Burulmalı bağlaşık çok katlı yapıların elastik deprem analizi
Elastic earthquake analysis torsionally coupled multistorey buildings
- Tez No: 46410
- Danışmanlar: DOÇ.DR. NECMETTİN GÜNDÜZ
- Tez Türü: Yüksek Lisans
- Konular: İnşaat Mühendisliği, Civil Engineering
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 1995
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 102
Özet
SUMMARY ELASTIC EARTHQUAKE ANALYSIS TORSIONALLY COUPLED MULTISTOREY BUILDINGS It is usual to consider planar models of the structure in each of the two orthogonal directions and to independently analyze the response of each model to the in plan horizontal component of ground motion. Analysis on this basis is strictly valid only for buildings with coincident centre of mass and resistance. Multistorey buildings with eccentric centers of mass and resistance requires three dimensional analysis, even when the motion is uniform over the base. In addition to torsion in a story due to any known eccentric of the center of mass with respect to the center of rigidity, and even in nominally symmetrical buildings, codes require that a torsional moment corresponding to a minimum eccentricity be considered in the design of vertical lateral-load-resisting elements. This“ accidental eccentricity ”is intented to account for such factors as the rotational component of ground motion, unaccounted for effects due to unfavorable distribution of dead and live load masses, and differences betweencomputed and actual values of stiffnesses and yield strengths. This study consist of six chapters. In the first chapter the subject and the introduction is given. In chapter two the assumptions for the method for computating the tall buildings which have orthogonal unsymmetrical moment resistings frames under the static lateral loads, guidelines of codes about minimum eccentricity for torsional effect are given, and one example has been solved. The third chapter consist of an approximate method for the elastic earthquake analysis of the idealized one storey building which is torsionally coupled. In the fourth chapter, the approximate method is applicated to the particular class of multistorey building with torsional effects. And for application one example has been made. In the fifth chapter an alternative is given for the SRSS ( square root of sum of squares method in seismic analysis. In the sixth chapter conclusion of the study are explained. VHl
Özet (Çeviri)
SUMMARY ELASTIC EARTHQUAKE ANALYSIS TORSIONALLY COUPLED MULTISTOREY BUILDINGS It is usual to consider planar models of the structure in each of the two orthogonal directions and to independently analyze the response of each model to the in plan horizontal component of ground motion. Analysis on this basis is strictly valid only for buildings with coincident centre of mass and resistance. Multistorey buildings with eccentric centers of mass and resistance requires three dimensional analysis, even when the motion is uniform over the base. In addition to torsion in a story due to any known eccentric of the center of mass with respect to the center of rigidity, and even in nominally symmetrical buildings, codes require that a torsional moment corresponding to a minimum eccentricity be considered in the design of vertical lateral-load-resisting elements. This“ accidental eccentricity ”is intented to account for such factors as the rotational component of ground motion, unaccounted for effects due to unfavorable distribution of dead and live load masses, and differences betweencomputed and actual values of stiffnesses and yield strengths. This study consist of six chapters. In the first chapter the subject and the introduction is given. In chapter two the assumptions for the method for computating the tall buildings which have orthogonal unsymmetrical moment resistings frames under the static lateral loads, guidelines of codes about minimum eccentricity for torsional effect are given, and one example has been solved. The third chapter consist of an approximate method for the elastic earthquake analysis of the idealized one storey building which is torsionally coupled. In the fourth chapter, the approximate method is applicated to the particular class of multistorey building with torsional effects. And for application one example has been made. In the fifth chapter an alternative is given for the SRSS ( square root of sum of squares method in seismic analysis. In the sixth chapter conclusion of the study are explained. VHlTorsion is normally assumed to occur when the centroid of rigidity of the various vertical resisting elemente in a story fails to coincide with the center of gravity. The distance between the two center, called the eccentricity e, times the amount of lateral force is a torsional moment that must be resisted in addition to and simultaneously with the normal design lateral forces. Torsion is simply a tvvisting about the vertical axis. A buiding has natural torsional modes in addition to its translational modes. it is desirable to eliminate torsion as much as possible by achieving a design with liftle ör no eccentricity. However, some torsion may develop accidentally and provisions should be made for it. Turkey code 1975 and ANSI-82 requires only that the 5% eccentricity be based of the building perpendicular to the direction of the applied forces. The UBS requires diaghram-connected shear resisting elemente to be designed for an accidental horizontal torsion corresponding to an eccentricity of 5% of the minimum building dimension between the centers of mass and rigidity at any level. SEAOC-90, UBC-91, BOCA-87, EUROCODE NO 8-1984 codes which are gıven require that a torsional moment corresponding to a minimum eccentricity be considered in the design of vertical lateral load resisting elemente. in the method for computing building which have orthogonal unsymmetrical