Düzensiz yapıların dinamik hesabı kolon taşıyan konsollar
Design of irregular buildings under earthquake forces-cantilever beams supporting columns
- Tez No: 55688
- Danışmanlar: PROF. DR. FARUK KARADOĞAN
- Tez Türü: Yüksek Lisans
- Konular: İnşaat Mühendisliği, Civil Engineering
- Anahtar Kelimeler: Deprem yönetmelikleri, Dinamik analiz, Konsol kirişler, Yönetmelikler, Earthquake regulations, Dynamic analysis, Cantilever beams, Regulations
- Yıl: 1996
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: Belirtilmemiş.
Özet
Bu çalışmada kolon taşıyan konsollardan oluşan düzensiz bir yapının statik ve betonarme hesabı yapılmış daha sonra yapının deprem altındaki davranışı incelenmiştir. Statik hesapta açı yöntemi ile ön boyutlandırma, sabit yükler için hesap, ve hareketli yükler için ayrı ayrı hesaplar yapılmıştır. Daha sonra 1975 Deprem Yönetmeliğine göre yapıya etkiyecek yatay yükler bulunup bu yükler altındaki kesit tesirleri belirlenmiştir. Bu hesaplar sonucu elde edilen değerler yönetmeliklere göre düzenlenerek en elverişsiz kesit tesirleri bulunmuştur. Üçüncü bölümde, en elverişsiz kesit tesirleri bulunan sistemin betonarme hesabı yapılmıştır. Betonarme hesabı sonucu elde edilen donatı değerleri kiriş ve kolon kesit şekillerinde verilmiştir. Dördüncü bölümde, sistemin serbest titreşimi ve zorlanmış titreşimi incelenmiştir. Öncelikle serbest titreşime ait mod şekilleri bulunmuş ve daha sonra zorlanmış titreşimde bu mod şekillerine karşı gelen yük değerleri belirlenmiştir. Modların süperpozisyonu yöntemi ile de kesitlere gelen en muhtemel kesit zorları belirlenmiştir. Daha sonra Elcentro 1940 ve Latino Americano Tower deprem kayıtları ile zaman artırımı metodlarından Lineer ivme ve Runge Kutta metodları kullanılarak sistemin bu deprem kayıtları altındaki davranışı incelenmiştir.
Özet (Çeviri)
in structural engineering, both safety and economic factors are considered in the design of structures, för it is known that these two basic factors considerably effect each other. Due to the development of structural analysis methods and computer technology, the behavior of structures is determined more precisely. Therefore, the problem of economical design becomes more important. For this reason, structural engineers use the design methods which consider both material and geometrical non-linearities. This study consists of three majör parts: Statical Analysis of Irregular Buildings, Reinforced Concrete Design of Buildings, and Dynamic and Semi-Dynamic Procedures and their Comparisons. in the first part, the analysis of a two-story irregular concrete frame subjected to various combinations of dead and live loads is presented. The preliminary cross-sectional dimension of the frame has been determined through the utilization of the Slope-deflection Method. Then, predesigned structure has been analyzed by the same method under dead loads and live loads respectively. At the end, the predesigned structure subjected to lateral load has been analyzed in accordance with 1975 Specifications for Structures to be Built in Disaster Areas by the same method used for the preliminary design. The dimensions of the critical cross-sections obtained from the preliminary analysis are checked under the most unsuitable loading conditions as are some combinations which consider different external effects acting in certain proportions according to Turkish Design Code. in this study, it is observed that the most unsuitable loading condition is obtained from the folloving combination: 1.4*6 + 1.6*Q where G: Dead weight Q: Live load xiiiin the second part of the work, reinforced concrete design for the system has been made according to the most unsuitable cross-sectional effects. The placement of the reinforcing bars for the cross-sectional areas for columns are also given at the end of this part. The third part of the work consists of the solution of frames by dynamic methods and its comparison to the loads found by using 1975 Specifications for Structures to be Built in Disaster Areas. Generally, in order to determine the response of the structures caused by an earthguake, the dynamic approaches are used. in semi-dynamic procedures, fictitious static loads due to the first natural period (specific) of the structure are taken into