Taşıyıcı sistemi düzensiz çok katlı bir yapının projelendirilmesi - Cin, Şenol (Fen Bilimleri Enstitüsü, 1998)
Yüksek lisans tezi olarak, Prof. Dr. Zeki HASGÜR yönetiminde taşıyıcı sistemi düşeyde düzensiz olan perde ve çerçevelerden oluşan 7 katlı bir yapının yatay ve düşey yükler altında statik ve betonarme hesaplan yapılmıştır. Taşıyıcı sistemin düzensizliği, düşey süreksizlik olup 5. katta kenar ve köşe kolonların eksenlerinin 4.kat kolonlarına mesnetli konsollara oturmasıyla eksenlerin kaydırılması şeklinde meydana gelmiştir. Yapının statik hesaplarında üç boyutlu model oluşturularak SAP90 (yapı analiz programı ) bilgisayar programı yardım ile statik ve dinamik hesap yapılmıştır. Modal analizde Erzincan spektrumu ve 1996 yönetmeliği karşılaştınlmıştır. Yapının konsol boylan arttınlarak (2m, 2,5m,3m) modal katılım faktörleri incelenmiştir. Konsol boyunun 2m olması durumunda z yönündeki depremin en büyük modal etkisi 13 modda, 2,5m için llmodda, 3m için 10 modda ortaya çıktığı görülmüştür. Yapı 6 normal kat ve 1 bodrum katından oluşmuş bir sistemdir. Yapının bodrum katinin çevresi perde duvarlarla çevrilidir. Döşeme tipi olarak nervürlü döşeme tipi uygun görülmüştür. Kat yüksekliği 3m olup temel alanı 384 m2dir. Yapının duvarlannda, iç kısımlarda yanm, dış kısımlarda tam tuğla kullanılmıştır. Çatı düz terastır. Betonarmeye esas malzeme BÇIII ve BÇI kullanılmıştır. Temel sistemi olarak İm kalınlığında kirişsiz radye olarak hesaplanmıştır. Temelin statik hesabında elastik zemine oturan plak hesabı yapılmıştır. Ko^OOOO kN/m3 alınmıştır. Zemin emniyet gerilmesi 150 kN/m2 dir Yapı 1. derece deprem bölgesindedir.

In this thesis, the static and reinforced concrete design calculation of an irregular sevenstorey building under vertical and horizontal loads is carried out. The vertical irregularity of the structural system comes into being due to the axes of the columns around periphery of the building do not coincide with each other on the fourth and fifth floors. The columns of these two floors connected through corbels beetwen two offset columns. The static and dynamic calculation are made by the use of computer software SAP90 Modal superposition is carried out by taking into account Erzincan E-W spectrum and 1996 Turkish Earthquake code. The result from the dynamic analysis are compared with those obtained from the static analysis. The building has six normal storeys and one basement storey. Basement is surrounded by shear walls. Load carrying system of building is composed of columns, shear walls and core in which staircase is located. The building under consideration is seven stories high with floor area of 16 meters by 24 meters. The building consists of the basement, the ground floor as a store floor and the others as offices. Buldmg is supposed to be constructed m the first degree seismic zone according to the map appended to the " specifications for the bulding to be natural disaster ". Design loads are taken from Turkish Standart 498 for live loads and dead loads. The design is based on these specification, as well as TS 500 /'Building Code Requirements for Reinforced Concrete ". A frame -shear wall system is chosen as structural system and C25, BÇIII are as materials for being concrete and steel respectively. The behaviour of the system is supposed elastic. First of all The calculation of the system under the vertical loads is achieved. For this purpose design computations start from the floors and go toward the foundation according to the flow of the loads. The internal forces at the cross section of the beams colums and shear walls are determined. The structure is defined totaly as a three dimensional frame which is composed of beams which connects columns and shear walls. Live loads are arranged producing the most unfavourable effects. [2] As a final design of the system vertical load solution and horizontal load results are combined taking into account the maximum reinforcement ratio at the colum and beam sections. The method involved in the software program for solving the system statically is matrix displasement method and by this method the solution of the system of linear equation represented by: {K}{U}={R} Where {K} is the stiffness matrix {U} is the vector of resulting displacement {R} is the vector of applied loads, Each joint of the structural model has six displacement components, X, Y and Z and three global rotations. RX, RY and RZ. Three dimensional system have 942 degrees of freedom. Under earthquke forces behaviour of the building below the ground level is different than that above the ground level. In order to design the building for earthquake,the forces acting on each floor due to earthquake and coefficent of structural behaviour, K, are determined assuming ground surfaces to be as foundation of the structure for the upper part of the structure above ground level and for the basement separetely. Since the basement's rigidity is bigger than the upper part due to the shear walls around the basement, the coefficent K is assumed to be 1,5 At the calculation of the staticaly equivalent earthquake loads, some other effects must be taken into consideration as the earthquake forces in x,y,z directions do not effect in the main directions separately to the construction. With this purpose, according to a calculation style in USA code, 30 % of the earthquake forces acting in other directions is added to the inter effect that is formed in one direction. The natural period of the building is determined with SAP 90 construction analysis, by using those values for different X and Y directions. In this acceptance, to calculate the earthquake effect in vertical direction and to find the eartquake load in the Z direction ; 2/3 of the average of the total horizontal load that effects to the construction