Betonarme kirişsiz döşemeli yapıların zımbalama kayma mukavemetlerinin ve yatay ötemelerinin hesabı için birer yöntem

Abstract

Betonarme kirişsiz döşemeli yapılar, özellikle A.B.D.'de ve Batı Avrupa ülkelerinde yaygın kullanım alanı bulan taşıyıcı sistemlerdir. Tercihin nedeni, mimari eğilimin yanı sıra, kalıp hazırlanmasından dolayı pahalı olan işçilikten tasarruf sağlamak şeklinde açıklanabilir, ülkemizde de uzun yıllardan bu yana daha çok "mantar döşeme" olarak adlandırılan kirişsiz döşemeli sistemler, genellikle resmi binalarda, büro tipi yapılarda kullanılmaktadır. Kirişsiz döşemeli yapılarda, en önemli problemin, "zımbalama" olduğu bilinmektedir. Altmışlı yılların başından bu yana çeşitli araştırmacılar tarafından yapılan deneysel ağırlıklı çalışmalar, kolon-döşeme birleşimlerinin zımbalama mukavemetini hesaplayan çeşitli bağıntıların geliştirilmesine ışık tutmuşlardır. Deprem bölgelerinde ise çok katlı kirişsiz döşemeli yapıların tasarlanmasında çeşitli endişeler vardır. Kirişleri olmayan yapının deprem esnasında önemli ölçüde yatay ötelemeler yapacağı, bunun sonu cunda en azından taşıyıcı olmayan elemanların hasar göreceği ya da birleşimlerde zımbalama hasarlarının oluşacağı düşünülmektedir. Bu nedenlerden, kirişsiz döşemeli betonarme yapıların taşıyıcı sistem düzenlenmesine birtakım kısıtlamalar getirilmiştir. Düzenli aks sis temine sahip olması istenen, bu tür yapıların perdelerle rijitleştirilmesi, bir doğrultuda en az üç açıklıklı olarak düzenlenmesi, döşeme kalınlıklarının minumum 15 cm olması yönetme! i ki erce bağlayıcı hale getirilmiştir. Çalışmanın 1. Bölümünde literatürdeki benzer araştırmalar hak kında kısaca bilgi verildikten sonra, 2. Bölümde."zımbalama mekaniği", ana hatlarıyla açıklanmış, bir sonraki bölüme temel oluşturacak de neysel çalışmalar özetlenerek yorumlanmıştır. 3. Bölümde kolon-döşeme birleşimlerinin zımbalama kayma mukavemetini taşıma gücünde hesaplamak amacıyla üç tip birleşim için analitik bağıntılar elde edilmiştir. 4. Bölümde, çerçeve tipi yapı örneği üzerinde, rüzgâr ve deprem yüklemesi altında kirişsiz döşemeli yapıların yatay ötelemeleri hesaplanmış, kirişli döşemeli sistemlerle karşılaştırılmış, yatay ötelemelerin hesabı için yaklaşık yöntem önerisi ile birlikte, yatay öteleme kriteri getirilmiştir. Çalışmada, kirişsiz döşemeli sistemlerin tasarımında oldukça önemli yer tutan "zımbalama kayması" ve 'yatay öteleme" hesaplarına mühendislik uygulamalarında kullanılabilecek öneriler getirilirken, önerilerin 3. Bölümde literatürdeki deney verileriyle, 4. Bölümde ise Açı Yöntemi ile prezisyonlu olduğu sonucuna varılmaktadır.

