Axial Restraint Research Articles

Analytical model for RC coupling beam considering axial restraint

A novel three-dimensional distributed plasticity model element is formulated and implemented into an open-source computational platform (OpenSees) to enhance nonlinear modeling approaches for lateral force resisting systems utilizing diagonally reinforced concrete coupling beams. The model incorporates a fiber-based concrete cross-section along with truss elements to represent the diagonal reinforcement and contact elements to model reinforcing bar slip at the beam-wall interface. The model is validated using test results from five different experiments that include variations in cross-section geometries, reinforcement configurations, and boundary conditions. Notably, two test specimens shared identical attributes except for their cross-sectional shapes (with and without a slab), whereas another pair were identical except for the degree of axial restraint provided. The final specimen utilized both longitudinal and diagonal reinforcement along the length of the beam. The model accurately predicted overall shear versus chord rotation responses with errors < 5 % and axial growth responses with errors < 30 %. The proposed model provides enhanced modeling options for nonlinear analysis by enabling sensitivity studies to address the potential impacts of coupling beam axial restraint on coupling beam and coupled wall behavior.

Review of design approaches for steel columns subjected to localised fires: Insights from the 2nd generation Eurocode model

Complex temperature fields may develop inside structural steel elements in fire, severely affecting the local and global response of the structure. However, simplified yet well-accepted design procedures allow for uniform temperature distributions in the steel elements. The second generation of Eurocodes provides advanced models for localised fires where non-negligible thermal gradients both inside the sections and along the elements are expected to influence the resistance of steel elements, especially those critical to the stability of the entire structure, such as vertical members. This paper sheds some light on the consequences of employing procedures with increasing complexity in the design of unprotected axially compressed steel columns subjected to localised fires for which the effect of the smoke layer is not significant. Five procedures were compared, considering a refinement in both the thermal and the mechanical models, culminating in the application of a procedure enabling complex temperature fields both in the section and along the column, namely the LOCAFI model, and exploiting numerical simulation in SAFIR. A parametric study was conducted, encompassing different fire scenarios and structural characteristics, resulting in 27468 analyses. It was shown that in the case of localised fire scenarios that induce significant thermal gradients in the structure advanced modelling is recommended because it better captures the thermomechanical response. Detailed considerations on relevant outcomes, such as the temperature at failure, were provided. Finally, the influence of the surrounding structure on the effectiveness of the procedures was investigated extending the parametric analysis to columns with various degrees of axial restraints.

Local buckling of the bottom flange in steel-concrete composite beams with trapezoidal corrugated webs subjected to end restraint at high temperatures

Steel-concrete composite beams with trapezoidal corrugated webs (SCBCW) are prone to rapid failure at high temperatures due to local instability of the bottom flange. The failure mechanism of SCBCW, which is an integral part of the holistic structure and subject to axial and rotational restraints from adjacent members at elevated temperatures, differs from conventionally simply supported steel-concrete composite beams with straight webs. To investigate the evolution of local buckling in the compressed flange of SCBCW under high temperature conditions, a composite beam model with frame restraints was developed using ABAQUS finite element software. In this model, the composite beam is connected to restraint frame columns through high-strength bolts. The changes in axial stress, bending moment, and deflection of the compressed flange of SCBCW were analyzed as temperature increased. Results indicate that at elevated temperatures, additional bending moments occur in the flange plane due to axial restraints, section temperature gradients, section negative bending moments and accordion effect caused by corrugated web on compressed bottom flange of SCBCW. This leads to a gradual increase in axial compressive stress before local buckling occurs followed by a decrease due to internal force redistribution upon onset of buckling. Studies show that initial buckling of bottom flange occurs on one side of flat section of web where axial compressive stress is relatively high while restraint effect on web is low; Subsequent local buckling of the beam then appears on opposite side adjacent flat section of web after initial buckle occure on one side. After local buckling appears on both sides of web tension bands appear on both sides where bottom flange experiences localized bucking. The setting of longitudinal stiffeners (LS) can effectively improve the local stability of the bottom flange of the composite beam, while the setting of transverse stiffeners (TS) has no significant impact.

