Column Slenderness Ratio Research Articles

Experimental Investigation on Behavior of Slender Steel Reinforced Concrete Columns Subjected to Eccentric Load

The objectives of this research were to investigate the structural behavior of slender steel reinforced concrete (Referred to as SRC)composite columns subjected to eccentric axial loading. The test consisted of 10 slender columns, with rectangular section160×180mm, and steel shape I10 encased in concrete. The stirrup spacing was 150 mm; its diameter was 6 mm. The diameter of longitudinal reinforcing bars was 10 mm. Details of the experimental investigations including description of the test columns, failure modes and mechanisms, strain characteristics, and load-deformation responses are discussed. Effects of concrete strength, slenderness of columns, and eccentricity of axial loads on the load-carrying capacity of slender column are then presented. Based on these results, a range of slenderness ratio and eccentric ratio of slender SRC column is proposed.

Lateral pressure effect on average compressive strength of stiffened panels for in-service vessels

This paper presents the estimation of the average compressive strengths of three types of stiffened panels under axial compression and lateral pressure based on simplified formulae in the CSR for tankers (common structural rules for double hull oil tankers) and nonlinear finite element analyses (FEAs). Basic scenarios are determined based on the slenderness ratios of the stiffened panels used for in-service ships. Secondary scenarios are subdivided by external pressures that are applied to finite element model by increasing 1 bar, assuming 30 m water height. The total number of FEAs for flat bar (FB)-, angle bar (AB)- and tee bar (TB)-stiffened panels is 189. FEA results show that the existence of pressure can cause a significant reduction of ultimate strength, while CSR formulae do not take into account the effect of lateral pressure. The lateral pressure is more detrimental to the ultimate strength of stiffened panels with a higher column slenderness ratio than those with a smaller column slenderness ratio. A new concept of the relative average compressive strain energy, instead of the ultimate strength, is introduced in order to rationally compare the average compressive strength through a complete compressive straining history. The differences in the ultimate strengths between CSR formulae and FEA results are relatively small for FB- and AB-stiffened panels, but larger discrepancies of relative average compressive strain energies are obtained.

Inelastic stability analysis of high strength rectangular concrete-filled steel tubular slender beam-columns

There is relatively little numerical study on the behavior of eccentrically loaded high strength rectangular concrete-filled steel tubular (CFST) slender beam-columns with large depth-to-thickness ratios, which may undergo local and global buckling. This paper presents a multiscale numerical model for simulating the interaction local and global buckling behavior of high strength thin-walled rectangular CFST slender beam-columns under eccentric loading. The effects of progressive local buckling are taken into account in the mesoscale model based on fiber element formulations. Computational algorithms based on the M<TEX>$\ddot{u}$</TEX>ller's method are developed to obtain complete load-deflection responses of CFST slender beam-columns at the macroscale level. Performance indices are proposed to quantify the performance of CFST slender beam-columns. The accuracy of the multiscale numerical model is examined by comparisons of computer solutions with existing experimental results. The numerical model is utilized to investigate the effects of concrete compressive strength, depth-to-thickness ratio, loading eccentricity ratio and column slenderness ratio on the performance indices. The multiscale numerical model is shown to be accurate and efficient for predicting the interaction buckling behavior of high strength thin-walled CFST slender beam-columns.

Thermoelastic buckling of steel columns with load-dependent supports

The in-plane elastic buckling of a steel column with load-dependent supports under thermal loading is investigated. Two elastic rotational springs at the column ends are used to model the restraints which are provided by adjacent structural members or elastic foundations. The temperature is assumed to be linearly distributed across the section. Based on a nonlinear strain–displacement relationship, both the equilibrium and buckling equations are obtained by using the energy method. Then the limits for different buckling modes and the critical temperature of columns with different cases are studied. The results show that the proposed analytical solution can be used to predict the critical temperature for elastic buckling. The effect of thermal loading on the buckling of steel columns is significant. Furthermore, the thermal gradient plays a positive role in improving the stability of columns, and the effect of thermal gradients decreases while decreasing the modified slenderness ratios of columns. It can also be found that rotational restraints can significantly affect the column elastic buckling loads. Increasing the initial stiffness coefficient α or the stiffening rate β of thermal restraints will increase the critical temperature.

