Betonarme çerçeve sistemlerde uygunluk burulmasının incelenmesi

Abstract

Burulma etkisi betonarme yapı elemanlarının tasarımında karşı laşılan önemli problemlerden biridir. Rapor edilen bu çalışmada taşı-' yıcı sistemi betonarme çerçevelerden oluşan çok katlı bir yapıda kenar akslarda beton hacmi sabit tutularak farklı olarak düzenlenen kiriş - döşeme sistemlerinin' ana kirişe yapmış olduğu etkiler teorik olarak incelenmiş itir. Birinci bölümde burulma rijitliği tarif edilmiş ve burulma etkisi altında çatlayan kesitin burulma rijitliğindeki değişimi gösterilmiştir. Bir sınır durumu gösteren basit burulma tarif edilerek, bu moment et kisi nedeniyle kesitte olaşan gerilme dağılımları grafik olarak verilmiş tir. İkinci bölümde denge ve uygunluk burulmaları açıklanmış ve uy gunluk burulması etkisindeki elemanların gerilme ve kesit hesabında kullanılmak üzere geliştirilen. Eğik Eğilme ve Uzay Kafes Benzeşimi teorileriyle ilgili gerekli bağıntılar verilmiştir. Daha sonra bu bağıntı lar yardımıyla burulma momentinin beton ve donatı arasında hangi oranda bölüşülerek karşılandığı hesaplanmıştır. Burulma teorilerinin incelenmesinden sonra bileşik burulma hal leri sırasıyla: kesme - burulma ve eğilme - burulmanın birlikte olması halleri incelenmiş ve bunlar için geliştirilen gerilme ve deformasyon bağıntılan verilmiştir. Daha sonra üç etkinin yani kesme, eğilme ve burulma etkisinin birlikte olması hali için verilen karşılıklı etkileşim diyagramları gösterilmiştir. Burulma etkisinin genel bağıntıları çıkartıldıktan sonra burulma etkisi altında betonarme elemanların taşıma gücü ilkesine göre kesit hesabının yapılması için izlenecek hesap esasları verilmiştir.

