Restrained Steel Beams Research Articles

Experimental, numerical and analytical analysis of a single-span steel portal frame exposed to fire

The thermo-mechanical behaviour of single-span steel portal frames in fire conditions illustrates a sequential transition from an ambient temperature state through to eventual collapse, encompassing axial forces, moments and deformations. To investigate the thermo-mechanical behaviour, a fire test on an 8 m × 6 m steel portal frame assembly is conducted. Detailed thermal and structural responses of the frame are measured and presented. The experimental results reveal that the frame collapses post 31-min heating with a peak temperature approximating 800 °C. A typical inward collapse mode is observed. 2D and 3D finite element models are established and validated against experimental results, respectively. The numerical model is divided into three heating regions to mimic the behaviour exhibited during the fire scenario. Furthermore, a thermo-mechanical theory is proposed to analyse the fire behaviour of a single-span steel portal frame. Based on the fire response of a restrained steel beam, the thermo-mechanical behaviour can be segmented into four stages: the ambient temperature stage, thermal expansion stage, elasto-plastic stage and catenary stage. A comprehensive series of calculation formulas determine the displacement, internal forces and moments at different stages. The analytical computations exhibit a close consistence with the numerical results, within the deviation of 10% for the majority. This analytical method can be effortlessly employed for both the fire-resistant design and assessment of the current state of steel portal frames in fire conditions.

Fire and post-fire performance of blind-bolted concrete-filled steel tubular joints with restrained steel beams: Experiment and simulation

Blind-bolted connection is a type of new developed prefabricated beam-column connection, which can be used to connect the concrete filled steel tubular (CFST) columns and the steel beams easily. The static and dynamic performance of CFST column to steel beam joints with blind-bolted connections have been well explored, but limited research has been conducted to investigate the fire and post-fire performance of this type of composite joint. In this paper, a series of reversed T-shaped joint fire tests were conducted to investigate the fire and post-fire performance of blind-bolted CFST joints with axially restrained steel beams. The influence of restrained effect from adjacent members in the entire frame structure on the response of blind-bolted joints in and after fire could be reasonably considered by the reversed T-shaped joint fire test. The joint temperature, failure modes, beam and column displacements and temperature internal force development during the entire loading and fire stage were recorded and discussed. The test results indicated that the blind-bolted connections showed very good working performance in and after fire, and no bolt shank fracture or bolt pull-out failure was observed. Finite element analysis (FEA) models were established to simulate the fire and post-fire performance of blind-bolted CFST T-shaped joints with axially restrained steel beams, and the joint moment versus relative rotation angle relationship curves of the blind-bolted joints during the entire fire and loading process were extracted and discussed based on the FEA models. The results indicated that the joint negative moment generated by the axially restrained beam boundary in the heating and cooling phases could go up to around 1.4 times the joint negative moment at ambient temperature.

Experimental study on behavior of restrained high strength Q690 steel beams exposed to fire

In comparison to the isolated steel beam, the restrained steel beam is able to sustain fire loads using the effect of the surrounding restraints. However, Q690 steel has lower resistance to high temperatures than other types of carbon steel. To address this gap, a series of experimental tests on restrained high-strength Q690 steel beams subjected to fire are reported in this paper. Four full-scale restrained high-strength Q690 steel beams were investigated under several fire scenarios, and one was tested at room temperature. In this study, three transient tests and one steady-state test were chosen to fully comprehend the behavior of the restrained high-strength Q690 steel beams exposed to fire. Under the two test conditions, the impact of the steady-state and transient conditions on the fire response of the restrained Q690 steel beams are compared, and the variation of axial peak force, bearing capacity, and deflection were analyzed. The results showed that the critical temperature of the steady-state test is close to the critical temperature of the transient test, and the maximum axial force of the steady-state test is comparable to the one of the transient test. Due to the combined action of load and axial forces, the restrained Q690 steel beam generally develops flexural-torsional buckling failure after reaching the critical temperature in transient tests. In comparison, the steady-state test exhibits early flexural-torsional buckling behavior before reaching the critical temperature.