Collapse analysis of restrained concrete-filled steel tubular columns in fire conditions

This paper presents numerical analyses of the thermo-mechanical behavior of restrained square concrete-filled steel tubular (CFST) columns subjected to standard fire. It is found that the behavior is significantly influenced by the load ratio and axial restraint level. The collapse of restrained columns in fire conditions can be defined as the axial force in columns reaching 0 or the axial contraction deformation reaching a hundredth of column length. Three collapse modes are discovered, i.e., the expansion deformation collapse mode, contraction deformation collapse mode, and load-bearing capacity loss collapse mode. Under a low load ratio, three distinct modes of collapse are possible. Conversely, at a high load ratio, only the contraction deformation collapse mode and the load-bearing capacity loss collapse mode are observed. Through analytical and numerical approaches, a method for identifying the collapse mode based on geometric dimensions, axial restraint level, and load ratio has been established. This identification method can significantly contribute to optimizing fire protection strategies for CFST columns in structural designs.

Behaviour of axially-restrained slender steel tubes exposed to fire

The behaviour of axially-restrained slender steel tubes exposed to fire was studied. Fire tests and corresponding finite element (FE) simulations were conducted on four specimens with varying slenderness ratios and axial restraint stiffness. The accuracy of FE simulation was validated against the test results. Both the test and numerical results showed that the axially-restrained slender steel tubes buckled at much lower temperatures than steel columns. Continuous temperature elevation was then required to complete their buckling, because the steel maintains considerable stiffness at the buckling temperature. Parametric analysis was conducted based on FE simulations to investigate the effect of the slenderness ratio, axial restraint stiffness, and peak temperature on the behaviour of axially-restrained slender steel tubes exposed to fire. Empirical equations were established for the buckling temperature and post-fire residual lateral displacement using response surface methodology. These equations demonstrated a strong ability to fit the experimental data and predict the responses for new scenarios.

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.

Buckling and critical temperatures of restrained H-section steel columns in fire considering dynamic effect

In this paper, a parametric analysis on the buckling and critical temperatures of restrained H-section steel columns in fire, considering the dynamic effect, is presented. The developed finite element model of steel columns was verified by test results. Then, the buckling and critical temperatures of steel columns, obtained by static and explicit dynamic analyses, were compared. Moreover, the effects of rotational and axial restraint stiffness ratios, as well as load ratios, were studied. It was found that as the rotational restraint stiffness ratio increased, the buckling and critical temperatures both rose, and the rotational restraint stiffness ratio affected the critical temperature more than the buckling temperature. Besides, when the axial restraint stiffness ratio and load ratio rose, the buckling and critical temperatures dropped significantly. Finally, by combining the findings of the research and existing calculation formulas in literatures, new simplified formulas for buckling and critical temperatures were proposed, respectively. The prediction results of the proposed calculation formulas agreed well with the parametric analysis results. The proposed formulas were further verified by test data. According to the comparative results, the proposed formulas could well predict the buckling and critical temperatures of steel columns in fire.

Numerical Analysis of Restrained Continuous Steel Columns under Standard Fire

The steel column performance in realistic structures during a fire has yet to be fully understood because existing research emphasizes single-story performance, thereby disregarding the influence of continuous steel columns in multi-story configurations devoid of fire. This paper presents a numerical study to comprehend the overall structural fire performance of continuous steel columns, considering the effect of loading ratios, restraint ratios, column continuity, and single-sided lateral moments. An advanced numerical model was initially developed using ABAQUS and validated against experimental tests. The validated numerical model was subsequently employed to investigate the effects of several parameters, including axial restraint ratios (α = 0.05–0.35) and axial load ratios (n = 0.3–0.8). The study findings indicated that the restraint ratios within the designed range have a slightly beneficial impact on the fire resistance of continuous steel columns. The column continuity did not exert a significant impact on the performance of steel columns in fire. Additionally, the comparison showed that the current design approach in EN 1993-1-2 was conservative for predicting the limiting temperature of internal and edge columns.

Blast resistance of RC columns for varied detonation scenarios: Effect of shear detailing

The growing threat of accidental and malevolent blast loading to building structures has necessitated the consideration of blast-resistant design. Columns are the most vulnerable and critical component of a building, so they must be designed against blast to achieve defined performance goals. The influence of transverse rebar detailing on the ultimate capacity and failure modes of rectangular reinforced concrete (RC) columns against blast loads was investigated under different detonation scenarios. The performance of the columns was quantified using the failure charge mass and post-blast residual axial capacity. Pressure–impulse diagrams were used to study the failure modes. The analyses showed that special transverse detailing measures were the most effective for columns subjected to near-field surface bursts. The confinement of concrete due to ties and axial restraint played a critical role in improving the blast performance of columns. The provision of diagonal rebar improved the blast resistance by preventing direct shear failure, and was most effective when coupled with closely spaced lateral ties. Finally, the performance of code-compliant columns against blast was studied to determine the blast safety margin and the scenarios under which it would be necessary to undertake blast retrofitting of the columns in existing critical buildings.

