Planda düzensiz çok katlı kaset döşemeli bir betonarme yapının boyutlandırılması

Abstract

Bu çalışmada düzensiz geometriye sahip kaset döşemeli çok katlı bir betonarme binanın statik ve betonarme hesabı yapılarak projelendirilmiştir. Projelendirilen bina bir simetri eksenini bulunan tüm katlarında aynı açıklıklara sahip olan altı katlı betonarme bir binadır. Binada iki tip kat planı mevcuttur. 1., 3. ve 5. katlarında orta kısmında bir boşluğa sahip kat planı, 2., 4. ve 6. katlarında ise orta kısmı kaset döşeme ile kapatılmış bir kat planı mevcuttur. Kat yüksekliği tüm katlarda aynı ve 3.5m'dir.. Binada deprem yönetmeliğinde tanımlanan Al türü burulma düzensizliği ile A4 türü (taşıyıcı eleman eksenlerinin paralel olmaması) düzensizlik bulunmaktadır. Düşey doğrultuda ise herhangi bir düzensizlik bulunmamaktadır. Binanın X ekseni doğrultusunda en uzak iki noktası arasındaki mesafe 22.0 m'dir. Y ekseni doğrultusunda ise bu mesafe 17.0 m'dir. Yapı malzemesi olarak beton için BS20 ve tüm elemanların donatımı için BÇIII kullanılmıştır. Bina, birinci derece deprem bölgesinde bulunduğu varsayılarak bu etkiler altında projelendirilmiştir. Bina yerel zemin sınıfının Z2 olduğu duruma göre analiz edilmiştir. Yapı önem katsayısı I=1.0'dir (konut, işyeri). Yatay yüklere göre hesap "Eşdeğer Statik Deprem Yükü" ve "Dinamik Analiz" olmak üzere iki yöntemle yapılmış ve bu iki yöntemin verdiği sonuçların karşılaştırılması mümkün olmuştur. 1997 Deprem Yönetmeliği'ne göre bu tip bir yapıda dinamik analiz yapılması zorunludur. Tüm çözümler için sistemin SAP90 programında modeli kurulmuştur. Tüm katlarda kat kütle merkezinde "master joint" tanımı yapılmış ve döşemelerin rijit diyafram olarak davranacağı varsayılarak tüm elemanların uçlarındaki yerdeğiştirmeler bu düğüm noktalarına bağlanmıştır. Dinamik analiz için kat kütleleri kat kütle merkezinde toplanmış tekil kütleler olarak alınmıştır. Modlann birleştirilmesi yöntemine göre yapılan dinamik analizde, her bir mod için hesaplanan etkin kütle 'lerin toplamının toplam kütlenin %90'ından az olmaması şartı göz önüne alınarak herbir deprem doğrultusu için ilk altı mod kullanılmıştır.