A consistent creep model for high strength steels and numerical investigation of creep on restrained steel beams

Even though creep behavior in steel at elevated temperatures has been widely observed, the effect of creep on steel members is not fully understood yet due to the extensive range of steel grades. In this paper, a tension creep test on high-strength Q960 steel at high temperatures was performed. Based on the test data in this paper and available creep data on Q345, Q460, and Q690 steels, a consistent creep model for each steel according to the Fields & Fields creep model was proposed and validated by the comparison with the test data. In order to quantitatively investigate the effect of creep on fire response of restrained steel beams, a finite element model (FEM) was established to analyze the critical temperature of restrained steel beams in fire conditions, with and without considering creep strain generated in steel beams. This was also carried out to better understand the impact of high-temperature on steel beams with various steel grades under the influence of the same load. The verification of the FEM was achieved by comparing the results with experimental data on a restrained Q235 steel beam and Q690 cantilever steel beam. The study reveals that creep has a noticeable effect on the fire resistance of the restrained steel beams and that the effect varies from one type of steel to another. A comparison has been made to observe the effect of high-temperature creep on the critical temperature for each steel type.

A Practical Approach for Fire Resistance Design of Restrained High-Strength Q690 Steel Beam Considering Creep Effect

Most of the previous studies on restrained steel beam behaviour in fire conditions have neglected the creep effect due to the lack of applicable creep models. A finite element model (FEM) is determined in this study to investigate fire resistance and the behaviour of restrained high-strength (RHS) Q690 steel beams in fire considering the high-temperature Fields & Fields creep model. A comparison of the results obtained by the FEM with those from previous tests proved the validity of the FEM. A second FEM without a creep model is also established to study the influence of creep on the fire resistance of restrained steel beams. Results showed that creep has a serious effect on the behaviour of restrained steel beams in fire. Thus, ignoring creep will possibly lead to unsafe designs. Several parametric studies are carried out using the validated FEM with the aim to investigate the influencing factors on the fire response of RHS Q690 steel beams. Analysis shows that some of the investigated factors, such as heating rate, cross-section temperature distribution, rotational restraint stiffness and span-to-depth ratio, have been found crucial in the fire resistance of RHS Q690 steel beams. Furthermore, a simplified approach is presented for RHS Q690 steel beams based on the results of the FEM, including the creep effect, to calculate the moment capacity. This approach is also suitable for calculating the critical temperature of RHS Q690 steel beams.

Research on the Judgement Method for Catenary Action of Restrained Steel Beams in Fire

Based on fire tests, a parametric numerical simulation on the catenary action of restrained steel beams in fire was performed by the finite element software ABAQUS. It can be known that axial constraint stiffness, rotational constraint stiffness and load ratio are key factors that affect the catenary action in fire. The formation mechanism of catenary action under ISO-834 standard fire was studied; and the judgement method for catenary action in fire was presented. The results show that: (1) when axial constraint stiffness reaches a certain value, the catenary action of restrained steel beams will occur almost at the same time; (2) with the increase of rotational constraint stiffness or load ratio, the catenary action of steel beams will occur earlier; (3) for restrained steel beams under a small load ratio, the catenary action usually occurs in fire when the mid-span deformation reaches 1/15 of the span; but for restrained steel beams under a large load ratio, the catenary action usually occurs when the mid-span deformation reaches 1/18 of the span; (4) for restrained steel beams with a large rotational constraint stiffness, the judgement method for catenary action in fire can still adopt the same method as above, which will be a little conservative.

Behaviour of restrained steel beam at elevated temperature – parametric studies

Purpose This paper aims to investigate computationally and analytically how different levels of restraint from surrounding structure, via catenary action in beams, affect the survival of steel framed structures in fire. This study focuses on examining the mid-span deflection and the tensile axial force of a non-composite heated steel beam at large deflection that is induced by the catenary action during exposure to fires. The study also considers the effect of the axial horizontal restraints, load-ratio, beam temperature gradient and the span/depth ratio. It was found that these factors influence the heated steel beam within steel construction and its catenary action at large deflection. The study suggests that this may help the beam to hang to the surrounding cold structure and delay the run-away deflection when the tensile axial force of the beam has been overcome. Design/methodology/approach This paper is part one of the parametric study and discusses both the effect of the axial horizontal restraints and load-ratio on the heated steel-beam. Reliance on the prescriptive standard fire solutions may lead to an unpredicted behaviour of the structure members if the impact of potential real fires is not considered. Findings Variation of the horizontal end-restraint level has a major effect on the behaviour of the beam at high deflection, and the loading on a beam at large displacement can be carried effectively by catenary behaviour. An increase of axial horizontal stiffness helps the catenary action to prevent run-away at lower deflections. The studies also investigated the influence of varying the load ratio on the behaviour of the heated beam at large deflection and how it affects the efficacy of the catenary action. The study suggests that care should be taken when selecting the load ratio to be used in the design. Originality/value In a recent work, the large deflection behaviours of axially restrained corrugated web steel beam (CWSB) at elevated temperatures were investigated using a finite element method (Wang et al., 2014). Parameters that greatly affected behaviours of CWSB at elevated temperatures were the load ratio, the axial restraint stiffness ratio and the span–depth ratio. Other works included numerical studies on large deflection behaviours of restrained castellated steel beams in a fire where the impact of the catenary action is considered (Wang, 2002). The impact of the induced axial forces in the steel beam during cooling stage of a fire when the beam temperature decreases, if thermal shortening of the beam is restrained, large tensile forces may be induced in the beam (Wang, 2005; Allam et al., 2002). A performance-based approach is developed for assessing the fire resistance of restrained beams. The approach is based on equilibrium and compatibility principles, takes into consideration the influence of many factors, including fire scenario, end restraints, thermal gradient, load level and failure criteria, in evaluating fire resistance (Dwaikat and Kodur, 2011; Allam et al., 1998).

