Nonlinear stability analysis of the frame structures

In this paper the phenomenon of instability of frames in elasto-plastic domain was investigated. Numerical analysis was performed by the finite element method. Stiffness matrices were derived using the trigonometric shape functions related to exact solution of the differential equation of bending according to the second order theory. When the buckling of structure occurs in plastic domain, it is necessary to replace the constant modulus of elasticity E with the tangent modulus Et. Tangent modulus is stress dependent function and takes into account the changes of the member stiffness in the inelastic range. For the purposes of numerical investigation in this analysis, part of the computer program ALIN was created in a way that this program now can be used for elastic and elasto-plastic stability analysis of frame structures. This program is developed in the C++ programming language. Using this program, it is possible to calculate the critical load of frames in the elastic and inelastic domain. In this analysis, the algorithm for the calculation of buckling lengths of compressed columns of the frames was also established. The algorithm is based on the calculation of the global stability analysis of frame structures. Results obtained using this algorithm were compared with the approximate solutions from the European (EC3) and national (JUS) standards for the steel structures. By the given procedure in this paper it is possible to follow the behavior of the plane frames in plastic domain and to calculate the real critical load in that domain

Column Buckling Investigation of Plane Frames

This paper deals with elastic stability analysis of the plane frame structures. The main aim is to investigate the accuracy of related parts of European and domestic codes for steel and concrete structures. Numerical analysis of frame structures is performed using the self-developed Matlab computer program. Matrix analysis of the whole structure according to the second order theory, based on the application of trigonometric shape functions, is applied. As opposed to that, the dominant approach given in most structural codes is based upon the stability analysis of compressed structural elements isolated from the structure as a whole. Several numerical examples are given in the paper and comparative analyses presented herein show that, in some cases, solutions given in domestic and European codes are rather inaccurate. For example, the error in the determination of the effective buckling length of frame columns can sometimes exceed even 100%. Finally, it is concluded that innovation of actual codes should be done in the part where the effective buckling length of frame columns is considered. Improvement of this calculation could be achieved using the global stability approach and the corresponding calculation of the critical load for complete structure, as it is presented in the paper

Nelinearna analiza stabilnosti okvirnih nosača

In this paper the phenomenon of instability of frames in elasto-plastic domain was investigated. Numerical analysis was performed by the finite element method. Stiffness matrices were derived using the trigonometric shape functions related to exact solution of the differential equation of bending according to the second order theory. When the buckling of structure occurs in plastic domain, it is necessary to replace the constant modulus of elasticity E with the tangent modulus Et. Tangent modulus is stress dependent function and takes into account the changes of the member stiffness in the inelastic range. For the purposes of numerical investigation in this analysis, part of the computer program ALIN was created in a way that this program now can be used for elastic and elasto-plastic stability analysis of frame structures. This program is developed in the C++ programming language. Using this program, it is possible to calculate the critical load of frames in the elastic and inelastic domain. In this analysis, the algorithm for the calculation of buckling lengths of compressed columns of the frames was also established. The algorithm is based on the calculation of the global stability analysis of frame structures. Results obtained using this algorithm were compared with the approximate solutions from the European (EC3) and national (JUS) standards for the steel structures. By the given procedure in this paper it is possible to follow the behavior of the plane frames in plastic domain and to calculate the real critical load in that domain.U ovom radu istraživan je fenomen gubitka stabilnosti okvirnih nosača u elasto-plastičnoj oblasti. Numerička analiza je sprovedena primenom metode konačnih elemenata. Matrice krutosti su izvedene korišćenjem trigonometrijskih interpolacionih funkcija koje se odnose na tačno rešenje diferencijalne jednačine savijanja štapa prema teoriji drugog reda. U slučaju kada se izvijanje konstrukcije dešava u plastičnoj oblasti, konstantan modul elastičnosti E u matrici krutosti zamenjen je tangentnim modulom Et koji prati promenu krutosti štapa u neelastičnoj oblasti i funkcija je nivoa opterećenja u štapu. Za potrebe ove analize formiran je deo računarskog programa ALIN koji može da se koristi za elastičnu i elasto-plastičnu analizu stabilnosti okvirnih konstrukcija. Program je napisan u C++ programskom jeziku. Primenom ovog programa omogućeno je i određivanje kritičnog opterećenja okvirnih nosača u elastičnoj i neelastičnoj oblasti. U ovom istraživanju formiran je i algoritam za proračun dužina izvijanja pritisnutih štapova stubova okvirnih nosača, a koji se bazira na proračunu globalne analize stabilnosti okvirne konstrukcije. Rezultati dobijeni primenom ovog algoritma upoređeni su s rešenjima koja se dobijaju korišćenjem evropskih EC3 i domaćih JUS standarda za okvirne čelične konstrukcije, a koja su približnog karaktera. Na osnovu postupka koji je dat u ovom radu moguće je praćenje fenomena gubitka stabilnosti okvirnog nosača u plastičnoj oblasti i direktno određivanje njegove kritične sile u toj oblasti

