• Earthquakes and Structures
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• v.5 no.2
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• pp.239-259
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• 2013

Typically, beams that form part of structural systems are subjected to vertical distributed loading along their length. Distributed loading affects moment and shear distribution, and consequently spread of inelasticity, along the beam length. However, the finite element models developed so far for seismic analysis of frame structures either ignore the effect of vertical distributed loading on spread of inelasticity or consider it in an approximate manner. In this paper, a beam-type finite element is developed, which is capable of considering accurately the effect of uniform distributed loading on spreading of inelastic deformations along the beam length. The proposed model consists of two gradual spread inelasticity sub-elements accounting explicitly for inelastic flexural and shear response. Following this approach, the effect of distributed loading on spreading of inelastic flexural and shear deformations is properly taken into account. The finite element is implemented in the seismic analysis of plane frame structures with beam members controlled either by flexure or shear. It is shown that to obtain accurate results the influence of distributed beam loading on spreading of inelastic deformations should be taken into account in the inelastic seismic analysis of frame structures.

• Steel and Composite Structures
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• v.18 no.1
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• pp.213-233
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• 2015

A nonlinear finite element analysis (FEA) model is presented for simulating the behaviour of recycled aggregate concrete-filled steel tube (RACFST) beam-columns subjected to constant axial compressive load and cyclically increasing flexural loading. The FEA model was developed based on ABAQUS software package and a displacement-based approach was used. The proposed engineering stress versus engineering strain relationship of core concrete with the effect of recycled coarse aggregate (RCA) replacement ratio was adopted in the FEA model. The predicted results of the FEA model were compared with the experimental results of several RACFST as well as the corresponding concrete-filled steel tube (CFST) beam-columns under cyclic loading reported in the literature. The comparison results indicated that the proposed FEA model was capable of predicting the load versus deformation relationship, lateral bearing capacity and failure pattern of RACFST beam-columns with an acceptable accuracy. A parametric study was further carried out to investigate the effect of typical parameters on the mechanism of RACFST beam-columns subjected to cyclic loading.

• Structural Engineering and Mechanics
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• v.41 no.6
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• pp.775-789
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• 2012

This paper focuses on post-buckling analysis of functionally graded Timoshenko beam subjected to thermal loading by using the total Lagrangian Timoshenko beam element approximation. Material properties of the beam change in the thickness direction according to a power-law function. The beam is clamped at both ends. The considered highly non-linear problem is solved by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. As far as the authors know, there is no study on the post-buckling analysis of functionally graded Timoshenko beams under thermal loading considering full geometric non-linearity investigated by using finite element method. The convergence studies are made and the obtained results are compared with the published results. In the study, with the effects of material gradient property and thermal load, the relationships between deflections, end constraint forces, thermal buckling configuration and stress distributions through the thickness of the beams are illustrated in detail in post-buckling case.

• Structural Engineering and Mechanics
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• v.87 no.2
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• pp.165-172
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• 2023

This paper presents a novel method for modeling elastic wave propagation in long beams. The proposed method derives a solution for the transient transverse displacement of the beam's neutral axis without assuming the separation of variables (SV). By mapping the governing equation from the space domain to the frequency domain using Fourier transformation (FT), the transverse displacement function is determined as a convolution integral of external loading functions and a combination of trigonometric and Fresnel functions. This method determines the beam's response to general loading conditions as a linear combination of the analytical response of a beam subjected to an abrupt localized loading. The proposed solution method is verified through finite element analysis (FEA) and wave propagation patterns are derived for tone burst loading with specific frequency contents. The results demonstrate that the proposed solution method accurately models wave dispersion, reduces computational cost, and yields accurate results even for high-frequency loading.

• Journal of the Korean Society for Precision Engineering
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• v.20 no.3
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• pp.140-148
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• 2003

An analysis fur the warping process has been performed to design the warper beam. Nonlinear material response is included in the physical model of polyester yarn. Large deformation finite element simulation considering contact and frictional analysis are used to obtain the pressure on the barrel of the warper beam. Loading condition on the flange is assumed by using the pressure on the barrel, winding number of yarn, Poisson's ratio of fiber, and fiber volume fraction. By using the above loading conditions NASTRAN finite element simulation is performed to calculate stress distribution and deformation of the warper beam. By comparing the deformed shape of the flange with experimental result, loading condition on the flange has been obtained. The obtained loading conditions on the barrel and flange can be utilized to design the warper beam.

