• Structural Engineering and Mechanics
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• v.12 no.3
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• pp.329-339
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• 2001

The present paper deals with the effective slenderness ratio of telescopic cylinders as a long column having different cross sections. Firstly, the slenderness ratio defined in the current standard for the telescopic cylinders is discussed to point out some difficulties which arise when the ratio is applied to the column having different cross sections. Secondly, a new effective slenderness ratio is proposed for columns having different cross sections by introducing a partial effective slenderness ratio. Finally, the proposed slenderness ratio is applied, for extending and development of discussion, to a two-staged column having piece-wise constant cross sections and a cylindrical column having linearly varying diameters.

• Structural Engineering and Mechanics
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• v.50 no.2
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• pp.201-214
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• 2014

Due to the confinement effects, Steel-Straps Tensioning Technique (SSTT) can significantly enhance the strength and ductility of high-strength concrete (HSC) members (Moghaddam et al. 2008). However, the enhancement especially in strength may result in slender member and more susceptible to instability (Jiang and Teng 2012a). This instability is particularly significant in HSC member as it inherent the brittle nature of the material (Galano et al. 2008). The current slenderness limit expression used in the design is mainly derived from the experiment and analysis results based on Normal strength concrete (NSC) column and therefore the direct application of these slenderness limit expressions to the HSC column is being questioned. Besides, a particular slenderness limit for the SSTT-confined HSC column which incorporated the pre-tensioned force and multilayers effects is not yet available. Hence, an analytical study was carried out in the view of developing a simple equation in order to determine the slenderness limit for HSC column confined with SSTT. Based on the analytical results, it was concluded that the existing slenderness limit expressions used in the design are appropriate for neither HSC columns nor SSTT-confined HSC columns. In this paper, a slenderness limit expression which has incorporated the SSTT-confinement effects is proposed. The proposed expression can also be applied to unconfined HSC columns.

• Proceedings of the Korea Concrete Institute Conference
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• 1992.10a
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• pp.167-172
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• 1992

To analyze the effects compressive strength of concrete and longitudinal steel ratio on second-order moment of columns, 30tied rein reinforced concrete columns with hinged ends were tested. The 80mm square cross section was used and the amount of eccentricity was 24mm. The compressive strengths of column specimens with slenderness ratios of 10, 60, and 100were 250, 648 and 880kg/$\textrm{cm}^2$, and the longitudinal steel ratios were 1.98%(4-D6) and 3.95%(8-D6). The ratio of ultimate load capacity to that of short column with the same eccentricity (Pu/Pn) was much decreased at high slenderness ratio with increasing the compressive strength of concrete. And the lateral displacement of slender column at the ultimate load was decreased as the strength was increased. These are due to that at high slenderness ratio the load capacity and behavior of column are affected by flexural rigidity. And, it was also found that with increasing steel ratio, the value of Pu/Pn and the lateral displacement at the ultimate load were larger for the same slenderness ratio.

• Structural Engineering and Mechanics
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• v.50 no.3
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• pp.287-304
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• 2014

A computer based iterative numerical procedure has been developed to analyse reinforced high strength concrete columns subjected to horizontal wave loads and eccentric vertical load by taking the material, geometrical and wave load non-linearity into account. The behaviour of the column has been assumed, to be represented by Moment-Thrust-Curvature relationship of the column cross-section. The formulated computer program predicts horizontal load versus deflection behaviour of a column up to failure. The developed numerical model has been applied to analyse several column specimens of various slenderness, structural properties and axial load ratios, tested by other researchers. The predicted values are having a better agreement with experimental results. A simplified user friendly hydrodynamic load model has been developed based on Morison equation supplemented with a wave slap term to predict the high frequency non-linear impulsive hydrodynamic loads arising from steep waves, known as ringing loads. A computer program has been formulated based on the model to obtain the wave loads and non-dimensional wave load coefficients for all discretised nodes, along the length of column from instantaneous free water surface to bottom of the column at mud level. The columns of same size and material properties but having different slenderness ratio are analysed by the developed numerical procedure for the simulated wave loads under various vertical thrust. This paper discusses the results obtained in detail and effect of slenderness in resisting wave loads under various vertical thrust.

• Journal of Korean Association for Spatial Structures
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• v.3 no.3 s.9
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• pp.85-93
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• 2003

Steel, concrete and their combination materials are the most 6commonly used materials for civil engineering structural systems such as buildings, bridge structures and other structures. Recently, however, fiber reinforced polymer (FRP) composites, a relatively new composite material made of fibers and polymer resins, have been gradually used in structural systems as an alternative structural material. This paper describes a comparison of design strength equations for steel column and FRP composite column based on design philosophies. The safety factors used in allowable stress design (ASD) are relatively higher in FRP structural design than steel structural design. Column critical stress equations of FRP composites column from an experimental study can be represented by Euler elastic buckling equation at the long-range of slenderness, and an exponential form at the short-range of slenderness as defined in Load and Resistance Factor Design (LRFD) of steel column. The column strength of steel and FRP composite columns in large slenderness is independent of material strength, this result verified the elastic buckling equation as derived by Eq. (15) and Eq. (5).

