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The purpose of this study is to investigate the influence of progressive collapse under high temperature for a reinforced concrete (RC) frame. An analytical programme was analysed for a two-bay five-storey RC frame exposed to high temperature at different column locations.

The effects of high temperature protections and locations (i.e. corner, middle and intermediate) on collapse conditions and load distributions were studied for the steady-state linear analysis using finite element software.

The results show that the frame will not collapse suddenly at temperatures up to 400°C. This is attributed to an increase in the deflections of the column, which increases the lateral displacement of adjacent heated columns and governs their buckling. This indicates that the temperature rating in the column against collapse can occur at a range of 500°C-600°C compared to that of individual members. The collapse pattern of RC frames designed as ordinary moment resisting frames, and under ordinary load, combinations is based on GSA guidelines. The results for displacement, stress and axial force were collected and discussed.

The two-bay five-storey frame has been created in finite element software, and linear analysis is used to perform this study with a different temperature.

This paper explains why the data with which thermal designers have to work is uncertain and incomplete. It then describes how accepting this uncertainty unlocks the shackles of accurate temperature prediction and gives the designer the freedom to tackle the different aspects of thermal design at an appropriate and simple level. The latter part of the paper concentrates on the thermal design of circuit boards, first for steady state and then for transient operation.

This paper delineates a literature review on fire-induced progressive collapse on structures and the effect of high temperature on structures and elements. After the occurrences of fire in the World Trade Center in the USA, the researchers started concentrating on the progressive collapse that happens due to high temperature. Currently, most of the researchers are working on fire-induced progressive collapse on structures using high-temperature behavior on materials which are used for construction. The researchers have been doing an intensive study to find a better strategy to prevent the building from structural fire damage or collapse with available codes and guidelines throughout the world. This paper aims to provide a better understanding and analytical solutions on the basis of the recent works done by researchers in fire-induced progressive collapse and methods adopted to find the collapse mechanism.

This paper is written by studying different literature papers of 109 related to progressive collapse on structures and fire-induced progressive collapse.

The behavior of structures due to high temperature and collapse conditions due to fire in different scenarios is identified.

This paper fulfills an identified need to study how the structure can withstand high-temperature conditions in our day-to-day lives.

In this study, the bending strength, flexural buckling strength and collapse temperature of small steel specimens with rectangular cross-sections were examined by steady and transient state tests with various heating and deformation rates.

The engineering stress and strain relationships for Japan industrial standard (JIS) SN400 B mild steels at elevated temperatures were obtained by coupon tests under three strain rates. A bending test using a simple supported small beam specimen was conducted to examine the effects of the deformation rates on the centre deflection under steady-state conditions and the heating rates under transient state conditions. Flexural buckling tests using the same cross-section specimen as that used in the bending test were conducted under steady-state and transient-state conditions.

It was clarified that the bending strength and collapse temperature are evaluated by the full plastic moment using the effective strength when the strain is equal to 0.01 or 0.02 under fast strain rates (0.03 and 0.07 min^–1). In contrast, the flexural buckling strength and collapse temperature are approximately evaluated by the buckling strength using the 0.002 offset yield strength under a slow strain rate (0.003 min^–1).

Regarding both bending and flexural buckling strengths and collapse temperatures of steel members subjected to fire, the relationships among effects of steel strain rate for coupon test results, heating and deformation rates for the heated steel members were minutely investigated by the steady and transient-state tests at elevated temperatures.

The paper aims to give an insight into the behaviour of reinforced concrete columns during and after the cooling phase of a fire. The study is based on numerical simulations as these tools are frequently used in structural engineering. As the reliability of numerical analysis largely depends on the validity of the constitutive models, the development of a concrete model suitable for natural fire analysis is addressed in the study.

The paper proposes theoretical considerations supported by numerical examples to discuss the capabilities and limitations of different classes of concrete models and eventually to develop a new concrete model that meets the requirements in case of natural fire analysis. Then, the study performs numerical simulations of concrete columns subjected to natural fire using the new concrete model. A parametric analysis allows for determining the main factors that affect the structural behaviour in cooling.

Failure of concrete columns during and after the cooling phase of a fire is a possible event. The most critical situations with respect to delayed failure arise for short fires and for columns with low slenderness or massive sections. The concrete model used in the simulations is of prime importance and the use of the Eurocode model would lead to unsafe results.

The paper includes implications for the assessment of the fire resistance of concrete elements in a performance‐based environment.

The paper provides original information about the risk of structural collapse during cooling.

In this study, engineering stress-strain relationships considering an effect of strain rate on steel materials at elevated temperatures were formulated and a simplified analytical model using a two-dimensional beam element to analytically examine the effect of strain rate on the load-bearing capacity and collapse temperature was proposed.

The stress-strain relationships taking into account temperature, strain, and strain rate were established based on the past coupon test results with strain rate as the test parameter. Furthermore, an elasto-plastic analysis using a two-dimensional beam element, which considered the effect on strain rate, was conducted for both transient- and steady-state conditions.

