• Steel and Composite Structures
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• v.6 no.5
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• pp.367-386
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• 2006

This paper describes the results of a numerical investigation of the large deflection behaviour of steel beams under fire conditions, taking into consideration the effect of catenary action provided by the surrounding structures. The main focus is on the development, validation and application of a simplified calculation method that may be adopted in design calculations. Because no experimental result is available for validation of the simplified calculation method, the finite element program ABAQUS has been used to simulate the large deflection behaviour of a number of steel beams so as to provide alternative results for validation of the proposed method. Utilising catenary action has the potential of eliminating fire protection to all steel beams without causing structural failure in fire. However, practical application of catenary action will be restricted by concerns over large beam deflection causing integrity failure of the fire resistant compartment and additional cost of strengthening the connections and the surrounding structures to resist the catenary forces in the steel beams. This paper will provide a discussion on practical implications of utilising catenary action in steel beams as a means of eliminating fire protection. A number of examples will then be provided to illustrate the type of steel framed structure that could benefit the most from exploiting catenary action in fire resistant design.

• Steel and Composite Structures
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• v.42 no.2
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• pp.161-172
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• 2022

In this paper, four specimens of CFST column joints with endplates and long bolts are tested in the scenario of progressive collapse. Flush endplate and extended endplate are both adopted in this study. The experimental results show that increasing the thickness of the endplate could improve the behavior of the joint, but delay the mobilization of catenary action. The thickness of the endplate should not be relatively thick in comparison to the diameter of the bolts, otherwise catenary action would not be mobilized or work effectively. Effective bending deformation of the endplate could help the formation and development of catenary action in the joints. The performance of flexural action in the joint would affect the formation of catenary action in the joint. Extra middle-row bolts set at the endplates and structural components set below the bottom beam flange should be used to enhance the robustness of joints. A special weld access hole between beam and endplate should be adopted to mitigate the chain damage potential of welds. It is suggested that the structural components of joints should be independent of each other to enhance the robustness of joints. Based on the component method, a formula calculating the stiffness coefficient of preloaded long bolts was proposed whose results matched well with the experimental results.

• Structural Engineering and Mechanics
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• v.35 no.6
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• pp.699-715
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• 2010

This paper investigates the structural responses of axially restrained steel beams under fire conditions by a nonlinear finite element method. The axial restraint is represented by a linear elastic spring. Different parameters which include beam slenderness ratio, external load level and axial restraint ratio are investigated. The process of forming a mid-span plastic hinge at the mid-span under a rising temperature is studied. In line with forming a fully plastic hinge at mid-span, the response of a restrained beam under rising temperature can be divided into three stages, viz. no plastic hinge, hinge forming and rotating, and catenary action stage. During catenary action stage, the axial restraint pulls the heated beam and prevents it from failing. This study introduces definitions of beam limiting temperature $T_{lim}$, catenary temperature $T_{ctn}$ and warning time $t_{wn}$. Influences of slenderness ratio, load level and axial restraint ratio on $T_{lim}$, $T_{ctn}$ and $t_{wn}$ are examined.

• Steel and Composite Structures
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• v.30 no.3
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• pp.253-269
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• 2019

This paper investigates the effects of the tensile catenary action on dynamic increase factor (DIF) in the nonlinear static analysis for progressive collapse of steel-frame buildings. Numerical analyses were performed to verify the accuracy of the empirical and analytical expressions proposed in the literature in cases where the catenary action is activated. For this purpose, nonlinear static and dynamic analyses of a series of steel moment frame buildings with a different number of spans and stories were carried out following the alternate path method. Different column removal scenarios were considered as separate load cases. The dynamic increase factor that approximately compensates for the dynamic effects in the nonlinear static analysis was selected so to match results from the nonlinear dynamic analysis. The study results showed that the many expressions in literature may not work in cases where the catenary stage is fully developed.

• International Journal of Concrete Structures and Materials
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• v.10 no.2
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• pp.237-247
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• 2016

Progressive collapse resistance of RC buildings can be analyzed by considering column loss scenarios. Using finite element analysis and a static test, the progressive collapse process of a RC frame under monotonic vertical displacement of a side column was investigated, simulating a column removal scenario. A single-story 1/3 scale RC frame that comprises two spans and two bays was tested and computed, and downward displacement of a side column was placed until failure. Our study offers insight into the failure modes and progressive collapse behavior of a RC frame. It has been noted that the damage of structural members (beams and slabs) occurs only in the bay where the removal side column is located. Greater catenary action and tensile membrane action are mobilized in the frame beams and slabs, respectively, at large deformations, but they mainly happen in the direction where the frame beams and slabs are laterally restrained. Based on the experimental and computational results, the mechanism of progressive collapse resistance of RC frames at different stages was discussed further. With large deformations, a simplified calculation method for catenary action and tensile membrane action is proposed.

