Abstract: A comparative study was undertaken of selected computational methods for predicting the strength determined from more than 500 physical tests of rectangular, tied structural concrete columns available in the literature. The study included 354 reinforced concrete and 150 composite steel-concrete columns. The computational methods compared were those of CSA A23.3-94 and Eurocode 2 for reinforced concrete and those of CSA A23.3-94 and Eurocode 4 for composite columns. The physical tests used for comparison were conducted on columns that were braced, pinned at both ends, subjected to short-term loads, and constructed using normal-density concrete with a compressive strength between approximately 17 and 57 MPa. Major variables included the concrete strength, the end eccentricity ratio, the slenderness ratio, the longitudinal reinforcing steel index for reinforced concrete or the structural steel index for composite columns, and the transverse reinforcement (tie/hoop) volumetric ratio. The study provided insights into the reliability of the computational methods examined. Recommendations for improving the CSA A23.3-94 procedure for the design of reinforced concrete and composite steel-concrete columns are also presented.
Key words: columns, composite construction, computations, physical tests, reinforced concrete, reliability, strength.
Resume : Une etude comparative a ete entreprise sur des methodes de calcul selectionnees pour predire la resistance a partir de plus de 500 essais physiques de poteaux structuraux rectangulaires, lies, en beton et disponibles dans la litterature. Cette etude comprenait 354 poteaux en beton arme et 150 poteaux composites acier-beton. Ces methodes de calcul etaient la CSA A23.3-94 et l'Eurocode 2 pour le beton arme et CSA A23.3-94 et Eurocode 4 pour les poteaux composites. Les essais physiques utilises pour la comparaison ont ete realises sur des poteaux qui etaient contreventes, goupilles aux deux extremites, soumis a des charges temporaires et batis en utilisant un beton de densite normale ayant une resistance en compression entre 17 et 57 MPa. Les principales variables comprenaient la resistance du beton, le rapport d'excentricite des extremites, le rapport d'elancement, l'indice d'acier d'armature de renforcement longitudinal pour le beton arme ou l'indice d'acier d'armature pour les poteaux composites ainsi que le rapport volumetrique de renforcement transversal (<< tie/hoop >>). L'etude a fournit un apercu de la fiabilite des methodes de calcul examinees. Des recommandations pour ameliorer la procedure CSA A23.3-94 pour calculer les poteaux en beton arme et composites acier-beton sont egalement presentees.
Mots cles : poteaux, construction composite, calculs, essais physiques, beton arme, fiabilite, resistance.
[Traduit par la Redaction] Mirza 747
Introduction
To examine the accuracy of selected methods for computing the strengths of reinforced concrete and composite steel-concrete columns in which steel sections are encased in concrete, a comparative study was conducted. The computational methods compared included those of CSA A23.3-94 (CSA 1994) and Eurocode 2 (CEN 1992) for reinforced concrete columns and those of CSA A23.3-94 and Eurocode 4 (CEN 1994) for composite columns. The CSA design method is strongly influenced by the column effective flexural stiffness (EI), which varies as a result of cracking, creep, and nonlinearity of the concrete stress-strain curve. To account for some of these variables, Mirza (1989) and Mirza and Tikka (1998a, 1998b) proposed refined equations for calculating the flexural stiffness of reinforced concrete and composite columns, respectively, designed according to the CSA procedures. These equations were also included in the study reported here.
The 354 physical tests of rectangular reinforced concrete columns reported in 25 investigations and the 150 physical tests of rectangular concrete-encased steel composite columns reported in 8 investigations were taken from the literature and used for the comparative study. The study included only those column tests for which the complete information required for analysis was available from the published data. No new physical tests were conducted as part of this study. The columns were braced, pin-ended, and subjected to shortterm loads producing pure axial force, combined axial force and symmetrical single-curvature bending, or pure bending. The columns used in this investigation are graphically represented in Fig. 1.
