Effect Of Axial Restraint Research Articles

Nonlinear Behavior Study of Reinforced Concrete Coupling Beams Subjected to the Effect of Wind Loading

Reinforced concrete shear walls connected by coupling beams are considered an efficient structural system for tall buildings subjected to lateral loads. For seismic design of such buildings, performance-based design has been commonly used in regions with strong earthquakes for its ability to achieve economical and safe design, however the use of performance-based wind design (PBWD), which permits nonlinear response of ductile elements at specific locations under wind loads is still hindered due to the lack of information regarding the performance of these elements. In addition to that, there is still a need for developing an analytical model that can represent nonlinear behavior of these elements when subjected to wind loads. Therefore, in this study two analytical models using two different methods to consider bond slip effect (Bond SP01 (BS) model and steel modification factor (SMF) model) were developed and implemented in OpenSees software and validated with a tested specimen of reinforced concrete coupling beam subjected to a simulated windstorm loading protocol. Then, a parametric study was conducted using the SMF model to investigate the effect of axial restraint, and modification of the ductility demand. Results showed that both of the models showed good agreement with the experiment, however results of the SMF model were more accurate. As for the parametric study, it was concluded that with axial restraint, the beam behavior was dominated by shear, and a slight increase of strength was observed. At ductility demand of 1.8 θ y , the beam performed well with no significant damage and minor residual rotations.

Numerical modeling of the fire behavior of reinforced concrete tunnel slabs during heating and cooling

This paper examines different modeling approaches to simulate the behavior of reinforced concrete (RC) tunnel slabs under fire during both the heating and cooling phases. Three modeling strategies are investigated by using beam, shell, and solid elements in addition to different methods to capture the effect of axial restraint on the slabs. The models consider temperature-induced plastic deformations and irrecoverable degradation of materials. The models also utilize distinct concrete properties for heating and cooling as well as account for the transient creep strain explicitly in the calculations. The results obtained from different modeling strategies are compared to five recent fire tests on loaded and restrained large-scale RC tunnel slabs, with varying concrete strengths, restraint levels, and fire scenarios. Temperature and displacement evolutions during heating and cooling obtained from the numerical models are compared with the experimental test data. When considering model accuracy and efficiency as the primary performance metrics, using shell elements to analyze the fire performance of reinforced concrete tunnel segments resulted in the best balance between the two. The numerical models and techniques developed in this paper will enable practicing engineers to reliably and rapidly assess fire damage to reinforced concrete tunnel linings, and to explore cost-effective designs of tunnels for fire.

Effect of Axial Restraint and Loading History on the Behavior of Short Reinforced Concrete Coupling Beams

Effect of Axial Restraint and Loading History on the Behavior of Short Reinforced Concrete Coupling Beams

Analytical assessment of restraint forces and crack widths in end-restrained building slabs

This paper deals with the analytical assessment of restraint forces and crack widths in end-restrained building slabs. The analysis concentrates on the service limit state (SLS) and the challenge is hereby the appropriate consideration of the combined effect of axial restraint due to imposed deformations and bending cracking due to loading. As for the imposed deformations, the paper regards the drying shrinkage of concrete under indoor conditions, although any other temperature deformation or combination of shrinkage and temperature could be included accordingly.A deformation-based approach is presented, in which imposed deformations are made compatible with the released deformations of the slab due to opening of loading-induced bending cracks. The solution aims an appropriate inclusion of the most relevant effects while still providing a practicable and verifiable solution for the complex problem of assessing the restraint forces as well as the crack widths in end-restrained building slabs.The result of this approach is an analytical quantification of restraint forces to be transferred in the restraining members. In addition, the presented approach enables the determination of crack widths in the restrained conditions. An important asset of the analytical nature of this approach is the explicit correlation between individual system parameters, especially concrete properties and surrounding conditions, member dimensions and provided reinforcement, loading in the SLS and restraining condition.The paper includes the presentation of the general idea of a deformation-based assessment of end-restrained building slabs; the demonstration of this approach with an example from the literature; and the comparison of the analytical design solution with experimental results on the combined effect of bending and axial restraint in slab-like specimens.