Axial restraint performance of small span-to-depth ratio coupling beams reinforced with diagonal and rhombic bars

High ductility is necessary for coupling beams because they are the key energy dissipating components in shear wall structures. However, the axial restraint by the coupled wall piers with high stiffness at both ends negatively affects ductility. Moreover, effectively obtaining the variation laws of the seismic performance of coupling beams under variable axial force using the existing methods is difficult. This study established a statically indeterminate strut and tie model of axial restraint hybrid reinforced coupling beams with a span-to-depth ratio less than 1.5, and the analysis program was compiled. The model was validated by the comparative results of four test examples with span-to-depth ratios ranging from 0.8 to 1.5. Key responses of deformation, bearing capacity, relationship between the axial force and axial deformation, and ductility characteristics subjected to different axial restraints were investigated through combination analysis of the shear-compression, span-to-depth, longitudinal to diagonal bar, and diamond to diagonal bar ratios. The results demonstrated that the axial and lateral forces of the coupling beams with axial restraint were greater than those of the unrestraint, and their amplitude first increased and then decreased with the axial deformation. The stronger is the axial restraint, the greater the yield deformation. Moreover, the smaller is the failure deformation, the more prominent the shear deformation in the total deformation and the worse the ductility. The results also showed that the ductility of the coupling beam in the coupled wall structure designed according to the current specification was insufficient when the wall stiffness was large, requiring more strict measures to be taken under rare earthquakes.

Behavior of FeCrAl-ODS cladding tube under loss-of-coolant accident conditions

To evaluate the behavior of an oxide-dispersion-strengthened FeCrAl (FeCrAl-ODS) cladding tube under loss-of-coolant accident (LOCA) conditions of light-water reactors (LWRs), the following two laboratory-scale LOCA-simulated tests were performed: the burst and integral thermal shock tests. Four burst and three integral thermal shock tests were performed on unirradiated, stress-relieved FeCrAl-ODS cladding tube specimens, simulating ballooning and rupture, oxidation, and quenching, which were postulated during a LOCA. The burst temperature of the FeCrAl-ODS cladding tube was 200–▪ higher than that of the Zircaloy cladding tube, and the FeCrAl-ODS cladding tube's maximum circumferential strain was smaller than or equal to that of the Zircaloy-4 cladding tube. These results indicate that the FeCrAl-ODS cladding tube has higher strength at high temperatures than the conventional Zircaloy cladding tube. The FeCrAl-ODS cladding tube did not fracture after being subjected to an axial restraint load of ∼▪, which is more than 10 times higher than the axial restraint load estimated for existing LWRs, during quenching, following isothermal oxidation at ▪ for ▪. The FeCrAl-ODS cladding tube was hardly oxidized during this isothermal oxidation condition. However, it melted after a short oxidation at ▪ and fractured after abnormal oxidation at ▪ for ▪. Based on these results, the FeCrAl-ODS cladding tube should not fracture in the time range expected during LOCAs below ▪, where no melting or abnormal oxidation occurs.

Numerical study on the fire behaviour of restrained steel-concrete composite beams

An elaborate solid-shell finite element model was developed to investigate the fire behavior of restrained steel-concrete composite beams. The model was validated against experimental results in literatures. Parametric studies were also performed to study the parameters including restraint stiffness, load ratio, span, exposure length, embedding depth, steel beam height and protective layer on the fire behavior of restrained composite beam. The analysis results show that the mechanical response of restrained composite beams goes through four phases: elastic, elasto-plastic, rapid plastic deformation and plastic catenary action phase. With the decrease of restraint stiffness, the increase of load and span, the failure mode of the restrained composite beam changes from overall lateral instability to a sharp increase in deformation rate, and the code BS476-20 and ISO834 underestimate the fire resistance of restrained composite beams. The negative bending moment at the beam end increases sharply and reaches the peak value within a short fire time. Therefore, reinforcement shall be provided at the top of the concrete slab near the support section. Furthermore, the difference in fire resistance of restrained composite beams is mainly reflected in the plastic catenary action phase. When the load ratio is less than 0.5, the fire resistance of restrained composite beams can be improved by reducing the fire range, beam height and span, and increasing the axial restraint stiffness. When the load ratio is 0.7, the fire resistance of restrained composite beam is hardly affected by the axial restraint stiffness and span, while with the exposure length reducing from 5 m to 4 m, embedded depth increasing from 0 mm to 50 mm, and the protective layer increasing from 0 mm to 10 mm, the fire resistance of the composite beams increases by 114 min and 160 min and 76 min, respectively.

