• Structural Engineering and Mechanics
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• v.32 no.5
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• pp.635-648
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• 2009

This paper describes fire performance of eight axially restrained reinforced concrete (RC) columns under a combination of two different load ratios and two different axial restraint ratios. The eight RC columns were all concentrically loaded and subjected to ISO834 standard fire on all sides. Axial restraints were imposed at the top of the columns to simulate the restraining effect of the rest of the whole frame. The axial restraint was effective when the column was expanding as well as contracting. As the results of the experiments have shown, the stiffness of the axial restraint and load level play an important role in the fire behaviors of both HSC and NSC columns. It is found that (a) the maximum deformations during expanding phase were influenced mostly by load ratio and hardly by axial restraint ratio, (b) For a given load ratio, axial restraint ratio had a great impact on the development of axial deformation during contraction phase beyond the initial equilibrium state, (c) increasing the axial restraint increased the value of restraint force generated in both the NSC and HSC columns, and (d) the development of column axial force during the contracting and cooling phase followed nearly parallel trend for columns under the same load ratio.

• Structural Engineering and Mechanics
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• v.35 no.6
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• pp.699-715
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• 2010

This paper investigates the structural responses of axially restrained steel beams under fire conditions by a nonlinear finite element method. The axial restraint is represented by a linear elastic spring. Different parameters which include beam slenderness ratio, external load level and axial restraint ratio are investigated. The process of forming a mid-span plastic hinge at the mid-span under a rising temperature is studied. In line with forming a fully plastic hinge at mid-span, the response of a restrained beam under rising temperature can be divided into three stages, viz. no plastic hinge, hinge forming and rotating, and catenary action stage. During catenary action stage, the axial restraint pulls the heated beam and prevents it from failing. This study introduces definitions of beam limiting temperature $T_{lim}$, catenary temperature $T_{ctn}$ and warning time $t_{wn}$. Influences of slenderness ratio, load level and axial restraint ratio on $T_{lim}$, $T_{ctn}$ and $t_{wn}$ are examined.

• Structural Engineering and Mechanics
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• v.55 no.1
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• pp.1-27
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• 2015

This article presents a theoretical parametric analysis on the ultimate torsional behaviour of axially restrained reinforced concrete (RC) beams. This analysis is performed by using a computing procedure based on a modification of the Variable Angle Truss Model. This computing procedure was previously developed to account for the influence of the longitudinal compressive stress state due to the axial restraint conditions provided by the connections of the beams to other structural members. The presented parametric study aims to check the influence of some important variable studies, namely: torsional reinforcement ratio, compressive concrete strength and axial restraint level. From the results of this parametric study, nonlinear regression analyses are performed and some design charts are proposed. Such charts allow to correct the resistance torque of RC beams (rectangular sections with small height to width ratios) to account for the favorable influence of the axial restraint.

• Steel and Composite Structures
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• v.23 no.3
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• pp.331-338
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• 2017

Cold-formed lipped channel columns (CFLCCs) have been widely used in light gauge steel constructions. The distortional buckling is one of the important buckling modes for CFLCCs and the distortional buckling critical load depends significantly on the rotational restrain stiffness generated by the web to the lipped flange. First, a simplified explicit expression for the rotational restraint stiffness of the lipped flange has been derived. Using the expression, the characteristics of the rotational restraint stiffness of the lipped flange have been investigated. The results show that there is a linear coupling relationship between the applied forces and the rotational restraint stiffness of the lipped flange. Based on the explicit expression of the rotational restraint stiffness of the lipped flange, a simplified analytical formula has been derived which can determine the elastic distortional buckling critical stress of the CFLCCs subjected to axial compression. The simplified analytical formula developed in this study has been shown to be accurate through the comparisons with results from the distortional buckling analyses using the ANSYS finite element software. The developed analytical formula is easy to apply, and can be used directly in practical design and incorporated into future design codes and guidelines.

• Steel and Composite Structures
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• v.9 no.2
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• pp.89-101
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• 2009

This paper presents a simplified model to study post-buckling behaviours of the axially restrained steel column at elevated temperatures in fire. The contribution of axial deformation to the curvature of column section is included in theoretical equations. The possible unloading at the convex side of the column when buckling occurs is considered in the stress-strain relationship of steel at elevated temperatures. Parameters that affect structural behaviours of the axial restrained column in fire are studied. The axial restraint cause an increase in the axial force before the column buckles; the buckling temperature of restrained columns will be lower than non-restrained steel columns. However, the axial force of a restrained column decreases after the column buckles with the elevation of temperatures, so make use of the post-buckling behaviour can increase the critical temperature of restrained columns. Columns with temperature gradient across the section will produce lower axial force at elevated temperatures.