• Proceedings of the Korea Concrete Institute Conference
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• 1998.10a
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• pp.571-576
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• 1998

This paper is a part of a research plan aimed at the verification of basic design rules of high-strength concrete columns. A total of 19 slender column specimens were tested to measure secondary moment and stiffness of eccentrically loaded reinforced concrete tied columns. Main variables included in this test program were concrete compressive strength, steel amount, eccentricity, and slenderness ratio. The concrete compressive strength varied from 356kg/$\textrm{cm}^2$ to 951kg/$\textrm{cm}^2$, the longitudinal steel ratios were between 1.13% and 5.51%, and slenderness ratios were 40 and 61. Calculated moment magnification factors and column stiffness based on design codes are higher than the test results for high axial load under small eccentricity, for higher slenderness ratio, for lower longitudinal steel ratio, and for high-strength concrete. The moment magnification method of the current design codes may provide a very conservative design for high-strength concrete slender column.

• Structural Engineering and Mechanics
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• v.22 no.2
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• pp.169-184
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• 2006

A close form solution of the maximum deflection for cracked columns with rectangular cross-sections was developed and thus the elastic buckling behavior and ultimate bearing capacity were studied analytically. First, taking into account the effect of the crack in the potential energy of elastic systems, a trigonometric series solution for the elastic deflection equation of an arbitrary crack position was derived by use of the Rayleigh-Ritz energy method and an analytical expression of the maximum deflection was obtained. By comparison with the rotational spring model (Okamura et al. 1969) and the equivalent stiffness method (Sinha et al. 2002), the advantages of the present solution are that there are few assumed conditions and the effect of axial compression on crack closure was considered. Second, based on the above solutions, the equilibrium paths of the elastic buckling were analytically described for cracked columns subjected to both axial and eccentric compressive load. Finally, as examples, the influence of crack depth, load eccentricity and column slenderness on the elastic buckling behavior was investigated in the case of a rectangular column with a single-edge crack. The relationship of the load capacity of the column with respect to crack depth and eccentricity or slenderness was also illustrated. The analytical and numerical results from the examples show that there are three kinds of collapse mechanisms for the various states of cracking, eccentricity and slenderness. These are the bifurcation for axial compression, the limit point instability for the condition of the deeper crack and lighter eccentricity and the fracture for higher eccentricity. As a result, the conception of critical transition eccentricity $(e/h)_c$, from limit-point buckling to fracture failure, was proposed and the critical values of $(e/h)_c$ were numerically determined for various eccentricities, crack depths and slenderness.

• Steel and Composite Structures
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• v.19 no.5
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• pp.1299-1319
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• 2015

This paper presents a detailed parametric study, conducted using finite element tools to cover a range of several geometric and material parameters, on the behaviour of thin-walled partially encased composite (PEC) columns. The PEC columns studied herein are composed of thin-walled built-up H-shaped steel sections with concrete infill cast between the flanges. Transverse links are provided between the opposing flanges to improve resistance to local buckling. The parametric study is confined to eccentrically-loaded columns subjected to major axis bending only. The parameters that were varied include the overall column slenderness ratio (L/d), load eccentricity ratio (e/d), link spacing-to-depth ratio (s/d), flange plate slenderness ratio (b/t) and concrete compressive strength ($f_{cu}$). The overall column slenderness ratio was chosen to be the primary variable with values of 5, 10 and 15. Other parameters were varied within each case of L/d ratio. The effects of the selected parameters on the behaviour of PEC columns were studied with respect to the failure mode, peak axial load, axial load versus average axial strain response, axial load versus lateral displacement response, moment versus lateral displacement behaviour and the axial load-moment interaction diagram. The results of the parametric study are presented in the paper and the influences of each of the parameters investigated are discussed.

• Proceedings of the Korea Concrete Institute Conference
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• 1993.10a
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• pp.284-289
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• 1993

To analyze the effects of compressive strength of concrete and longitudinal steel ratio on buckling behavior of columns, 36tied reinforced concrete columns with hinged ends were tested. The 100mm square cross section was used and the amount of eccentricity was 10mm. The compressive strengths of column specimens with slenderness ratios of 15, 30 and 50 were 202, 513 and 752 kg/$\textrm{cm}^2$. The longitudinal steel ratio of columns with bending about a section diagonal and about a principal axis were 2.85%(4-D10). The ratio of ultimate load capacity to that of short column with the same eccentricity was much decreased at high slenderness ratio with increasing the compressive strength of concrete. And the lateral displacement of column at the ultimate load was decreased as the strength was increased. These are due to that at high slenderness ratio, the load capacity and behavior of column are affected by flexural rigidity. And, it was also found that for the same quantity of confining steel and level of axis load, there is little difference between the flexural strength for bending about a section diagonal and for bending about principal axis.

• Computers and Concrete
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• v.19 no.5
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• pp.537-544
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• 2017

The strength and deformational capacity of slender reinforced concrete (RC) columns greatly rely on their slenderness ratios, while an additional secondary moment (i.e., the $P-{\delta}$ effect) can be induced especially when the RC column members are exposed to fire. To evaluate the fire-resisting performances of RC columns, this study proposed an axial force-flexural moment (i.e., P-M) interaction curve model, which can reflect the fire-induced slenderness effects and the nonlinearity of building materials considering the level of stress and the magnitude of temperature. The P-M interaction model proposed in this study was verified in detail by comparing with the fire test results of RC column specimens reported in literature. The verification results showed that the proposed model can properly evaluate the fire-resisting performances of RC column members.