Strengthening of Laterally Restrained Steel Beams Subjected to Flexural Loading Using Low-Modulus CFRP

AbstractUpgrading the flexural design strength of the structural member for increased live load without disrupting the functionality of the structure is an arduous task. One such problem was invest...

Structural performance of steel beams and frames with slant end-plate connections at elevated temperature

Thermal expansion remains as one of the most hazardous conditions a restrained steel beam could experience throughout its service life. In this regard, the design of connections plays an important role in dissipating the thermal axial force resulted from such deformation. In this paper, the finite element method (FEM) has been employed to investigate the thermal performance of the steel beam with slant connections under gravity and thermal loads. The numerical outcomes agree very well with the analytical and experimental approaches, thus demonstrating a good reliability of the model to assess the thermal performance of the steel frames with slant end-plate connections. In addition, the proposed and conventional end-plate connections are modelled separately in two 7-storey steel frames to examine their comparative thermal performance. The numerical results conclude that the thermal behaviour of steel frame with the slant end-plate connection is superior to that using conventional since it is capable to dissipate considerably the experienced additional thermal axial forces.

A Numerical Investigation on Restrained High Strength Q460 Steel Beams Including Creep Effect

Most of previous studies on fire resistance of restrained steel beams neglected creep effect due to lack of suitable creep model. This paper presents a finite element model (FEM) for accessing the fire resistance of restrained high strength Q460 steel beams by taking high temperature Norton creep model of steel into consideration. The validation of the established model is verified by comparing the axial force and deflection of restrained beams obtained by finite element analysis with test results. In order to explore the creep effect on fire response of restrained Q460 steel beams, the thermal axial force and deflection of the beams are also analyzed excluding creep effect. Results from comparison infer that creep plays a crucial role in fire response of restrained steel beam and neglecting the effect of creep may lead to unsafe design. A set of parametric studies are accomplished by using the calibrated FEM to evaluate the governed factors influencing fire response of restrained Q460 steel beams. The parametric studies indicate that load level, rotational restraint stiffness, span–depth ratio, heating rate and temperature distribution pattern are key factors in determining fire resistance of restrained Q460 steel beam. A simplified design approach to determine the moment capacity of restrained Q460 steel beams is proposed based on the parametric studies by considering creep effect.

Parametric study on load ratio effect on the flexural bending behaviour of axially-restrained HSS steel beams subjected to fire

Purpose In fire condition, the limiting temperature of a restrained steel beam depends on a few parameters, e.g. temperature distributions along and across the beam, beam’s load ratio and span length. The purpose of this study is to investigate the structural fire behaviour of axially restrained steel beams under different beam’s load ratios, taking into consideration the effect of the beam’s end connections configuration. Design/methodology/approach A three-dimensional finite element (FE) computer model has been developed to simulate the structural fire behaviour of axially restrained steel beams and their end connections. After successfully validating the developed model against the outcomes of the available large-size fire resistance experiments, the FE model has been used in a parametric study to investigate the beam’s load ratio effect on the behaviour of the axially restrained steel beams and their end connections. Findings The parametric study showed that increasing the beam loading level significantly increased the beam deflections at elevated temperatures; where, increasing the beam’s load ratio from 0.5 to 0.9 reduced the beam fire resistance by about 100 s. In contrast, decreasing the beam’s load ratio from 0.5 to 0.3 allowed the beam to easily achieve a 30-min fire resistance rating with no fire protection applied. Originality/value Experimental parametric studies are difficult to control in a laboratory setting and are also expensive and time consuming. Therefore, the reasonable accuracy of the validated FE model in reproducing the experimental fire behaviour of steel beams and their end connections makes it a very useful tool for both numerical and analytical studies.