• International Journal of High-Rise Buildings
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• v.3 no.3
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• pp.231-241
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• 2014

Ductile fracture is one of the most common failure modes of steel beam-to-column connections in moment resisting frames. Most proposed evaluation methods of the plastic deformation capacity of a beam until ductile fracture are based on steel beam tests, where the material's yield strength/ratio, the beam's moment gradient, and loading history are the most important parameters. It is impossible and unpractical to cover all these parameters in real tests. Therefore, a new attempt to evaluate a beam's plastic deformation capacity through analysis is introduced in this paper. Another important issue is about the loading histories. Recent years, the effect on the structural component under long-duration ground motion has drawn great attentions. Steel beams tends to experience a large number of loading cycles with small amplitudes during long-duration earthquakes. However, current research often focuses on the beam's behavior under standard incremental loading protocols recommended by respective countries. In this paper, the plastic deformation capacity of steel beams subjected to long duration ground motions was evaluated through analytical methodology.

• Computers and Concrete
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• v.30 no.4
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• pp.277-287
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• 2022

Due to the scarcity of extortionate experimental data, fatigue failure of the reinforced concrete (RC) element might be achieved economically adopting nonlinear finite element (FE) analysis as an alternative approach. However, conventional implicit dynamic analysis is expensive, quasi-static method overlooks interaction effects and inertia, direct cyclic analysis computes stabilized responses. Apart from this, explicit dynamic analysis may provide a numerical operating system for factual long-term responses. The study explores the fatigue behavior based on a simplified explicit dynamic solution employing nonlinear time domain analysis. Among fourteen RC beams, one beam is selected to validate under static loading, one under fatigue with the experimental study and other twelve to check the detail fatigue behavior. The SWOT (Strength, Weakness, Opportunities, Threats) analysis has been carried out to pinpoint the detail scenario in the adoption of numerical approach as an alternative to the experimental study. Excellent agreement of FE and experimental results is seen. The 3D nonlinear RC beam model at service fatigue limits is truthful to be used as an expedient contrivance to envisage the precise fatigue behavior. The simplified analysis approach for RC beam under fatigue offers savings in computation to predict responses providing acceptable accuracy rather than the complicated laboratory investigation. At higher frequency, the flexural failure occurs a bit earlier gradually compared to the repeated loading case of lower frequency. The deflection increases by 6%-10% at the end of first cycle for beams with increasing frequency of cyclic loading. However, at the end of fatigue loading, greater deflection occur earlier for higher load range because of more rapid stiffness degradation. For higher frequency, a slight boost in concrete compressive strains at an initial stage of loading has been seen indicating somewhat stepper increment. Stiffness degradation in larger loading cycle at same duration escalates the upsurge of the rate of strain in case of higher frequency.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1990.04a
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• pp.12-17
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• 1990

Stepped bean with immovable ends for large amplitude of vibration including effects of longitudinal displacement, shear deformation and rotary inertia is investigated for free and forced vibration using finite element method. Modified harmonic force matrix is introduced for analysis of vibration with finite amplitude of the stepped beam under uniform hamonic loading and beam with nonuniform harmonic loading. Numerical examples of stepped beam with various support conditions are analysed for deflections and natural frequencies. Results show that the proposed method is valid and efficient.

• Steel and Composite Structures
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• v.1 no.1
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• pp.145-158
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• 2001

An experimental study was conducted to evaluate the effects of loading sequence and lateral bracing on the behavior of reduced beam section (RBS) steel moment frame connections. Four full-scale moment connections were cyclically tested-two with a standard loading history and the other two with a near-fault loading history. All specimens reached at least 0.03 radian of plastic rotation without brittle fracture of the beam flange groove welds. Two specimens tested with the nearfault loading protocol reached at least 0.05 radian of plastic rotation, and both experienced smaller buckling amplitudes at comparable drift levels. Energy dissipation capacities were insensitive to the types of loading protocol used. Adding a lateral bracing near the RBS region produced a higher plastic rotation; the strength degradation and buckling amplitude were reduced. A non-linear finite element analysis of a one-and-a-half-bay beam-column subassembly was also conducted to study the system restraint effect. The study showed that the axial restraint of the beam could significantly reduce the strength degradation and buckling amplitude at higher deformation levels.

• Structural Engineering and Mechanics
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• v.2 no.1
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• pp.95-112
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• 1994

This paper describes the formulation and application of a dynamic model for a conventional rail track subjected to arbitary loading functions that simulate wheel/rail impact forces. The rail track is idealized as a periodic elastically coupled beam system resting on a Winkler foundation. Modal parameters of the track structure are first obtained from the natural vibration characteristics of the beam system, which is discretized into a periodic assembly of a specially-constructed track element and a single beam element characterized by their exact dynamic stiffness matrices. An equivalent frequency-dependent spring coefficient representing the resilient, flexural and inertial characteristics of the rail support components is introduced to reduce the degrees of freedom of the track element. The forced vibration equations of motion of the track subjected to a series of loading functions are then formulated by using beam bending theories and are reduced to second order ordinary differential equations through the use of mode summation with non-proportional modal damping. Numerical examples for the dynamic responses of a typical track are presented, and the solutions resulting from different rail/tie beam theories are compared.