Perdeli çerçeve sistemlerde temel dönmelerinin üst yapıya etkisi
Effect on the foundation rotations on the superstructure in the wall-frame systems
- Tez No: 39641
- Danışmanlar: PROF. DR. KAYA ÖZGEN
- Tez Türü: Doktora
- Konular: İnşaat Mühendisliği, Civil Engineering
- Anahtar Kelimeler: Elastik zemin, Elastoplastik davranış, Çerçeve sistemi, Elastic ground, Elastoplastic behavior, Frame system
- Yıl: 1994
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: Belirtilmemiş.
Özet
ÖZET Bu çalışmada elastik zemine oturan boşluklu perde sistemlerin elastik ve elasto-plastik analizi yapılmış ve çeşitli plastikleşme durumlarında kesit tesirlerini veren bağıntılar elde edilmiştir. Bunun yanında elastik zemine oturan perde-çerçeve sistemlerde temel dönme ve çökmelerinin üst yapının kesit tesirlerine etkileri matris- deplasman yöntemiyle sayısal olarak incelenmiştir. Birinci bölümde çalışmanın konusu, yapılan araştırmalar, kullanılan yöntemler ve varsayımlar belirtilmiştir. ikinci bölümde yüksekliği boyunca üçgen, düzgün yayılı yatay yüklemelerle birlikte tepede tekil yük etkisindeki boşluklu perdenin elastik ve elasto-plastik davranışları incelenmiştir. Üçüncü bölümde yine aynı yüklemeler altındaki sistemin kat kirişlerinden birinin daha rijit olması durumu dikkate alınarak elastik ve elasto-plastik davranışlarına ilişkin kesit etkileri bağlantıları elde edilmiştir. Çalışmanın dördüncü bölümünde H mertebe etkileri de dikkate alınarak boşluklu perdenin elastik davranışına ilişkin, esası ardışık yaklaşım yöntemine dayanan bir çözüm geliştirilmiştir. Beşinci bölümde uygulamada sıkça karşılaşılan 3 tip perde-çerçeve sistem ele alınarak bu sistemlere ilişkin geometri, yükleme durumları ve varsayımlar belirtilmiş, ayrıca matris-deplasman yöntemine ilişkin bağıntılar kısaca özetlenmiştir. Altına bölümde bulunan ve bilinen bağıntılar örnek sistemlere uygulanarak kesit etkileri ve diyagramları elde edilmiştir. Son bölümde elde edilen sonuçlar değerlendirilmiştir. ıx
Özet (Çeviri)
These four terms represent the relative displacement due to the bending of the walls, the relative displacement caused by the deformation of the laminas, the relative displacement due to the axial deformation of the walls, the relative settlement of the walls at the foundation respectively. From the equilibrium of moment consideration at any section, the following expression is obtained: M0(x) = -EI0^.+LT(x) Finally, the shear force intensity, q(x), in the connecting medium and the axial force, T(x), in the walls are related by: / » dT Eliminating the variables y(x), q(x) and replacing by e= x / H, following differential equation is obtained for the axial force, T(s): d2T de2 -a2T=-B2M0(s) where H2 = 12EI*bL / 'he3, a2 = Lfi' EI I V1+M<J H2 B2=^H2 / = /,+/, J_ 1_ J_ A~ A* A, For the loading considered, the external moment at any cross-section is given by: 7 wff2 M0(e) = FH(I-e)+-PH2(l-e)2+--(e3-3e+2) 2 6 A solution to the differential equation with the applied external moment expression is given by T(s) = Bshas+Cchas + T/e) where the particular integral is given by: fi' Tp(e) = -2 a Pff“ wH2 3 W FH(l-e)+ (1-sf + (e -3s + 2)+-y(P + ws) 2 6 a The values of the arbitrary constant B and C are to be determined by the boundary conditions of the problem: Xllregions over the height of the structure. If the stiffening beam is at the lower regions; one upper and two lower elastic and one middle plastic zones are developed in the system. 7- The flexible soil conditions bring the second order moments to an important case, and causes great moment increments at the base of the wall espacially. As the base soil becomes relatively rigid, these effects get down as to be neglected. However in the second order solution, with reducing the foundation and soil rigidity, it is seen that the axial forces decrease and the moments increase at the base of the wall. These results are opposite of the first degree solutions. 8- In wall-frame systems which are used commonly in practice, when the walls are on flexible soil the wall moments decrease considerably. Therefore, great moment increments occur at frame struts due to influences remaining from the wall. As expected, these effects are not seen as the soil becomes rigid. From all these, it is seen that soil, structure and foundation must be taken together into account in the analysis of structural systems. It appears that reversing poor soils into a better state is very important for the behaviour of the system. Hence, the importance of soil investigations is also seen clearly. xvxixThese four terms represent the relative displacement due to the bending of the walls, the relative displacement caused by the deformation of the laminas, the relative displacement due to the axial deformation of the walls, the relative settlement of the walls at the foundation respectively. From the equilibrium of moment consideration at any section, the following expression is obtained: M0(x) = -EI0^.+LT(x) Finally, the shear force intensity, q(x), in the connecting medium and the axial force, T(x), in the walls are related by: / » dT Eliminating the variables y(x), q(x) and replacing by e= x / H, following differential equation is obtained for the axial force, T(s): d2T de2 -a2T=-B2M0(s) where H2 = 12EI*bL / 'he3, a2 = Lfi' EI I V1+M<J H2 B2=^H2 / = /,+/, J_ 1_ J_ A~ A* A, For the loading considered, the external moment at any cross-section is given by: 7 wff2 M0(e) = FH(I-e)+-PH2(l-e)2+--(e3-3e+2) 2 6 A solution to the differential equation with the applied external moment expression is given by T(s) = Bshas+Cchas + T/e) where the particular integral is given by: fi' Tp(e) = -2 a Pff”wH2 3 W FH(l-e)+ (1-sf + (e -3s + 2)+-y(P + ws) 2 6 a The values of the arbitrary constant B and C are to be determined by the boundary conditions of the problem: Xllregions over the height of the structure. If the stiffening beam is at the lower regions; one upper and two lower elastic and one middle plastic zones are developed in the system. 