• Journal of the Korea Concrete Institute
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• v.17 no.3 s.87
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• pp.435-444
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• 2005

This paper predicted the shear behavior of reinforced concrete columns using Transformation Angle Truss Model (TATM) considered the effects of bending moment and axial force. Nine columns with various shear span- to-depth ratios and axial force ratios were tested to verify the theoretical results obtained from TATM. Fine linear displacement transducers (LVDT) were attached to a side of the column near the shear critical region to measure the curvature, the longitudinal and transverse axial deformations, and the shear deformation of the column. The test was terminated when the value of the applied load dropped to about $85\%$ of the maximum-recorded load in the post-peak descending branch. All the columns were failed in shear before yielding of the flexural steel. The shear strength and the stiffness of the columns increased, as the axial force increased and the shear span-to-depth ratio decreased. Shear stress-shear strain and shear stress-strain of shear reinforcement curves obtained from TATM were agreed well with the test results in comparison to other truss models (MCFT, RA-STM, and FA-STM).

• Structural Engineering and Mechanics
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• v.64 no.2
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• pp.145-153
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• 2017

In this article, a novel simple higher-order shear deformation theory for bending and free vibration analysis of functionally graded (FG) beams is proposed. The beauty of this theory relies on its 2-unknowns displacement field as the Euler-Bernoulli beam theory, which is even less than the Timoshenko beam theory. A shear correction factor is, therefore, not needed. Equations of motion are obtained via Hamilton's principle. Analytical solutions for the bending and free vibration analysis are given for simply supported beams. Efficacy of the proposed model is shown through illustrative examples for bending and dynamic of FG beams. The numerical results obtained are compared with those of other higher-order shear deformation beam theory results. The results obtained are found to be accurate.

• Earthquakes and Structures
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• v.13 no.5
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• pp.509-518
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• 2017

The objective of the present paper is to investigate the bending behavior with stretching effect of carbon nanotube-reinforced composite (CNTRC) beams. The beams resting on the Pasternak elastic foundation, including a shear layer and Winkler spring, are considered. The single-walled carbon nanotubes (SWCNTs) are aligned and distributed in polymeric matrix with different patterns of reinforcement. The material properties of the CNTRC beams are estimated by using the rule of mixture. The significant feature of this model is that, in addition to including the shear deformation effect and stretching effect it deals with only 4 unknowns without including a shear correction factor. The single-walled carbon nanotubes (SWCNTs) are aligned and distributed in polymeric matrix with different patterns of reinforcement. The material properties of the CNTRC beams are assessed by employing the rule of mixture. The equilibrium equations have been obtained using the principle of virtual displacements. The mathematical models provided in this paper are numerically validated by comparison with some available results. New results of bending analyses of CNTRC beams based on the present theory with stretching effect is presented and discussed in details. the effects of different parameters of the beam on the bending responses of CNTRC beam are discussed.

• Steel and Composite Structures
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• v.41 no.5
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• pp.697-711
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• 2021

In this work, a simple quasi 3-D parabolic shear deformation theory is developed to examine the bending response of antisymmetric cross-ply laminated composite plates under different types of mechanical loading. The main feature of this theory is that, in addition to including the transverse shear deformation and thickness stretching effects, it has only five-unknown variables in the displacement field modeling like Mindlin's theory (FSDT), yet satisfies the zero shear stress conditions on the top and bottom surfaces of the plate without requiring a shear correction factor. The static version of principle of virtual work was employed to derive the governing equations, while the bending problem for simply supported antisymmetric cross-ply laminated plates was solved by a Navier-type closed-form solution procedure. The adequacy of the proposed model is handled by considering the impact of side-to-thickness ratio on bending response of plate through several illustrative examples. Comparison of the obtained numerical results with the other shear deformation theories leads to the conclusion that the present model is more accurate and efficient in predicting the displacements and stresses of laminated composite plates.

• Structural Engineering and Mechanics
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• v.45 no.3
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• pp.355-371
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• 2013

Single- and multi-span orthotropic functionally graded hollow cylinders subjected to axisymmetrical bending are investigated on the basis of a unified shear deformable shell theory, in which the transverse displacement is expressed by means of a general shape function. To approach the through-thickness inhomogeneity of the hollow cylinder, a laminated model is employed. The shape function therefore shall be determined for each fictitious layer. To improve the computational efficiency, we resort to a transfer matrix method. Based on the principle of minimum potential energy, equilibrium equations are established, which are then solved analytically using the transfer matrix method for arbitrary boundary conditions. Numerical comparisons among a third-order shear deformable shell theory, an exact elastic theory and the present theory are provided for a simply supported hollow cylinder, from which the present theory turns out to be superior in stress estimation. Distributions of displacements and stresses in single- and three-span hollow cylinders with different boundary conditions are also illustrated in numerical examples.