Effect of axial restraint on the performance of Elliptical Hollow Section steel columns, in hydrocarbon fire

This paper presents the findings from a novel experimental programme that examines the influence of axial restraint on the loading and buckling capacity of Elliptical Hollow Section (EHS) steel columns, when exposed to the hydrocarbon fire curve. When fire occurs in a structure, the steel columns are subject to thermal expansion, and in practice this thermal expansion is normally restrained by the cooler surrounds of the structure. Restraining this thermal expansion, subsequently introduces restraint forces, which are not present in the structural element prior to heating. This experimental programme comprised of 12 EHS column tests of two slenderness λ z = 40.1 and λ z = 50.8 , under three different loading levels ( α L = 0.3 , 0.45 and 0.6), exposed to a hydrocarbon heating regime. Initially, six EHS columns were tested unrestrained followed by six restrained EHS column tests. The fire resistance of the restrained columns were subsequently compared with the previous unrestrained column tests, tested under the same mechanical and thermal loading conditions. This paper will provide the recorded axial displacements, temperature profiles and induced axial forces of the restrained EHS columns, comparing these findings with the unrestrained EHS columns.

Effect of Heating and Cooling on Axially Restrained RC Columns with Special-Shaped Cross Section

This paper describes the performance of 12 axially restrained RC columns (four for each type of cross section, i.e., +-, T- and L-shaped cross section) under fire conditions that were recently finished in South China University of Technology. The main objective of the paper is to investigate the effect of axial restraint on RC columns during both expanding and contracting phases. The RC columns were all initially 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. Different degrees of axial restraint were obtained by varying the length of the restraining beam. The boundary conditions of the columns were considered as fixed–fixed for all tests. It is found that restrained RC columns behave quite differently to isolated ones. No typical ‘runaway’ failure of isolated RC columns was observed in the fire test. Finally, the finite element software, SAFIR, is employed to conduct a numerical analysis of the tests.

Effect of axial restraint in composite bars under nonlinear inelastic uniform torsion by BEM

In this paper, the effect of axial restraint in the elastic–plastic uniform torsion analysis of cylindrical bars taking into account the effect of geometric nonlinearity is presented employing the boundary element method. The bar is axially elastically supported at the centroids of its end cross sections, treating the cases of free axial boundary conditions (vanishing axial force), restrained axial shortening or given axial force as special ones. The cross section of the bar is an arbitrary doubly symmetric composite one, consisting of materials in contact, each of which can surround a finite number of inclusions, while the case of a homogeneous cross section is treated as a special one. The stress–strain relationships for the materials are assumed to be elastic–plastic-strain hardening. The incremental torque–rotation relationship is computed based on the finite displacement (finite rotation) theory, that is the transverse displacement components are expressed so as to be valid for large rotations and the longitudinal normal strain includes the second-order geometrically nonlinear term, often described as the “Wagner strain”. The proposed formulation does not stand on the assumption of a thin-walled structure and therefore the cross section’s torsional rigidity is evaluated exactly without using the so-called Saint-Venant’s torsional constant. The torsional rigidity of the cross section is evaluated directly employing the primary warping function of the cross section depending on both its shape and the progress of the plastic region. A boundary value problem with respect to the aforementioned function is formulated and solved employing a BEM approach. The developed procedure retains most of the advantages of a BEM solution over a pure domain discretization method, although it requires domain discretization, which is used only to evaluate integrals. The significant increase of the torsional rigidity of the bar and the arising axial force due to the axial restraint are concluded.

Effect of axial restraint on flexural and shear behaviour of high-strength concrete members

This paper was developed to examine the effect of sequential axial restraint on flexural and shear behaviour of high-strength concrete beams. This study includes flexural and shear tests conducted under both restrained and unrestrained conditions to provide a comparison in test results. In the early stage of the tests, the bending stiffness of the fully-restrained beam was lower than that of the unrestrained beam due to a crack generated by tensile restraint during concrete curing. However, as the transverse load increased, the restraint force changed from tension to compression, causing the stiffness to be higher. Even though the displacement capacity of the restrained beam at failure decreased, the yield load and displacement of the restrained beam was higher than that of the unrestrained beam. Additionally, it was observed that shear crack propagation and shear capacity were not affected by cracks less than 0·1 mm in width, which penetrated due to the restraining tensile stress that occurred before loading.

Effect of axial restraint on flexural and shear behaviour of high-strength concrete members

Effect of axial restraint on flexural and shear behaviour of high-strength concrete members

Effect of support conditions on the fire behaviour of steel and composite beams

AbstractThe fire behaviour of a structural steel beam or a steel and concrete composite beam in a fire compartment depends on many factors including the nature of the supports at the ends of the beam.This paper describes a detailed analytical investigation into the effects of support conditions on the fire performance of steel and composite steel‐concrete beams exposed to linearly increasing temperature with time, as well as to standard and parametric fires.The support conditions include simply supported, fully fixed, and a range of intermediate cases, providing varying levels of axial and flexural restraint. In each case, a comparison of the deflected shape with the evolving internal forces shows unusual but predictable behaviour, strongly dependent on the stress–strain relationship of the steel. In addition to the standard support conditions, a spring was used to simulate the effect of axial restraint provided by adjacent spans of a multi‐span beam. This case showed that the spring stiffness had a very considerable influence on the behaviour of the beam and the time to failure under an increasing fire temperature.This paper gives new insight into the structural performance of steel and composite beams, observed in recent fires such as the eight storey steel frame at Cardington. There are major implications for structural designers. Copyright © 2004 John Wiley & Sons, Ltd.