• Structural Engineering and Mechanics
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• v.78 no.4
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• pp.403-411
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• 2021

Ties are mandated by many design guidelines and codes to prevent the progressive collapse of buildings initiated by local failures. This study develops a model to estimate catenary/cable action capacity and the required ties in continuous reinforced concrete beams to bridge above the potential failed interior columns. The developed model is derived based on virtual work method and verified using test results presented in the literature. Also, parametric investigations are conducted to estimate the required ties in continuous reinforced concrete beams supporting one-way slab systems. A comparison is conducted between the estimated tie reinforcement using the developed model and that provided by satisfying the integrity provisions of the ACI 318-14 (2014) code. It is shown that the required tie reinforcements to prevent progressive collapse using the developed model are obviously larger than that provided by the integrity requirements of the ACI 318-14 (2014) code. It has been demonstrated that the increases in the demanded tie reinforcements over that provided by satisfying ACI 318-14 (2014) integrity provisions are varied between 1.01 and 1.46.

• Structural Engineering and Mechanics
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• v.53 no.1
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• pp.173-188
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• 2015

Several structural calamities in the second half of the 20th century have shown that adequate collapse-resistance cannot be achieved by designing the individual elements of a structure without taking their interconnectivity into consideration. It has long been acknowledged that membrane behaviour of reinforced concrete structures can significantly increase the robustness of a structure and delay a complete collapse. An experimental large-scale test was conducted on a horizontally restrained, continuous reinforced concrete slab exposed to an artificial failure of the central support and subsequent loading until collapse of the specimen. Within this investigation the development of catenary action associated with the formation of large displacements was observed to increase the ultimate load capacity of the specimen significantly. The development of displacements, strains and horizontal forces within this investigation confirmed a load transfer process from an elastic bending mechanism to a tension controlled catenary mechanism. In this contribution a special focus is directed towards strain and crack development at critical sections. The results of this contribution are of particular importance when validating numerical models related to the development of catenary action in concrete slabs.

• 한국신재생에너지학회:학술대회논문집
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• 2005.06a
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• pp.529-533
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• 2005

A railway catenary system which supplies a train with electric power is an important system in determining the maximum speed of an electric train. However, a pantograph could be separated from a contact wire because of reciprocal action between a pantograph with constant upward force and a catenary system. The contact loss of a pantograph-catenary system is mainly affected by the dynamic characteristics of damping and wave propagation velocity of contact wire. For increasing speed of an electrical train, it is necessary to establish the techniques to identify the modal parameter of a catenary system through experiment. However, it is difficult to decouple each mode and to extract respect ive damping rat io since a catenary system has an extremely high modal density. For this reason, mode decoupling process to identify modal parameters is a principal technique in analyzing a catenary system. In this paper, the damping extract ion method for a catenary system using the continuous wavelet transform is discussed.

• Steel and Composite Structures
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• v.1 no.4
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• pp.427-440
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• 2001

The growing use of unprotected or partially protected steelwork in buildings has caused a lively debate regarding the safety of this form of construction. A good deal of recent research has indicated that steel members have a substantial inherent ability to resist fire so that additional fire protection can be either reduced or eliminated completely. A performance based philosophy also extends the study into the effect of structural continuity and the performance of the whole structural totality. As part of the structural system, thermal expansion during the heating phase or contraction during the cooling phase in most beams is likely to be restrained by adjacent parts of the whole system or sub-frame assembly due to compartmentation. This has not been properly addressed before. This paper describes an experimental programme in which unprotected steel beams were tested under load while it is restrained between two columns and additional horizontal restraints with particular concern on the effect of catenary action in the beams when subjected to large deflection at very high temperature. This paper also presents a three-dimensional mathematical modelling, based on the finite element method, of the series of fire tests on the part-frame. The complete analysis starts with an evaluation of temperature distribution in the structure at various time levels. It is followed by a detail 3-D finite element analysis on its structural response as a result of the changing temperature distribution. The principal part of the analysis makes use of an existing finite element package FEAST. The effect of columns being fire-protected and the beam being axially restrained has been modelled adequately in terms of their thermal and structural responses. The consequence of the beam being restrained is that the axial force in the restrained beam starts as a compression, which increases gradually up to a point when the material has deteriorated to such a level that the beam deflects excessively. The axial compression force drops rapidly and changes into a tension force leading to a catenary action, which slows down the beam deflection from running away. Design engineers will be benefited with the consideration of the catenary action.

• Structural Engineering and Mechanics
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• v.58 no.2
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• pp.327-345
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• 2016

Many experimental and analytical studies have been conducted with beam-column subassemblages composed of a two-span beam to investigate the progressive collapse resistance of RC frames. Most study results reveal a strength-decreased transition phase in the nonlinear static load-deflection curve, which may induce dynamic snap-through response and increase the chord rotation demand for effective catenary action (ECA). In this study, the nonlinear static response is idealized as a piecewise linear curve and analytical pseudo-static response is derived for each linearized region to investigate the rotation demands for the ECA of the two-span RC beams. With analytical parameters determined from several published test results, numerical analysis results indicate that the rotation demand of 0.20 rad recommended in the design guidelines does not always guarantee the ECA. A higher rotation demand may be induced for the two-span beams designed with smaller span-to-depth ratios and it is better to use their peak arch resistance (PAR) as the collapse strength. A tensile reinforcement ratio not greater than 1.0% and a span-to-depth ratio not less than 7.0 are suggested for the two-span RC beams bridging the removed column if the ECA is expected for the collapse resistance. Also, complementary pseudo-static analysis is advised to verify the ECA under realistic dynamic column loss even though the static PAR is recovered in the nonlinear static response. A practical empirical formula is provided to estimate an approximate rotation demand for the ECA.