• Steel and Composite Structures
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• v.11 no.6
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• pp.489-504
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• 2011

This paper presents a theoretical investigation in free vibration of sigmoid functionally graded beams with variable cross-section by using Bernoulli-Euler beam theory. The mechanical properties are assumed to vary continuously through the thickness of the beam, and obey a two power law of the volume fraction of the constituents. Governing equation is reduced to an ordinary differential equation in spatial coordinate for a family of cross-section geometries with exponentially varying width. Analytical solutions of the vibration of the S-FGM beam are obtained for three different types of boundary conditions associated with simply supported, clamped and free ends. Results show that, all other parameters remaining the same, the natural frequencies of S-FGM beams are always proportional to those of homogeneous isotropic beams. Therefore, one can predict the behaviour of S-FGM beams knowing that of similar homogeneous beams.

• 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.7 no.1
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• pp.53-70
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• 2007

This paper presents a analysis of the problem of optimal design of the beams with two I-type cross section shapes. These types of beams are simply supported and subject to pure bending. The strength and stability conditions were formulated and analytically solved in the form of mathematical equations. Both global and selected types of local stability forms were taken into account. The optimization problem was defined as bicriteria. The cross section area of the beam is the first objective function, while the deflection of the beam is the second. The geometric parameters of cross section were selected as the design variables. The set of constraints includes global and local stability conditions, the strength condition, and technological and constructional requirements in the form of geometric relations. The optimization problem was formulated and solved with the help of the Pareto concept of optimality. During the numerical calculations a set of optimal compromise solutions was generated. The numerical procedures include discrete and continuous sets of the design variables. Results of numerical analysis are presented in the form of tables, cross section outlines and diagrams. Results are discussed at the end of the work. These results may be useful for designers in optimal designing of thin-walled beams, increasing information required in the decision-making procedure.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2000.04b
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• pp.389-396
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• 2000

A three-dimensional finite element dynamic analysis was conducted to evaluate the effects of reducing cross beams from a simply supported straight P.S.C girder bridge. Two analyses were performed on the P.S.C girder bridge; one with 7 cross beams which is commonly used as current standard, and the other with 3 cross beams. A frequency analysis was conducted first in order to establish the dynamic characteristics of the bridge and determine an appropriate time step to use in the time history analyses. To assess the function and effectiveness of the cross beams, time history analysis was conducted for aforementioned two analysis cases. In the analysis, the complete model was subjected to a loading condition corresponding to the one passing truck loading. Several results of deflection, bending moment and shear forces were compared for two cases. From the analysis results, reduction of cross beams was found to have only a minimum effect on the response of the bridge. The maximum deck slab bending moment was found to decrease. This decrease should result in smaller flexural crack widths in the deck slab, which may lead to an improved deck performance.

• Structural Engineering and Mechanics
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• v.67 no.5
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• pp.465-479
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• 2018

In a previous study, design charts where proposed to help the torsional design of axially restricted reinforced concrete (RC) beams with squared cross section. In this article, new design charts are proposed to cover RC beams with rectangular cross section. The influence of the height to width ratio of the cross section on the behavior of RC beams under torsion is firstly shown by using theoretical and experimental results. Next, the effective torsional strength of a reference RC beam is computed for several values and combinations of the study variables, namely: height to width ratio of the cross section, concrete compressive strength, torsional reinforcement ratio and level of the axial restraint. To compute the torsional strength, the modified Variable Angle Truss Model for axially restricted RC beams is used. Then, an extensive parametric analysis based on multivariable and nonlinear correlation analysis is performed to obtain nonlinear regression equations which allow to build the new design charts. These charts allow to correct the torsional strength in order to consider the favourable influence of the compressive axial stress that arises from the axial restraint.