Nelinearna analiza stabilnosti okvirnih nosača

The research related to work on my doctoral thesis is presented in this paper. The basic subject of proposed PhD research is related to the numerical simulation of elastic and non-elastic stability analysis of frame structures. The existing structural codes neither observe the structural stability of frame structures in general and nor take into account the contemporary potential available for structural engineers. So, the global nonlinear stability analysis of the frame structures is suggested. This numerical analysis will be performed using the suitable combination of commercial software and the corresponding home-made programming. .U ovom radu ukratko je prikazan sadržaj istraživanja koji će biti sastavni deo doktorske disertacije. Predmet istraživanja predložene disertacije je numerička simulacija problema stabilnosti okvirnih nosača u elastičnoj i neelastičnoj oblasti. Postojeći način proračuna konstrukcija, na osnovu aktuelnih propisa, ne uzima u obzir mogućnosti savremenih kompjutera koji su dostupni građevinskim inženjerima. Zato se u ovom radu analizira mogućnost nelinearne analize okvirnih nosača u celini. Numerička analiza će biti obavljena korišćenjem kombinacije komercijalnog softvera i sopstvenog programa

Elasto-plastična analiza stabilnosti okvirnih nosača pomoću programa ALIN

This paper presents the procedure for stability analysis of frame structures in elasto-plastic domain. This analysis is performed using the code ALIN, developed in the C++ programming language. In this code the stiffness matrix is derived using interpolation functions related to the exact solution of the differential equation of bending of a beam according to the second-order theory. Also, the concept of tangent modulus is applied for the stability calculation in the inelastic domain.Zbornik radova Građevinskog fakultet

Parametarska analiza stabilnosti čeličnih okvirnih nosača

In this paper it is presented parametric stability analysis of frame structures with accuracy assessment of solutions given in codes for design of steel structures. Method for calculating the critical load and the effective buckling length of the frame structures that is based on the global stability analysis is formulated. According to results of analysis of the whole structure, the critical load and effective buckling length for each column member can be obtained. The numerical analysis in this paper is based on the calculation of the critical load in elaso-plastic domain.Zbornik radova Građevinskog fakultet

Proračun stabilnosti okvirnih nosača

Poslednjih nekoliko decenija značajno su se unapredila saznanja u vezi proračuna stabilnosti okvirnih nosača. Zato je u ovom radu dat pregled postupaka iz ove oblasti. Prikazane su tradicionalne metode koje se baziraju na teoriji izolovanog štapa, ali i savremene metode koje se primenjuju metodu konačnih elemenata. Posebno je istraživan fenomen gubitka stabilnosti okvirnih nosača u elasto-plastičnoj oblasti. Tako je numerička analiza obavlјena primenom metode tangetnog modula, što znači da je konstantan modul elastičnosti u matrici krutosti zamenjen tangentnim modulom koji prati promenu krutosti štapa u neelastičnoj oblasti. Matrice krutosti su izvedene korišćenjem trigonometrijskih interpolacionih funkcija koje se odnose na tačno rešenje diferencijalne jednačine savijanja štapa prema teoriji drugog reda. Prikazani proračun se zasniva na analizi globalne stabilnosti okvirnih nosača