In this study, the reinforced concrete design of a six-storey building which has a one- axis-symmetry and irregular plan. The building has two types of storey plans. The first type has slab on the center region of the plan and the other has an opening at the same region. Storey height for all storeys are the same and 3.5 meters. Total height of the building is 21.0 meters. The building has Al type torsional irregularity and A4 type irregularity (the axes of load bearing members are not paraleli to each other) in plan. There are no irregularities in elevation. In the X-direction, the distance between the two-most-far-points of the building is 22.0 meters. The distance for Y-direction is 17.0 meters. The typical configurations can be seen in Figure 1 and 2. The concrete quality used is BS20 which has a design value compressive strength of 133 kgf/cm2. The steel used for all members is BCIII which has a design value of 3650 kgf/cm2 tensile strength. The building is designed assuming that it will be built in a first degree earthquake zone. The local soil conditions are considered as the soil class Z2 in Turkish Earthquake Code ABYYHY. XIV The building has a structural system which consists of shear walls located at the inner region and columns located at circumference. All these vertical members are connected to each other by beams which have a rectengular cross-section of 30cm/70cm. For the analysis of the structural system the loads on the floors defined in TS498 is assumed. The dead loads include the weight of the covering material and the weight of slab itself. A live load of 200kgf/m2 is considered. For the analysisof the slabs SAP90 computer program is used by considering several loading conditions to obtain the largest internal forces. In order to find vertical loads that each column will carry it is assumed that vertical loads are first applied onto the slabs then transmitted to beams that surround the slab. The beams are carried by two supporting columns at each end of the beam. Each column must bear the the vertical loads caused by the column itself, the weight of the slabs of different types, the beams supported by the column, and the weight of the section walls carried by the beams. The vertical members of the structure are dimensioned by considering the total factored vertical load that the member is subjected to. Later the vertical loads are applied onto the beams in the three-dimension-model of the system in order to find the internal forces caused by vertical loads. This type of analysis gives more realistic results than the analysis of seperate frames. The structural system is analysed under seven different load combinations that give the largest internal forces. To obtain the largest beam span moment, a loading configuration is considered where both dead and live loads are applied on the beam span and only dead loads on the adjacent beam are applied by providing a full- empty-full loading sequence. Lastly an analysis is carried out for a loading condition where all spans are loaded with dead and live loads together. It is seen that the results of the last loading combination differs only 8% from the largest result xv obtained by the detailed analysis. This last loading combination is used for the design of the cross-section because it is more suitable to combine with lateral loads. The internal forces due to lateral earthquake loading are obtained using two different methods: 1. Equivalent Static Earthquake Load 2. Dynamic Analysis This gives an opportunity to compare results of two methods for the structure in question. In the Turkish Code, Dynamic Analysis is the method to be used for such systems that have irregularities mentioned above. In the Equivalent Static Earthquake Load Method, the total weight of the structure is obtained. Then, a total static lateral force is calculated considering the weight of the building, the earthquake zone, the response spectrum characteristics and the structural system itself. This resultant total load splitted into the storey loads that act on each storey level. The system is analyzed under these static forces using SAP90 computer program and the joint displacements and frame element forces are calculated. The first natural period of the system is calculated using joint displacementsby using Rayleigh Method. Then, it is checked whether the spectrum coefficient selected for calculating equivalent static load is appropriate or not. If not, the internal forces are modified by the ratio of the two spectrum coefficients. In Dynamic Analysis, the storey masses are supposed to be concentrated at the center of mass. Mod Superposition Method is used for Dynamic Analysis. According to the Turkish Earthquake Code, the total participating mass value must be more than 90% of the total mass of the building. In order to satisfy this condition,the first six modes of the structural system are considered. Mode shapes and participating masses are given in appendixes. For the exentric earthquake loadings, the point where all the mass of the building is supposed to be concentrated is shifted depending on the earthquake direction and the XVI distance of the building in direction vertical to earthquake excitation. All loading conditions are taken into account is SAP90 data file one-by-one. Each data file gives solution to only one loading condition. Unlike the "Equivalent Static Earthquake Load", the superposition is carried out manually. The same model is used in SAP90 for all solutions except different loading conditions. The geometry of the system does not change at all whereas the mass center is shifted so that exentricity can be taken into account. The shear walls are taken into account in the analysis as one column which has the same cross-section as the shear wall.The rigid part of the beams which connect the shear walls to the neighbouring columns is considered as beams which have cross- section heights equal to the storey height. Three nodes are required for such modelling of shear walls, one in the middle and two at the ends. For all storeys a master joint is defined at the mass center of the storey. This results that the slabs are expected to behave as rigid diaphrams. So all the joint displacements end the frame elements are tied to the master joint of the related storeys. To find the most largest internal forces at elements that the structure consists of, the following loading combinations are considered: 1- 1.4G + 1.6Q factord vertical loads, 2- 1.OG + 1.OQ ± 1.0EX Earthquake excitation applied on mass-center in X-direction 3- LOG + 1.0Q ± 1.0E0.o5x Earthquake excitation applied on shifted-mass- centerin X-direction XVI! 4- 1.OG + 1.OQ ± 1.OEy Earthquake excitation applied on mass center in Y-direction 5- 1.OG + 1.OQ ± 1.0E0 osy Earthquake excitation applied on shifted-mass- center in Y-direction For the exantric earthquake excitation the storey mass which are concentrated at the mass center are shifted 5% of the building length on axis perpendicular to the excitation. In all of these analysis and design calculations the following CODES are used: TS500 (Building Code Requirements For Reinforced Concrete Structures, April 1984) TS498 (Design Loads For Buildings, November 1987) ABYYHY (Building Code Requirements For Reinforced Concrete Structures in Earthquake Zones, June 1997)