Post-buckling of variable stiffness curvilinear fibre-reinforced general lay-up composite beams by sinusoidal shear flexible theory

The mechanical post-buckling behaviour of variable stiffness layered composite beams reinforced by curvilinear fibres subjected to compressive loads is investigated here using a sine function-based shear flexible beam model. The neutral axis stretching force stemming from the axial movement restraints is accounted for through von Karman’s assumption based geometrical nonlinearity. Furthermore, the modified beam constitutive equation arising from the consideration of the Poisson’s effect is introduced in the formulation for the laminated beam analysis with general lay-up or ply sequences. The governing equations incorporating the incremental stiffness matrices are formed through the minimization of total potential energy principle and are solved by numerical method. The solutions for the developed governing equations are evaluated iteratively based on eigenvalue analysis and the characteristics of post-buckling of laminated beams can be inferred through the relationship between the beam deflection level and post-buckling axial load. An in-depth analysis selecting many design parameters for instance lamina’s curvilinear fibre angles, beam slenderness ratio, lay-up and edge conditions, load type and so on is dealt with in bringing out the behaviour of variable stiffness laminated beam in linear and post-buckling regions. Also, the influence of flexible end supports by restraining elastically against ends rotation is studied on the beam elastic stability behaviour.

Influence of H-column stiffness on the anti-collapse performance of composite frame in the minor-axis direction

This study is the first attempt to investigate the resistance mechanism in the minor axis of H-columns and aims to provide essential information for improving the reliability of the anti-collapse transmission path of spatial structures. A one-third scale composite frame extending in the minor-axis direction of the H-column, comprising a welded flange and bolted web beam–beam connection, was investigated through monotonic static loading test to clarify the resistance transmission mechanism of structures. Based on the progress in the internal force under different displacements, the minor-axis specimen experienced stages of elasticity, compression arch, and mixed mechanism. The influence of column stiffness on the resistance and internal force development in the minor-axis specimen was comparatively significant with respect to the results of the major-axis specimen. For parametric analysis, a full-scale model was developed, which confirmed the influence of column stiffness and boundary axial restraint stiffness on collapse performance of composite frames in the minor-axis direction, providing an underlying mechanism for anti-collapse design and optimization research. Furthermore, a multispan solid model was developed to reflect the attenuation law of the axial restraint stiffness provided by the external substructure (surroundings) with the appropriate number of spans, which assisted in formulating a simplified modeling process. To avoid or delay the negative impact of potential defects on the structure, local weakening strategies were applied to the minor-axis direction based on the experimental and simulation results, and the collapse resistance mechanism was verified using the developed model.

Development of design equations for ultra-high strength steel CHS columns under transient fire conditions considering thermal creep and axial restraint effects

Despite their potential for widespread structural applications, the use of ultra-high strength steel (UHSS) members in buildings is currently hindered by the lack of suitable design relationships for these components. In response to this technical gap, this paper presents design equations for Grade 1200 UHSS circular hollow section (CHS) columns under transient fire conditions. The design relationships are derived from an extensive parametric study on the in-fire behavior of UHSS tube columns using advanced finite element (FE) simulations in ABAQUS software. However, to verify the FE modeling framework, experiments are also conducted on axially-compressed UHSS tube specimens. The thermal creep of the UHSS tubes is explicitly included as a user-defined subroutine in the modeling by a robust creep model exclusively developed for the UHSS material under transient fire conditions. In addition to the utilization factor, the effects of non-dimensional slenderness, heating rate (or thermal creep), and axial restraint stiffness ratio are also studied and considered in the design equations obtained for the UHSS CHS columns. Finally, it is shown that the present design relationships can predict the columns' buckling and failure temperatures with a maximum absolute error (MAE) of 4%.