7- The flexible soil conditions bring the second order moments to an important case, and causes great moment increments at the base of the wall espacially. As the base soil becomes relatively rigid, these effects get down as to be neglected. However in the second order solution, with reducing the foundation and soil rigidity, it is seen that the axial forces decrease and the moments increase at the base of the wall. These results are opposite of the first degree solutions. 8- In wall-frame systems which are used commonly in practice, when the walls are on flexible soil the wall moments decrease considerably. Therefore, great moment increments occur at frame struts due to influences remaining from the wall. As expected, these effects are not seen as the soil becomes rigid. From all these, it is seen that soil, structure and foundation must be taken together into account in the analysis of structural systems. It appears that reversing poor soils into a better state is very important for the behaviour of the system. Hence, the importance of soil investigations is also seen clearly. xvxixÖZET Bu çalışmada elastik zemine oturan boşluklu perde sistemlerin elastik ve elasto-plastik analizi yapılmış ve çeşitli plastikleşme durumlarında kesit tesirlerini veren bağıntılar elde edilmiştir. Bunun yanında elastik zemine oturan perde-çerçeve sistemlerde temel dönme ve çökmelerinin üst yapının kesit tesirlerine etkileri matris- deplasman yöntemiyle sayısal olarak incelenmiştir. Birinci bölümde çalışmanın konusu, yapılan araştırmalar, kullanılan yöntemler ve varsayımlar belirtilmiştir. İkinci bölümde yüksekliği boyunca üçgen, düzgün yayılı yatay yüklemelerle birlikte tepede tekil yük etkisindeki boşluklu perdenin elastik ve elasto-plastik davranışları incelenmiştir. Üçüncü bölümde yine aynı yüklemeler altındaki sistemin kat kirişlerinden birinin daha rijit olması durumu dikkate alınarak elastik ve elasto-plastik davranışlarına ilişkin kesit etkileri bağlantıları elde edilmiştir. Çalışmanın dördüncü bölümünde H mertebe etkileri de dikkate alınarak boşluklu perdenin elastik davranışına ilişkin, esası ardışık yaklaşım yöntemine dayanan bir çözüm geliştirilmiştir. Beşinci bölümde uygulamada sıkça karşılaşılan 3 tip perde-çerçeve sistem ele alınarak bu sistemlere ilişkin geometri, yükleme durumları ve varsayımlar belirtilmiş, ayrıca matris-deplasman yöntemine ilişkin bağıntılar kısaca özetlenmiştir. Altına bölümde bulunan ve bilinen bağıntılar örnek sistemlere uygulanarak kesit etkileri ve diyagramları elde edilmiştir. Son bölümde elde edilen sonuçlar değerlendirilmiştir. ıxthe moment diagram of the walls and struts in the wall-frame systems have been calculated. In the seventh chapter the main results of the study have been summarized as follows: 1- Foundation type plays an important role on the behaviour of shear walls under the poor soil conditions: For example, in the case where the foundation of the lateral loaded shear wall is continuous, great increments in the bending moments (M) are seen while axial force (Tq) at the base of the wall decreases according to single foundation case. As the foundation soil is relatively stiff, this effect is also decreases because of the decrease of the foundation rotations, and falls down to the zero under rigid soil conditions. 2- For single foundations on a poor soil, with increasing axial force (Tq) at the base of the coupled shear wall, the moments becomes lower. This ratio decrease is greater than the ration of the incerement in the axial force. In the continuous foundation formation, a completely opposite case occurs; the axial force decreases and the moment increases at the base of the wall. 3- In the elasto-plastic behaviour of coupled shear walls, three different plastification states develop over the height of the structure: a) State-I consists of an upper elastic, middle plastic, lover elastic zone; it occurs as the result of relatively stiff soil conditions. b) State-II consists of a lower plastic, upper elastic zones; it occurs as the result of either poor soil conditions or in a system which the flexural regidity of coupling beam is big enough. c) State-m consists of la lower elastic, upper plastic zones; it develops under the rigit soil, continuouns foundation conditions and in the system which the flexural rigidity of coupling beams are relatively small. 4- It can be said that optimal solution can be achieved by installing the stiffening beam at about 0.2 to 0.5 of the structural height in the case where one of the floor beams is relatively stiff. However, installing the stiffening beam appears to be a more suitable solution at the lower zone if the base soil is poor, and at the middle zone if the base soil is rigid. 5- When one of the floor beams is relatively rigid, there are again three different plastification states in the system. The foundation type, soil conditions, coupling beam rigidity and the location of stiffening beam determine these cases. 