account and so the dynamic problem turns into an eguivalent static problem. The method used in this thesis is the method of the Modal Superposition, which is öne of dynamic procedures. Modal Superposition is a method in which the eguations of motions are transferred from a set of n simultaneous differential eguations to a set of n independent eguations by the use of so-called normal coordinates. These eguations are solved for the response of each mode and the total response of the system is obtained by superposing individual solutions. in the Method of Modal Superposition, the shapes and the periods of the structures normal modes, and in the semi- dynamic procedures the natural period should be known. in order to find the natural period, various methods are developed, such as; the Stodolo-Vianello Method, The Rayleigh Ritz Method. in the dynamic procedure studied in this thesis, frequencies and corresponding mode shapes have been calculated using Stodola-Vienola method. For this purpose a computer program, STODOLA.BAS, has been written. After calculating the mode shapes and freguencies, the loads for forced vibration have been obtained by using gı = mi*di*o>2 eguation. The Modal Superposition Method has been used to obtain the earthguake forces. in the Modal Superposition Method, for every mode there is a natural period and displacement vector. The main system vibrates according to proper Superposition of these displacement modes. The participation factors determine the natural percentage of the contribution mode of vibration. For the natural period value of each mode and accepted damping percentage, the Sa acceleration spectrum value is read from the ground's acceleration spectrum curves drawn for Elcentro 1940. Then, the earthguake force is calculated from the definition of force formula. Generally, the maximum value for some normal modes can be determined as the sguare root of the addition of the sguares (namely the root-mean-square method). xivin the 1975 Specifications for Structures to be Built in Disaster Areas, the effects of earthguakes are taken as horizontal static loads acting at floor levels. in dimensioning the structural elements against earthguake loading, the total static horizontal load coming to the structure is calculated by the given F-force formula. F force, which is calculated according to the structure's natural period for first normal mode, is then distributed to the storey along the height. in practice, the horizontal loads can be calculated by dynamic ör semi-dynamic methods. The ductility factor can be determined according to the type and the geometry of the system as well as the reinforcement of the cross sections. in the last part, Elcentro 1940 NS and Latino Americano Tower earthguakes' records have been applied to the structure to get the actual behavior of the system under an earthguake. First of ali we have to write the eguation of motion for the system. The coupled eguation of motion can be written in the following form: Mxx+Cxx+Kxx= -M x p« in order to obtain the uncoupled eguation of motion the above eguation must be rewritten in the following form: MM-Mı [MM,[Î],+(cM,[ j],+[*]tö,m, = -[A/][C/]& [<[A/M[f],+«lcl[«iı[5],+«M Mimi - -«MM* [î],+«[cW[#]ı+k]m, = -W,[M]lu]3*“f(l) l \2çma)w ooo Tt(1) l fû,”'2 ooo Tt'“ ~ f”O 2Çwo>w OO tmO ö>'“2 O O t<2) + ooo+ooo f<*> L O00 2£”“û>”“_.İ”(J“_ L O 00 û)”“'ir**'. ”d>“ o”<PIJ <D'“TM, o o o Ti”O“ <D”«Dlv O1* O M* O 01.. <0“ <D;I O* <D/W O O Mİ O l O”1 (D“1 O* O**i O O O M.Ll. where; O is the normalized modal displacement vector, and OT is the transpose of the normalized modal displacement vector. XVThen the problem converges to the solution of the equation of motion for a single degree of freedom system. Coupled equation of motion is solved by using step by step integration methods to obtain the displacements of the system under earthquake records. In order to solve the coupled equation of motion the damping matrix must be determined. For this purpose proportional viscous damping matrix has been constructed. Clearly the simplest way to formulate a proportional damping matrix is to make it proportional to either the mass or stiffness matrix because the undamped mode shapes are orthogonal with respect to each of these. Thus the damping