Modele obliczeniowe stalowych ram płaskich z węzłami podatnymi

• Autorzy: Giżejowski M.
• Języki publikacji: PL

Abstrakty

PL

Warunkiem wdrożenia zintegrowanych procedur projektowania ram stalowych metodą stanów granicznych jest opracowanie jakościowo nowych modeli obliczeniowych konstrukcji. Modele te umożliwiają zaawansowaną analizę całych układów nośnych. W rozprawie skoncentrowano się na opracowaniu zaawansowanych modeli obliczeniowych stalowych prętów i ram płaskich. Uwzględniono podatność postaciową prętów oraz podatność obrotową połączeń prętów w węzłach. Macierze sztywności wyprowadzono dla superelementu (elementu pręta traktowanego integralnie z węzłami podatnymi) na podstawie ogólniejszych założeń, niż spotykane dotychczas w literaturze. Uwzględniono tzw. współczynnik sztywności zamocowania pręta w węźle końcowym, który zmienia się w granicach (0,1), a nie w granicach (O, oo), gdy stosuje się fizyczną sztywność węzłów. Dzięki temu uzyskano dobrze uwarunkowane macierze sztywności konstrukcji, które nie stwarzają kłopotów numerycznej stabilności rozwiązania. Macierze sztywności metody przemieszczeń, do analizy płaskiej postaci zginania, wyprowadzono z rozwiązania równań różniczkowych pręta podatnego na odkształcenia postaciowe, dla przypadku zginania bez udziału siły osiowej (teoria I rzędu) oraz z udziałem siły osiowej ściskającej lub rozciągającej (teoria II rzędu). Linie ugięcia pręta określono w funkcji przemieszczeń punktów końcowych superelementu, a następnie korzystając z definicji sił przekrojowych, wyznaczono lokalne macierze sztywności. Do zbudowania macierzy sztywności początkowych naprężeń w przemieszczeniowej wersji MES wykorzystano zasadę prac wirtualnych i funkcje kształtu o geometrycznych stopniach swobody, tzn. funkcję opisującą linię ugięcia superelementu w przypadku zerowej siły osiowej. Całkowitą macierz sztywności MES zdefiniowano jako energetycznie konsystentną, tzn. jako sumę macierzy początkowej sztywności (według teorii I rzędu) oraz macierzy początkowych naprężeń, uzyskanej z zasady prac wirtualnych. Zastosowanie wyprowadzonych zależności przedstawiono na przykładzie eulerowskiej utraty stateczności ram zbudowanych z prętów o przekroju złożonym.

EN

Integrated design strategy of steel frames by the limit states method is possible m practice on condition that new quality computational models are worked out for the advanced structural analysis of the whole frame system. In the investigations presented herein, the focus was on the development of advanced computational models of steel members and piane frame structural systems. The member shear deformation and partial fixity in joints (connection semi-rigidity) were taken into consideration. A stiffness matrix of line superelement (member element treated integrally with its semi-rigid end connections) was developed on the basis of more general assumptions than have usually been made in other relevant formulations known from the subject literature. The fixity factor based formulation was used in which the stiffness factor changes in the range of (0,1), instead of (O, oo), as in the case of physical connection stiffness range. It allowed for the structure stiffness matrix to be postively defined, regardless of the actual connection stiffness, and also for a stable numerical solution when the structural matrices are inverted. Slope deflection based stiffness matrices for in-plane bending were developed on the basis of an accurate solution of the differential equilibrium equation of the shear flexible member in the case of zero axial force (first-order theory) and also in the case of compressive or tensial axial force (second-order theory). The deflection curve was expressed in terms of nodal displacements of the line superelement, and the element stiffness matrices were next derived on the basis of defmitions of member stress resultants, independently for the three cases defined by the axial force type. The initial stress stiffness matrix in the displacement version of FEM was derived on the V.W. principle, taking into account the geometrie DOF based shape functions, i.e. the deflection curve of the superelement subjected to zero axial force. The total element stiffness FEM matrix was developed via an energy consistent approach as a product of the first-order initial stiffness matrix and the initial stress stiffness matrix derived on the V.W. principle. Examples of Eulerian buckling case studies of frames composed of shear flexible members were given. The main goal of the investigations described herein aimed at the development of a computational model capable of capturing the effect of the continuous stiffness degradation of structural members and joints and its influence on the frame ultimate limit state. The model developed by the author is of a more general nature than those suggested in other relevant formulations. The modified section ciassification system and the member stiffness degradation model accounted for inelastic deformations and the postbuckling stress redistribution in slender plate segments, after their distortion due to local buckling, were introduced. A failure criterion has been included in the analysis with regard to the lack of required rotation capacity of the member section of class greater than l. New joint ductility requirements were introduced and verified by parametric studies of a two-storey and two-bay frame. Noneulerian buckling modes and the failure caused by the lateral-torsional deformation state of insufficiently restrained frame systems in the out-of-plane direction were also examined. The element out-of-plane FEM stiffness matrix was developed on the basis of an energy consistent approach, as in the Eulerian model. The constitutive component of the torsional part of the stiffness matrix was derived on the basis of an accurate solution of the differential equilibrium equation of member nonuniform torsion of a finite St. Venant sectional rigidity. The computational model developed uses in-plane and out-of-plane degradation functions together with a number of safety factors associated with these functions. In addition to the theoretical modelling, the experimental investigations were carried out for portal frame models with welded and bolted beam-to-column connections, tested upside-down.The experimental setup allowed for investigations of in-plane bending and out-of-plane stability of frame specimens. The testing stand was equipped with a computer on-line guiding system in order to facilitate the testing procedure. Special devices were installed to measure the rotation of the connection as a whole, the total rotation of the connection and the member close-to-the-connection length, as well as the contribution of various joint components to the rotation of the whole joint. A total of 15 frame specimens were tested in the main series which was divided into 4 gropus, depending upon the beam axial force sign and the type of out-of-plane beam restraints. Experimental results, stored on computer hard disc in files compatible with the calculation sheet EXCEL of Microsoft Office, were used for graphical postprocessing. As a result, the following graphs have been developed: frame load-deflection characteristics, connection rotations, components of displacements in the mid-span section of the frame beam as well as bolt elongations. The test results have been used for verification of the computational models developed by the author for an estimation of the semi-continuous plane frame ultimate strength. Fistly, the verification of a semi-rigid joint with M- characteristics is presented and the results compared with the component method of the Annex J of Eurocode 3. Next, the load-deflection frame characteristics of tested specimens are evaluated by means of the computational model developed. The stiffness degradation functions and their safety factors were verified accordingly. Finally, at the end, general remarks and detailed conclusions have been drawn directed towards the partical utilisation of the theoretical and experimental investigations carried out.

Słowa kluczowe

PL

modele obliczeniowe; węzły podatne; układy ramowe; układy imperfekcyjne

• Wydawca: Oficyna Wydawnicza Politechniki Warszawskiej
• Czasopismo: Prace Naukowe Politechniki Warszawskiej. Budownictwo
• Rocznik: 2000
• Tom: z. 136
• Strony: 3--285
• Opis fizyczny: Bibliogr. 216 poz., rys., tab.

Twórcy

autor

Giżejowski M.

• Instytut Konstrukcji Budowlanych PW