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The purpose of this paper is to recover the deficiency of existing tie force (TF) methods by considering the decrease in section strength due to cracking and by selecting limit state of collapse according to section properties.

A substructure is selected by isolating the connected beams from the entire structure. For interior joints, the TFs in the orthogonal beams are obtained by catenary action. For corner joints, the TFs are assessed by beam action. For edge joints, however, the resistance is gained by greater of the resistance under catenary action for periphery beams and beam action for all the connecting beams in both directions. For catenary action, the TF capacities must satisfy Equation (20). On the other hand, for beam action, the TF must satisfy Equation (16), while R is calculated from Equation (17). In the case where the length of the connecting beams is similar, Equation (19) can be used.

Closed form solutions are available for TFs on both beam and catenary stages.

The proposed formulation makes designing more practical and convenient. However, the proposed formulation had good agreement with experimental results.

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.

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.

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.

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).

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.

The robustness of building structures in a fire has recently drawn wide attention. This study presents the progressive collapse analysis of steel frame building structures under localised fire. The main objective of this study is to propose methods to enhance the structural collapse resistance of such structures in fire.

A modelling method was developed and validated against both experimental and analytical studies. Then, a series of robustness analyses were performed to investigate the interaction among the members and the pattern of load distribution within the structures. These analyses show that lateral resistance and load redistribution have a vital role in the robustness of the building. Thus, two approaches have been adopted to enhance the robustness of the focused steel frame during a fire.

It is found that increased size of floor beams and vertical bracing systems are effective measures in preventing whole structure collapse. The larger beam section is able to prevent catenary action so that the load in the failed columns can safely transfer to the adjacent columns without buckling. On the other hand, the bracing system improves the lateral resistance that can accommodate the lateral force when catenary action occurs in the beam.

Previous studies have focused on the collapse mechanism of steel frame structures. However, the parameters affecting the structural robustness in a fire have not yet been explored. To address this gap, this study adopted numerical modelling to undertake parametric studies to identify effective methods to improve the robustness of such structures under fire conditions.

This study aims to investigate the thermal creep behavior of steel frame assemblies with shear tab connections subjected to transient-state fire temperatures. Different key parameters are investigated to study their effect on the global response of the steel frames in fire.

Finite element (FE) models of connection assemblies are first analyzed using Abaqus under transient-state temperature conditions and validated against experimental work available in the literature. Upon acquiring the validated conditions, parametric studies are carried out to study the effect of key geometric and heating parameters on the overall response of the frame assembly to fire temperatures. Thermal creep material is also incorporated in the analyses through a user-defined subroutine, and a comparison between including and excluding creep material is illustrated to show the effect of thermal creep on the structural behavior.

The results reported herein indicate that having a rigid column increases the thermal-induced axial forces, thus increasing the development of thermal creep strains. Slow heating rates can cause axial stress relaxation in the restrained beam and increase the mid-span deflection and consequently the development of beam catenary action. The results also show that reaching higher initial cooling temperatures and having longer cooling phase durations result in more tensile forces at the end of the cooling phase.

Previous studies were limited to isolated steel connections under steady-state conditions. This study investigates the creep behavior of shear tab connection assemblies under transient-state conditions of fire when creep effects are explicitly considered. This can provide a rational and realistic assessment of the steel behavior in fire events.

In this paper a robust 2-noded connection element has been presented for modelling the bolted end-plate connections between steel beam and column at elevated temperatures. The connection element allows the element nodes to be placed at the reference plane with offset and the non-uniform temperature distributions within the connection. In this model the connection failure due to bending, axial tension, compression and vertical shear are considered. The influence of the axial tensile force of the connected beam on the connection is also taken into account. This model has the advantages of both the previous simple and component-based models. A series of numerical studies was carried on a 2D steel frame under ISO834 and Natural fires. The results indicated that the deflections of beams are significantly affected by using different types of the connections. However, the axial forces of the connected beam are less significantly affected by different types of the connections. Another finding is that the axial tensile force in the beams generated due to catenary action is relative small compared to the forces caused by the thermal shrinkage of the beam during cooling phase of the real fire.