Influence of Slenderness on the Behavior of a FRP-Encased Steel-Concrete Composite Column

AbstractThe compressive behavior of a steel-concrete composite column encased in a fiber reinforced polymer (FRP) tube is evaluated experimentally for columns with various slenderness ratios. The composite column consists of a FRP tube surrounding a steel I-section that is subsequently filled with concrete. A total of nine column specimens were tested ranging between 500 and 3,000 mm in height. Confinement and composite action resulted in enhanced compressive behavior of the composite columns. Maximum confinement occurred in the short column (slenderness ratio less than 0.2). Confinement action reduced with increased height of the column specimens. The column load- carrying capacity, ultimate axial strain, and compressive strength of the confined concrete core in the longest specimen (slenderness ratio of 0.9) were reduced to approximately 59, 14, and 51% of the short column values, respectively. A buckling strength curve of the composite columns was developed on the basis of the experimental results.

High strength thin-walled rectangular concrete-filled steel tubular slender beam-columns, Part II: Behavior

Experimental and numerical research on full-scale high strength thin-walled rectangular steel slender tubes filled with high strength concrete has not been reported in the literature. In a companion paper, a new numerical model was presented that simulates the nonlinear inelastic behavior of uniaxially loaded high strength thin-walled rectangular concrete-filled steel tubular (CFST) slender beam-columns with local buckling effects. The progressive local and post-local buckling of thin steel tube walls under stress gradients was incorporated in the numerical model. This paper presents the verification of the numerical model developed and its applications to the investigation into the fundamental behavior of high strength thin-walled CFST slender beam-columns. Experimental ultimate strengths and load-deflection responses of CFST slender beam-columns tested by independent researchers are used to verify the accuracy of the numerical model. The verified numerical model is then utilized to investigate the effects of local buckling, column slenderness ratio, depth-to-thickness ratio, loading eccentricity ratio, concrete compressive strengths and steel yield strengths on the behavior of high strength thin-walled CFST slender beam-columns. It is demonstrated that the numerical model is accurate and efficient for determining the behavior of high strength thin-walled CFST slender beam-columns with local buckling effects. Numerical results presented in this study are useful for the development of composite design codes for high strength thin-walled rectangular CFST slender beam-columns.

Study on the Behaviors of Steel Reinforced Concrete Cloumns

The influence on columns behaviors of slenderness ratio are analyzed, and the influence on columns’ anti-seismic behavior of axial compression ratio, stirrup ratio and steel form are analyzed through the test on bearing capacity and level load of low cycle reverse of steel reinforced high-strength concrete columns. The bearing capacity of the long columns reduces along with the slenderness ratio increasing and augments along with concrete strength increasing. Probability of suddenly destruct increases along with the column slenderness ratio augmenting through the test. In addition, anti-seismic behavior of columns are effected not only axial compression ratio, but also steel form. Axial compression coefficien of the steel reinforced high-strength concrete columns with different steel form may be adjusted, however, the influence of stirrup ratio is very little on anti-seismic behavior of columns.

Behavior of long confined concrete column

The behavior of concrete columns confined by fiber reinforced plastic/polymer (FRP) depends on several parameters, including concrete strength, types of fibers, volume and orientation of fiber in the jacket, jacket thickness and shape of cross section, length-to-diameter (slenderness) ratio of the column. In this paper, the behavior of long concrete columns confined by means of proper plastic tube is investigated including failure mechanisms and subsequently their failure mode with theoretical model for calculation of the column capacity. The influence of column slenderness ratio on their axial load capacity, axial strains, and radial strains is also investigated. The experimental program was classified into three different groups with slenderness ratios from 9 to 18. Test results show that, utilizing plastic tube for confinement significantly influences the failure mechanisms of concrete columns. Results also show that the stiffness of the tested long confined concrete columns specimens increases as slenderness ratio decreases.

