regions mentioned above should be taken into account at the design stage in order to keep the values inside the concrete strength limits. The strength of the interface between concrete and steel bars should be taken into account.
The continuity of the material at the aforementioned regions should be checked with non-destructive testing.
The values of the ultimate shear stresses at the anchorage zone are dependent parameters of the used materials' elastic constants and design values of the prestressing. Variation of shear stresses along the transfer length is not linear but decreases with following a hyperbola equation. Results presented herein can be used in the design of prestressed concrete element.