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Prefabrike kolon kiriş birleşiminin elastik dönme redörünün hesabı

Prefabrike kolon kiriş birleşiminin elastik dönme redörünün hesabı

##### Dosyalar

##### Tarih

1996

##### Yazarlar

Çolak, Mustafa

##### Süreli Yayın başlığı

##### Süreli Yayın ISSN

##### Cilt Başlığı

##### Yayınevi

Fen Bilimleri Enstitüsü

##### Özet

Yüksek lisans tezi olarak sunulan bu çalışma üç ana bölümden oluşmaktadır. Çalışmada, Prefabrike Betonarme bir endüstri yapışırım kolon-kiriş birleşimi incelenerek, hesapta kullanılacak elastik dönme redörünün tayini amaçlanmıştır. Aynı birleşim ile ilgili önceden yapılmış deney çalışmasına yer verilerek, teorik çalışma ile deney çalışması karşılaştırılmıştır. Çalışmanın ilk bölümünde, Prefabrikasyon Teknolojisi tanıtılarak, tarihsel gelişimi, avantajları, kullanım alanları sıralanmış, Prefabrike Betonarme İskelet Sistemler başlığı altında tek ve çok açıklıktı endüstri yapılarının tasarım kriterleri açıklanmıştır. Çalışmada konu olan birleşime benzer bazı kolon-kiriş birleşim detayları literatürden incelenerek, şekillerle anlatılmıştır. Yan rijit düğüm noktaları başlığı altında, konu ile ilgili literatürde mevcut bazı çalışmalara yer verilerek, elastik birleşimlerle ilgili yapılmış teorik ve deneysel çalışmalar sonucunda elde edilen kabul edilebilir elastik dönme redörü formülü verilmiştir. Prefabrike betonarme düğüm noktalarının çeşitli açılardan incelenmesi ile ilgili, günümüze kadar yapılan çalışmalardan örnekler sunulmuştur. İkinci bölümde, örnek olarak ele alman Prefabrike Betonarme kolon-kiriş birleşimi incelenmiştir. Seçilen sistemin özellikleri tanıtılmış, birleşime neden olan etkenler açıklanmış, birleşim bölgesi sonlu dörtgen elemanlara bölünerek idealleştirilmiş ve düzlemi içindeki yükler etkisinde bir levha problemi olarak çözülmüştür. Hesap kabulleri ve yardımcı bilgisayar programı hakkında kısaca bilgi verilmiştir. Kolon-kiriş birleşimin elastik dönme redörü, iki farklı uygulama için hesapla tayin edilmiştir. Aynı amaçla daha önceden yapılmış deneysel çalışmanın adımlan bölümler halinde anlatılmıştır. İki farklı uygulama için bulunan hesap sonuçlan tablo ve grafikler yardımıyla sunulmuştur. Üçüncü bölümde ise ikinci bölümde verilen hesap sonuçlan değerlendirilmiş, deneysel çalışmada bulunan sonuçlarla karşılaştırılmış ve birleşimin kullanılabilir elastik dönme redörünün değeri hakkında önerilerde bulunulmuştur.

