ࡱ> 7967 *bjbjUU Z7|7|%lfffffff4h$ |"NNNNNNNC"E"E"E"E"E"E"$# %i"!fNNNNNi"ffNN"NfNfNC"NC"66ff N CӃt!`N ,"0"~&~& ffff RELIABILITY OF COMPOSITE COLUMNS AND BEAM-COLUMNS IN EC-4 Marta Sulyok Professor of Structural Engineering, University of Zagreb, Faculty of Architecture 10000 Zagreb, Ka ieva 26, Croatia Summary The reliability of the design methods in EUROCODE 4, Composite Construction, for composite columns is studied in this paper. The investigation is made for both concrete-filled tubes and concrete encased profiles. The research compares the available test-results with the design model of EC-4 using the second order reliability method. Introduction Since the 1950's, researchers have tested and tried to explain the behavior of composite columns loaded axially and eccentrically. Tests have included both circular and rectangular steel tubes filled with concrete as well as shapes surrounded by concrete, sometimes including steel reinforcing bars within the sections. By the EC-4 approach evaluated predicted strength have to be compared to available composite column and beam-column test results in order to find out how well this design code models actual behavior. This will also give the statistical basis, which is needed in the reliability study. Reliability index will be determined by the given statistics of the basic variables and this will also indicate how well the design model of EC-4 meet the target value =3.8 which is prescribed. As in the codes of practice exist different methods for the design of composite columns, EC-4 is analyzed and the results are compared with AISC of LRFD criteria of model design. Available experimental results Composite columns can be broadly classified as either steel sections encased in concrete, or hollow sections filled with concrete, which are circular, square and rectangular tubes. From the published test results the information are gathered, which include tests on fifty-two encased steel I shapes and one hundred forty-six concrete filled circular steel tubes in axial compression analyzed in this paper. The experiments for the encased steel I-shapes included in SSRC report (1979) and for the concrete-filled steel tube columns, the tests were published by Gardner and Jacobson (1967) with the very high yield stress on steel tubes. The experiments are made with the varied diameters of concrete filled circular tubes, and the overall results of these specimens compare fairly well with the expectation. The tests for the circular steel tubes are selected in eighty specimens. Eurocode 4 design model for composite column From European Committee for standardization publicized ENV-1994 for EC-4, defined the model design for Composite Structure of Steel and Concrete and the design rules for the composite columns are analyzed in this paper in order to verify the probabilistic concepts of safety for the resistance model through the use of partial safety factors in following format:  EMBED Equation.2  (1) where are adopted respectively partial safety factors applied to steel, concrete and reinforcing steel: (a , (c , (s and (RD, the additional partial safety factor to be introduced when stability is concerned. Ultimate limit state design is applied with the partial safety factors for the actions and for use in this paper only the combination of the permanent and one variable action is made as:  EMBED Equation.2  (2) with Gk and Qkl -as characteristic values of permanent action and one variable action. The general method of the design takes account of second order effects including imperfections and the non-linear material behaviour. The need to simplify design methods leads to basic design curves for composite columns under certain assumptions, and adopts the European buckling curves originally established for bare steel columns. Both design methods assume full composite action up to failure without slip at the steel-concrete interface. These methods are derived from German practice specified in DIN 18806[3]. The reduced concrete properties are used to account for the effects of creep and the use of the un-cracked concrete section in stiffness calculation. Slenderness effects are accounted for the use of a non-dimensional slenderness parameter with equivalent stiffness and the code recognized the confinement effect in-filled columns. Consequently, the method is applicable to symmetric sections and is restricted to the range of sections catered for in the European buckling curves. The simplified design method gives the plastic resistance of the cross-section to compression by the sum of the resistances of the components as follows:  EMBED Equation.2  (3) where:  EMBED Equation.2  The design strength of the respective materials are defined with partial safety factors given in Eq (1). fyyield strength of the steel sectionfccompressive strength of the concrete(cstrength coefficient for concrete is:fsyield strength of the reinforcing steelAaarea of steel sectionAcarea of concrete sectionAsarea of reinforcing bars An important design parameter is the steel contribution ratio (, which is defined as follows:  EMBED Equation.2  (4) Effective elastic flexural stiffness (EI)e as defined in [1] Eq (11) and is used in Eq (10) under EC-4 clause 4.8.3.5(1) for elastic critical buckling load Ncr and for the evaluation of the non-dimensional slenderness of the column  EMBED Equation.2 , defined in [1] Eq (14) EC-4 clause 4.8.3.7(2) with the plastic resistance of the cross-section to compression NplR according to Eq(3) and the coefficients (a=(c=(s=1.0 .Resistance of members to axial compression must be verified:  EMBED Equation.2  (5) ( reduction factor due to the composite column buckling according to the European curves a, b, c  Reliability analysis for realized reliability index ( In order to evaluate the influence of the model for the designed resistance by EC-4 of composite columns, the tested-to-predicted load ratio is calculate for each of the specified and grouped specimens taken from the available experimental results. They are analyzed for the predicted load capacity of axial compression using the actual section and material properties. The statistics are defined by mean value and standard deviation in the expression of the resistance as the basic random variable with normal distribution function. In the case of the reliability of the axial compressed composite columns, the resistance as random variable is defined by equivalent ( strength reduction derived using the European Steel Buckling Curves in the conjunction with the composite cross-sectional properties in the form of slenderness parameters  EMBED Equation.2 . The reliability index (, measures the probability that g is less or equal to zero.  EMBED Equation.2  (6) Monte Carlo simulation technique is used to generate 10000 samples with the normal distribution density function and the given statistics. The realized index ( for encased I shapes is 3.28 (n=52) and for concrete filled tubes 3.18 (n=146). As (s are lower than prescribed by EC-4 it is necessary to reexamine the statistics for the basic random variables. The basic random variables were assumed to be mutually independent and Monte Carlo simulation is used for the non-linear g-function. The reliability index was shown to be independent of the system parameters. Comparing with the realized AISC-LRFD values of the (s, which are lower than by design model of EC-4, and are 2.7 for encased steel-sections and 2.5 for concrete filled steel tubes, EC-4 is more on conservative side. By the mentioned technique of simulation, if we want to achieved reliability index 3.80, the statistics of tested-to-predicted ratios must have mean value 2.0 and standard deviation 0.2, which is impossible to realize by the used groups of the experiments data. The results are in Tab.1. Conclusion As the realized reliability indices for composite columns are lower than by EC-4 prescribed target value 3.80, it is necessary to re-examine the statistics of actual-to-nominal parameters as well as on resistance and load action side. The reliability index (=3.28 (n=52) for encased I-sections is near to the reduced reliability level, which may exist from the limited number of specimens and various quality of concrete included in the test results. The large number of specimens for concrete filled steel tubes (n=146) give the scattering in results (SX(1)=0.238) which leads to (=3.18. As for the beam-columns, reliability indices are 2.88 and 2.99 adequately for the same sections, which are less on the conservative side, and also lower than prescribed. Table 1 Reliability indices for composite columns in axial compression TYPE OF COLUMNSMX (1)SX (1)n( for EC-4( for LRFDEncased steel I-sections1.4900.181523.282.7Concrete filled circular tubes1.5690.2381463.182.5 References: Chung, K. F and Narayanan, R.,1994,Composite Column Design to Eurocode 4, The Steel Construction Institute Publication 142. ENV 1994-1-1:1992: Eurocode 4, Design of Composite Steel and Concrete Structures-Part 1-1: General rules and rules for buildings, European Committee for Standardization. DIN 18806 Teil 1. Verbundkonstruktionen, Verbundsttzen. (3.84). 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