Fire Resistances of Restrained Steel Beams Subjected to Fire Loads

Conventional fire loads and fire resistances of a steel beam still lack an adequate correlation. This paper has established the relationship between the responses of restrained steel beams and fire actions by using a new definition of fire resistances and a new expression of fire loads. By using reduction factors of elastic modulus and yield strengths, has presented three critical equations to predict the limit state of a restrained steel beam in a fire. Based on these equations and the heat transfer formula, the paper provided a new definition of fire resistances. By using the heat release rate and effective rate coefficient of thermal absorption, a new expression of fire loads has been argued. Compared with tests, the proposed approach in this paper is in good agreement with the measured values in tests. The results show that the new fire resistances could be able to reflect the facts of heat transfers and duration time. In contrast to conventional fire loads, the new fire loads are more efficient to indicate a fire load.

Dynamic Behaviour and Catenary Action of Axially-restrained Steel Beam Under Impact Loading

In this paper, the dynamic response and catenary action of axially restrained steel beam under impact loadings is examined through a combination of experimental and numerical investigations. The results of six impact tests on the axially restrained welded H-beams by means of the drop hammer test machine are presented. The main behavioural patterns and the key response characteristics including the development of impact force, deformation and strain, as well as failure modes are examined, with emphasis on the effect of impact energy and the width to thickness ratio of beam flange. Finite element models are also developed and validated against the available testing results. It is demonstrated that the detailed FE model can reasonably capture the response of the welded H-beams under impact loadings. Moreover, the mechanism of catenary action was identified based on the development of the internal force in the welded H-beams.

An approach for evaluating fire resistance of steel beams considering creep effect

Most of previous studies on fire resistance of restrained steel beams neglected creep effect due to lack of suitable creep model. This paper presents a finite element model (FEM) for accessing the fire resistance of restrained high strength Q460 steel beams by taking high temperature Norton creep model of steel into consideration. The validation of the established model is verified by comparing the axial force and deflection of restrained beams obtained by finite element analysis with test results. In order to explore the creep effect on fire response of restrained Q460 steel beams, the thermal axial force and deflection of the beams are also analyzed excluding creep effect. Results from comparison infer that creep plays a crucial role in fire response of restrained steel beam and neglecting the effect of creep may leads to unsafe design. A simplified design approach to determine the moment capacity of restrained Q460 steel beams is proposed based on the results of parametric studies by considering creep effect.

Axially restrained steel beams with web openings at elevated temperatures, part 1: Behaviour and numerical simulation results

Steel beams with web openings are frequently used as floor and roof beams in building construction to achieve attractive, flexible and optimised design solutions for passage of services. In practical construction, such beams may be axially restrained by the surrounding structure. The presence of axial restraint can drastically change the behaviour of such beams in fire, but the behaviour of axially restrained steel beams with web opening has received little attention. This paper investigates the effects of openings on axially restrained steel beams at elevated temperatures through extensive numerical simulations. The examined parameters include opening shape, opening size and opening position, load ratio, level of axial restraint and cross-section temperature distribution profile. The results of this numerical investigation identify the key stages and quantities that should be evaluated in fire resistance design of axially restrained perforated steel beams.The simulation results show that axially restrained steel beam with web opening may enter catenary action at a much lower temperature than the commonly accepted critical temperature of the beam calculated assuming no axial restraint. This happens when the opening is slender (long and deep) and when it is placed at high bending moment regions of the beam. The effect is more severe as the level of end axial restraints increases. An important implication of this finding is that additional tensile forces may exist in such beams at the critical temperatures calculated without considering axial restraint.The results of this paper also indicate that when the maximum axial tension in the beam is reached, the top tee-section has almost zero axial force. At the same temperature, the bottom tee-section (in tension) has reached its maximum tensile capacity. Hence the maximum axial force in the beam is the same as the tensile capacity of the bottom tee-section. This finding can be used to determine the maximum tensile force against which the connections. The companion paper presents an analytical solution.

Axially restrained steel beams with web openings at elevated temperatures, part 2: Development of an analytical method

The companion paper has presented the results of an extensive numerical study to investigate the behaviour of axially restrained steel beams with web opening, and to identify how the key quantities of the behaviour are controlled by different design parameters, including size and location of the opening, level of axial restraint, load ratio and temperature distribution. This paper uses the numerical simulation results to derive an analytical method to evaluate the key quantities, including the initial slope of the beam axial force – temperature relationship (rate of increase in compressive force with respect to temperature increase), point of initial buckling of the Tee-section under compression, transition temperature from compression to tension, the maximum tensile force and the corresponding temperature.For practical design, the beam's limiting temperature is calculated without consideration of axial restraint. At this temperature, since there may be considerable axial tensile force in the beam with web opening, it is important to check the capacity of the connections against the maximum tensile force, which can be calculated accurately using the proposed method.

