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Keywords: high strength concrete, non-linear finite element analysis, inelastic buckling, effective buckling length.

Summary

The calculation of the effective buckling length in real concrete columns is not well studied. This is due to most of the performed research studied to obtain such a length are developed assuming a linear elastic material behaviour, which is far away for the case of reinforced concrete. In order to develop simplified models for analysis it is necessary to validate a numerical model which it will be able to recreate as much as possible the columns tested in the laboratory. To do that a bi-dimensional finite element numerical model in ATENA [1], was calibrated with our experiments. Hereinafter, this virtual laboratory allowed more tests to be performed to propose a new equation for the buckling length.

The buckling length is defined as L_b=beta L_o, where L_o is the real length of the element. If both, the column and the rotational springs are elastic, the buckling length agrees with the classical solution of the differential equation [2]. But if the column is inelastic, lower values of ß (effective buckling length) are observed. Conceptually this makes sense because the real concrete column has a lower stiffness due to cracking (and other effects) than the elastic one, therefore it is as though the rotational springs are more rigid, having a tendency toward the behaviour of the clamped-clamped column (which when elastic beta=0.5) .

The main problem is that the stiffness of concrete structures is not only dependent on the cracking, but also on the longitudinal reinforcement, the strength of concrete, etc.

If a sensitivity study is performed the strength of concrete and the longitudinal reinforcement ratio have the same influence in the inelastic beta coefficient, around 35 and 37%. However the yield stress of steel does not have any influence.

If a comparative study is performed between the numerical model and the different codes, it can be shown that there are representative differences with respect to all of them: the ACI code (between 37% and -3%), with the Spanish code EHE (26% and -9.26%), with the Euro code 2 (between the 14% and -14%) and regarding Traver and Bonet (14% and -7%) [3]. It was decided to propose a new equation for the effective buckling length for non-sway column.

Three types of equations are proposed for the inelastic effective buckling length: one complete and two simplified (checking and design). It can be noticed that the medium error is 2.6% for checking and around 7.6% for design in the safe side, which it improves greatly the existing methods in the codes.

References

1: Cervenka V., "Applied brittle analysis of concrete structures", In: Mihashi, H., Rokugo, K. (Eds.), Fracture Mechanics of Concrete Structures (Proc. 5th Int. Conf. FraMCoS-5, Gifu, Japan), vol. 4. postconf. Aedificatio Publ., Freiburg, Germany, pp. 1107-1116, 1998.
2: Chen W.F. and Lui E.M., Stability Design of Steel Frames, CRC Press, Boca Raton, FL, 1991.
3: Traver J., Bonet J.L., "Cálculo del factor de amplificación de momentos en soportes esbeltos intraslacionales de hormigón armado en flexo-compresión esviada", Master Thesis, E.T.S.I.C.C.P, Valencia 2002. (In Spanish)

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 86 PROCEEDINGS OF THE ELEVENTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING Edited by: B.H.V. Topping Paper 177 Numerical Analysis of the Inelastic Buckling Length of Non-Sway Reinforced Concrete Columns A. Bendito¹, M.L. Romero², J.L. Bonet², P.F. Miguel² and M.A. Fernandez² ¹Engineering Department, Núcleo Universitario Rafael Rangel, University of Los Andes, Venezuela ²Institute of Science and Technology of Concrete, Technical University of Valencia, Spain doi:10.4203/ccp.86.177 purchase the full-text of this paper Full Bibliographic Reference for this paper A. Bendito, M.L. Romero, J.L. Bonet, P.F. Miguel, M.A. Fernandez, "Numerical Analysis of the Inelastic Buckling Length of Non-Sway Reinforced Concrete Columns", in B.H.V. Topping, (Editor), "Proceedings of the Eleventh International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 177, 2007. doi:10.4203/ccp.86.177 Keywords: high strength concrete, non-linear finite element analysis, inelastic buckling, effective buckling length. Summary The calculation of the effective buckling length in real concrete columns is not well studied. This is due to most of the performed research studied to obtain such a length are developed assuming a linear elastic material behaviour, which is far away for the case of reinforced concrete. In order to develop simplified models for analysis it is necessary to validate a numerical model which it will be able to recreate as much as possible the columns tested in the laboratory. To do that a bi-dimensional finite element numerical model in ATENA [1], was calibrated with our experiments. Hereinafter, this virtual laboratory allowed more tests to be performed to propose a new equation for the buckling length. The buckling length is defined as L_b=beta L_o, where L_o is the real length of the element. If both, the column and the rotational springs are elastic, the buckling length agrees with the classical solution of the differential equation [2]. But if the column is inelastic, lower values of ß (effective buckling length) are observed. Conceptually this makes sense because the real concrete column has a lower stiffness due to cracking (and other effects) than the elastic one, therefore it is as though the rotational springs are more rigid, having a tendency toward the behaviour of the clamped-clamped column (which when elastic beta=0.5) . The main problem is that the stiffness of concrete structures is not only dependent on the cracking, but also on the longitudinal reinforcement, the strength of concrete, etc. If a sensitivity study is performed the strength of concrete and the longitudinal reinforcement ratio have the same influence in the inelastic beta coefficient, around 35 and 37%. However the yield stress of steel does not have any influence. If a comparative study is performed between the numerical model and the different codes, it can be shown that there are representative differences with respect to all of them: the ACI code (between 37% and -3%), with the Spanish code EHE (26% and -9.26%), with the Euro code 2 (between the 14% and -14%) and regarding Traver and Bonet (14% and -7%) [3]. It was decided to propose a new equation for the effective buckling length for non-sway column. Three types of equations are proposed for the inelastic effective buckling length: one complete and two simplified (checking and design). It can be noticed that the medium error is 2.6% for checking and around 7.6% for design in the safe side, which it improves greatly the existing methods in the codes. References 1 Cervenka V., "Applied brittle analysis of concrete structures", In: Mihashi, H., Rokugo, K. (Eds.), Fracture Mechanics of Concrete Structures (Proc. 5th Int. Conf. FraMCoS-5, Gifu, Japan), vol. 4. postconf. Aedificatio Publ., Freiburg, Germany, pp. 1107-1116, 1998. 2 Chen W.F. and Lui E.M., Stability Design of Steel Frames, CRC Press, Boca Raton, FL, 1991. 3 Traver J., Bonet J.L., "Cálculo del factor de amplificación de momentos en soportes esbeltos intraslacionales de hormigón armado en flexo-compresión esviada", Master Thesis, E.T.S.I.C.C.P, Valencia 2002. (In Spanish) purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £120 +P&P)
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