• Steel and Composite Structures
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• v.36 no.2
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• pp.143-161
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• 2020

In nanosized structures as the surface area to the bulk volume ratio increases the classical continuum mechanics approaches fails to investigate the mechanical behavior of such structures. In perforated nanobeam structures, more decrease in the bulk volume is obtained due to perforation process thus nonclassical continuum approaches should be employed for reliable investigation of the mechanical behavior these structures. This article introduces an analytical methodology to investigate the size dependent, surface energy, and perforation impacts on the nonclassical bending behavior of regularly squared cutout nanobeam structures for the first time. To do this, geometrical model for both bulk and surface characteristics is developed for regularly squared perforated nanobeams. Based on the proposed geometrical model, the nonclassical Gurtin-Murdoch surface elasticity model is adopted and modified to incorporate the surface energy effects in perforated nanobeams. To investigate the effect of shear deformation associated with cutout process, both Euler-Bernoulli and Timoshenko beams theories are developed. Mathematical model for perforated nanobeam structure including surface energy effects are derived in comprehensive procedure and nonclassical boundary conditions are presented. Closed forms for the nonclassical bending and rotational displacements are derived for both theories considering all classical and nonclassical kinematics and kinetics boundary conditions. Additionally, both uniformly distributed and concentrated loads are considered. The developed methodology is verified and compared with the available results and an excellent agreement is noticed. Both classical and nonclassical bending profiles for both thin and thick perforated nanobeams are investigated. Numerical results are obtained to illustrate effects of beam filling ratio, the number of hole rows through the cross section, surface material characteristics, beam slenderness ratio as well as the boundary and loading conditions on the non-classical bending behavior of perforated nanobeams in the presence of surface effects. It is found that, the surface residual stress has more significant effect on the bending deflection compared with the corresponding effect of the surface elasticity, Es. The obtained results are supportive for the design, analysis and manufacturing of perforated nanobeams.

• Steel and Composite Structures
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• v.14 no.4
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• pp.335-347
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• 2013

In this paper, the nonlinear cylindrical bending behavior of functionally graded nanocomposite plates reinforced by single-walled carbon nanotubes (SWCNTs) is studied using an efficient and simple refined theory. This theory is based on assumption that the in-plane and transverse displacements consist of bending and shear components in which the bending components do not contribute toward shear forces and, likewise, the shear components do not contribute toward bending moments. The material properties of SWCNTs are assumed to be temperature-dependent and are obtained from molecular dynamics simulations. The material properties of functionally graded carbon nanotube-reinforced composites (FG-CNTCRs) are assumed to be graded in the thickness direction, and are estimated through a micromechanical model. The fundamental equations for functionally graded nanocomposite plates are obtained using the Von-Karman theory for large deflections and the solution is obtained by minimization of the total potential energy. The numerical illustrations concern the nonlinear bending response of FG-CNTRC plates under different sets of thermal environmental conditions, from which results for uniformly distributed CNTRC plates are obtained as comparators.

• Structural Engineering and Mechanics
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• v.31 no.5
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• pp.545-566
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• 2009

Bridge columns are subjected to combined actions of axial force, shear force and bending moment during earthquakes, caused by spatially-complex earthquake motions, features of structural configurations and the interaction between input and response characteristics. Combined actions can have significant effects on the force and deformation capacity of RC columns, resulting in unexpected large deformations and extensive damage that in turn influences the performance of bridges as vital components of transportation systems. This paper evaluates the seismic response of three prototype reinforced concrete bridges using comprehensive numerical models that are capable of simulating the complex soil-structural interaction effects and nonlinear behavior of columns. An analytical approach that can capture the shear-flexural interacting behavior is developed to model the realistic nonlinear behavior of RC columns, including the pinching behavior, strength deterioration and stiffness softening due to combined actions of shear force, axial force and bending moment. Seismic response analyses were conducted on the prototype bridges under suites of ground motions. Response quantities of bridges (e.g., drift, acceleration, section force and section moment etc.) are compared and evaluated to identify the effects of vertical motion, structural characteristics and the shear-flexural interaction on seismic demand of bridges.

• Geomechanics and Engineering
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• v.18 no.2
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• pp.161-178
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• 2019

In this research, a simple quasi 3D hyperbolic shear deformation model is employed for bending and dynamic behavior of functionally graded (FG) plates resting on visco-Pasternak foundations. The important feature of this theory is that, it includes the thickness stretching effect with considering only 4 unknowns, which less than what is used in the First Order Shear Deformation (FSDT) theory. The visco­Pasternak's foundation is taken into account by adding the influence of damping to the usual foundation model which characterized by the linear Winkler's modulus and Pasternak's foundation modulus. The equations of motion for thick FG plates are obtained in the Hamilton principle. Analytical solutions for the bending and dynamic analysis are determined for simply supported plates resting on visco-Pasternak foundations. Some numerical results are presented to indicate the effects of material index, elastic foundation type, and damping coefficient of the foundation, on the bending and dynamic behavior of rectangular FG plates.

• Structural Engineering and Mechanics
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• v.2 no.1
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• pp.1-16
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• 1994

A unified theory has recently been developed for reinforced concrete structures (Hsu 1993), subjected to the four basic actions - bending, axial load, shear and torsion. The theory has five components, namely, the struts-and-ties model, the equilibrium (or plasticity) truss model, the Bernoulli compatibility truss model, the Mohr compatibility truss model and the softened truss model. Because the last three models can satisfy the stress equilibrium, the strain compatibility and the constitutive laws of materials, they can predict not only the strength, but also the load-deformation history of a member. In this paper the five models are summarized to illustrate their intrinsic consistency.