The aim of the study presented herein is to propose an approximate value for the elastic-rotational stiffness, to some accuracy, of the prefabricated concrete frame system which is under the experimental investigation in the laboratory scale experiment, along with the results which demonstrate the correspondance with the theoretical and experimental predictions. A widely applied system among the industrial structures where prefabrication technology utilized heavily has been chosen. For this system, a connection detail has been developed, the applicability of which has been evaluated by experimental and analytical studies. In the introduction part, theoretical background and the literature survey have been given briefly along with the purpose and the scope of the study. The definition of the prefabrication in the civil engineering field and the significant applications in the construction industry with increasing use of the techniques based on the advantages of the prefabrication have also been mentioned briefly. Prefabricated concrete-frame systems are classified as being defined in the literatures and the design criteria are depicted with the help of various figures. In general, the load-bearing system of the single story structures with large spans has three main types. They are frame, load bearing wall and the composite systems, respectively. The decision to choose the right one depends on many things, such as aesthetics, personal comfort, live loads, limitations or advantages of the structure and the serviceability form the construction system. Members of the prefabricated structures are based on the optimum serviceability, saving time and money. Members such as traditional brick, reformed or normal concrete load bearing walls, light-weight slabs, columns and load bearing facade elements, some of those may be used to construct the structure, for instance in the composite system. In the first chapter, connection details similar to the one under consideration are summarized briefly with the help of the figures. In static analysis, when frame or grill systems are analized, generally nodes connecting the members are assumed to be either complete rijid or hinged jomts. » However, connections at construction joints of the steel structures and the prefabricated concrete structures yield deformable rotations and connections are loosen due to either shrinkage or swelling effects as a result of the variational loading such as cyclic loading or variation of temparatures in members of the structure. Therefore, assumptions related to the joints in the static analysis do not reflect the reality. But, it is common to prescribe the behaviour of the construction joints as semi-rigid joints. This is an approximation that allows the engineer to define a new term, an elastic rotational stiffness. There are many experimental investigations and analytical studies conducted in the U.S.A, Japan and Turkey as well on this subject in the literature, and the main purpose of these studies is to verify the proposed solution and use it in different applications. Experimental studies satisfy the approximation that assumes the linear relationship between the applied moment and the corresponding rotation. This relationship is given by the equation M=R9, where M is the applied moment, R is used to define the semi-rigid stiffness and 9 indicates the rotation angle. The model used in the experimental investigation is idealized in finite element application by simplifying the column-beam connection as a plane problem for two different applications under different loading and bearing conditions. In the first application, epoxy with high adhesive property is not taken into account in the analysis of joints, while in the second application, impact of the epoxy on the force distribution over the elements implented in the joints is included. In the second chapter, the model used in the experimental study, computation procedure and assumptions are described briefly. Dimensions of the structural systems and loading play an important role to design the members. For the structures with short rigid columns and steep slope roofs of which the design load is not big, structure and span lengths are varied from 10 m. to 22 m. and 5 m. to 8 m., respectively. The height of the structure varies with respect to the cross-section of the columns and the loading conditions. For some systems of which have two or more than two spans, if point of inflection for the spans up to a certain span length is not far from the mid-column, to some extend, it is possible to cast the mid-column in a single piece. However, when span lengths are increased gradually, the point of the inflection of the system moves to somewhere in the span, mid-column cantilever system of which consists of two components namely column and the cantilever beam being fixed into the Cornell is generally casted separately. But, for columns of the single span frames, symmetrical loading is inevitable. In this study, under the light of the detail summarized above, 20 m. length of the structure with 6 m. span length and 6 m. height is chosen and analysis is carried out for one of construction joints in the beam-column connections. »1 In modelling stage, fictitious bars are placed horizontally in the construction joint are used to calculate the displacements between the column and the cantilever beam member. These fictitious bars take only axially acting compressional or tensile forces. Corresponding to the existence of the tensile forces on these fictitious bars, separation of the members at the joint may be decided. Elâstomeric bearings at the construction joint in which cantilever-beam is fitted into the Cornell are modelled by vertically designed fictitious bars which take only axial tensile and compressional forces. In this chapter, experimental study conducted previously are expounded. In the experimental study to find out the forces on the steel connectors, to evaluate the compression force caused deformations on the pressurized zone, the location of the resultant of the compressional stresses, failure loading level and the effect of the epoxy with high adhesive property on stress distribution are the main problems to