Most of the structural elements are subjected to torsional mo ment, in the systems whose bearing system is reinforced concrete. This moment arises due to the geometry of the system or due to the asymetric distrubition.of the loads. But mostly the amount of the torsional moment is so small that it can be neglected in the structural analyses. In this study, it has been attempted to investigate the effects of the compatibility torsion and the behoviour of the system under these loadings in amulti - story structure, a frame system of sub - beams 1.2.3 E CD £ o rn I. II. f- 6.0m CO o r-i o 6.0 m 5.0m 6.0 m III. £f in in t- " in Figure! System I.II.IH First of all. for specifying the strength of concrete sections aga inst torsional moments, the torsional stiffness, which is one of the VII most im portant parameters, have been defined and the variation of torsional stiffness be ore and after cracking has been explained Ro= 0 = GCI Pi xfo After the description of torsional stiffness, the torsion is devided into two catagories as equilibrium iorsion and compatibility Jtorsion. Both types of torsion are investigated in detail: - Equilibrium Torsion: For structures that are under the effect of this type of torsion, the- rejşa need for torsional moments for holding the structural system or element in eauilibrium. Equilibrium torsion is an unseperated part of the system It is not possible to decrease or neglect this type of torsi on. Compatibility Torsion: The difference of this torsion from the equilibrium torsion is as fallows: It may net be necessary to use torsional moment for equilibrium In the plastic joints that may be formed in certain areas without destro ying the stability of the system. By the formation of these joints, the system may rotate a certain amount and will come to a new equili brium state. İn this case there will be no need for torsional moment For this reason, if enough amount of reinforcement is put in the elements {to provide sufficient rotation) that are under the effect of tor sional moment in the system, the torsional moment can be neglected in the structural analyses. But the rotation of.he section must be rest ricted. Alter the description of torsion types, the behoviour of an element that is under the effect of a torsional moment is examined. For this rea son, although it is rarely encountered in practice, in order to form a bo undary condition, the important simple torsion effect and also compa- und torsion states have been examined. v i i 'ı - Simple Torsion The circular sections that are under the effect of simple torsion, the plane sections remain as plane after twisting. On the other hand, the rectangular sections, the plane sections do not remain as plane af ter twisting and this causes the solution to be more comDlex. For this reason the strain distribution differs from one section to another. Be cause of these shear stresses that are formed on the rectangular conc rete sections, the cracks under the effect of simple torsion start first as 45° on the wider surface of the section. Later they spread on the other surfaces. On the three surfaces of the element, perpendicular cracks to the principal tensional stresses occur and crushing forms on the fo urth surface. - Compound Torsion states: In the compound torsion states, apart from the torsion acting on the concrete section without reinforcement, the concrete section is re inforced with web and longitudinal reinforcements. In this case, the breakage doesn't occur immediately after the concrete is cracked. The loads are carried by the longitudinal and web reinforcements. Here, this subject is explained by two theories. - Skew Bending Theory: In this theory, an element of 45 J slope with the cracked surface be am axis formed of longitudinal reinforcement transmit loads and, the stirrups resist the tensile forces where the crack is termed and there is no tensional resistance. In the compression zone, the concrete toget her with the longitudinal reinforcement carries a certain part of torsio nal moment. The sum of the strengthes in both zones gives the strength (Tn) of the section against torsional moment. - Space Truss Analogy For the space truss anology, similar results are obtained as in the skew bending theory. ! X The results obtained in both of the theories are given below: Tn=Tc + Ts m 2A 2 \T7^ fxiyiAtfy. Tn=^ x2yV fed + -t { § - J After this subject, except for the simple torsion shear - torsion and bending - torsion states are examined. - Combined Bending and Torsion: « Generally, in aplication, both the bending and torsion are seen to gether. In case the bending and torsion act together, the diagram of mutual interactions gives good results. In these results, obtained from the mutual interaction diagrams, the necessary rein forcement can be found The area of the reinforcements are equal to the sumof the areas of the reinforcement that is necessary for the bending and torsion in the tension zone and to the difference of those in the compression zo ne. Tro Mro T (x2 + y2) \i As= 2(x2y2fy) fyl*-f) Also, as a simple solution, in case the bending and torsion act to gether, separate calculations are made for bending and torsion. By ad ding these two reinforcement areas, the Interaction of bending and tor sion may be neglected. Combined shear and Torsion: In case of combined shear and torsion, the mutual interaction diagram Is valid just as in case of combined bending and torsion This Interaction can be described as follows <#-)2 + b^)2=l V ' v T vcr xcr From here, the total strength of torsional m tment can be obtai-l ned. I l+( VxTUt * ld - CombinedShear, Bending.and Torsion The effect of combined shear - bending and torsion can be Jpest de-i fined by the mutual interaction surfaces. The behs-lour of the.element is defined according to. the torsional moments of efferent magnitudes acting on the section from these surfaces. Later, the solution for the problem has been explained according to the bearing capacity. After giving the torsional strength for rectan gular sections, the minimum reinforcements have been issued for the! section. The procedure to be followed according to ".he bearing capacity has. been given andihe systems with numbers..1.2 nd 3 have been sol ved according. to different column types and fol": wing results have been abtained. 1. The torsional moments on the supports ar.i span increase ag the stiffness of the columns increase when the bei.Ti that is under the: effect of torsional moment 2. When the system is formed of only one sub - beam, the rotation on the beam that is under the effect of torsional m.'ment. is larger than the other systems. This causes an increase of torsional moment x:\d accordingly an Increase In the needed reinforcement amount. 3. By making a comparison between the systems with respect to total amount of the reinforcement, the most suitable load bearing system is the system_n.umb_er 2 with two sub - beams.