Monotonik ve çevrimsel yüklemenin yüksek mukavemetli betonarme kiriş davranışına etkisi

Abstract

1975 Türk Deprem Yönetmeliği, deprem mühendisliğindeki gelişmeler ışığında yeniden gözden geçirilmiş ve 1998 Türk Deprem Yönetmeliği hazırlanmıştır. Yeni yönetmeliğin hedeflerinde birisi, betonarme yapıların güvenlik sınırlan içinde plastik şekil değiştirme yaparak deprem enerjisini yutmasını sağlamaktır, yani yapılarda sünekliği sağlamaktır. Bu amaçla yeni yönetmelikte yapı sistemleri ve yapı elemanları süneklik düzeyi yüksek olanlar ve süneklik düzeyi normal olanlar olarak ikiye ayrılmıştır. Bu çalışmada 1998 Türk Deprem Yönetmeliğinin, süneklik düzeyi yüksek kirişler için öngördüğü şartlara uyan ve özellikleri aynı olan, basit mesnetlenmiş iki adet betonarme kiriş üzerinde monotonik ve çevrimsel yükleme deneyleri yapılarak kirişlerin yük altındaki davranışları belirlenmeye çalışılmıştır. Deneyde kullanılan kirişlerin kesiti 40x40 cm2, kiriş uzunluğu 450 cm'dir. Kirişlerde çekme donatısı olarak 4 basınç donatısı olarak 216 S420 (BÇIII) kullanılmıştır. Kesme donatısı olarak 10 cm aralıkla yerleştirilmiş $8 S220 (BÇI) kullanılmıştır. Kullanılacak betonun karakteristik silindir dayanımı olarak 25 MPa seçilmiştir, ancak daha sonra malzeme üzerinde yapılan deneylerde bu dayanımın ortalama 42 MPa seviyesinde olduğu belirlenmiştir. Kirişlere kuvvet, orta bölgede 1 m aralıklı iki simetrik noktasal yük şeklinde uygulanmıştır, böylece iki tekil yük arasında kalan orta alanda kesme kuvvetinin olmadığı sabit bir moment bölgesi elde edilmiştir. Deney sırasında kirişler üzerinde oluşan şekil değiştirmeleri belirlemek için donatı çeliği üzerine ve beton üzerine birim uzama ölçerler yerleştirilmiştir. Kirişlerin yapacağı çökmenin belirlenmesi için değişik noktalara yer değiştirme ölçerler yerleştirilmiştir. Kirişler hazırlanırken alman altışar adet 15x15x15 cm3'lük küp beton numuneleri üzerinde basınç, çelik numuneleri üzerinde çekme deneyleri yapılarak gerçek malzeme özellikleri belirlenmiştir. Bu malzeme özelliklerinden yola çıkılarak donatı tarafından sarılmış ve sarılmamış betonun basınç altında davranışı; betonun çekme altındaki davranışı ve donatı çeliğinin basınç ve çekmedeki davranışı için gerçekçi malzeme modelleri hazırlanmıştır. MS-Excel'de yazılan bir bilgisayar programıyla, hazırlanan malzeme modelleri kullanılarak kirişler için moment-eğrilik diyagramı çizilmiştir.