Thermal creep of hybrid steel columns comprising ultra-high strength steel tubes and stainless steel plates under transient fire conditions

This paper investigates the behavior of an innovative steel column section both at room temperature and under the transient heating regime of building fires. The column consists of Grade 1200 ultra-high strength steel (UHSS) tubes welded to the corners of Grade 304 stainless steel plates, forming a square-shaped hybrid cross-section. First, through performing compressive tests on 780 mm long stub columns of the hybrid section at room temperature, its vulnerability to local buckling is assessed; accordingly, decision is made on the appropriate width of the plates. Then, six transient fire tests are conducted on the hybrid stub columns under three different compressive load levels. Due to the very fast heating rate of standard fire curves such as the ISO 834, the thermal creep of steel columns may be overlooked using these heating regimes, which may lead to an overestimation of the column’s resistance against building fires. Thus, a distinctive heating regime is adopted for the fire tests in this study; at any load level, two fast and slow heating rates are applied to the specimens. In this way, by comparing the results obtained, the effect of thermal creep on the fire resistance of the columns can be assessed. More importantly, the fire tests are used to verify finite element (FE) models developed for these hybrid columns in ABAQUS software; specifically, the creep model already developed for the UHSS tube and stainless steel plate materials is verified for component-level simulations. The verified FE modeling framework is then employed to perform an extensive parametric study on the effects of length, utilization factor, axial restraint stiffness ratio, and heating rate on the hybrid columns’ fire resistance. Finally, based on the results obtained from the parametric study, simplified design equations in the temperature domain are obtained for the axially-restrained hybrid steel columns under transient fire.

Analysis of axial and rotational restrained concrete-filled steel tube columns at elevated temperature

This paper has two aims, first, to develop a simplified finite element (FE) model to simulate and study the behaviour of restrained concrete-filled steel tube (CFST) columns subjected to axial force and fire, and second, to propose simplified design equations. FE model has been developed using the ABAQUS program and verified against published data. Furthermore, a parametric study has been conducted using the verified FE model to study different parameters that might affect the behaviour of restrained concrete-filled steel tube columns subjected to axial force under elevated temperatures. These parameters are load level, section type (circular and square), axial and/or rotational restraint ratio, type of steel tube (carbon and stainless steel), type of concrete (carbonate and siliceous concrete aggregate), steel yielding strength, concrete compressive strength, column dimension, width to thickness ratio and reinforcement ratio. Finally, simplified design equations are proposed to determine the buckling time, critical time and maximum load capacity of axial and rotational restrained CFST columns under fire.

Effect of axial and rotational restraint on performance of composite beams with fire protection coating

Effect of axial and rotational restraint on performance of composite beams with fire protection coating

Predicting equation of quasi-static and dynamic failures of steel columns under fire

Steel columns may fail in dynamic or quasi-static types under fire. The quasi-static failure of steel column could be considered as gradual column removal in the collapse assessment of structures, while the dynamic failure cannot. Hence, it is meaningful if the failure type of the column could be predicted. To identify the failure types of box-section steel columns under fire simply, this paper adopted a validated numerical model to conduct a systematic parametric analysis. The critical axial restraint stiffness ratio (βl,cr), which is used to predict the failure type of columns under fire conditions, is the main focus. Firstly, the values of βl,cr of columns with a representative section were studied, with various slenderness ratios and load ratios being considered. Then, the effects of width-thickness ratio, length–width ratio, sectional size, and bending moment load ratio on βl,cr were studied. The results indicate that βl,cr of columns with the representative section increases with the rise of the load ratio, and increases sharply after the load ratio exceeds a certain level. Besides, the dynamic effect during column buckling and βl,cr both increase with the rise of either the width-thickness ratio, length–width ratio, or sectional size. Moreover, based on the results, a predicting equation for βl,cr of box-section steel columns was proposed. The failure type of a steel column under fire can be easily predicted by the proposed equation. Finally, the proposed equation was verified by an additional series of case studies, and good agreement was achieved.

Generalised analytical solution for determining natural frequency of free span offshore pipelines considering non-homogeneity of seabed soil

The free spanning of the offshore pipelines caused by uneven seabed, ocean current and soil erosion, is one of the main factors of fatigue failure. The majority of researchers have presumed that the seabed soil is homogeneous but practically it is not homogeneous. In this article, a generalised analytical model of the free spanning has been proposed considering the effects of axial force, out of straightness and axial restraints for determining natural frequencies of the offshore pipelines. The novelty of this paper is that the developed analytical model is used for non-homogeneous soil conditions at the support of free span pipelines to find the lowest natural frequency. The proposed model has been validated with the well-used code DNVGL-RP-F105: 2017 and finite element analyses. The proposed analytical method has been found to be accurate under real-world circumstances and could be a helpful tool for evaluating the free span pipelines.