6- In the case where the stiffening beam is at the middle zone, when the structure is loaded beyond the elastic range, one middle plastic region, which contains this beam, is formed together with an upper and lower elastic zone. Response type of elasto- plastic range, which contains a middle plastic zone bounded by two upper and one lower elasti zones, occurs in the case where the stiffening beam is at the upper xviiregions over the height of the structure. If the stiffening beam is at the lower regions; one upper and two lower elastic and one middle plastic zones are developed in the system. 7- The flexible soil conditions bring the second order moments to an important case, and causes great moment increments at the base of the wall espacially. As the base soil becomes relatively rigid, these effects get down as to be neglected. However in the second order solution, with reducing the foundation and soil rigidity, it is seen that the axial forces decrease and the moments increase at the base of the wall. These results are opposite of the first degree solutions. 8- In wall-frame systems which are used commonly in practice, when the walls are on flexible soil the wall moments decrease considerably. Therefore, great moment increments occur at frame struts due to influences remaining from the wall. As expected, these effects are not seen as the soil becomes rigid. From all these, it is seen that soil, structure and foundation must be taken together into account in the analysis of structural systems. It appears that reversing poor soils into a better state is very important for the behaviour of the system. Hence, the importance of soil investigations is also seen clearly. xvxixthe moment diagram of the walls and struts in the wall-frame systems have been calculated. In the seventh chapter the main results of the study have been summarized as follows: 1- Foundation type plays an important role on the behaviour of shear walls under the poor soil conditions: For example, in the case where the foundation of the lateral loaded shear wall is continuous, great increments in the bending moments (M) are seen while axial force (Tq) at the base of the wall decreases according to single foundation case. As the foundation soil is relatively stiff, this effect is also decreases because of the decrease of the foundation rotations, and falls down to the zero under rigid soil conditions. 2- For single foundations on a poor soil, with increasing axial force (Tq) at the base of the coupled shear wall, the moments becomes lower. This ratio decrease is greater than the ration of the incerement in the axial force. In the continuous foundation formation, a completely opposite case occurs; the axial force decreases and the moment increases at the base of the wall. 3- In the elasto-plastic behaviour of coupled shear walls, three different plastification states develop over the height of the structure: a) State-I consists of an upper elastic, middle plastic, lover elastic zone; it occurs as the result of relatively stiff soil conditions. b) State-II consists of a lower plastic, upper elastic zones; it occurs as the result of either poor soil conditions or in a system which the flexural regidity of coupling beam is big enough. c) State-m consists of la lower elastic, upper plastic zones; it develops under the rigit soil, continuouns foundation conditions and in the system which the flexural rigidity of coupling beams are relatively small. 4- It can be said that optimal solution can be achieved by installing the stiffening beam at about 0.2 to 0.5 of the structural height in the case where one of the floor beams is relatively stiff. However, installing the stiffening beam appears to be a more suitable solution at the lower zone if the base soil is poor, and at the middle zone if the base soil is rigid. 5- When one of the floor beams is relatively rigid, there are again three different plastification states in the system. The foundation type, soil conditions, coupling beam rigidity and the location of stiffening beam determine these cases. 6- In the case where the stiffening beam is at the middle zone, when the structure is loaded beyond the elastic range, one middle plastic region, which contains this beam, is formed together with an upper and lower elastic zone. Response type of elasto- plastic range, which contains a middle plastic zone bounded by two upper and one lower elasti zones, occurs in the case where the stiffening beam is at the upper xviiregions over the height of the structure. If the stiffening beam is at the lower regions; one upper and two lower elastic and one middle plastic zones are developed in the system. 7- The flexible soil conditions bring the second order moments to an important case, and causes great moment increments at the base of the wall espacially. As the base soil becomes relatively rigid, these effects get down as to be neglected. However in the second order solution, with reducing the foundation and soil rigidity, it is seen that the axial forces decrease and the moments increase at the base of the wall. These results are opposite of the first degree solutions. 8- In wall-frame systems which are used commonly in practice, when the walls are on flexible soil the wall moments decrease considerably. Therefore, great moment increments occur at frame struts due to influences remaining from the wall. As expected, these effects are not seen as the soil becomes rigid. From all these, it is seen that soil, structure and foundation must be taken together into account in the analysis of structural systems. It appears that reversing poor soils into a better state is very important for the behaviour of the system. Hence, the importance of soil investigations is also seen clearly. xvxix
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