The Turkish Earthquake Code 1975, needed to be reevaluated by taking into account considerable advances that have been made in the earthquake engineering over the last twenty years. The new Turkish Earthquake Code 1998 is based on the modern aseismic design principles. One of the modern aseismic design's general requirements is to ensure plastic behavior capability to the reinforced concrete structures to dissipate earthquake energy by plastic deformations. At this point, ductility (//) term is defined and the structural systems are classified as follows. - systems with normal ductility level - systems with high ductility level. In the new code a beam is defined as a structural element which may carry design axial load which is equal to or lower than 0.1 Acf,*. In this study two structural members with no axial load were designed as beams with high ductility level, satisfying the requirements of the Turkish Eartquake Code 1998, for the beams with high ductility level. Those reinforced concrete beams were tested under monotonic and cyclic loads for comparing their behavior. These most common techniques have been choosen because of their simplicty to apply. The beams are simply supported and subjected to two point concentrated loads at the mid span. Before the construction of the beams, a calculation is made to ensure that the capacity of the loading actuator is higher than the beams' maximum strength. Both of the beams have the same geometrical transversal and longitudinal dimensions. Both of the beams has 40x40 cm2 cross-sections and 4.5 m of length. The details of the beams can be seen in Figure 1. CD O 400 mm 4)8/10 Figure 1 : Cross-section of the beams xvi In the Turkish Earthquake Code 1998, concrete must be characterized by at least 20 MPa of average cylindrical strength for the members of high level ductility systems. To satisfy that requirement, 25 MPa (BS25) was choosen and supplied from the factory of Yapı Merkezi Prefabrication Inc. by a completely computerized mixing system. For each beam, 6 cubes with dimensions of 15*15x15 cm3 have been taken to be subjected to compression tests at seventh, twenty-eigth days and on the days of the experiments. The compression test result show that the beams are at higher strength than the proposed strength. At the compression tests the average cylindirical strength of the concrete, in the day of loading experiments, was found to be 42 MPa. For the reinforcement steel 420 MPa of average tension strength is allowed in the Turkish Earthquake Code so S420 (BÇIII) deformed rebar was used for the beams' longitudinal reinforcement. 4Ş16 was used as tensional reinforcement and 216 was used as compressional reinforcement. S 220 (BÇI) was choosen for transversal reinforcement. (J)8 was used with spacing of 10 cm for stirrups. During the construction of beams, three specimens are taken from the longitudinal reinforcement and two specimens are taken from the transversal reinforcement to be tested under tension. As shown in the formula below, the percentage of reinforcement is 0.00558. p=Ai.,_"L = a005S8 bwd 40x36 When the beams are simply supported the span length is 4.1 m from support to support. The loads are 1.00 m apart with the ratio of shear span to depth of section (a/d) 4.31. The pattern of loading is shown in the Figure 2. As shown in the figure, by this type of loading a constant moment area can be obtained in the area between the concentrated singular loads. In this fixed moment area, no tensional force acts on the beam. And in the shear span both moment and tensional forces are acting on the beam. p'Zj_ J.P/2 Z^ 1.55n 1- -In 1 I.5?.m ^ A Û.775P P/'c Figure 2 : The force applied on the beam and resulting moment and shear force diagrams Acui/2 Ad rs; !, Acui/2 t' D Q S Ol Fa = Gsi Ab X3* ci - Occi Acci + Ccui Acı Fcti - (Tcü Acti Figure 3 : The algorithm of the computer program Using the results obtained from the tests on materials, realistic matematical models are developed for the stress-strain relationships of the unconfined concrete under compression, confined concrete under compression, concrete under tension and reinforcement steel. In the preperation of the models of confined concrete and unconfined concrete under compression, Kent and Park Model is used. A bi-linear model is used for concrete in tension and a tri-linear model is used for steel. The input data for steel are fy, fgu, e^ e^ and Es. These models are used in a spread sheet program developed to calculate analytical moment-curvature relationship of reinfoced concrete cross-sections subjected to flexure. In this program the cross-section is is divided into 26 filaments and for each filament confined core and unconfined cover areas are defined. For a given strain at the extreme fiber in compression, the depth of neutral axis which satisfies the force equilibrium is found by trial. For each filament average stresses are calculated at the centroids of the unconfined and confined portions of the filament. In doing this, first the strain at the centroid of the filament is calculated by using the compatibility requirements. This centroidal strain is later used along with the approporiate concrete models to calculate stresses acting on the confined and unconfined portions of the filament. Finite concrete forces for confined and unconfined portions of the filaments are found by multiplying the stress by the corresponding areas. Fcui=Ocuj.Acuj and Fcc;=accj.ACci. Stresses in reinforcement at a given level is found by entering the stress-strain diagram of steel with the strain value found from the compatibility requirements. Steel force at that level is found by multiplying the stress found with the area of the reinforcement at that level, Fsj=osi.Asi. Moments are calculated using the forces acting on the filaments at different strain values at the extreme fiber in compression. The curvatures are calculated by dividing the strain of the extreme fiber to the depth of the natural axis (bc/x). A theorical moment-curvature diagram is drawn using these values. The algorithm of the program is demonstrated in the Figure 3. where only some typical finite forces are shown. To determine the behavior of the beams during loading, special measurement systems are used such as strain gauges and LVDT's (linear voltage differential transducers). A strain gauge is constructed by bonding a fine electric resistance wire or photographically etched metallic resistance foil to an electrical base using an appropriate bonding material and attaching gauge leads. 10 mm strain gauges are placed on the longitudinal reinforcement, 5 mm strain gauges are placed on the tranvesal reinforcement and 60 mm strain gauges are placed to the top and bottom surfaces of mid points of the beams. A strain gauge can be seen in the Figure 4. Gaoge length Figure 4 : A foil strain gauge The strain generated in the specimen is relayed through the base to the fine wire or foil, where expansion or contraction occurs. As a result, the fine wire or foil experiences a variation in resistance. This variation is exactly proportional to the strain. Normally the resistance change is very small and requires a Wheatstone bridge curcuit to convert it to voltage output The voltage output due to the strain is given as follows. Ae = E = - Ke 4R 4 In this equation, Ae is the voltage output, E is the exciting voltage, R is the gauge resistance, AR is the resistance change due to strain, K is the gauge factor and 6 is the strain measured. The strain gauge is connected to a strainmeter (i.e. data logger or switch box), which provides the Wheatstone bridge circuit and exciting voltage. LVDT's are used to measure the displacement of the specific points choosen on the beams. An LVDT is composed of a stroke that contacts to the point on the beam and a spring mechanism in which the stroke moves. This movement creates a magnetic area and this causes a voltage output. The voltage outputs from strain gauges and LVDT's are collected by a switch box and transfered to data logger. Data logger is used to convert analog voltage changes of LVDT's and strain gauges to digital values. This digital data can be printed from the built-in printer of the data logger or can be transferred to a personal computer and recorded by a program. The load is applied to the beams by a servohydrolic actuators which has 25 ton of xix loading capacity. The monotonic tests have been carried out by increasing the displacement in order to investigate the descending branch of force-displacement relations. The cyclic tests have been carried out using displacement control properties of the actuator. A cyclic load is applied three times for a displacement level. During the monotonic test, while the displacement was increasing, a sudden reduction of stiffness referred to the yielding displacement. In this test the yielding displacement is 15.54 mm with the load of 163.42 kN. The failure of the specimen is identified by the drop of the force after reaching a maximum value. The maximum force is 200.5 kN. At about 126.2 mm of vertical displacement the tests have been stopped due to security reasons. In the cyclic test, yielding displacement is observed at 16.32 mm of vertical displacement at the load of 170.25 kN. The failure of the beam is observed at the load of 191.32 kN. The test have been stopped at about 118 mm of vertical displacement. In both tests the ductility term is defined as 5 -5 n=- - L 5v where 8U is the displacement at the maximum force and 8y is the displacement at the yielding force. For the monotonic test ductility is calculated as 7.01 and for the cyclic test ductility is calculated as 5.44. Other data recorded from the strain gauges and transducers are presented graphically