• Steel and Composite Structures
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• v.41 no.5
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• pp.625-636
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• 2021

This paper examines the fire performance of uninsulated and uncoated restrained steel-concrete composite beams supplemented with externally prestressed strands through advanced numerical simulation. In this work, a sequentially coupled thermo-mechanical analysis is carried out using ABAQUS. This analysis utilizes a highly nonlinear three-dimensional finite element (FE) model that is specifically developed and validated using full-sized specimens tested in a companion fire testing program. The developed FE model accounts for nonlinearities arising from geometric features and material properties, as well as complexities resulting from prestressing systems, fire conditions, and mechanical loadings. Four factors are of interest to this work including effect of restraints (axial vs. rotational), degree of stiffness of restraints, the configuration of external prestressed tendons, and magnitude of applied loading. The outcome of this analysis demonstrates how the prestressing force in the external tendons is primarily governed by the magnitude of applied loading and experienced temperature level. Interestingly, these results also show that the stiffness of axial restraints has a minor influence on the failure of restrained and prestressed steel-concrete composite beams. When the axial restraint ratio does not exceed 0.5, the critical deflection of the composite beam is lower than that of the composite beam with a restraint ratio of 1.0.

• Steel and Composite Structures
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• v.8 no.1
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• pp.19-34
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• 2008

This paper presents the results of a validation and parametric study for the theory presented in the companion paper. The parameters investigated include the stiffness of axial and rotational restraints, load ratio, depth-span ratio of the beam, the yield strength of steel, load type and the temperature distribution in the crosssection of the beam.

• Steel and Composite Structures
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• v.35 no.1
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• pp.29-41
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• 2020

Cross-beams of modern through truss bridges are connected to truss chord at its nodes and between them. It results in variable rotational end restraint for cross-beams, thus variable bending moment distribution. This feature is captured in three-dimensional modelling of through truss bridge structure. However, for preliminary design or rapid assessment of service load effects such technique of analysis may not be available. So an analytical method of assessment of rotational end restraint for cross-beam of through truss bridges was worked out. Two cases - nodal cross-beam and inter-nodal cross-beam - were analyzed. Flexural and torsional stiffness of truss members, flexural stiffness of deck members and axial stiffness of wind bracing members in the vicinity of the analyzed cross-beam were taken into account. The provision for reduced stiffness of the X-type wind bracing was made. Finally, general formula for assessment of rotational end restraint was given. Rotational end restraints for cross-beams of three railway through truss bridges were assessed basing on the analytical method and the finite element method (three-dimensional beam-element modelling). Results of both methods show good agreement. The analytical method is able to reflect effects of some structural irregularities. On the basis of the obtained results the general values of rotational end restraint for nodal and inter-nodal cross-beams of railway through truss bridges were suggested.

• Steel and Composite Structures
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• v.33 no.3
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• pp.403-432
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• 2019

Axially functionally graded (AFG) beams are a new class of composite structures that have continuous variations in material and/or geometrical parameters along the axial direction. In this study, the exact analytical solutions for the free vibration of AFG and uniform beams with general elastic supports are obtained by using Euler-Bernoulli beam theory. The elastic supports are modeled with linear rotational and lateral translational springs. Moreover, the material and/or geometrical properties of the AFG beams are assumed to vary continuously and together along the length of the beam according to the power-law forms. Accordingly, the accuracy, efficiency and capability of the proposed formulations are demonstrated by comparing the responses of the numerical examples with the available solutions. In the following, the effects of the elastic end restraints and AFG parameters, namely, gradient index and gradient coefficient, on the values of the first three natural frequencies of the AFG and uniform beams are investigated comprehensively. The analytical solutions are presented in tabular and graphical forms and can be used as the benchmark solutions. Furthermore, the results presented herein can be utilized for design of inhomogeneous beams with various supporting conditions.