figure out the behaviour of the connection. Experiment has been carried out on the floor in order to ensure easily, the stability of the experimental set-up under loading. In the numerical analysis, when type A in which epoxy has not been used is subjected to 20 KN. force at the begining. In the vertically connected adjacent surfaces at the joint, horizontally modeled fictitious bars under tension have been removed and the experiment under currently increasing loads is conducted. As a result of numerical analysis, in the vertical adjacent surfaces at the joint, the length change in each fictitious bars indicates the shape of the compressional regime, while in application B in which epoxy with the strong adhesive properties has been used is modeled by horizontal fictitious bars. Separation of the concrete and epoxy is controlled totally by the tensile strength of the concrete since the tensile strength of the epoxy is much greater than the one of the concrete in the experimental study. Therefore, for small P values, there is no separation between members at joint, but small displacements are monitored. As the increasing P value gradually approaches to a certain P limit value, members have been separated and deformations are continued at the limit value P. As a result of this separation, certain amount of the fictitious bars left in the compression zone. Analysis has been carried untitt a few of the fictitious bars left on that compression zone for the type A Experimental study with gradually increasing loads yields that there is a linear relationship between the applied moment and the rotation. In the third chapter, results obtained from experimental and analytical studies are utilized to interpret the each one of them and compare with each other. Calculation of the rotational stiffness factor of the prefabricated column-beam connection is performed first for the type A and the relationship of the applied moment and rotation is established. Xlll For this purpose, tensile bars in the construction joint under the constant load have been removed and only two single compressional bars have been left in the compressional zone, this indicates that the length of the compressional zone should be somewhere within the range of 5 cm. to 10 cm. This result demonstrates very good correspondance with the experimental study of the same beam-column connection of which the location of the resultant of the compressional stresses in the pressure caused deformation zone is located quite close to the connected adjacent edges with 9 cm. distance. Elastic rotational stiffiiess factor is evaluated approximately to be 90000 KNm/rad from M-0 curve of the type A. The elasticity modulus of the steel material which has the strongest influence on the value of the rotational stiffness has been observed throughout the alternate parametric study. Another important factor which influences the results is the physical properties of the bearing system. But, alternate parametric study shows that the values of the rotational stiflhess factors are very sensitive to the choice of the material elastic modulus. In the experimental study, as seen from the M-0 curves, one may deduce that the relationship between the applied moment and the rotation is nonlinear. This nonlinearity is mainly due to the settled parts of the bearing system and other deformations related to the connectors which hold the all parts of the connected beam-column system, but in the numeric analysis, because of this kind of effects, usually, are not taken into account so as to simplify the calculation algorithm, M-9 curve reflects strongly linear relationship. In experiments, the results obtained both from the experimental study and the numerical analysis start to demonstrate the incompatibility with the rotational deformations at the first loading-unloading cycle. Even, for the following loading, the system which experienced one loading unloading cycle demostrates much stiffer behaviour. The slopes of the M-0 curves for the first loading-unloading cycle and the reloading give us a very good prediction, in the case of this experimental study, the system under the consideration has been experienced large displacement at the very beginning. M-0 curve obtained from the numerical analysis shows similar shape with that obtained from the reloading experiment. In the numerical analysis of the system with epoxy, we suggested that the displacement of the connection almost depends on the material properties of the epoxy. Although, fictitious bars are used to simulate the epoxy, and they are also controlled by the tensile strength of the epoxy material as suggested, but the tensile strength of the concrete is found to be much less than the strength of the epoxy. Therefore, the concrete tensile strength became the control factor to conduct the analysis. XIV Under these circumstances, system shows highly stiff behaviour at the begining. However, for high P values, high tensile forces on the fictitious bars in the construction joint have been observed. This high tensile forces exceed the value of the concrete. Therefore the fictitious bars exceeding the tensile strength of the concrete have been removed and the experiment has been carried on with the constant loading up until three fictitious bars left in compression zone. M-0 curve for this experiment gives linear relation as seen in curves for type A. In the numerical analysis of the second experimental set, the effect of the epoxy is seen up to a certain P value, but for the following P values there is no influence over the behaviour of the system and also similarity between both set-up, type A and B can be easily distinguished. In general, typical errors due to the laboratory conditions, some deficiencies in the production and the assumptions result in small differences between the two sets. Although, it needs to be worked on with more experimental investigations the statical approach as to figure out the results and predictions seems a sound way. Finally, we may conclude that both studies, the numeric analysis and the experimental studies give valid results in an acceptable range and both results also reflect an indication of the general behaviour as expected.