in X and Y directions is taken and by dividing at the rates of the colum effect field, it is applied on the colums which are at the ends of cantilever in vertical direction. As an initial study to find the most inadequate earthquake combination at the solution in the dynamic load, all the load is accepted to be at the joining point of each other, in the three dimensional model. As a dynamic effect, response spectrum curves, with 0,05 damping ratio in East-West and Vertical direction of Erzincan 1992 earthquake, have been used. Different type of combinations such as X- Y/3-Z/3, Y-X/3-Z/3, Z- X/3-Y/3,V(X2+Y2), V(X2+Y2+Z2), V(X2+Y2)+Z/3 and I X | + 1 Y | + 1 Z ] are applied. The results for the cantilever elements are shown in the additional chapter. After all, the effect of X, Y and Z directions to the modes is compared in a situation like the cantilever lengths to be 2 meters, 2.5 meters and 3 meters. In dynamic xv solution, E-W component of Erzincan earthquake is applied to Z component in X and Y directions at vertical direction a total of 20 Modes are considered in this calculation İn the purpose of making the construction for the structural dynamic calculation lumped masses are gathered at the nodes and rijit diaphragm model is accepted in the joint points 903,...907, are accepted as the major joint point (master point) for to define the rigid diaphragm model. Master joint points are prevented from position changes in vertical direction and rotations around X and Y axis. Dynamical solution of structure is made by SAP 90 software with response spectrum analysis. Spectrum curves shaving the 0,05 rate in East- West and vertical direction of Erzincan 1992 earthquake, have been used as a dynamic outer effect. Construction style coefficient concerning the construction ductility is taken as 3 according to the given value for the ductility, frame-shear wall construction, at the earthquake code. In dynamic solution, as a result of act of East-West component of Erzincan earthquake on x,y directions, the construction has bean made affective to construction by giving console end point masses for to include the effect of the earthquake in vertical directions, at the consoles. SAP 90 solves this equation system with Modal superposition responce spectrum approach. Floor acceleration is given from the data as a responce spectrum curve showing the change of spectral acceleration relative to time period. In the first solution that is made by concerning the construction under the dynamic load; due to the story drifts violating the code limitations. The solution is repeated by increasing the rigidity of structure increasing the shear wall thickness, column dimensions and corner coloums are organized as L shaped. Data preparation for the structural analysis, basically involves : (1) describing geometry and (2) defining the static and dynamic load conditions for which the structure needs to analyzed. Basic geometric dimensions of the structure are established by placing joints ( for node points) on the structure each joints is given a unique identification number and is located in space with coordinates that are associated with a global three dimensional coordinate system, the structural geometry is completed by connecting the predifined joints with structural elements that are of a specific type ; namely beams, trusses. shell, plates, etc.. Each element has a unique identification number. When the structural damping is assumed as to be zero. Natural frequencies analysis spectrum require the undamped free vibration mode shapes. This involves the solution of the generalized eigen value problem. (K-©2m)4>=0 K is the stiffness matrix m is the mass matrix co is the diagonal matrix of the eigenvalues xvi  is the modal vector The dynamic equilibrium equations associated with the response of the structure to ground motion is given by, M û+C o+ K o =Müg where, M is the mass matrix C is the damping matrix iig is the ground accelarations, and û, û and n are the structural responses as accelerations, velocities and displacement respectively. SAP90 solve this system of equations using the mode superposition response spectrum approach, the gound acceleration is input as a digitized responce spectrum curve depending on natural period The ground excitation can occur simultaneously in three direction, namely any two mutually perpendicular direction in the X-Y plane and in the Z direction. To get the maxsimum displacement and member forces, first the modal responses associated with a particular direction of excitation are calculated. The nodal responses are then combined using the complete quadric combination using the complete quadric combination technique. The total responce is then calculated by summing the responces from the three directions by the square root of the sum of the squares method. The in-plane stiffness of most concrete floors in building structures, in general, very high. SAP90 has a special option for modelling such horizantal rijid floor diaphragm systems. A floor diaphragm is modeled as a rigid horizantal plane parallel to the global X-Y plane, so that all points on any one floor diaphragm cannot displace relative to each other in the X-Y plane. Typically, each floor diaphragm is established by a joint of the diaphragm. The location of the master joint on each floor diaphragm is arbitrary. All the other joints that exist on the diaphragm are connected to the master node by rijid links and their displacements are dependent upon the displacements of the master joints. This option is very useful in lateral dynamic analysis of building type structures. Lumping the story masses at the center of mass will result in a very small eigenvalue problem. Every joints of the structural model has six displacement componets. three global