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2016, vol. 59, br. 3, str. 27-44
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Nelinearna analiza stabilnosti okvirnih nosača
Nonlinear stability analysis of the frame structures
aUniverzitet u Beogradu, Građevinski fakultet, Srbija bDžavni univerzitet u Novom Pazaru, Srbija
e-adresa: cstanko@grf.bg.ac.rs
Sažetak
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.
Abstract
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.
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Reference
|
|
|
*** (1971) CRC Japan: Handbook of structural stability. Tokyo: Corona
|
|
|
*** (2006) Eurocode 3, design of steel structures - ENV 1993-1-1:2005. European Committee for Standardization
|
|
|
*** (1978) European convention for constructional steelwork (ECCS): European recommendations for steel structures
|
|
|
*** (1993) Eurocode 3, design of steel structures: ENV 1993-1-1:1992. European Committee for Standardization
|
|
|
Allen, H.G., Bulson, P.S. (1980) Backgroung to buckling. U.K: McGraw-Hill
|
|
4
|
Bathe, K.J. (1982) Finite Element Procedures in Engineering Analysis. Prentice Hall
|
|
|
Bazant, Z.P., Cedolin, L. (2003) Stability of structures. New York, USA: Dover Publications
|
|
|
Buđevac, D., Marković, Z., Bogavac, D., Tošić, D. (1999) Metalne konstrukcije. Beograd: Građevinski fakultet
|
|
 
|
Chen, W.F. (2000) Structural stability: from theory to practice. Engineering Structures, 22(2): 116-122
|
|
|
Ćorić, S. (2013) Nelinearna analiza stabilnost okvirnih nosača. Beograd: Građevinski fakultet, doktorska disertacija
|
|
|
Ćorić, S. (2006) Prilog određivanju dužina stubova okvirnih nosača. Beograd: Građevinski fakultet, magistarski rad
|
|
|
Engesser, F. (1892) Ueber die Knickfestigkeit Gerader Stabe. Zeistschrift fur Architektur und Ingenieurwesen, 35
|
|
|
Farshi, B., Kooshesh, F. (2009) Buckling analysis of structural steel frames with inelastic effects according to codes. Journal of Constructional Steel Research, 65(10-11): 2078-2085
|
|
|
Gallagher, R.H. (1975) Finite Element Analysis. New Jersey: Prentice Hall
|
|
|
Gantes, C., Mageirou, G. (2005) Improves stiffness distribution factors for evaluation of effective buckling lengths in multi-story sway frames. Engineering Structures, Vol. 27, 7, pp. 1113-1124
|
|
|
Horne, M.R. (1975) An approximate method for calculating the elastic critical loads of multi-storey plane frames. Structural Engineer, Vol. 56, 6, pp. 242-248
|
|
|
Horne, M.R., Merchant, W. (1965) The stability of frames. Oxford: Pergamon
|
|
|
Massonnet, C.E., Maquoi, R. (1978) Recent progress in the field of structural stability of steel structures. Zurich, Switzerland: IABSE
|
|
|
Mcguire, W., Gallagher, R., Ziemain, R. (2000) Matrix structural analysis. New York, USA: John Wiley & Sons, 2nd edition
|
|
|
Rondal, J., Maquoi, R. (1979) Single equation for SSRC column strength curves. ASCE J. Struct. Div, Vol.105, No.ST 1, pp.247-250
|
|
7
|
Timoshenko, S.P., Gere, J.M. (1961) Theory of elastic stability. New York: McGraw-Hill
|
|
|
White, D.W., Hajjar, J.F. (1997) Buckling models and stability design of steel frames: a unified approach. Journal of Constructional Steel Research, 42(3): 171-207
|
|
|
White, D.W., Hajjar, J.F. (1997) Accuracy and simplicity of alternative procedures for stability design of steel frames. Journal of Constructional Steel Research, 42(3): 209-261
|
|
|
Yoo, H., Choi, D.H. (2008) New method of inelastic buckling analysis for steel frames. Journal of Constructional Steel Research, Vol. 64, 7, pp. 1152-1164
|
|
|
Zarić, B., Buđevac, D., Stipanić, B. (2000) Čelične konstrukcije u građevinarstvu. Beograd: Građevinska knjiga
|
|
|
Žugić-Zornija, Lj. (2009) Nelinearna analiza mostova sa kosim kablovima. Beograd: Građevinski fakultet, doktorska disertacija
|
|
|
|
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