• Structural Engineering and Mechanics
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• v.49 no.6
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• pp.673-685
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• 2014

The topic of this study is to strengthen cracked beams with prefabricated RC U cross-sectional plates. The damaged beams were repaired by epoxy based glue. The repaired beams were strengthened using prefabricated plates. The strengthening plates were bonded to the bottom and side faces of the beams by anchorage rods and epoxy. The strengthened beams were incrementally loaded up to maximum load capacities. The experimental results were satisfactory since the load carrying capacities of damaged beams were increased approximately 76% due to strengthening. It was observed that strengthening plates had a dominant effect on the performance of beams in terms of both the post-elastic strength enhancement and the ductility. The experimental program was supported by a three-dimensional nonlinear finite element analysis. The experimental results were compared with the results obtained from the beam modeled with ANSYS finite element program.

• Journal of the Korean Wood Science and Technology
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• v.19 no.2
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• pp.40-55
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• 1991

To investigate the influence of cross section geometries on the behavior of composite beams in the case of small span to depth ratio and deep beams. the static flexural behavior of composite I-beams and Box- beams was evaluated. 12 types of composite I -beams composed of LVL flanges and particleboard or plywood web and 3 types of composite Box-beams composed of LVL flanges and plywood web were tested under one-point loading. The load-deflection curves were almost linear to failure, therefore, the behavior of tested composite beams was elastic. The theoretical flexural rigidity of composite beams was calculated and compared with observed flexural rigidity. The highest value was found in I-W type beams and the lowest value was found in G-P type beams. The difference between theoretical and observed flexural rigidity was small. Theoretical total deflection of tested composite beams was calculated using flexural rigidity and compared with actual deflection. Shear deflection of these beams was evaluated by the approximation method, solid crosss section method and elementary method. The difference between actual deflection and expected deflection was not found in D, E and F type beams. This defference was small in G, H and I type beams or Box-beam.

• Journal of the Korean Society of Safety
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• v.36 no.5
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• pp.27-35
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• 2021

This study investigated the change in stiffness and deflection of a scaffold working plate caused by damage to a cross-beam in the plate. Experiments were conducted considering various load and damage conditions of cross-beams. A cross-beam falling off from the working plate was considered damaged. The load-displacement curves of specimens at the center of the uniform load showed that the working plate stiffness decreased by 14.66%-1.89%, depending on the load interval due to the damage of one cross-beam. A reduction in the stiffness of 33.94%-40.76% resulted from the damage of two cross-beams. Moreover, the displacement increased by an average of 25% when one cross-beam was damaged and an average of 65% when two cross-beams were damaged. Therefore, damage to the cross-beam in the working plate can potentially cause accidents and harm workers. As the load increases, the risk of an accident due to the aforementioned damage also increases because the stiffness remarkably decreases with the load increase. Further, the damage to the cross-beam mainly reduces the stiffness but increases the displacement rather than the strength of the working scaffold plate.

• Journal of Ocean Engineering and Technology
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• v.18 no.2
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• pp.46-51
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• 2004

Natural frequencies of the transverse vibration of beams with step change in cross-section are obtained by using the asymptotic closed form solution. This closed form solution is found by using WKB method under the assumption of slowly varying properties, such as mass, cross-section, tension etc., along the beam length. However, this solution is found to be still very accurate even in the case of large variation in cross-section and tension. Therefore, this result can be easily applied to many engineering problems.

• Structural Engineering and Mechanics
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• v.68 no.6
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• pp.713-720
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• 2018

In this paper a new numerical method to determine the elastic curve of the simply supported beams of variable cross-section is demonstrated. In general case it needs to solve linear or small nonlinear second order differential equations with prescribed boundary conditions. For numerical solution the initial values of the slope and the deflection of the end cross-section of the beam is necessary. For obtaining the initial values a lively procedure is developed: it is a special application of the shooting method because boundary value problems can be transformed into initial value problems. As a result of these transformations the initial values of the differential equations are obtained with high accuracy. Procedure is applied for calculating of elastic curve of a simply supported beam of variable cross-section. Results of these numerical procedures, analytical solution of the linearized version and finite element method are compared. It is proved that the suggested procedure yields technically accurate results.