translation X, Y and Z, and three global rotationts. Rx, Ry and Rz. The directions associated with these six displacement compenents are known as the degrees of freedom of the joints. XVU Reinforced concrete design of the building is made by using the most unfavourable cross section effect resulted from the vertical and horizantal load combinations due to earthquake and vertical loads. Reinforced concrete design of the beams in the first story is done by the use of cross section effects of the beams at span and the supports and reasonable amount of bar determine from calculation is exceeded the minumum bar requirement which is Asmin=12/fyd*bw*d. If the magnitude of the shear stresses of the beams at the section which have a distance from the support surface is greater than the magnitude of Vcr=0.65 fctd bw d.shear design of beams are made by taking shear reinforcement mto consideration Reinforced concrete design of the columns earned out by using ultimate force- moment interaction graphs. Reinforced concrete of shear walls in the building is made like design of columns, and appropriate amount of bar is placed m the column heads at the shear walls. Foundation of the building is designed so that magnitude of soil stress formed under foundation of the building is less than 150 kM/m2 and tension stress is not formed through out the foundation. For that purpose, raft foundation is designed for the building. As a result, at the design of an earthquake resistant construction, it's important for a construction to have a symmetrical and regular structural system. It is not a voluntary situation of a structure to display a sudden mass and rigidity change at the plan and height. The constructions having mass and rigidity variation either in horizontal or in vertical, are named as irregular structural system. Although the calculations and details are fully arranged this style of constructions are negatively effected because of their irregularity. The most important particularity, in these constructions is the appropriate dimensions given to beams which are adjacent to the cantilevers and continue till to the inside of the construction.The vertical earthquake component in this type of structure increases the internal forces according to the results of effective horizontal earthquake records. Frame System is not formed in two directions at the systems which of their colons do not present in the same vertical axis. Because of this, these kind of systems must be avoided. The cantilever beams which are built under the columns should also be made to the adjacent internal beams. If an irregularity forms in the situation of not making haunch or lowering the beam rigidity, the section moment and shear force capacity becomes less than the calculated values and ifa balance is not provided at the joint-point, then it will cause formation of some other effects. The reinforcement of the joint which is as important as the static and dynamic calculations, also have to be prepared. The continuity of the reinforcement at the joint between the cantilever beam and the internal beam must be provided carefully. Three dimensional dynamic calculation must be made in the structures which of their structural systems are irregular. In this situation, cantilever beam should be examined under both horizontal and vertical earthquakes effect. According to the dynamic xvni calculation method, earthquake records that are taken from the similar grounds and spectrums obtained from these records can be used for an earthquake spectrum that will be base for calculation. In the regular constructions, it is enough to make the calculation according to the two major directions for the seismic effects to exist. When the seismic direction do not exist in these two major directions, it forms some additional effects. At the first degreel of seismic region and at the irregular constructions higher from 30 m, unless the seismic effects are parallel to the side of the construction at the plan, they have to be included in the calculation. This can be done by adding % 30 of the effects in other directions to the internal effects formed by seismic forces. In an irregular structural system, relative floor displacements have to be limited to lossen the damage as a result of a probable earthquake. It is seen that the behavior of a structure, having an regular structural system to an earthquake is not suitable. In this situation the rest of the parts and details of the system should be arranged in an appropriate way. Therefore the dispersion of the internal forces formed in the cantilever have to be included to the calculation. Shear forces at the same direction at the bottom and top column, form the tension forces, at the beam that connects the cantilever to the internal beam and therefore these forces exhibit the importance of design of the beam. For that reason, the rigidity of the beam must be at the cantilever rigidity or close to that, at least it should have a haunch. Beside, the cantilever placed and the colon according to the effects,have to be chosen enough to be rigid. After the internal force dispersion, between the components at the joint point of the settled cantilever, is calculated by appropriate models, the details belonging to the equipment, have to be arranged carefully according to this. As a result, the reinforcement arranged for the corbels is also considered properly, horizontal hook reinforcement and close stirrup have to be used in this as the several layers settled, to transform the cantilever to a triangle baffle is the most appropriate way instead of increasing the beam section or limitting the layers.
Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Sosyal Bilimler Enstitüsü, 1998
Keywords: Projelendirme; Yüksek yapılar; Projecting; High structures