Reinforced Concrete Flat Plate Structures are widely used structural systems especially in the United States of America and Western European countries. In our country moreoften medium-rise office and residential buildings employ flat plate reinforced concrete struc tures. Besides architectural tendency, the reason for its extensive usage and preference is the economy it brings in employment costs by cutting off the frameworking expenses. On the other hand, in the flat plate structures, the reinforcement is used much more extensively then it is the structures with beam. In reinforced concrete flat plates, it is necessary to consider two types of shear failures. Where the slab could act essentially as a wide beam, a shear failure could occur across the entire width or over substantial width. This type of failure is rarely critical in most cases, but it must however be checked. The shear strength of the slab in this case can be calculated as for a beam. The region of a slab in the vicinity of a column could fail in shear by developing a failure surface in the form of a truncated cone or pyramid. This type of failure, called a "punching shear failure", is usually the source of collapse of flat plate and flat slab buildings. Adequate design of this region of slab is therefore of paramount importance. In general, the region of a slab near a column must transfer both shear force and unbalanced bending moment to the column. Numerous tests have been carried out to evaluate the punching shear strength of slabs where the moment transfer is zero. In recent years, a significant amount of test data has also become available for the case where both shear and moment are transferred. Several theories, have been put forward to predict the strengths observed in these tests. ix - The ACI 318-83 |3| approach is an extrapolation of a working stress method of calculation to an ultimate strength situation and therefore it is not logical. Moreover, it does not cover all practical cases. In what follows, a brief description of the behav iour under load of a slab in the vicinity of a column is presented and the mechanism of failure is explained with the help of a physical model. This is followed by the development of design equations and correlation with test data. Based on these equations, recommendations for de sign are made. An example is presented to illustrate the application of the proposed design recommendations. With the aid of a physical model (Figure 3.1), the behaviour of the slab and the punching shear failure is initiated either by the failure of the slab at the side face of the critical section in combined torsion and shear, or by the failure of the slab at the front face (and the back face if any) in shear. Equations are developed for the calculation of punching shear strength of slabs in the presence of an unbalanced moment. The following cases are considered: a) Where the side face of the critical section contains no beam and no closed ties (e.g. a slab in the vicinity of an interior column). In this case, the equa tion for the punching shear strength, Vu is as follows: uo i+°-i25 b) where contains a beam amount of (3.18) the side face or slab strip v> minimum closed ties (e dniuuriu ut minimum c. ..- vicinity of an edge column). In fn«" the punching shear strength, VUmin is as follows: of the critical section provided with a certain (e.g. a slab in the for t ties, V Umi n A.(D/h).VU0 1+0.52 ud In this case, the equation with the minimum closed (3.31) b.b]V c) where the side face of the critical section contains a beam or slab strip provided with more than minimum closed ties (e.g. a heavily loaded slab in the the - x - vicinity of an edge column). The maximum punching shear strength, V umax is as fol 1 ows : umax = 2r8 V umin /x/y (3.38) The design expressions have been compared with available test results. The correlation between the test and the predicted strengths has been found to be conserva tive (Table 3.1). An example has been presented to illustrate the ease with which the proposed design recemmendati ons can be used in engineering practice. These subjects are investigated in the second and the third chapters. The control of lateral displacements (wind or earthquake) is an essential part of the design procedure in multistory flat plate reinforced concrete structures. For low-rise and mid-height buildings, experience has proven that an acceptable design may be prepared which satisfies buth displacements limitations and code provi sions for stresses, in very tall buildings, the lateral load design can become very sophisticated and usually requires wind tunnel or shaking table tests. In order to estimate the structural displacements and internal forces due to lateral loads, a common pro cedure has been to model the three-dimensional structure as a series of planar ones. The typical planar structure includes one row of columns, associated portions of the flat plate floors. One such method was developed by Cheoung-Siat-Moy |52J for unbraced steel frames where he developed a working formula to determine the relative story drift for unbraced steel frames. In this study, it is demonstrated that these formulas can also be used to calculate the story displacements for reinforced concrete flat plate plane frames. The concept upon which the method rests is that the stiffness of a story can be represented by the sum of the stiffnesses of its subassembl ages, with a subassembl age being a substructure consisting of one column and its restraining girders or beams. Obviously, a story with in columns will contain m subassembl ages. Also, an exterior subassembl age will have only one restraining beam and an interior subassembl age will have two restraining beams. xi width diffe that ture secon Cheou displ the s resul The w stori In equa rent takes given dly t ng-Si aceme ame r ts ob hol e es st this pa t i ons ( researc pi ace in | 51 his tim at-Moy nts of einforc tained process ructure rt of in par hers, in the I by u e, sim 1 52 | a unbrac ed con from t is re s and the s t 1.2 and t code sing plifi nd us ed st crete hese peate the r tudy,.2.). he eq s are the s ed me ed in eel f flat two m dais esul t first th devel ope ui valent employed 1 ope-def 1 thod, dev determin rames, is plate st ethods ar o for eig s are com e effective d by several frame method, to the struc- ection method eloped by ing the lateral employed to ructure and the e compared, ht and six pared. The simplified method described in fourth part reduces the complexity of analyzing multibay reinforced concrete flat plate frames for wind and earthquake loads. The value of P can be taken to be zero if the P-A effects is negl ected. In a preliminary analysis, the displacement equa tion, along with the frame model, can enable the engineer to obtain a relative story stiffness for a given lateral displacement. The displacement equation overestimates the value of displacement for the lower stories, while it appears to converge close to the actual value in its uppermost stori es. The method presented was compared with the value computed by slope-deflection method; a satisfactory agree ment was achieved in both cases. In addition, lateral displacements of the struc tures are investigated under the loads with the same total values but with rectangular (wind) and triangular (earth quake) distribution and the results obtained by the linear elastic analysis are compared with two seperate types of beam-column structures. The difference between the finite element solution of maximum total story displacement of the structure in |51| under wind loading and the slope-deflection method employed for the same structure is 18% whereas it is 19% for the simplified method. These differences are obtained by using the rigidity values determined from the equivalent frame method. The difference between the finite element solution of maximum total story displacement obtained by using the rigidity values of Pecknold's |36| effective width determination method, and the slope-deflection meth od is 27% while it is 28% for the simplified method. XT 1 - ments The percentage approximately normal story displace- can be stated as 0.001 o, 0.003. When the column dimensions of flat-plate framing systems is designed to be equal and with square sections through all stories. Safety is assured against lateral drifts up to ten stories. It is appropriate to take the depth of the slabs between 200-250 mm and to have column dimensions with 3 - 3.5 times these values. As a further research the equations (in Part 3.2) for punching shear strength can be improved by taking the effects of the bond slip, the dowel action and the aggregate interlock into account. Also, slab holes in the vicinity of a column can be taken into consideration and new design equations can be defined. It is in evitable to apply experimental methods in order to accomplish these further researches. The problem of lateral displacements in linear elastic analysis in asimetric structural systems (in plan and in elongation) can still be investigated. It is also advisable to work on the same problem in progressive collapse. A summary of conclusions and recommendations are given in fifth chapter.