Izvijanje okvirnih nosača u plastičnoj oblasti

This paper presents plastic buckling analysis of steel frames. Sway and non-sway frames were considered. It was shown that by applying the matrix analysis according to second order theory, critical load of the whole system and the effective buckling length of each frame column can be found. Numerical analysis was performed using the self-developed computer program based on the exact solution and transcendental shape functions were applied. The calculation was also carried out according to actual domestic and European codes. Comparative numerical analysis presented herein shows what kind of error can be obtained using the actual codes in the part which is related to effective length calculation of steel frames that buckle in plastic domain.U ovom radu prikazana je analiza izvijanja okvirnih čeličnih nosača u plastičnoj oblasti. Analizirani su nosači sa pomerljivim i nepomerljivim čvorovima. Pokazano je kako se primenom matrične analize po teoriji drugog reda može odrediti kritično opterećenje okvirnih sistema, a zatim i dužine izvijanja pojedinih štapova. Numerička analiza je obavljena pomoću sopstvenog programa koji se bazira na tačnom rešenju, pa su interpolacione funkcije usvojene u transcendetnom obliku. Takođe, proračun je sproveden i prema aktuelnim domaćim i evropskim propisima. Na kraju je izvršeno upoređivanje rezultata koji su dobijeni ovim postupcima i zaključeno je kolike greške mogu da se naprave primenom aktuelnih propisa u delu koji se odnosi na proračune dužine izvijanja stubova okvirnih čeličnih nosača koji se izvijaju u plastičnoj oblasti

Izvijanje okvirnih nosača u plastičnoj oblasti

This paper presents plastic buckling analysis of steel frames. Sway and non-sway frames were considered. It was shown that by applying the matrix analysis according to second order theory, critical load of the whole system and the effective buckling length of each frame column can be found. Numerical analysis was performed using the self-developed computer program based on the exact solution and transcendental shape functions were applied. The calculation was also carried out according to actual domestic and European codes. Comparative numerical analysis presented herein shows what kind of error can be obtained using the actual codes in the part which is related to effective length calculation of steel frames that buckle in plastic domain.U ovom radu prikazana je analiza izvijanja okvirnih čeličnih nosača u plastičnoj oblasti. Analizirani su nosači sa pomerljivim i nepomerljivim čvorovima. Pokazano je kako se primenom matrične analize po teoriji drugog reda može odrediti kritično opterećenje okvirnih sistema, a zatim i dužine izvijanja pojedinih štapova. Numerička analiza je obavljena pomoću sopstvenog programa koji se bazira na tačnom rešenju, pa su interpolacione funkcije usvojene u transcendetnom obliku. Takođe, proračun je sproveden i prema aktuelnim domaćim i evropskim propisima. Na kraju je izvršeno upoređivanje rezultata koji su dobijeni ovim postupcima i zaključeno je kolike greške mogu da se naprave primenom aktuelnih propisa u delu koji se odnosi na proračune dužine izvijanja stubova okvirnih čeličnih nosača koji se izvijaju u plastičnoj oblasti

Stability analysis of multi-story steel frames subjected to different axial load

This paper presents a stability analysis of multi-story steel frames in the elastic and elasto-plastic domain. The concept of the tangent modulus theory is applied. Numerical analysis is carried out using FEM where corresponding stiffness matrices are based upon the trigonometric and hyperbolic interpolation functions of normal forces. Also, the calculation algorithm is based on the global stability analysis of the considered frames. The numerical analysis is performed using the self-developed computer program ALIN. A six-story three-bay steel frame was chosen as a benchmark numerical example. Sway and non-sway frames that are clamped at the base are analyzed separately. Two load cases are considered: when the axial forces are applied at the top of the frame and when these forces are applied at each story of the frame. From the obtained results it is obvious the weakness of the traditional elastic stability analysis. Therefore, stability analysis in the inelastic domain is recommended, especially in the case of rigid structures