• Steel and Composite Structures
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• v.8 no.1
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• pp.1-18
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• 2008

Observations from experiments and real fire indicate that restrained steel beams have better fire-resistant capability than isolated beams. Due to the effects of restraints, a steel beam in fire condition can undergo very large deflections and the run away damage may be avoided. In addition, axial forces will be induced with temperature increasing and play an important role on the behaviour of the restrained beam. The factors influencing the behavior of a restrained beam subjected to fire include the stiffness of axial and rotational restraints, the load type on the beam and the distribution of temperature in the cross-section of the beam, etc. In this paper, a simplified model is proposed to analyze the performance of restrained steel beams in fire condition. Based on an assumption of the deflection curve of the beam, the axial force, together with the strain and stress distributions in the beam, can be determined. By integrating the stress, the combined moment and force in the cross-section of the beam can be obtained. Then, through substituting the moment and axial force into the equilibrium equation, the behavior of the restrained beam in fire condition can be worked out. Furthermore, for the safety evaluation and repair after a fire, the behaviour of restrained beams during cooling should be understood. For a restrained beam experiencing very high temperatures, the strength of the steel will recover when temperature decreases, but the contraction force, which is produced by thermal contraction, will aggravate the tensile stresses in the beam. In this paper, the behaviour of the restrained beam in cooling phase is analyzed, and the effect of the contraction force is discussed.

• Structural Engineering and Mechanics
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• v.5 no.4
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• pp.415-431
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• 1997

Stability equations that evaluate the elastic critical axial load of stepped columns under extreme and intermediate concentrated axial loads in any type of construction with sidesway totally inhibited, partially inhibited and uninhibited are derived in a classical manner. These equations can be utilized in the stability analysis of framed structures (totally braced, partially braced, and unbraced) with stepped columns with rigid, semirigid, and simple connetions. The proposed column classification and the corresponding stability equations overcome the limitations of current methods which are based on a classification of braced and unbraced columns. The proposed stability equations include the effects of: 1) semirigid connections; 2) step variation in the column cross section at the point of application of the intermediate axial load; and 3) lateral and rotational restraints at the intermediate connection and at the column ends. The proposed method consists in determining the eigenvalue of a $2{\times}2$ matrix for a braced column at the two ends and of a $3{\times}3$ matrix for a partially braced or unbraced column. The stability analysis can be carried out directly with the help of a pocket calculator. The proposed method is general and can be extended to multi-stepped columns. Various examples are include to demonstrate the effectiveness of the proposed method and to verify that the calculated results are exact. Definite minimum bracing criteria for single stepped columns is also presented.

• Structural Engineering and Mechanics
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• v.85 no.6
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• pp.825-835
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• 2023

The effective buckling length factor is an important parameter in the elastic buckling analysis of steel structures. The present article aims at developing a new method that allows the determination of the buckling factor values for frames. The novelty of the method is that it considers the interaction between the bracing and the elastic supports for asymmetrical frames in particular. The approach consists in isolating a critical column within the frame and evaluating the rotational and translational stiffness of its restraints to obtain the critical buckling load. This can be achieved by introducing, through a dimensionless parameter 𝜙_i, the effects of coupling between the axial loading and bending stiffness of the columns, on the classical stability functions. Subsequently, comparative, and parametric studies conducted on several frames are presented for assessing the influence of geometry, loading, bracing, and support conditions of the frame columns on the value of the effective buckling length factor K. The results show that the formulas recommended by different approaches can give rather inaccurate values of K, especially in the case of asymmetric frames. The expressions used refer solely to local stiffness distributions, and not to the overall behavior of the structure.

• Steel and Composite Structures
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• v.20 no.1
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• pp.57-70
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• 2016

The predominant type of buckling that I-steel concrete composite beams experience in the negative moment area is distortional buckling. The key factors that affect distortional buckling are the torsional and lateral restraints by the bottom flange. This study thoroughly investigates the equivalent lateral and torsional restraint stiffnesses of the bottom flange of an I-steel concrete composite beam under negative moments. The results show a coupling effect between the applied forces and the lateral and torsional restraint stiffnesses of the bottom flange. A formula is proposed to calculate the critical buckling stress of the I-steel concrete composite beams under negative moments by considering the lateral and torsional restraint stiffnesses of the bottom flange. The proposed method is shown to better predict the critical bending moment of the I-steel composite beams. This article introduces an improved method to calculate the elastic foundation beams, which takes into account the lateral and torsional restraint stiffnesses of the bottom flange and considers the coupling effect between them. The results show a close match in results from the calculation method proposed in this paper and the ANSYS finite element method, which validates the proposed calculation method. The proposed calculation method provides a theoretical basis for further research on distortional buckling and the ultimate resistance of I-steel concrete composite beams under a variable axial force.