횡압력을 받는 실선 보강판의 평균압축강도

This paper presents estimation of average compressive strengths of three types of stiffened panels under lateral pressure and axial compression based on simplified formulas from CSRs and nonlinear FEAs. FEA scenarios are prepared based on the slenderness ratios of the stiffened panels used for in-service vessels. The seven step lateral pressures by 1bar increment are imposed on FE models assuming maximum 30m water height. The number of FEAs for FB-, AB-, and TB-stiffened panels is totally 189 times. FEA results show that existence of pressure can evolves significant reduction of ultimate strengths, meanwhile CSR formulas do not take into account the lateral pressure effect. Lateral pressure acting on the stiffened panel with higher column slenderness ratio more reduces the ultimate strengths than those with smaller column slenderness ratio. A new concept of relative average compressive strain energy instead of the ultimate strength is introduced in order to rationally compare the average compressive strength through complete compressive straining regime. The differences of the ultimate strengths between CSR formulas and FEA results are relatively small for FB- and AB-stiffened panels, but larger discrepancies of relative average compressive strain energies are shown.

Experimental Study on Axial Compressive Behaviors of Steel Recycled Concrete Composite Columns

In order to reveal the performance of steel recycled concrete composite columns, 6 specimens were designed for axial compression loading experiment. And two factors which are recycled coarse aggregate replacement percentage and slenderness ratio of column are taken into consideration. The bearing capacity and load-displacement curves of composite columns are obtained. Based on the test, the failure patterns and the influence of recycled coarse aggregate replacement percentage and slenderness ratio to axial compression load-bearing capacity are analyzed. In the end, the calculation formula for axial compression load of steel recycled concrete composite columns is presented.

Stability of axially restrained steel columns under temperature action

The in-plane elastic buckling of a steel column under thermal loading is investigated. The column is pinned at its ends, with two linear elastic springs that model the restraint provided by adjacent members in a structural assemblage or an elastic foundation. Across a section, the temperature is assumed to be linearly distributed. Based on a nonlinear strain-displacement relationship, the energy method is used to obtain the equilibrium and buckling equations. Then the buckling of columns with three different thermal loading cases is studied. The results show that the analytical formulas can be used to evaluate the critical temperature for elastic buckling. The thermal gradient plays a positive role in improving the stability of columns. Comparing these predictions with uniform temperature distribution over cross section, it can be shown that the buckling load is seriously underestimated. It can also be found that axial restraints can significantly affect the column elastic buckling loads. The critical temperature decreases with an increase of restraint stiffness. Furthermore, the effect of axial stiffness increases when increasing the thermal gradients and decreasing the slenderness ratio of columns.

High strength circular concrete-filled steel tubular slender beam–columns, Part II: Fundamental behavior

There is relatively little experimental and numerical research on the fundamental behavior of high strength circular concrete-filled steel tubular (CFST) slender beam–columns. In a companion paper, a new numerical model for predicting the nonlinear inelastic behavior of high strength circular CFST slender beam–columns under axial load and bending was presented. The numerical model developed accounts for confinement effects on the strength and ductility of the concrete core and on circular steel tubes as well as initial geometric imperfections of beam–columns. This paper presents the verification of the numerical model and extensive parametric studies on the fundamental behavior of high strength circular CFST slender beam–columns. The ultimate strengths and axial load–deflection responses of circular CFST slender beam–columns under eccentric loading predicted by the numerical model are verified by corresponding experimental results. The computer program implementing the numerical model is used to investigate the fundamental behavior of high strength circular CFST slender beam–columns in terms of load–deflection responses, ultimate strengths, axial load–moment interaction diagrams, and strength increase due to concrete confinement. Parameters examined include column slenderness ratio, eccentricity ratio, concrete compressive strengths, steel yield strengths, steel ratio and concrete confinement. It is demonstrated that the numerical model developed is an efficient computer simulation and design tool for high strength circular CFST slender beam–columns. Benchmark numerical results presented in this paper are valuable in the development of composite design codes for high strength circular CFST slender beam–columns.