Large deflection response of restrained steel beams under fire and explosion loads.

A numerical study on the response of steel beams to fire and explosion is presented in this paper. First, a unified computing model, which can be used to simulate the behaviour of beams under four loading scenarios that involve fire and explosion or impact, is constructed. The proposed technique allows complete transparency of the influence of the various parameters on the structural behaviour. Second, the effects of load level on critical temperature are analyzed for various static and explosion load ratios. Two cases of explosion and fire loading sequences are compared, it is shown that the critical temperature of the beam subjected to fire followed by an explosion is lower than that of the beam subjected to an explosion followed by fire. The influence of temperature on the p–i diagram is investigated, an iso-damage surface is introduced to distinguish safe and unsafe regions. Third, the limiting temperature criteria are further examined. That is, the first and second limiting temperatures can be determined when the dimensional catenary force is equal to zero or to one, which corresponds to the bending or stretching plastic hinge, respectively.

Behaviour of restrained steel beam with reduced beam section exposed to fire

Reduced beam section (RBS) is one of the connection types, which is economical and popular for use in steel moment frames in seismic regions. By cutting some portions of the beam flanges near the column face, the RBS connections are designed to form plastic hinge within the RBS zone so that it could enhance the structural seismic performance. However, the steel beams with RBS connections have to provide robustness when exposed to fire. Although the responses of ordinary steel beams to elevated temperatures have been investigated over the last few decades, there has been very limited research on the behaviour of steel beams, with RBS connections in fire. This study includes a series of numerical analysis, to investigate the high-temperature performance of steel beams with RBS connections, compared to the responses of ordinary steel beams to fire. Various parameters have been considered, including the types of fire curves, the levels of beam-end restraints and the cutting profiles of the RBS connections. Overall, the deformation shape of RBS beams at high temperature is similar to that of ordinary steel beams, whereas the RBS beams could have longer period of fire resistance. The cut section actually provides both rotational and axial ductility/deformability to the connection, enhancing its fire resistance. Moreover, the cutting length, proposed by EC8, is also adequate for fire design. The minimum distance, between the RBS zone and the beam-end, proposed by FEMA-350 has been shown sufficient.

Stability of steel beams using the continuous strength method

Through a programme of experiments, numerical modelling and parametric studies, the implications of allowing for strain-hardening in the design of partially restrained steel beams are investigated. A total of fourteen tests were performed on simply supported beams that were partially restrained against lateral torsional buckling. Four different restraint spacings were considered in the tests to give non-dimensional lateral torsional slenderness values of 0.1, 0.2, 0.3 and 0.4 for the unrestrained lengths. In all tests, bending resistances in excess of the plastic moment capacity were observed, but in order to attain the levels of resistance predicted by the continuous strength method (CSM), which allows for strain-hardening, closer restraint spacing than the minimum specified by EN 1993-1-1 (2005) is required. Using additional data generated as part of an analytical and numerical study, as well as test data collected from the literature, a basic design approach was presented that incorporated a limiting lateral torsional slenderness for the CSM of 0.2, as well as a simple transition function from bending resistances predicted by plastic theory to those predicted by the CSM.

A B-splines-based GBT formulation for modeling fire behavior of restrained steel beams

An implicit finite element model based on the generalized beam theory (GBT) is developed to simulate the fire behavior of restrained steel beams. The model considers both material and geometric nonlinearities. A bilinear stress–strain curve is used to represent the material behavior at elevated temperatures. The GBT cross-section deformation modes are utilized to construct the mid-surface displacements of each wall, where the longitudinal variations of the mode amplitudes are approximated by the cubic B-splines. The bending related displacements are established by using assumptions of the Kirchhoff's plate theory. The Green–Lagrangian strain tensor is employed to represent the deformation at each quadrature point, and therefore the geometric nonlinearity can be included. A weak-form of the nonlinear equilibrium equations is derived by the Principle of Virtual Work and is solved by employing an implicit iterative procedure. The current model can capture local deformation because higher-order cross-section deformation modes are used. The fidelity of the developed GBT formulation has been evaluated by comparing the predictions with three benchmark results available in the literature, and case studies have been performed. It is found that the local buckling can influence the overall behavior of beams in fire, which is different to the finding of the conventional beam-element-based analysis. The current GBT approach is an alternative to the shell finite element formulation, but exhibits higher computational efficiency.