The aim of the study presented herein is to propose an approximate value for the elastic-rotational stiffness, to some accuracy, of the prefabricated concrete frame system which is under the experimental investigation in the laboratory scale experiment, along with the results which demonstrate the correspondance with the theoretical and experimental predictions. A widely applied system among the industrial structures where prefabrication technology utilized heavily has been chosen. For this system, a connection detail has been developed, the applicability of which has been evaluated by experimental and analytical studies. In the introduction part, theoretical background and the literature survey have been given briefly along with the purpose and the scope of the study. The definition of the prefabrication in the civil engineering field and the significant applications in the construction industry with increasing use of the techniques based on the advantages of the prefabrication have also been mentioned briefly. Prefabricated concrete-frame systems are classified as being defined in the literatures and the design criteria are depicted with the help of various figures. In general, the load-bearing system of the single story structures with large spans has three main types. They are frame, load bearing wall and the composite systems, respectively. The decision to choose the right one depends on many things, such as aesthetics, personal comfort, live loads, limitations or advantages of the structure and the serviceability form the construction system. Members of the prefabricated structures are based on the optimum serviceability, saving time and money. Members such as traditional brick, reformed or normal concrete load bearing walls, light-weight slabs, columns and load bearing facade elements, some of those may be used to construct the structure, for instance in the composite system. In the first chapter, connection details similar to the one under consideration are summarized briefly with the help of the figures. In static analysis, when frame or grill systems are analized, generally nodes connecting the members are assumed to be either complete rijid or hinged jomts. » However, connections at construction joints of the steel structures and the prefabricated concrete structures yield deformable rotations and connections are loosen due to either shrinkage or swelling effects as a result of the variational loading such as cyclic loading or variation of temparatures in members of the structure. Therefore, assumptions related to the joints in the static analysis do not reflect the reality. But, it is common to prescribe the behaviour of the construction joints as semi-rigid joints. This is an approximation that allows the engineer to define a new term, an elastic rotational stiffness. There are many experimental investigations and analytical studies conducted in the U.S.A, Japan and Turkey as well on this subject in the literature, and the main purpose of these studies is to verify the proposed solution and use it in different applications. Experimental studies satisfy the approximation that assumes the linear relationship between the applied moment and the corresponding rotation. This relationship is given by the equation M=R9, where M is the applied moment, R is used to define the semi-rigid stiffness and 9 indicates the rotation angle. The model used in the experimental investigation is idealized in finite element application by simplifying the column-beam connection as a plane problem for two different applications under different loading and bearing conditions. In the first application, epoxy with high adhesive property is not taken into account in the analysis of joints, while in the second application, impact of the epoxy on the force distribution over the elements implented in the joints is included. In the second chapter, the model used in the experimental study, computation procedure and assumptions are described briefly. Dimensions of the structural systems and loading play an important role to design the members. For the structures with short rigid columns and steep slope roofs of which the design load is not big, structure and span lengths are varied from 10 m. to 22 m. and 5 m. to 8 m., respectively. The height of the structure varies with respect to the cross-section of the columns and the loading conditions. For some systems of which have two or more than two spans, if point of inflection for the spans up to a certain span length is not far from the mid-column, to some extend, it is possible to cast the mid-column in a single piece. However, when span lengths are increased gradually, the point of the inflection of the system moves to somewhere in the span, mid-column cantilever system of which consists of two components namely column and the cantilever beam being fixed into the Cornell is generally casted separately. But, for columns of the single span frames, symmetrical loading is inevitable. In this study, under the light of the detail summarized above, 20 m. length of the structure with 6 m. span length and 6 m. height is chosen and analysis is carried out for one of construction joints in the beam-column connections. »1 In modelling stage, fictitious bars are placed horizontally in the construction joint are used to calculate the displacements between the column and the cantilever beam member. These fictitious bars take only axially acting compressional or tensile forces. Corresponding to the existence of the tensile forces on these fictitious bars, separation of the members at the joint may be decided. Elâstomeric bearings at the construction joint in which cantilever-beam is fitted into the Cornell are modelled by vertically designed fictitious bars which take only axial tensile and compressional forces. In this chapter, experimental study conducted previously are expounded. In the experimental study to find out the forces on the steel connectors, to evaluate the compression force caused deformations on the pressurized zone, the location of the resultant of the compressional stresses, failure loading level and the effect of the epoxy with high adhesive property on stress distribution are the main problems to figure out the behaviour of the connection. Experiment has been carried out on the floor in order to ensure easily, the stability of