The analytical results agreed relatively well with the test results, which used small steel beam specimens with a rectangular cross-section under various heating rates (transient-state condition) and deformation rates (steady-state condition). It was found that the bending strength and collapse temperature obtained from the parametric analyses agreed relatively well with those evaluated using the effective strength obtained from the coupon tests with strain equal to 0.01 or 0.02 under the fast strain rates.

The effect of stress degradation, including the stress-strain relationships at elevated temperature, was mitigated by considering the effect of strain rate on the analytical model. This is an important point to consider when considering the effect of strain rate on steel structural analysis at elevated temperatures to maintain analytical stability unaccompanied by the stress degradation.

The purpose of this paper is to study numerically the effects of heat transfer on the strength of shock waves emitted upon spherical bubble collapse.

The motion of bubble under ultrasound is predicted by solutions of the Navier‐Stokes equations for the gas inside a spherical bubble. The Gilmore model and the method of characteristics are used to model the shock wave emitted at the end of the bubble collapse.

The theory permits one to predict correctly the bubble radius‐time curve and the characteristics of shock wave in sulphuric acid solution. These simulations indicated that the heat transfer inside the bubble and the liquid layer plays a major role in the bubble behaviour and the strength of the shock waves. Also, the developed numerical scheme is checked for different gas bubble like air, Argon and Xenon. It is observed that the gas thermal conductivity plays an important role in the shock wave strength. A good agreement is observed by comparison of the results with the experimental data.

The effect of heat transfer on the emitted shock wave strength has not been studied previously. In this paper, a numerical scheme is developed to consider heat transfer on the shock. Also, this simulation is checked for different gas conductivities.

The main purpose of this study was to propose theoretical calculation models to evaluate the theoretical bending strengths of welded wide-flange section steel beams with local buckling at elevated temperatures.

Steady-state tests using various test parameters, including width-thickness ratios (Class 2–4) and specimen temperatures (ambient temperature, 400, 500, 600, 700, and 800°C), were performed on 18 steel beam specimens using roller supports to examine the maximum bending moment and bending strength after local buckling. A detailed calculation model (DCM) based on the equilibrium of the axial force in the cross-section and a simple calculation model (SCM) for a practical fire-resistant design were proposed. The validity of the calculation models was verified using the bending test results.

The strain concentration at the local buckling cross-section was mitigated in the elevated-temperature region, resulting in a small bending moment degradation after local buckling. The theoretical bending strengths after local buckling, evaluated from the calculation models, were in good agreement with the test results at elevated temperatures.

The effect of local buckling on the bending behaviour after the maximum bending strength in high-temperature regions was quantified. Two types of calculation models were proposed to evaluate the theoretical bending strength after local buckling.

In this study, the effects of strain rate on the bending strength of full-scale wide-flange steel beams have been examined at elevated temperatures. Both full-scale loaded heating tests under steady-state conditions and in-plane numerical analysis using a beam element have been employed.

The load–deformation relationships in 385 N/mm²-class steel beam specimens was examined using steady-state tests at two loading rate values (0.05 and 1.00 kN/s) and at two constant member temperatures (600 and 700 °C). Furthermore, the stress–strain relationships considering the strain rate effects were proposed based on tensile coupon test results under various strain rate values. The in-plane elastoplastic numerical analysis was conducted considering the strain rate effect.

The experimental test results of the full-scale steel beam specimens confirmed that the bending strength increased with increase in strain rate. In addition, the analytical results agreed relatively well with the test results, and both strain and strain rate behaviours of a heated steel member, which were difficult to evaluate from the test results, could be quantified numerically.

The novelty of this study is the quantification of the strain rate effect on the bending strength of steel beams at elevated temperatures. The results clarify that the load–deformation relationship of steel beams could be evaluated by using in-plane analysis using the tensile coupon test results. The numerical simulation method can increase the accuracy of evaluation of the actual behaviour of steel members in case of fire.

This paper describes the results of non-linear elasto-plastic implicit dynamic finite element analyses that are used to predict the collapse behaviour of cold-formed steel portal frames at elevated temperatures. The collapse behaviour of a simple rigid-jointed beam idealisation and a more accurate semi-rigid jointed shell element idealisation are compared for two different fire scenarios. For the case of the shell element idealisation, the semi-rigidity of the cold-formed steel joints is explicitly taken into account through modelling of the bolt-hole elongation stiffness. In addition, the shell element idealisation is able to capture buckling of the cold-formed steel sections in the vicinity of the joints. The shell element idealisation is validated at ambient temperature against the results of full-scale tests reported in the literature. The behaviour at elevated temperatures is then considered for both the semi-rigid jointed shell and rigid-jointed beam idealisations. The inclusion of accurate joint rigidity and geometric non-linearity (second order analysis) are shown to affect the collapse behaviour at elevated temperatures. For each fire scenario considered, the importance of base fixity in preventing an undesirable outwards collapse mechanism is demonstrated. The results demonstrate that joint rigidity and varying fire scenarios should be considered in order to allow for conservative design.