Kutu kesitli kirişlerin eğilme, burulma ve bozulma etkilerine göre analizi

Abstract

ÖZET Bu çalışmada kutu kesitli kirişlerin eğilme, burulma ve bozulma etkilerine göre analizleri incelenmiştir. Kutu kesitli kirişler genellikle köprü inşaatında kulla nılmaktadır. Kiriş kesitinin içi bos ve ince duvarlı olarak yapılması, malzemeden ekonomi sağlanmasının yanısıra kirisin hem eğilme ve hem de burulma etkilerine karsı yeterli ve elve rişli şekilde dayanmasını da sağlamaktadır. Çalışmada önce konu ile ilgili önceki çalışmalar tarana rak incelenmiştir. ikinci bölümde ince duvarlı ve çok gözlü kutu kesitli ki rişlerin basit eğilme ve St Venant burulması analizleri açık lanmıştır. üçüncü bölümde ince duvarlı kapalı veya açık kesitli ki rişlerin çarpılmalı burulma analizi verilmiştir. Dördüncü bölümde ince duvarlı tek gözlü veya çok gözlü kirişlerin çarpılmalı burulma analizi için gerekli olan kayma merkezinin hesabı konusu incelenmekte ve kesmeli eğilme teori sine dayalı bir bilgisayar programı verilerek açık ve kapalı kesitlere ilişkin çözülmüş örnekler sunulmaktadır. Beşinci bölümde ince duvarlı kirişlerde normal kuvvet, eğilme ve çarpılmalı burulma bileşik halinin matris formülas- yonu verilmektedir. Böylelikle ince duvarlı kirişlerin analizi bilgisayar programlamasına uygun hale getirilmiş olmaktadır. Altıncı bölümde kutu kesitli kirişlerde bozulma etkileri nin analizi, elastik zemine oturan kiriş analoj isiyle yapıl maktadır. Yedinci bölümde uygulamadan alman tek gözlü kapalı ke sitli bir kutu kiriş köprü örneği üzerinde özellikle burulma ve bozulma etkilerine göre sayısal alarak yapılmış bir analiz ayrıntılı bir şekilde sunulmaktadır. Sekizinci bölümde bu çalışmadan elde edilen sonuçlar yer almaktadır. Kutu kesitli kirişlerin eğilme ve burulma etkilerine göre analizi konusunda Türkçe yayınlanmış pek az kaynak bulunduğu, bozulma etkisine göre analiz konusunda ise Türkçe kaynak bu lunmadığı göz önünde tutulursa; bu çalışmada toplu olarak ve sayısal örnekleriyle verilen eğilme, burulma ve bozulma ana lizlerinin karayolu köprülerinin projelendirilmesinde yardım cı olacağına inanılmaktadır. -vi

SUMMARY Thin-walled box beams are usually used in bridge deck construction. The advantage of the hollow section is that the material has efficiently been used in bending and torsion. As spans of bridges increase in the range where dead load dominates, economies in self -weight will become more important. In this study, the generalized co-ordinate method of Vlasov and simple beam theory has been extended to treat torsional and distortional effects in straight, thin-walled box beams of uniform section. Single-cell or multi-cell sec tions with side cantilevers can be analysed, and the structure can be single-span or continuous. The calculations by the methods presented have been done by hand, and if necessary a micro-computer is enough. Because, the theoretical formulations used for torsional and distortional analyses are such that only small matrices arise, requiring relatively low storage capacity in the computer. In the study of single-cell box beams made by Maisel and Roll (1974), it was concluded that torsional warping and distortional warping should both be considered in the treatment of concrete box beams. The thesis is composed of eight chapters. In the first chapter, the subject is introduced and a short survey on related works is given. In the second chapter, simple bending and St Venant torsional analyses of thin-walled multi-cell box beams are explained. Since simple bending and torsional analysis of single-cell box beam are treated on an example in the seventh chapter, only analyses of multi-cell box beams are given in this chapter. The normal stresses in longitudinal bending of a thin-walled beam is obtained easily by using engineers* theory of bending. For the shear stresses arising in longitudinal bending, imaginary cuts are inserted for each cell and thus the closed cross-section is transformed to a fully open one. The statically indeterminate shear flows are required to restore compatibility at these cuts. Then, in order to obtain unknown shear flows in each cell, a system of simultaneous equations is set up, corresponding to the condition that there is no twist of the section. To evalute the shear stresses in bending due to horizontal loading, a similar procedure are used to obtain the statically indeterminate shear flows. For the St Venant torsion of thin-walled multi-cell box beams, the shear flows in St Venant torsion in each cell are defined and an equation is set up for each cell. For the case of a multi- -vii-cell section, the solution of simultaneous equations gives the St Venant torsional shear flows. In the third chapter, the torsional warping analysis of thin-walled beams of closed or open crass-section is explained. The torsional warping (longitudinal) stresses and torsional warping shear stresses are obtained in terms of the applied torsional moment, the bimoment and section properties known as the sectorial-coordinate and the torsional warping moment of inertia. The algebraic expressions for obtaining these section properties and stresses, and also the St Venant torsional shear stresses are given. In the fourth chapter, the subject of the determination of shear center which is required in the analysis of thin-walled beams has been treated. The center may be defined as the point of the cross-section of a thin-walled beam, through which the external forces should be applied in order not to produce twist of the beam. Two different approaches to determine the shear center are explained in detail. The approach which is based on the theory of bending and shear is preferred, as it is suitable for computer programming. The list of computer programme are given and two examples of the determination of the shear center of open and closed sections are presented. In the fifth chapter, the analysis of torsional warping and simple bending, including axial loading are jointly formulated by using matrix notation. Distortional effects are excluded here, and are treated in the sixth chapter by extension of matrix formulation. There is a close relationship between torsional warping analysis and theory of bending. Similar expressions for cross-sectional displacement due to torsion and to bending may be developed by using orthogonali- zation (normalization) procedures. A matrix differential equation for the non-distortional behaviour of a prismatic, thin-walled beam is also developed. The solution of this equation yields the expression for longitudinal normal stress. In sixth chapter, analysis of box beams for distortional effects is given. Distortional effects comprise distortional warping and transverse bending, and arise in concrete box beam construction as a result of the usual practice of inserting diaphragms only at the supports, or at large spacings within the span of the beam. These effects have to be superimposed upon the effects of longitudinal bending and torsional warping. A method of distortional analysis developed by Sedlacek (1971) is explained in matrix notation. A generalized differantial equation representing combined bending, torsional and distortional behavior is given. Beam-on-elastic-f oundation analogy is used for this analysis. The solutions for each distortional mode of the box-beam behaviour are then viii-superimposed to give the complete picture of distortional action, together with the non-distortional effects. In the seventh chapter, a single-span box beam whose cross-section has one cell is numerically analysed for bending, torsional and distortional effects. In chapter eight, the results of this study are outlined. -ix-