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

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

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

Elasto-plastic stability analysis of the frame structures using the tangent modulus approach

This paper presents the procedure for stability analysis of frames in elastic-plastic domain using the concept of the tangent modulus. 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. Formulation of the corresponding stiffness matrices is based upon the solution of the equation of bending of the beam according to the second order theory. Numerical analysis was performed using the code ALIN, developed in the C++ programming language

Iterative displacement coefficient method: mathematical formulation and numerical analyses

U radu je prikazana matematička formulacija i numerička analiza originalno razvijene iterativne metode koeficijenata pomaka (IDCM - Iterative Displacement Coefficient Method). IDCM je postupak iz područja istraživanja utjecaja potresa na građevine primjenom nelinearne statičke pushover analize. Razina ciljanog pomaka prema IDCM se određuje primjenom dvostrukog iterativnog postupka. Prvi iterativni postupak provodi se simultano po silama i po pomaku, dok se drugi iterativni postupak provodi korekcijom dobivenog rješenja za razinu ciljanog pomaka po pushover krivulji. IDCM je implementirana u racunalni program Nonlin Quake TD.The mathematical formulation and numerical tests of the originally developed Iterative Displacement Coefficient Method (IDCM) are presented in the paper. The IDCM method is a procedure in the field of seismic analysis of structures that is based on the Nonlinear Static Pushover Analysis. The target displacement level is determined by means of a double iterative procedure developed in the IDCM. The first iterative procedure is carried out simultaneously by forces and displacements, while the second iterative procedure is conducted by correction of the solution obtained for the level of target displacement along a pushover curve. The IDCM method is incorporated in the computer code Nonlin Quake TD

Metodologija pripreme i obrade akcelerograma za linearne i nelinearne seizmičke analize konstrukcija

U radu je dat prikaz metodologije za pripremu i obradu akcelerograma koji se koriste za seizmički proračun konstrukcija. Definisani su termini i detaljnije obrazložene procedure koje se sprovode nad akcelerogramima kao što su: selekcija, formatiranje, konvertovanje, skaliranje, kalkulacija, procesiranje, kompatibilizacija, normalizacija, filtriranje, generisanje i transformacija. Ove procedure se izvršavaju u vremenskom, frekventnom, FFT frekventnom, FFT frekventno- vremenskom i kapacitativnom domenu. Jasno su postavljene granice između procedura definisanjem termina za svaku po na osob, tako da su pojedine procedure međusobno autonomne, ali sa druge strane matematičke formulacije i fizikalnost problema određenih procedura se preklapaju ili su komplementarne

HE DEVELOPMENT OF CONTROLLED DAMAGE MECHANISMS-BASED DESIGN METHOD FOR NONLINEAR STATIC PUSHOVER ANALYSIS

Abstract. This paper presents the original method of controlled building damage mechanisms based on Nonlinear Static Pushover Analysis (NSPA-DMBD). The optimal building damage mechanism is determined based on the solution of the Capacity Design Method (CDM), and the response of the building is considered in incremental situations. The development of damage mechanism of a system in such incremental situations is being controlled on the strain level, examining the relationship of current and limit strains in concrete and reinforcement steel. Since the procedure of the system damage mechanism analysis according to the NSPA-DMBD method is being iteratively implemented and designing checked after the strain reaches the limit, for this analysis a term Iterative-Interactive Design (IID) has been introduced. By selecting, monitoring and controlling the optimal damage mechanism of the system and by developed NSPA-DMBD method, damage mechanism of the building is being controlled and the level of resistance to an early collapse is being increased.Key words: damage mechanisms, strains, Capacity Design Method, Nonlinear Static Pushover Analysis, Iterative-Interactive Design

Analiza mehanizama loma zgrada razmatranjem statičke neodređenosti i kinematičke stabilnosti

U radu je prikazan koncept analize mehanizama loma zgrada bazirajući se na osnovnim stavovima iz statike konstrukcija, razmatrajući statičku neodređenost i kinematičku stabilnost. Istraživanje je sprovedeno modelirajući mehanizme loma koji se uobičajeno javljaju kod zgrada izloženih dejstvu zemljotresa: prema metodi programiranog ponašanja (CDM - Capacity Design Method), “jaki stubovi - slabe grede”, “slabi stubovi - jake grede”, “meki sprat”, “fleksibilno prizemlje”, “diskontinuitet krutosti”, uticaj krutog parapeta, sistem sa konzolnim delom, sistemi neregularni po visini, sistem ukrućen vertikalnim armiranobetonskim zidom i sa izmeštenim delom zida u prizemlju. Takođe, razmatrani su i složeni mehanizmi loma koji se javljaju kao kombinacija čistih ili parcijalno razvijenih više prethodno nabrojanih mehanizama loma