• Structural Engineering and Mechanics
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• v.67 no.5
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• pp.465-479
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• 2018

In a previous study, design charts where proposed to help the torsional design of axially restricted reinforced concrete (RC) beams with squared cross section. In this article, new design charts are proposed to cover RC beams with rectangular cross section. The influence of the height to width ratio of the cross section on the behavior of RC beams under torsion is firstly shown by using theoretical and experimental results. Next, the effective torsional strength of a reference RC beam is computed for several values and combinations of the study variables, namely: height to width ratio of the cross section, concrete compressive strength, torsional reinforcement ratio and level of the axial restraint. To compute the torsional strength, the modified Variable Angle Truss Model for axially restricted RC beams is used. Then, an extensive parametric analysis based on multivariable and nonlinear correlation analysis is performed to obtain nonlinear regression equations which allow to build the new design charts. These charts allow to correct the torsional strength in order to consider the favourable influence of the compressive axial stress that arises from the axial restraint.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.9 s.252
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• pp.1134-1141
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• 2006

This paper presents the model for evaluating restraint effect of pressure induced bending (PIB) on the circumferential through-wall crack opening displacement (COD), which considers plastic behavior of crack. This study performed three-dimensional elastic-plastic finite element (FE) analyses for different crack angle, restraint length, pipe geometry, stress level, and material conditions, and evaluated the influence of each parameter on the PIB restraint effect on COD. Based on these evaluations and additional perfectly-plastic FE analyses, a closed-form model to evaluate the restraint effect of PIB on the plastic crack opening of circumferential through-wall crack, was proposed as functions of crack angle, restraint length, radius to thickness ratio, axial stress corresponding to an internal pressure, and normalized COD evaluated from linear-elastic crack opening condition.

• Nuclear Engineering and Technology
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• v.39 no.1
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• pp.75-84
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• 2007

This paper presents a closed-form model for evaluating the restraint effect of pressure induced bending on the opening of a circumferential through-wall crack, which is considered plastic deformation behavior. Three-dimensional finite element analyses with different crack lengths, restraint conditions, pipe geometries, magnitudes of internal pressure, and tensile properties were used to investigate the influence of each parameter on the pressure-induced bending restraint on the crack opening displacement. From these investigations, an analytical model based on elastic-perfectly plastic material was developed in terms of the crack length, symmetric restraint length, mean radius to thickness ratio, axial stress corresponding to the internal pressure, and normalized crack opening displacement evaluated from a linear-elastic crack opening condition. Finite element analyses results demonstrate that the proposed analytical model reliably estimated the restraint effect of pressure-induced bending on the plastic crack opening of a circumferential through-wall crack and properly reflected the dependence on each parameter within the range over which the analytical expression was derived.

• Magazine of the Korea Concrete Institute
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• v.8 no.5
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• pp.111-122
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• 1996

The effects of external restraint on the thermal stresses i n mass concrete are investigated through a series of parametric study. Two major factors affecting the degree of external restraint such as the ratio of length to height of the placed structure (L/H) and the elastic modulus of base structure ($E_r$) are employed as the parameters in a condition which a placing height H is 1.0m. Various conditions of I,/H and E, are analysed by a FEM program and the relationship between these two parameters is examined. The shape of stress distribution due to the external restraint is shown as linearity on the height direction of the section, and is influenced by L/H, $E_r$, and strength development of placed concrete. The external restraint can be devided by two part. One is an axial restraint and the other is a flexural restraint. When the level of external restraint is low, the structure behavior is mainly governed by flexural restraint, otherwise it is dependent on axial restraint. Comparing the calculated stress by the method of the ACI 207 committee with a finite element analysis, the fbrmer overestimates the external restraint stress when the degree of external restraint is weak, and underestimates when it is strong.

• Steel and Composite Structures
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• v.4 no.1
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• pp.23-36
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• 2004

The inelastic lateral-distortional buckling of doubly-symmetric hot-rolled I-section beam-columns subjected to a concentric axial force and uniform bending with elastic restraint which produce single curvature is investigated in this paper. The numerical model adopted in this paper is an energy-based method which leads to the incremental and iterative solution of a fourth-order eigenproblem, with very rapid solutions being obtained. The elastic restraint considered in this paper is full restraint against translation, but torsional restraint is permitted at the tension flange. Hitherto, a numerical method to analyse the elastic and inelastic lateral-distortional buckling of restrained or unrestrained beam-columns is unavailable. The prediction of the inelastic lateral-distortional buckling load obtained in this study is compared with the inelastic lateral-distortional buckling of restrained beams and the inelastic lateral-torsional buckling solution, by suppressing the out-of-plane web distortion, is published elsewhere and they agree reasonable well. The method is then extended to the lateral-distortional buckling of continuously restrained doubly symmetric I-sections to illustrate the effect of web distortion.