moment resisting frames under the static lateral loads, material is homogen, isotropic and linear elastic, the floors are infinitely rigid in their planes, the frames are shear frames, vertical resisting elemente are orthogonal, and rigid deck supported on massless axially in extensible columns and walls, are assumed. The additional shears due to horizontal torsional momente may be calculated approximately by assuming the vertical elemente at each story to be fixed at their ends to parallel rigid plates. The torsional shear force acting on each element may then be taken as proportional to ite lateral stiffhess and ite distance from the center of rigidity of the story considered. These torsional shears are to be added to the shears due to lateral loading ör motion. For application öne example have been made. The lateral ör translational and torsional motions of the structure are coupled if the centre of mass and resistance is not coincide. Analysis of torsionally coupled building requires that in additional to the two translational degrees of freedom, the torsional degree of freedom be included for each floor. Most of the previous work on the coupled lateral torsional response of buildings to earthquakes has been based on a shear beam idealization of the structure (e.g., Tso and Meng 1982 ; Rutenberg 1978). i.\in this part of this study, a simpler method relative to the standart procedures of dynamic analysis is presented for elastic analysis of torsionally coupled buidings by taking advantage of features characteristic of many multistorey buildings : a-) Ali floors of the building have essentially the same geometry in plane and the same locations for columns and shear walls. b-)The ratio of the story stiffhesses in x and y directions is about the same for ali stories. in this simpler method, the forces developed in the torsionally coupled building are expressed in terms of the forces in a corresponding torsionally uncoupled system ( a system with coincident centers of mass and resistance with ali other properties identical to the actual building ) and those in an associated öne story torsionally coupled system. The special class of building is assumed to satisfy the following restrictions: a-) The prencipal axes of resistance for ali the stories are identically oriented, along the x and y axes, b-) The center of mass of the floor ali lie on öne vertical axis, c-) Ali floors have the same radius of gyration r about the vertical axis through the center of mass and ratio of the three stifrhess quantities translational stiffhesses in x and y direction, and torsional stifrhess for any story are independent of the story number. d-) The center of resistance of the stories ali lie on another vertical axis. The natural frequencies and the mode shapes for coupled lateral torsional motions of the class of multistory buildings are described earliear can, therefore be determined in three steps: 1-) Solve an eigenvalue problem of order N to obtain the frequencies and the mode shapes for the corresponding torsionally uncoupled system, b-) Solve an eigenvalue problem of order 3 to obtain the normalized frequencies and the mode shapes of the associated öne story system, c-)Compute natural frequencies and mode shapes of the torsionally coupled system from the results of steps before. The possibility of such simplification in calculation of natural frequencies and mode shapes for a class of building was apparently first noticed by Shiga [ 18 ] and then by hoerner [ 19]. XThe sequence of steps in the analysis of response of a N story buılding to the ground motion component along the x principal axis of resistance are summarized as follows [ 3 ]: 1-) Define the corresponding uncoupled system : a system with coincident centers of mass and resistance, but ali other properties identical to the actual system. 2-) Analyze the vibration properties of the first j modes of the torsionally uncoupled system defined in step l for motion in the x direction by solving the eigenvalue problem of order N. 3-) Define the öne storey system associated with the j th group of three coupled vibration modes as having the properties defined. 4-) Solve an eigenvalue problem of order 3 for each of the associated öne storey system defined in steps 3, to determine the vibration frequencies and the mode shapes. 5-) Determine the maximum forces at the floor levels for nj modes of vibration of the N storey torsionally coupled system. 6-) Compute for each of the nj modes of vibration to be included, the maximum values of any desired storey force by stsandart statics procedures from the floor level forces computed to step 5 for that mode. 7-) Compute the maximum of the total value of any desired storey force by combining the values of modal maxima for that force by special combination tecnique. To illustrate the application and accuracy of this procedure öne numerical example are presented. For the comparison the results, the same problem modelling with rigid diaphragm floors is solved using the time history and response spectrum options of SAP90 [20]. it is well known that the application of the square root of sum of squares (SRSS) method in seismic analysis for combining modal maxima can cause signifıcant errors especially for torsionally coupled multıstorey buildings. A complete quadratic combination (CQC) method is proposed which reduces errors in modal combination [ 4 ]. xiThe CQC method only involves a small increas in numerical effort, it is recommended that the new approach be used as a replacement for the SRSS method in ali response spectrum calculations. it should be pointed out that a method similar to the CQC method was first proposed by Rosenblueth and Elorduy in 1969 [ 16 ]. in the last chapter conclusions of the study are explained.y are explained. VHl
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