[FIGURE 1 OMITTED]
Major variables investigated in this study include the concrete strength (f'.sub.c]), the end eccentricity ratio (e/h), the slenderness ratio (l/h), the longitudinal reinforcing steel index ([[rho].sub.rs][f.sub.yrs/[f'.sub.c]) for reinforced concrete columns or the structural steel index ([[rho].sub.ss][f.sub.yss]/[f'.sub.c]) for composite columns, and the transverse reinforcement (tie/hoop) volumetric ratio ([rho]"), where e is the eccentricity of the axial load at column ends; h is the overall depth of the column cross section taken perpendicular to the axis of bending; l is the length of the column; [f.sub.yrs] is the yield strength of longitudinal reinforcing steel bars; [f.sub.yss] is the yield strength of the structural steel section; [[rho].sub.rs] is the ratio of the cross-sectional area of longitudinal reinforcing bars to the overall area of the column cross section (longitudinal reinforcing steel ratio); and [[rho].sub.ss] is the ratio of the cross-sectional area of the structural steel section to the overall area of the column cross section (structural steel ratio). Comparisons of different computational methods, as well as evaluations of major variables affecting the strength, were based on statistical analyses of the ratios of tested strengths to computed strengths (strength ratios). These evaluations and comparisons provided insights for the critical review of the reliability and related statistics of the computational methods examined and are presented and discussed in detail in this paper. As the column specimens were constructed with normal-density, normal-strength concrete with compressive strengths between approximately 17 and 57 MPa, the results of the study are limited to such columns. A similar study on high-strength concrete columns is in the initial stage.
Physical tests used
The experimental results used in this study for rectangular, tied reinforced concrete column specimens were taken from 354 short-term physical tests reported by Bresler (1960), Bresler and Gilbert (1961), Bunni (1975), Chang and Ferguson (1963), Cusson and Paultre (1994), Drysdale and Huggins (1971), Ernst et al. (1953), Fang et al. (1994), Gaede (1958), Goyal and Jackson (1971), Green and Hellesland (1975), Heimdahl and Bianchini (1975), Hognestad (1951), Hudson (1965), Kim and Yang (1995), Martin and Olivieri (1965), Mehmel et al. (1969), Pfister (1964), Ramu et al. (1969), Razvi and Saatcioglu (1989), Roy and Sozen (1964), Scott et al. (1982), Sheikh and Uzumeri (1980), Todeschini et al. (1964), and Viest et al. (1956). Of these test specimens, 163 were subjected to pure axial load, and the remaining 191 were subjected to combined axial load and symmetrical single-curvature bending. The geometric and material properties of the reinforced concrete test specimens are summarized in Table 1. The experimental data used in this study for rectangular, tied composite column specimens were taken from 150 short-term physical tests reported by Anslijn and Janss (1974), Morino et al. (1984), Procter (1967), Roderick and Loke (1974), Roik and Mangerig (1987), Roik and Schwalbenhofer (1988), Stevens (1965), and Suzuki et al. (1984). These tests were conducted on composite column specimens with steel sections encased in concrete. Of these test specimens, 58 were subjected to pure axial load, 76 were subjected to axial load combined with symmetrical single curvature bending, and the remaining 16 were subjected to pure bending. Note that the specimens tested under pure bending had cross-sectional details normally used for columns and were included in this study so that the entire P-M interaction diagram could be investigated. The geometric and material properties of the composite specimens are summarized in Table 2. The physical failure strength of a column specimen was defined as the peak strength reached on the load-deflection or moment-deflection response curve.
In this study, the concrete strength (f'.sub.c]) was defined as the strength obtained from the standard 150 mm diameter x 300 mm cylinder tests or as the equivalent standard cylinder strength computed from cube tests. For some of the physical tests, the cube test strengths were reported. In such cases, the reported strengths were converted to the equivalent standard cylinder strengths by using the following procedure, documented by Mirza et al. (1979). The strength of a cube of a given size was first converted to the strength of a 150 mm cube by using an equation proposed by Bolotin (1969), and this computed strength of the 150 mm cube was then converted to the equivalent strength of a standard cylinder by using an equation proposed by L'Hermite (1955). The longitudinal reinforcing and structural steel yield strengths ([f.sub.yrs] and [f.sub.yss]) were taken as those for bar and coupon sample tests reported in individual studies.
Calculation procedures examined
The computed strengths were based on CSA A23.3-94 (CSA 1994) and Eurocode 2 (CEN 1992) for reinforced concrete and CSA …
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