the experimental set-up under loading. In the numerical analysis, when type A in which epoxy has not been used is subjected to 20 KN. force at the begining. In the vertically connected adjacent surfaces at the joint, horizontally modeled fictitious bars under tension have been removed and the experiment under currently increasing loads is conducted. As a result of numerical analysis, in the vertical adjacent surfaces at the joint, the length change in each fictitious bars indicates the shape of the compressional regime, while in application B in which epoxy with the strong adhesive properties has been used is modeled by horizontal fictitious bars. Separation of the concrete and epoxy is controlled totally by the tensile strength of the concrete since the tensile strength of the epoxy is much greater than the one of the concrete in the experimental study. Therefore, for small P values, there is no separation between members at joint, but small displacements are monitored. As the increasing P value gradually approaches to a certain P limit value, members have been separated and deformations are continued at the limit value P. As a result of this separation, certain amount of the fictitious bars left in the compression zone. Analysis has been carried untitt a few of the fictitious bars left on that compression zone for the type A Experimental study with gradually increasing loads yields that there is a linear relationship between the applied moment and the rotation. In the third chapter, results obtained from experimental and analytical studies are utilized to interpret the each one of them and compare with each other. Calculation of the rotational stiffness factor of the prefabricated column-beam connection is performed first for the type A and the relationship of the applied moment and rotation is established. Xlll For this purpose, tensile bars in the construction joint under the constant load have been removed and only two single compressional bars have been left in the compressional zone, this indicates that the length of the compressional zone should be somewhere within the range of 5 cm. to 10 cm. This result demonstrates very good correspondance with the experimental study of the same beam-column connection of which the location of the resultant of the compressional stresses in the pressure caused deformation zone is located quite close to the connected adjacent edges with 9 cm. distance. Elastic rotational stiffiiess factor is evaluated approximately to be 90000 KNm/rad from M-0 curve of the type A. The elasticity modulus of the steel material which has the strongest influence on the value of the rotational stiffness has been observed throughout the alternate parametric study. Another important factor which influences the results is the physical properties of the bearing system. But, alternate parametric study shows that the values of the rotational stiflhess factors are very sensitive to the choice of the material elastic modulus. In the experimental study, as seen from the M-0 curves, one may deduce that the relationship between the applied moment and the rotation is nonlinear. This nonlinearity is mainly due to the settled parts of the bearing system and other deformations related to the connectors which hold the all parts of the connected beam-column system, but in the numeric analysis, because of this kind of effects, usually, are not taken into account so as to simplify the calculation algorithm, M-9 curve reflects strongly linear relationship. In experiments, the results obtained both from the experimental study and the numerical analysis start to demonstrate the incompatibility with the rotational deformations at the first loading-unloading cycle. Even, for the following loading, the system which experienced one loading unloading cycle demostrates much stiffer behaviour. The slopes of the M-0 curves for the first loading-unloading cycle and the reloading give us a very good prediction, in the case of this experimental study, the system under the consideration has been experienced large displacement at the very beginning. M-0 curve obtained from the numerical analysis shows similar shape with that obtained from the reloading experiment. In the numerical analysis of the system with epoxy, we suggested that the displacement of the connection almost depends on the material properties of the epoxy. Although, fictitious bars are used to simulate the epoxy, and they are also controlled by the tensile strength of the epoxy material as suggested, but the tensile strength of the concrete is found to be much less than the strength of the epoxy. Therefore, the concrete tensile strength became the control factor to conduct the analysis. XIV Under these circumstances, system shows highly stiff behaviour at the begining. However, for high P values, high tensile forces on the fictitious bars in the construction joint have been observed. This high tensile forces exceed the value of the concrete. Therefore the fictitious bars exceeding the tensile strength of the concrete have been removed and the experiment has been carried on with the constant loading up until three fictitious bars left in compression zone. M-0 curve for this experiment gives linear relation as seen in curves for type A. In the numerical analysis of the second experimental set, the effect of the epoxy is seen up to a certain P value, but for the following P values there is no influence over the behaviour of the system and also similarity between both set-up, type A and B can be easily distinguished. In general, typical errors due to the laboratory conditions, some deficiencies in the production and the assumptions result in small differences between the two sets. Although, it needs to be worked on with more experimental investigations the statical approach as to figure out the results and predictions seems a sound way. Finally, we may conclude that both studies, the numeric analysis and the experimental studies give valid results in an acceptable range and both results also reflect an indication of the general behaviour as expected.

##### Açıklama

Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 1996

##### Anahtar kelimeler

İnşaat Mühendisliği,
Elastik dönme redörü,
Kiriş-kolon birleşimi,
Prefabrikasyon,
Engineering,
Elastic rotational stiffness,
Beam-column collection,
Prefabrication