Investigation of concrete encased steel composite columns at elevated temperatures

This paper presents a nonlinear 3-D finite element model investigating the behaviour of concrete encased steel composite columns at elevated temperatures. The composite columns were pin-ended axially loaded columns having different cross-sectional dimensions, different structural steel sections, different coarse aggregates and different load ratios during fire. The nonlinear material properties of steel, concrete, longitudinal and transverse reinforcement bars as well as the effect of concrete confinement at ambient and elevated temperatures were considered in the finite element models. The interface between the steel section and concrete, the longitudinal and transverse reinforcement bars, and the reinforcement bars and concrete were also considered allowing the bond behaviour to be modelled and the different components to retain its profile during the deformation of the column. The initial overall (out-of-straightness) geometric imperfection was carefully included in the model. The finite element model has been validated against published tests conducted at elevated temperatures. The time–temperature relationships, deformed shapes at failure, time–axial displacement relationships, failure modes and fire resistances of the columns were evaluated by the finite element model. It has been shown that the finite element model can accurately predict the behaviour of the columns at elevated temperatures. Furthermore, the variables that influence the fire resistance and behaviour of the composite columns comprising different load ratios during fire, different coarse aggregates and different slenderness ratios were investigated in parametric studies. It is shown that the fire resistance of the columns generally increases with the decrease in the column slenderness ratio as well as the increase in the structural steel ratio. It is also shown that the time–axial displacement relationship is considerably affected by the coarse aggregate. The fire resistances of the composite columns obtained from the finite element analyses were compared with the design values obtained from the Eurocode 4 for composite columns at elevated temperatures. It is shown that the EC4 is conservative for all the concrete encased steel composite columns, except for the columns having a load ratio of 0.5 as well as the columns having a slenderness ratio of 0.69 and a load ratio of 0.4.

Ultimate strength of orthogonal stiffened plates subjected to axial and lateral loads

Orthogonal stiffened plates present in the ship deck are subjected to axial compression due to hogging and sagging bending moments and, lateral load due to cargo load. The main objective of this investigation is to determine the ultimate load carrying capacity and study the interactive behaviour of orthogonal stiffened plates under axial and lateral loads. Tests were conducted on six stiffened plates with plate slenderness ratios of 80 and 64, and corresponding column slenderness ratios of 24 and 26. Hydraulic jacks and inflatable air balloon with load control mechanism were fabricated to apply axial and lateral loads on the test specimens respectively. All the specimens were tested up to ultimate load and the mode of failure was determined based on the initial yielding observed in the plate and/or stiffener. Nonlinear finite element analysis of test specimens was performed using the general purpose FE software ANSYS®. Both material and geometric nonlinearities were considered in the FE analysis of test specimens. The ultimate loads obtained from the finite element analysis were compared with experimental data and found to be satisfactory. It was also observed that the mode of failure obtained from finite element analysis is similar as observed from experiments. It was concluded that the increase in lateral load beyond two thirds of ultimate lateral load significantly reduces the axial ultimate load carrying capacity of stiffened panels. The interactive effect of stiffened plates subjected to combined action of axial and lateral loads is determined as nonlinear.

Thermal buckling of rotationally restrained steel columns

The in-plane elastic buckling of a steel column under thermal loading is investigated. Two elastic rotational springs at the column ends are used to model the restraints which are provided by adjacent structural members or an elastic foundation. The temperature is assumed to be linearly distributed across the section. Based on a nonlinear strain-displacement relationship, both the equilibrium and buckling equations are obtained by using the energy method. Then the buckling of columns in three different thermal loading cases is studied. The results show that the proposed analytical solution can be used to predict the critical temperature for elastic buckling. The thermal gradient plays a positive role in improving the stability of columns. Furthermore, the effect of thermal gradients decreases while increasing the rotational restraint stiffness and decreasing the slenderness ratios of columns. It can also be found that rotational restraints can significantly affect the column elastic buckling loads. Increasing the rotational stiffness of thermal restraints will increase the critical temperature.

Empirical formulations for estimation of ultimate strength of continuous stiffened aluminium plates under combined in-plane compression and lateral pressure

The present research was undertaken based on the results obtained by the same authors in a sensitivity study on the buckling and ultimate strength of continuous stiffened aluminium plates. Empirical expressions are developed for predicting ultimate compressive strength of welded stiffened aluminium plates used in marine applications under combined in-plane axial compression and different levels of lateral pressure. Existing data of the ultimate compressive strength for stiffened aluminium plates numerically obtained by the authors through the previously performed sensitivity analysis are used for deriving formulations that are expressed as functions of two parameters, namely the plate slenderness ratio and the column (stiffener) slenderness ratio. Regression analysis is used in order to derive the empirical formulations. The formulae implicitly include effects of the weld on initial imperfections, and the heat-affected zone.