Effect of axial restraint on mechanical behavior and average crack spacing of reinforced concrete flexural members

This study was performed to verify the effect of axial restraint on the mechanical behavior and average crack spacing of reinforced concrete (RC) flexural members. Experiments for mechanical behavior have been performed on axially restrained and unrestrained RC beams. And, the average crack spacing has also been investigated in other RC beam tests under the axially restrained condition. The test results show that the capacity of the axially restrained beam was higher than that of the unrestrained beam. For restrained flexural members, axial deformation was restrained, deformation capacity was decreased, plastic behavior was delayed, and possibility of compressive failure was increased due to the axial restraint force. The major variables affecting the average crack spacing were steel stress, axial force, circumference of reinforcing bar, and effective tension area of concrete. However, the effect of concrete compressive strength was minimal. A prediction equation utilizing the identified variables was proposed for determining the average crack spacing of the axially restrained RC flexural members.

Effect of Axial Restraint on Mechanical Behavior of High- Strength Concrete Beams

This study was performed to verify the effect of restraint of axial deformation (that is, thermal and time-dependent volume change after concrete placing and axial elongation caused by lateral loading) on mechanical behavior of high-strength concrete beams. For this purpose, the characteristics of concrete beams (the development of the restrained stress and the mechanism of crack formation caused by the restrained stress) were studied on the basis of the experiments and numerical analyses of the data for high-strength concrete beams at an early age. When a high-strength concrete member is axially restrained, a crack might propagate in the member not demolded at an early age. This is caused by a drop of temperature that results from the hydration heat of cement and autogenous shrinkage and not by drying shrinkage, which would not have started as yet. The restrained stress of a member is accurately obtained by calculating the externally restrained force and the steel stress. The maximum restrained stress is determined by the cracking strength of concrete. It is concluded that the additional restrained stress is released and the axial rigidity of member is reduced with formation of additional cracks.

The effect of axial restraint on the fire resistance of steel columns

The paper represents the outcomes of a joint research between the University of Ulster and the University of Sheffield into the performance of axially restrained steel columns during fire. The Ulster experimental program incorporates 37 high temperature tests that investigate three parameters: slenderness ratio (λ=49,75,98), degree of axial restraint (αk=0, 0.1,0.2,0.3) and loading ratio (αL=0,0.2,0.4,0.6). A unique test rig which allows the application of both axial restraint and loads, either separately or at the same time has been especially designed for the experimental program. Typical results from the fire tests are presented, which illustrates characteristic response of the columns to the imposition of axial restraint, coupled with the temperature increase. In addition, trend graphs charting generic response are discussed. An associated computational study by Sheffield provides satisfactory accurate computer simulations of fire tests, using standard materiel property input data. The computer modelling exercises has been extended to parametric studies, to include the effects of many more levels of axial restrain. The linked experimental and computational study has thus validated a computational model, which can be used to provide the basis design guidance of the behaviour of restrained columns in fire situations.

Stiffening of bent beams due to partial and complete end restraint

A study of the effect of axial restraint on the bending deflections of centrally-loaded 3inned beams is presented. Exact and approximate solutions are given for the cases of no, partial, and full axial restraint. It is demonstrated that even moderate restraint can significantly increase the stiffness of the beam in response to transverse loading.

Pressure Transients in Hydraulic Pipelines

Equations of motion for a cylindrical tube containing a fluid are developed from a consideration of the forces and moments in the tube wall. These equations are solved for boundary conditions representing the situation where the fluid is flowing steadily through a horizontal pipe and a valve at the downstream end is closed instantaneously. The solution gives theoretical results for the usual water-hammer wave but also predicts the existence of a precursor wave. Expressions are derived for the velocities of propagation of both transients and their associated pressure changes. A comprehensive series of experiments has been carried out. Some interesting and probably unique results were obtained, which demonstrate the behavior of both transients. Measurements of velocity and pressure change have been made. The effect of axial restraint on the pipe is demonstrated.

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