The purpose of this paper is to present a finite element formulation of enhanced two‐node parabolic cable element for the static analysis of cable structures.

Unlike the assumed polynomial displacement interpolation functions, the present approach uses the analytical cable dynamic stiffness matrix to obtain the explicit expression of the static stiffness matrix of an inclined sagging cable by setting the frequency at zero. The Newton‐Raphson‐based iterative method is used to obtain the solution.

It is demonstrated that the present results agree well with those obtained from the nonlinear analytical theory of a parabolic cable and previous reported methods in the literature.

This paper proposes a two‐node parabolic cable element. For comparable accuracy with the truss element method, fewer numbers of such cable elements are needed.

First, a synopsis of the major changes of natural science, mathematics and philosophy within the 17th century shall highlight the birth of the new age of science and technology. Based on Fermat's principle of the shortest light‐way and Galilei's first attempt of an approximative solution of the so‐called Brachistochrone problem using a quarter of the circle, Johann Bernoulli published a competition for this problem in 1696, and six solutions were submitted by the most famous scientists of the time and published in 1697, even though the variational calculus was only published in 1744 by Euler for the first time. Especially the analytical solution of Jakob Bernoulli contains already the main idea of Euler's variational calculus, i.e. to vary only one function value at a time using a finite difference method and proceeding to the infinitesimal limit. Also Leibniz' geometric solution is very remarkable, realizing a direct discrete variational method geometrically which was invented numerically much later in the 19th century by Ritz and Galerkin and generalized to the finite element method by introducing test and trial functions in finite subspaces. A new finite element solution of the non‐linear Brachistochrone problem concludes the paper. It is important to recognize that besides the roots of variational calculus also the first formulations of conservation laws in mechanics and their applications originated in the 17th century.

The paper aims to report a fire test conducted on a three-dimensional frame in order to investigate the behaviour of bare steel flush end-plate connections with relatively low thickness at elevated temperatures.

A half-scale model was fabricated and exposed to modified (scaled) ISO 834 heating curve using a semi-open furnace. The maximum temperature inside the furnace reached 1,026 °C.

The rotations of connections are reported and compared with those of a previous study on an exactly the same model with thick end-plates. Various modes of failure such as local buckling of the beams flanges and lateral-torsional buckling of beams were observed during the test. Finally, the structure collapsed after 29 min of heating due to the fracture of weld between one of the beams and one of its attached end-plates whilst the other beam had undergone a maximum deflection of 35 cm (≈ 1/6 span length). Other observed failure modes included bolt fracture, bolt thread stripping and large inelastic deformation of the end-plates.

Although the adoption of thin end-plates increased the rotational capacity of the connections, it did not improve the robustness of the structure under fire conditions.

Progressive collapse refers to a phenomenon, in which local damage in a primary structural component leads to total or partial structural system failure, without any proportionality between the initial and final damage. Robustness is a measure that demonstrates the strength of a structure to resist progressive collapse. Static pushdown and nonlinear dynamic analysis were two main procedures to calculate the capacity of structures to resist progressive collapse. According to previous works, static analysis would lead to inaccurate results. Meanwhile, capacity analysis by dynamic analysis needs several reruns and encountering numerical instability is inevitable. The purpose of this paper is to present the formulation of a solution procedure to determine robustness of steel moment resisting frames, using plastic limit analysis (PLA).

This formulation utilizes simplex optimization to solve the problem. Static pushdown and incremental dynamic methods are used for verification.

The results obtained from PLA have good agreement with incremental analysis results. While incremental dynamic analysis is a very demanding method, PLA can be utilized as an alternative method.

The formulation of progressive collapse resistance of steel moment frames by means of PLA is not proposed in previous research works.