Structural behavior of centrally loaded steel columns at elevated temperature

A series of experimental studies is conducted to examine the behavior of SN490 steel column subjected to axial load in the fire condition. This experimental work is aimed at examining the effect of the width-to-thickness ratio of flanges, the slenderness ratio of steel columns and residual stresses on the ultimate strength of an SN490 steel column at a specified temperature. From these studies, it is found that the column strength decreases with the increase of width-to-thickness ratio and slenderness ratio. Column behavior is sensitive to width-to-thickness ratios and the slenderness ratio at temperatures below 550 ∘C. However, the influence of width-to-thickness ratios and the slenderness ratios is not severe when the temperature is higher than 550 ∘C. When the temperature is above 550 ∘C, the column strength deteriorates rapidly. It is also found that the failure mode of steel columns changes from inelastic global buckling at room temperature to inelastic local buckling at elevated temperature, due to the release of residual stress in a fire. Based on the results of this study, local buckling criteria and column strength at specified temperatures are suggested.

Interaction curves for stiffened panel with circular opening under axial and lateral loads

Stiffened panels in ships and offshore oil platforms are provided with circular openings for repair, access and maintenance. This paper presents the numerical study carried out on the ultimate strength of stiffened panel with central circular opening subjected to axial load, lateral load and a combination of axial and lateral loads. Ultimate strength of the panel was evaluated considering both geometric and material non-linearities using FEA software ANSYS. Plates of varied widths and open section unequal angle stiffeners covering plate and column slenderness ratios in the practical range of 1.0–4.5 and 0.32–1.00, respectively, keeping the opening ratio equal to 1.0 are the parameters considered in this study. On the basis of the study, interaction curves were developed for normalised axial load and normalised lateral load. The developed interaction curves for stiffened panels with angle stiffeners and circular opening were found to be non-linear for lower plate slenderness ratio up to 2.0 and for the range of column slenderness ratio covered in the present study. Interaction equations were also proposed based on non-linear regression analysis for determining the ultimate strength of stiffened panel under axial, lateral and also under combined axial and lateral loads.

POST-EARTHQUAKE ULTIMATE TEMPERATURES OF MULTI-STORY AND MULTI-SPAN FRAMES SUBJECTED TO WHOLE FLOOR FIRE

To clarify post-earthquake fire resistance of steel frames, this paper studies analytically the ultimate temperatures of seismically designed multi-story and multi-span steel frames which have suffered some or severe damages due to preceding earthquakes. Refined finite element analysis and simplified theoretical analysis have both been conducted assuming that the frames, which have undergone permanent relative story displacement and/or fracture of beam-end-connection due to earthquakes, are next subjected to whole floor fire at the first floor. It is found that the lowering in ultimate temperature of the damaged frames is caused by P-Δ effect depending on the amount of the residual relative story displacement of the floor in fire. Their ultimate temperatures are therefore affected solely by the amount of axial forces and slenderness ratios of columns, but they are almost independent of the number or length of spans or of the number of stories. Theoretical consideration aims to analyze simply the post-earthquake P-Δ effect of the heated columns and the resulting predicted ultimate temperatures are found in good agreement with finite element solutions for all cases.

EFFECTS OF IMPACT VELOCITY AND SLENDERNESS RATIO ON DYNAMIC BUCKLING LOAD FOR LONG COLUMNS

In this research, the buckling behavior of long columns under dynamic load was investigated both experimentally and numerically, and an effective buckling criterion for dynamic load was derived from the results in terms of the impact velocity and the slenderness ratio. In the experiments, a free fall drop-weight type impact testing machine was employed. The dynamic buckling loads were measured by the load sensing block, and the displacements were measured by a high speed magnetic-resistance device. In the numerical analyses, dynamic FEM code 'MSC-Dytran' was used to simulate the typical experimental results, and the validity and the accuracy of the simulations were checked. The dynamic buckling loads at various impact velocities were then systematically investigated. From both experimental and simulated results, it was found that the dynamic to static buckling load ratios can be successfully described as a square function of the slenderness ratio of the columns, while they can be also described by a power law of the applied impact velocity.