matrix might be given by c = a0xm or c = axxk in which the proportionality constants a0 and ax have units of sec”1 and sec, respectively. These are called mass proportional and stiffness proportional damping, and the damping behavior associated with them may be recognized by evaluating the generalized modal damping value for each. Then we can obtain the following expressions: sn = a0/(2xcon) or En = a!X(an/2 where; sn is damping ratio, and (0n is the frequency These expressions show that for mass proportional damping, the damping ratio is inversely proportional to the frequency while for stiffness proportional damping it is directly in proportion with the frequency. In this regard it is important to note that the dynamic response generally will include contributions from all N modes even though only a limited number of modes are included in the uncoupled equations of motion. Thus, neither of these types of damping matrix is suitable for use with multidegree of freedom (MDOF) system in which the frequencies of the significant modes span a wide range because the relative amplitudes of the different modes will be seriously distorted by inappropriate damping ratios. If it is assumed that the damping is proportional to a combination of the mass and stiffness matrices, we can obtain the following equations : c = a0xm + aixk 6n = a0/(2xcan) + aiXon/2 Now it is apparent that the two damping factors a0 and ai, can be evaluated by the solution of a pair of simultaneous xviequations if the damping ratios 8m and en associated with two specific frequencies eom/ con are known. In applying this proportional damping matrix procedure in practice, it is recommended that com generally be taken as the fundamental frequency of the MDOF system and that <an be set among the higher frequencies of the modes that contribute significantly to the dynamic response. When constructing the damping matrix for the system first and second modes' frequencies have been used. After the construction of proportional damping matrix, Linear Acceleration and Runge-Kutta step by step integration methods have been used to solve the coupled equation of motion. At first, these two methods have been compared in order to see which one of them is more stable for this system. After using these two methods for At=0.04 sec and At=0.02 sec, it's seen that Runge-Kutta method is more stable. Linear Acceleration method proves instability especially under long time periods. Because of this the Runge-Kutta method is used for the solution of the coupled equation of motion. Four different conditions have been taken into account to evaluate the response of the system to the earthquake records. For this purpose the stiffness of the first floor columns have been increased and decreased and the results have been compared to the real system. This study has been made to evaluate the pounding (also known as battering or hammering) effect when, by any reason, the stiffness matrix of the system is changed. When the stiffness matrix is decreased the maximum displacements of the system becomes higher than the real system. At the end, relative displacements of the floors have been checked to evaluate weather it is under the limit values or not. For the second floor, the relative displacement is seen to be higher than the limit value during the response of the system to the used earthquakes' records.
Benzer Tezler
- Planda düzensiz betonarme bir yapının düşey ve yatay yükler altında davranışının incelenmesi
Assessment of an irregular reinforced concrete building under vertical and horizontal loads
CİHAN NAM
- Planda düzensiz yapılarda kat döşemelerinin deprem etkileri altındaki davranışı
Seismic behaviour of floor slabs in multy-story buildings with plan irregulality
MUSTAFA SERDAR ATABEY
- Planda düzensiz yapıların deprem davranışının incelenmesi
Başlık çevirisi yok
MEHMET YAŞAR GÜR
Yüksek Lisans
Türkçe
1998
İnşaat Mühendisliğiİstanbul Teknik ÜniversitesiYapı Mühendisliği Bilim Dalı
PROF. DR. ZEKAİ CELEP
- Planda düzensiz çok katlı kaset döşemeli bir betonarme yapının boyutlandırılması
Design of an irregular multi-storey building
GÖKHAN SİVRİ
Yüksek Lisans
Türkçe
1999
İnşaat Mühendisliğiİstanbul Teknik Üniversitesiİnşaat Mühendisliği Ana Bilim Dalı
PROF. DR. ZEKAİ CELEP